Update online docs for release version

author: Johannes Ranke <jranke@uni-bremen.de> 2020-10-15 12:53:23 +0200
committer: Johannes Ranke <jranke@uni-bremen.de> 2020-10-15 12:53:23 +0200
commit: 5b1179f0daff9077e1370065f9b9f03a2d0e0450 (patch)
tree: 01f30f5763c279b942458843939d4f02be6ca455 /docs
parent: 272aba066f0d7502e319b7e7f14009318cd44348 (diff)
140 files changed, 2725 insertions, 2295 deletions
diff --git a/docs/404.html b/docs/404.html
index 29b71104..55b92696 100644
--- a/docs/404.html
+++ b/docs/404.html
@@ -71,7 +71,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="https://pkgdown.jrwb.de/mkin/index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -108,6 +108,9 @@
     <li>
       <a href="articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -116,7 +119,7 @@
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -157,7 +160,7 @@ Content not found. Please use links in the navbar.
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/articles/FOCUS_D.html b/docs/articles/FOCUS_D.html
index cdd85f43..dd5fe08e 100644
--- a/docs/articles/FOCUS_D.html
+++ b/docs/articles/FOCUS_D.html
@@ -31,7 +31,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -68,6 +68,9 @@
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -76,7 +79,7 @@
       </ul>
 <ul class="nav navbar-nav navbar-right">
 <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -97,18 +100,19 @@
       <h1 data-toc-skip>Example evaluation of FOCUS Example Dataset D</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2020-05-27</h4>
+            <h4 class="date">2020-10-15</h4>
       
-      <small class="dont-index">Source: <a href="http://github.com/jranke/mkin/blob/master/vignettes/FOCUS_D.Rmd"><code>vignettes/FOCUS_D.Rmd</code></a></small>
-      <div class="hidden name"><code>FOCUS_D.Rmd</code></div>
+      <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/master/vignettes/FOCUS_D.rmd"><code>vignettes/FOCUS_D.rmd</code></a></small>
+      <div class="hidden name"><code>FOCUS_D.rmd</code></div>
 
     </div>
 
     
     
 <p>This is just a very simple vignette showing how to fit a degradation model for a parent compound with one transformation product using <code>mkin</code>. After loading the library we look at the data. We have observed concentrations in the column named <code>value</code> at the times specified in column <code>time</code> for the two observed variables named <code>parent</code> and <code>m1</code>.</p>
-<div class="sourceCode" id="cb1"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/library.html">library</a></span>(<span class="no">mkin</span>, <span class="kw">quietly</span> <span class="kw">=</span> <span class="fl">TRUE</span>)
-<span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">FOCUS_2006_D</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb1"><pre class="downlit">
+<span class="kw"><a href="https://rdrr.io/r/base/library.html">library</a></span><span class="op">(</span><span class="va"><a href="https://pkgdown.jrwb.de/mkin/">mkin</a></span>, quietly <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>
+<span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">FOCUS_2006_D</span><span class="op">)</span></pre></div>
 <pre><code>##      name time  value
 ## 1  parent    0  99.46
 ## 2  parent    0 102.04
@@ -156,29 +160,37 @@
 ## 44     m1  120  33.31</code></pre>
 <p>Next we specify the degradation model: The parent compound degrades with simple first-order kinetics (SFO) to one metabolite named m1, which also degrades with SFO kinetics.</p>
 <p>The call to mkinmod returns a degradation model. The differential equations represented in R code can be found in the character vector <code>$diffs</code> of the <code>mkinmod</code> object. If a C compiler (gcc) is installed and functional, the differential equation model will be compiled from auto-generated C code.</p>
-<div class="sourceCode" id="cb3"><html><body><pre class="r"><span class="no">SFO_SFO</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../reference/mkinmod.html">mkinmod</a></span>(<span class="kw">parent</span> <span class="kw">=</span> <span class="fu"><a href="../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"m1"</span>), <span class="kw">m1</span> <span class="kw">=</span> <span class="fu"><a href="../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>))</pre></body></html></div>
+<div class="sourceCode" id="cb3"><pre class="downlit">
+<span class="va">SFO_SFO</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>parent <span class="op">=</span> <span class="fu"><a href="../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"m1"</span><span class="op">)</span>, m1 <span class="op">=</span> <span class="fu"><a href="../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span><span class="op">)</span></pre></div>
 <pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
-<div class="sourceCode" id="cb5"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">SFO_SFO</span>$<span class="no">diffs</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb5"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">SFO_SFO</span><span class="op">$</span><span class="va">diffs</span><span class="op">)</span></pre></div>
 <pre><code>##                                                    parent 
 ##                          "d_parent = - k_parent * parent" 
 ##                                                        m1 
 ## "d_m1 = + f_parent_to_m1 * k_parent * parent - k_m1 * m1"</code></pre>
 <p>We do the fitting without progress report (<code>quiet = TRUE</code>).</p>
-<div class="sourceCode" id="cb7"><html><body><pre class="r"><span class="no">fit</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span>(<span class="no">SFO_SFO</span>, <span class="no">FOCUS_2006_D</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb7"><pre class="downlit">
+<span class="va">fit</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOCUS_2006_D</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></pre></div>
 <pre><code>## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, quiet = TRUE): Observations with value
 ## of zero were removed from the data</code></pre>
+<pre><code>## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, quiet = TRUE): Shapiro-Wilk test for
+## standardized residuals: p = 0.0165</code></pre>
 <p>A plot of the fit including a residual plot for both observed variables is obtained using the <code>plot_sep</code> method for <code>mkinfit</code> objects, which shows separate graphs for all compounds and their residuals.</p>
-<div class="sourceCode" id="cb9"><html><body><pre class="r"><span class="fu"><a href="../reference/plot.mkinfit.html">plot_sep</a></span>(<span class="no">fit</span>, <span class="kw">lpos</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="st">"topright"</span>, <span class="st">"bottomright"</span>))</pre></body></html></div>
+<div class="sourceCode" id="cb10"><pre class="downlit">
+<span class="fu"><a href="../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">fit</span>, lpos <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="st">"topright"</span>, <span class="st">"bottomright"</span><span class="op">)</span><span class="op">)</span></pre></div>
 <p><img src="FOCUS_D_files/figure-html/plot-1.png" width="768"></p>
 <p>Confidence intervals for the parameter estimates are obtained using the <code>mkinparplot</code> function.</p>
-<div class="sourceCode" id="cb10"><html><body><pre class="r"><span class="fu"><a href="../reference/mkinparplot.html">mkinparplot</a></span>(<span class="no">fit</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb11"><pre class="downlit">
+<span class="fu"><a href="../reference/mkinparplot.html">mkinparplot</a></span><span class="op">(</span><span class="va">fit</span><span class="op">)</span></pre></div>
 <p><img src="FOCUS_D_files/figure-html/plot_2-1.png" width="768"></p>
 <p>A comprehensive report of the results is obtained using the <code>summary</code> method for <code>mkinfit</code> objects.</p>
-<div class="sourceCode" id="cb11"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">fit</span>)</pre></body></html></div>
-<pre><code>## mkin version used for fitting:    0.9.50.2 
-## R version used for fitting:       4.0.0 
-## Date of fit:     Wed May 27 07:05:33 2020 
-## Date of summary: Wed May 27 07:05:34 2020 
+<div class="sourceCode" id="cb12"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span><span class="op">(</span><span class="va">fit</span><span class="op">)</span></pre></div>
+<pre><code>## mkin version used for fitting:    0.9.50.3 
+## R version used for fitting:       4.0.3 
+## Date of fit:     Thu Oct 15 12:42:00 2020 
+## Date of summary: Thu Oct 15 12:42:00 2020 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent * parent
@@ -186,7 +198,7 @@
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 421 model solutions performed in 0.166 s
+## Fitted using 421 model solutions performed in 0.172 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -210,6 +222,11 @@
 ##      value  type
 ## m1_0     0 state
 ## 
+## 
+## Warning(s): 
+## Observations with value of zero were removed from the data
+## Shapiro-Wilk test for standardized residuals: p =  0.0165
+## 
 ## Results:
 ## 
 ##        AIC      BIC    logLik
@@ -225,11 +242,11 @@
 ## 
 ## Parameter correlation:
 ##                  parent_0 log_k_parent   log_k_m1 f_parent_ilr_1      sigma
-## parent_0        1.000e+00    5.174e-01 -1.688e-01     -5.471e-01 -3.190e-07
+## parent_0        1.000e+00    5.174e-01 -1.688e-01     -5.471e-01 -3.214e-07
 ## log_k_parent    5.174e-01    1.000e+00 -3.263e-01     -5.426e-01  3.168e-07
-## log_k_m1       -1.688e-01   -3.263e-01  1.000e+00      7.478e-01 -1.406e-07
-## f_parent_ilr_1 -5.471e-01   -5.426e-01  7.478e-01      1.000e+00 -1.587e-10
-## sigma          -3.190e-07    3.168e-07 -1.406e-07     -1.587e-10  1.000e+00
+## log_k_m1       -1.688e-01   -3.263e-01  1.000e+00      7.478e-01 -1.410e-07
+## f_parent_ilr_1 -5.471e-01   -5.426e-01  7.478e-01      1.000e+00  5.093e-10
+## sigma          -3.214e-07    3.168e-07 -1.410e-07      5.093e-10  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -313,7 +330,7 @@
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/articles/FOCUS_D_files/figure-html/plot-1.png b/docs/articles/FOCUS_D_files/figure-html/plot-1.png
index 306244b3..60433c42 100644
--- a/docs/articles/FOCUS_D_files/figure-html/plot-1.png
+++ b/docs/articles/FOCUS_D_files/figure-html/plot-1.png
diff --git a/docs/articles/FOCUS_D_files/figure-html/plot_2-1.png b/docs/articles/FOCUS_D_files/figure-html/plot_2-1.png
index 158e3c50..f4937894 100644
--- a/docs/articles/FOCUS_D_files/figure-html/plot_2-1.png
+++ b/docs/articles/FOCUS_D_files/figure-html/plot_2-1.png
diff --git a/docs/articles/FOCUS_L.html b/docs/articles/FOCUS_L.html
index 2a58b4e5..77774263 100644
--- a/docs/articles/FOCUS_L.html
+++ b/docs/articles/FOCUS_L.html
@@ -31,7 +31,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -68,6 +68,9 @@
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -76,7 +79,7 @@
       </ul>
 <ul class="nav navbar-nav navbar-right">
 <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -97,10 +100,10 @@
       <h1 data-toc-skip>Example evaluation of FOCUS Laboratory Data L1 to L3</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2020-05-27</h4>
+            <h4 class="date">2020-10-15</h4>
       
-      <small class="dont-index">Source: <a href="http://github.com/jranke/mkin/blob/master/vignettes/FOCUS_L.Rmd"><code>vignettes/FOCUS_L.Rmd</code></a></small>
-      <div class="hidden name"><code>FOCUS_L.Rmd</code></div>
+      <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/master/vignettes/FOCUS_L.rmd"><code>vignettes/FOCUS_L.rmd</code></a></small>
+      <div class="hidden name"><code>FOCUS_L.rmd</code></div>
 
     </div>
 
@@ -110,42 +113,44 @@
 <h1 class="hasAnchor">
 <a href="#laboratory-data-l1" class="anchor"></a>Laboratory Data L1</h1>
 <p>The following code defines example dataset L1 from the FOCUS kinetics report, p. 284:</p>
-<div class="sourceCode" id="cb1"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/library.html">library</a></span>(<span class="st">"mkin"</span>, <span class="kw">quietly</span> <span class="kw">=</span> <span class="fl">TRUE</span>)
-<span class="no">FOCUS_2006_L1</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html">data.frame</a></span>(
-  <span class="kw">t</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/rep.html">rep</a></span>(<span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="fl">0</span>, <span class="fl">1</span>, <span class="fl">2</span>, <span class="fl">3</span>, <span class="fl">5</span>, <span class="fl">7</span>, <span class="fl">14</span>, <span class="fl">21</span>, <span class="fl">30</span>), <span class="kw">each</span> <span class="kw">=</span> <span class="fl">2</span>),
-  <span class="kw">parent</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="fl">88.3</span>, <span class="fl">91.4</span>, <span class="fl">85.6</span>, <span class="fl">84.5</span>, <span class="fl">78.9</span>, <span class="fl">77.6</span>,
+<div class="sourceCode" id="cb1"><pre class="downlit">
+<span class="kw"><a href="https://rdrr.io/r/base/library.html">library</a></span><span class="op">(</span><span class="st"><a href="https://pkgdown.jrwb.de/mkin/">"mkin"</a></span>, quietly <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>
+<span class="va">FOCUS_2006_L1</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html">data.frame</a></span><span class="op">(</span>
+  t <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/rep.html">rep</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">1</span>, <span class="fl">2</span>, <span class="fl">3</span>, <span class="fl">5</span>, <span class="fl">7</span>, <span class="fl">14</span>, <span class="fl">21</span>, <span class="fl">30</span><span class="op">)</span>, each <span class="op">=</span> <span class="fl">2</span><span class="op">)</span>,
+  parent <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="fl">88.3</span>, <span class="fl">91.4</span>, <span class="fl">85.6</span>, <span class="fl">84.5</span>, <span class="fl">78.9</span>, <span class="fl">77.6</span>,
              <span class="fl">72.0</span>, <span class="fl">71.9</span>, <span class="fl">50.3</span>, <span class="fl">59.4</span>, <span class="fl">47.0</span>, <span class="fl">45.1</span>,
-             <span class="fl">27.7</span>, <span class="fl">27.3</span>, <span class="fl">10.0</span>, <span class="fl">10.4</span>, <span class="fl">2.9</span>, <span class="fl">4.0</span>))
-<span class="no">FOCUS_2006_L1_mkin</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span>(<span class="no">FOCUS_2006_L1</span>)</pre></body></html></div>
+             <span class="fl">27.7</span>, <span class="fl">27.3</span>, <span class="fl">10.0</span>, <span class="fl">10.4</span>, <span class="fl">2.9</span>, <span class="fl">4.0</span><span class="op">)</span><span class="op">)</span>
+<span class="va">FOCUS_2006_L1_mkin</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span><span class="op">(</span><span class="va">FOCUS_2006_L1</span><span class="op">)</span></pre></div>
 <p>Here we use the assumptions of simple first order (SFO), the case of declining rate constant over time (FOMC) and the case of two different phases of the kinetics (DFOP). For a more detailed discussion of the models, please see the FOCUS kinetics report.</p>
 <p>Since mkin version 0.9-32 (July 2014), we can use shorthand notation like <code>"SFO"</code> for parent only degradation models. The following two lines fit the model and produce the summary report of the model fit. This covers the numerical analysis given in the FOCUS report.</p>
-<div class="sourceCode" id="cb2"><html><body><pre class="r"><span class="no">m.L1.SFO</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span>(<span class="st">"SFO"</span>, <span class="no">FOCUS_2006_L1_mkin</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)
-<span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">m.L1.SFO</span>)</pre></body></html></div>
-<pre><code>## mkin version used for fitting:    0.9.50.2 
-## R version used for fitting:       4.0.0 
-## Date of fit:     Wed May 27 07:05:36 2020 
-## Date of summary: Wed May 27 07:05:36 2020 
+<div class="sourceCode" id="cb2"><pre class="downlit">
+<span class="va">m.L1.SFO</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="va">FOCUS_2006_L1_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>
+<span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span><span class="op">(</span><span class="va">m.L1.SFO</span><span class="op">)</span></pre></div>
+<pre><code>## mkin version used for fitting:    0.9.50.3 
+## R version used for fitting:       4.0.3 
+## Date of fit:     Thu Oct 15 12:42:03 2020 
+## Date of summary: Thu Oct 15 12:42:03 2020 
 ## 
 ## Equations:
-## d_parent/dt = - k_parent_sink * parent
+## d_parent/dt = - k_parent * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 133 model solutions performed in 0.031 s
+## Fitted using 133 model solutions performed in 0.032 s
 ## 
 ## Error model: Constant variance 
 ## 
 ## Error model algorithm: OLS 
 ## 
 ## Starting values for parameters to be optimised:
-##               value   type
-## parent_0      89.85  state
-## k_parent_sink  0.10 deparm
+##          value   type
+## parent_0 89.85  state
+## k_parent  0.10 deparm
 ## 
 ## Starting values for the transformed parameters actually optimised:
-##                       value lower upper
-## parent_0          89.850000  -Inf   Inf
-## log_k_parent_sink -2.302585  -Inf   Inf
+##                  value lower upper
+## parent_0     89.850000  -Inf   Inf
+## log_k_parent -2.302585  -Inf   Inf
 ## 
 ## Fixed parameter values:
 ## None
@@ -156,25 +161,25 @@
 ##   93.88778 96.5589 -43.94389
 ## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
-##                   Estimate Std. Error  Lower  Upper
-## parent_0            92.470    1.28200 89.740 95.200
-## log_k_parent_sink   -2.347    0.03763 -2.428 -2.267
-## sigma                2.780    0.46330  1.792  3.767
+##              Estimate Std. Error  Lower  Upper
+## parent_0       92.470    1.28200 89.740 95.200
+## log_k_parent   -2.347    0.03763 -2.428 -2.267
+## sigma           2.780    0.46330  1.792  3.767
 ## 
 ## Parameter correlation:
-##                     parent_0 log_k_parent_sink      sigma
-## parent_0           1.000e+00         6.186e-01 -1.712e-09
-## log_k_parent_sink  6.186e-01         1.000e+00 -3.237e-09
-## sigma             -1.712e-09        -3.237e-09  1.000e+00
+##                parent_0 log_k_parent      sigma
+## parent_0      1.000e+00    6.186e-01 -1.516e-09
+## log_k_parent  6.186e-01    1.000e+00 -3.124e-09
+## sigma        -1.516e-09   -3.124e-09  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
 ## t-test (unrealistically) based on the assumption of normal distribution
 ## for estimators of untransformed parameters.
-##               Estimate t value    Pr(&gt;t)    Lower   Upper
-## parent_0      92.47000   72.13 8.824e-21 89.74000 95.2000
-## k_parent_sink  0.09561   26.57 2.487e-14  0.08824  0.1036
-## sigma          2.78000    6.00 1.216e-05  1.79200  3.7670
+##          Estimate t value    Pr(&gt;t)    Lower   Upper
+## parent_0 92.47000   72.13 8.824e-21 89.74000 95.2000
+## k_parent  0.09561   26.57 2.487e-14  0.08824  0.1036
+## sigma     2.78000    6.00 1.216e-05  1.79200  3.7670
 ## 
 ## FOCUS Chi2 error levels in percent:
 ##          err.min n.optim df
@@ -206,38 +211,38 @@
 ##    30   parent      2.9     5.251  -2.3513
 ##    30   parent      4.0     5.251  -1.2513</code></pre>
 <p>A plot of the fit is obtained with the plot function for mkinfit objects.</p>
-<div class="sourceCode" id="cb4"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">m.L1.SFO</span>, <span class="kw">show_errmin</span> <span class="kw">=</span> <span class="fl">TRUE</span>, <span class="kw">main</span> <span class="kw">=</span> <span class="st">"FOCUS L1 - SFO"</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb4"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">m.L1.SFO</span>, show_errmin <span class="op">=</span> <span class="cn">TRUE</span>, main <span class="op">=</span> <span class="st">"FOCUS L1 - SFO"</span><span class="op">)</span></pre></div>
 <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-4-1.png" width="576"></p>
 <p>The residual plot can be easily obtained by</p>
-<div class="sourceCode" id="cb5"><html><body><pre class="r"><span class="fu"><a href="../reference/mkinresplot.html">mkinresplot</a></span>(<span class="no">m.L1.SFO</span>, <span class="kw">ylab</span> <span class="kw">=</span> <span class="st">"Observed"</span>, <span class="kw">xlab</span> <span class="kw">=</span> <span class="st">"Time"</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb5"><pre class="downlit">
+<span class="fu"><a href="../reference/mkinresplot.html">mkinresplot</a></span><span class="op">(</span><span class="va">m.L1.SFO</span>, ylab <span class="op">=</span> <span class="st">"Observed"</span>, xlab <span class="op">=</span> <span class="st">"Time"</span><span class="op">)</span></pre></div>
 <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-5-1.png" width="576"></p>
 <p>For comparison, the FOMC model is fitted as well, and the <span class="math inline">\(\chi^2\)</span> error level is checked.</p>
-<div class="sourceCode" id="cb6"><html><body><pre class="r"><span class="no">m.L1.FOMC</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span>(<span class="st">"FOMC"</span>, <span class="no">FOCUS_2006_L1_mkin</span>, <span class="kw">quiet</span><span class="kw">=</span><span class="fl">TRUE</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb6"><pre class="downlit">
+<span class="va">m.L1.FOMC</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"FOMC"</span>, <span class="va">FOCUS_2006_L1_mkin</span>, quiet<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span></pre></div>
 <pre><code>## Warning in mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet = TRUE): Optimisation did not converge:
 ## false convergence (8)</code></pre>
-<div class="sourceCode" id="cb8"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">m.L1.FOMC</span>, <span class="kw">show_errmin</span> <span class="kw">=</span> <span class="fl">TRUE</span>, <span class="kw">main</span> <span class="kw">=</span> <span class="st">"FOCUS L1 - FOMC"</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb8"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">m.L1.FOMC</span>, show_errmin <span class="op">=</span> <span class="cn">TRUE</span>, main <span class="op">=</span> <span class="st">"FOCUS L1 - FOMC"</span><span class="op">)</span></pre></div>
 <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-6-1.png" width="576"></p>
-<div class="sourceCode" id="cb9"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">m.L1.FOMC</span>, <span class="kw">data</span> <span class="kw">=</span> <span class="fl">FALSE</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb9"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span><span class="op">(</span><span class="va">m.L1.FOMC</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></pre></div>
 <pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
 <pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
 <pre><code>## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
 ## doubtful</code></pre>
-<pre><code>## mkin version used for fitting:    0.9.50.2 
-## R version used for fitting:       4.0.0 
-## Date of fit:     Wed May 27 07:05:36 2020 
-## Date of summary: Wed May 27 07:05:36 2020 
-## 
-## 
-## Warning: Optimisation did not converge:
-## false convergence (8) 
-## 
+<pre><code>## mkin version used for fitting:    0.9.50.3 
+## R version used for fitting:       4.0.3 
+## Date of fit:     Thu Oct 15 12:42:03 2020 
+## Date of summary: Thu Oct 15 12:42:03 2020 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 899 model solutions performed in 0.204 s
+## Fitted using 380 model solutions performed in 0.086 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -258,34 +263,39 @@
 ## Fixed parameter values:
 ## None
 ## 
+## 
+## Warning(s): 
+## Optimisation did not converge:
+## false convergence (8)
+## 
 ## Results:
 ## 
 ##        AIC      BIC    logLik
-##   95.88835 99.44984 -43.94418
+##   95.88778 99.44927 -43.94389
 ## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
 ##           Estimate Std. Error  Lower  Upper
-## parent_0     92.47     1.2800 89.730 95.220
-## log_alpha    10.58        NaN    NaN    NaN
-## log_beta     12.93        NaN    NaN    NaN
-## sigma         2.78     0.4507  1.813  3.747
+## parent_0     92.47     1.2820 89.720 95.220
+## log_alpha    16.92        NaN    NaN    NaN
+## log_beta     19.26        NaN    NaN    NaN
+## sigma         2.78     0.4501  1.814  3.745
 ## 
 ## Parameter correlation:
-##           parent_0 log_alpha log_beta   sigma
-## parent_0   1.00000       NaN      NaN 0.01452
-## log_alpha      NaN         1      NaN     NaN
-## log_beta       NaN       NaN        1     NaN
-## sigma      0.01452       NaN      NaN 1.00000
+##           parent_0 log_alpha log_beta    sigma
+## parent_0  1.000000       NaN      NaN 0.002218
+## log_alpha      NaN         1      NaN      NaN
+## log_beta       NaN       NaN        1      NaN
+## sigma     0.002218       NaN      NaN 1.000000
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
 ## t-test (unrealistically) based on the assumption of normal distribution
 ## for estimators of untransformed parameters.
-##           Estimate  t value    Pr(&gt;t)  Lower  Upper
-## parent_0     92.47 72.13000 1.052e-19 89.730 95.220
-## alpha     39440.00  0.02397 4.906e-01     NA     NA
-## beta     412500.00  0.02397 4.906e-01     NA     NA
-## sigma         2.78  6.00000 1.628e-05  1.813  3.747
+##           Estimate t value Pr(&gt;t)  Lower  Upper
+## parent_0 9.247e+01      NA     NA 89.720 95.220
+## alpha    2.223e+07      NA     NA     NA     NA
+## beta     2.325e+08      NA     NA     NA     NA
+## sigma    2.780e+00      NA     NA  1.814  3.745
 ## 
 ## FOCUS Chi2 error levels in percent:
 ##          err.min n.optim df
@@ -293,8 +303,8 @@
 ## parent     3.619       3  6
 ## 
 ## Estimated disappearance times:
-##         DT50  DT90 DT50back
-## parent 7.249 24.08    7.249</code></pre>
+##        DT50  DT90 DT50back
+## parent 7.25 24.08     7.25</code></pre>
 <p>We get a warning that the default optimisation algorithm <code>Port</code> did not converge, which is an indication that the model is overparameterised, <em>i.e.</em> contains too many parameters that are ill-defined as a consequence.</p>
 <p>And in fact, due to the higher number of parameters, and the lower number of degrees of freedom of the fit, the <span class="math inline">\(\chi^2\)</span> error level is actually higher for the FOMC model (3.6%) than for the SFO model (3.4%). Additionally, the parameters <code>log_alpha</code> and <code>log_beta</code> internally fitted in the model have excessive confidence intervals, that span more than 25 orders of magnitude (!) when backtransformed to the scale of <code>alpha</code> and <code>beta</code>. Also, the t-test for significant difference from zero does not indicate such a significant difference, with p-values greater than 0.1, and finally, the parameter correlation of <code>log_alpha</code> and <code>log_beta</code> is 1.000, clearly indicating that the model is overparameterised.</p>
 <p>The <span class="math inline">\(\chi^2\)</span> error levels reported in Appendix 3 and Appendix 7 to the FOCUS kinetics report are rounded to integer percentages and partly deviate by one percentage point from the results calculated by mkin. The reason for this is not known. However, mkin gives the same <span class="math inline">\(\chi^2\)</span> error levels as the kinfit package and the calculation routines of the kinfit package have been extensively compared to the results obtained by the KinGUI software, as documented in the kinfit package vignette. KinGUI was the first widely used standard package in this field. Also, the calculation of <span class="math inline">\(\chi^2\)</span> error levels was compared with KinGUII, CAKE and DegKin manager in a project sponsored by the German Umweltbundesamt <span class="citation">(Ranke 2014)</span>.</p>
@@ -303,19 +313,21 @@
 <h1 class="hasAnchor">
 <a href="#laboratory-data-l2" class="anchor"></a>Laboratory Data L2</h1>
 <p>The following code defines example dataset L2 from the FOCUS kinetics report, p. 287:</p>
-<div class="sourceCode" id="cb14"><html><body><pre class="r"><span class="no">FOCUS_2006_L2</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html">data.frame</a></span>(
-  <span class="kw">t</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/rep.html">rep</a></span>(<span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="fl">0</span>, <span class="fl">1</span>, <span class="fl">3</span>, <span class="fl">7</span>, <span class="fl">14</span>, <span class="fl">28</span>), <span class="kw">each</span> <span class="kw">=</span> <span class="fl">2</span>),
-  <span class="kw">parent</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="fl">96.1</span>, <span class="fl">91.8</span>, <span class="fl">41.4</span>, <span class="fl">38.7</span>,
+<div class="sourceCode" id="cb14"><pre class="downlit">
+<span class="va">FOCUS_2006_L2</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html">data.frame</a></span><span class="op">(</span>
+  t <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/rep.html">rep</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">1</span>, <span class="fl">3</span>, <span class="fl">7</span>, <span class="fl">14</span>, <span class="fl">28</span><span class="op">)</span>, each <span class="op">=</span> <span class="fl">2</span><span class="op">)</span>,
+  parent <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="fl">96.1</span>, <span class="fl">91.8</span>, <span class="fl">41.4</span>, <span class="fl">38.7</span>,
              <span class="fl">19.3</span>, <span class="fl">22.3</span>, <span class="fl">4.6</span>, <span class="fl">4.6</span>,
-             <span class="fl">2.6</span>, <span class="fl">1.2</span>, <span class="fl">0.3</span>, <span class="fl">0.6</span>))
-<span class="no">FOCUS_2006_L2_mkin</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span>(<span class="no">FOCUS_2006_L2</span>)</pre></body></html></div>
+             <span class="fl">2.6</span>, <span class="fl">1.2</span>, <span class="fl">0.3</span>, <span class="fl">0.6</span><span class="op">)</span><span class="op">)</span>
+<span class="va">FOCUS_2006_L2_mkin</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span><span class="op">(</span><span class="va">FOCUS_2006_L2</span><span class="op">)</span></pre></div>
 <div id="sfo-fit-for-l2" class="section level2">
 <h2 class="hasAnchor">
 <a href="#sfo-fit-for-l2" class="anchor"></a>SFO fit for L2</h2>
 <p>Again, the SFO model is fitted and the result is plotted. The residual plot can be obtained simply by adding the argument <code>show_residuals</code> to the plot command.</p>
-<div class="sourceCode" id="cb15"><html><body><pre class="r"><span class="no">m.L2.SFO</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span>(<span class="st">"SFO"</span>, <span class="no">FOCUS_2006_L2_mkin</span>, <span class="kw">quiet</span><span class="kw">=</span><span class="fl">TRUE</span>)
-<span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">m.L2.SFO</span>, <span class="kw">show_residuals</span> <span class="kw">=</span> <span class="fl">TRUE</span>, <span class="kw">show_errmin</span> <span class="kw">=</span> <span class="fl">TRUE</span>,
-     <span class="kw">main</span> <span class="kw">=</span> <span class="st">"FOCUS L2 - SFO"</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb15"><pre class="downlit">
+<span class="va">m.L2.SFO</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="va">FOCUS_2006_L2_mkin</span>, quiet<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span>
+<span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">m.L2.SFO</span>, show_residuals <span class="op">=</span> <span class="cn">TRUE</span>, show_errmin <span class="op">=</span> <span class="cn">TRUE</span>,
+     main <span class="op">=</span> <span class="st">"FOCUS L2 - SFO"</span><span class="op">)</span></pre></div>
 <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-8-1.png" width="672"></p>
 <p>The <span class="math inline">\(\chi^2\)</span> error level of 14% suggests that the model does not fit very well. This is also obvious from the plots of the fit, in which we have included the residual plot.</p>
 <p>In the FOCUS kinetics report, it is stated that there is no apparent systematic error observed from the residual plot up to the measured DT90 (approximately at day 5), and there is an underestimation beyond that point.</p>
@@ -325,22 +337,24 @@
 <h2 class="hasAnchor">
 <a href="#fomc-fit-for-l2" class="anchor"></a>FOMC fit for L2</h2>
 <p>For comparison, the FOMC model is fitted as well, and the <span class="math inline">\(\chi^2\)</span> error level is checked.</p>
-<div class="sourceCode" id="cb16"><html><body><pre class="r"><span class="no">m.L2.FOMC</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span>(<span class="st">"FOMC"</span>, <span class="no">FOCUS_2006_L2_mkin</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)
-<span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">m.L2.FOMC</span>, <span class="kw">show_residuals</span> <span class="kw">=</span> <span class="fl">TRUE</span>,
-     <span class="kw">main</span> <span class="kw">=</span> <span class="st">"FOCUS L2 - FOMC"</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb16"><pre class="downlit">
+<span class="va">m.L2.FOMC</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"FOMC"</span>, <span class="va">FOCUS_2006_L2_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>
+<span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">m.L2.FOMC</span>, show_residuals <span class="op">=</span> <span class="cn">TRUE</span>,
+     main <span class="op">=</span> <span class="st">"FOCUS L2 - FOMC"</span><span class="op">)</span></pre></div>
 <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-9-1.png" width="672"></p>
-<div class="sourceCode" id="cb17"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">m.L2.FOMC</span>, <span class="kw">data</span> <span class="kw">=</span> <span class="fl">FALSE</span>)</pre></body></html></div>
-<pre><code>## mkin version used for fitting:    0.9.50.2 
-## R version used for fitting:       4.0.0 
-## Date of fit:     Wed May 27 07:05:37 2020 
-## Date of summary: Wed May 27 07:05:37 2020 
+<div class="sourceCode" id="cb17"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span><span class="op">(</span><span class="va">m.L2.FOMC</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></pre></div>
+<pre><code>## mkin version used for fitting:    0.9.50.3 
+## R version used for fitting:       4.0.3 
+## Date of fit:     Thu Oct 15 12:42:04 2020 
+## Date of summary: Thu Oct 15 12:42:04 2020 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 239 model solutions performed in 0.047 s
+## Fitted using 239 model solutions performed in 0.049 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -375,10 +389,10 @@
 ## 
 ## Parameter correlation:
 ##             parent_0  log_alpha   log_beta      sigma
-## parent_0   1.000e+00 -1.151e-01 -2.085e-01 -7.637e-09
+## parent_0   1.000e+00 -1.151e-01 -2.085e-01 -7.436e-09
 ## log_alpha -1.151e-01  1.000e+00  9.741e-01 -1.617e-07
-## log_beta  -2.085e-01  9.741e-01  1.000e+00 -1.387e-07
-## sigma     -7.637e-09 -1.617e-07 -1.387e-07  1.000e+00
+## log_beta  -2.085e-01  9.741e-01  1.000e+00 -1.386e-07
+## sigma     -7.436e-09 -1.617e-07 -1.386e-07  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -404,15 +418,17 @@
 <h2 class="hasAnchor">
 <a href="#dfop-fit-for-l2" class="anchor"></a>DFOP fit for L2</h2>
 <p>Fitting the four parameter DFOP model further reduces the <span class="math inline">\(\chi^2\)</span> error level.</p>
-<div class="sourceCode" id="cb19"><html><body><pre class="r"><span class="no">m.L2.DFOP</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span>(<span class="st">"DFOP"</span>, <span class="no">FOCUS_2006_L2_mkin</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)
-<span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">m.L2.DFOP</span>, <span class="kw">show_residuals</span> <span class="kw">=</span> <span class="fl">TRUE</span>, <span class="kw">show_errmin</span> <span class="kw">=</span> <span class="fl">TRUE</span>,
-     <span class="kw">main</span> <span class="kw">=</span> <span class="st">"FOCUS L2 - DFOP"</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb19"><pre class="downlit">
+<span class="va">m.L2.DFOP</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"DFOP"</span>, <span class="va">FOCUS_2006_L2_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>
+<span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">m.L2.DFOP</span>, show_residuals <span class="op">=</span> <span class="cn">TRUE</span>, show_errmin <span class="op">=</span> <span class="cn">TRUE</span>,
+     main <span class="op">=</span> <span class="st">"FOCUS L2 - DFOP"</span><span class="op">)</span></pre></div>
 <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-10-1.png" width="672"></p>
-<div class="sourceCode" id="cb20"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">m.L2.DFOP</span>, <span class="kw">data</span> <span class="kw">=</span> <span class="fl">FALSE</span>)</pre></body></html></div>
-<pre><code>## mkin version used for fitting:    0.9.50.2 
-## R version used for fitting:       4.0.0 
-## Date of fit:     Wed May 27 07:05:37 2020 
-## Date of summary: Wed May 27 07:05:37 2020 
+<div class="sourceCode" id="cb20"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span><span class="op">(</span><span class="va">m.L2.DFOP</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></pre></div>
+<pre><code>## mkin version used for fitting:    0.9.50.3 
+## R version used for fitting:       4.0.3 
+## Date of fit:     Thu Oct 15 12:42:04 2020 
+## Date of summary: Thu Oct 15 12:42:04 2020 
 ## 
 ## Equations:
 ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -421,7 +437,7 @@
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 572 model solutions performed in 0.132 s
+## Fitted using 572 model solutions performed in 0.139 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -452,18 +468,18 @@
 ## Optimised, transformed parameters with symmetric confidence intervals:
 ##          Estimate Std. Error      Lower     Upper
 ## parent_0  93.9500  9.998e-01    91.5900   96.3100
-## log_k1     3.1370  2.376e+03 -5616.0000 5622.0000
+## log_k1     3.1370  2.376e+03 -5615.0000 5622.0000
 ## log_k2    -1.0880  6.285e-02    -1.2370   -0.9394
 ## g_ilr     -0.2821  7.033e-02    -0.4484   -0.1158
 ## sigma      1.4140  2.886e-01     0.7314    2.0960
 ## 
 ## Parameter correlation:
 ##            parent_0     log_k1     log_k2      g_ilr      sigma
-## parent_0  1.000e+00  5.155e-07  2.371e-09  2.665e-01 -6.849e-09
-## log_k1    5.155e-07  1.000e+00  8.434e-05 -1.659e-04 -7.791e-06
-## log_k2    2.371e-09  8.434e-05  1.000e+00 -7.903e-01 -1.262e-08
-## g_ilr     2.665e-01 -1.659e-04 -7.903e-01  1.000e+00  3.241e-08
-## sigma    -6.849e-09 -7.791e-06 -1.262e-08  3.241e-08  1.000e+00
+## parent_0  1.000e+00  5.157e-07  2.376e-09  2.665e-01 -6.837e-09
+## log_k1    5.157e-07  1.000e+00  8.434e-05 -1.659e-04 -7.786e-06
+## log_k2    2.376e-09  8.434e-05  1.000e+00 -7.903e-01 -1.263e-08
+## g_ilr     2.665e-01 -1.659e-04 -7.903e-01  1.000e+00  3.248e-08
+## sigma    -6.837e-09 -7.786e-06 -1.263e-08  3.248e-08  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -482,8 +498,8 @@
 ## parent      2.53       4  2
 ## 
 ## Estimated disappearance times:
-##          DT50  DT90 DT50_k1 DT50_k2
-## parent 0.5335 5.311 0.03009   2.058</code></pre>
+##          DT50  DT90 DT50back DT50_k1 DT50_k2
+## parent 0.5335 5.311    1.599 0.03009   2.058</code></pre>
 <p>Here, the DFOP model is clearly the best-fit model for dataset L2 based on the chi^2 error level criterion. However, the failure to calculate the covariance matrix indicates that the parameter estimates correlate excessively. Therefore, the FOMC model may be preferred for this dataset.</p>
 </div>
 </div>
@@ -491,18 +507,20 @@
 <h1 class="hasAnchor">
 <a href="#laboratory-data-l3" class="anchor"></a>Laboratory Data L3</h1>
 <p>The following code defines example dataset L3 from the FOCUS kinetics report, p. 290.</p>
-<div class="sourceCode" id="cb22"><html><body><pre class="r"><span class="no">FOCUS_2006_L3</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html">data.frame</a></span>(
-  <span class="kw">t</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="fl">0</span>, <span class="fl">3</span>, <span class="fl">7</span>, <span class="fl">14</span>, <span class="fl">30</span>, <span class="fl">60</span>, <span class="fl">91</span>, <span class="fl">120</span>),
-  <span class="kw">parent</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="fl">97.8</span>, <span class="fl">60</span>, <span class="fl">51</span>, <span class="fl">43</span>, <span class="fl">35</span>, <span class="fl">22</span>, <span class="fl">15</span>, <span class="fl">12</span>))
-<span class="no">FOCUS_2006_L3_mkin</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span>(<span class="no">FOCUS_2006_L3</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb22"><pre class="downlit">
+<span class="va">FOCUS_2006_L3</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html">data.frame</a></span><span class="op">(</span>
+  t <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">3</span>, <span class="fl">7</span>, <span class="fl">14</span>, <span class="fl">30</span>, <span class="fl">60</span>, <span class="fl">91</span>, <span class="fl">120</span><span class="op">)</span>,
+  parent <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="fl">97.8</span>, <span class="fl">60</span>, <span class="fl">51</span>, <span class="fl">43</span>, <span class="fl">35</span>, <span class="fl">22</span>, <span class="fl">15</span>, <span class="fl">12</span><span class="op">)</span><span class="op">)</span>
+<span class="va">FOCUS_2006_L3_mkin</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span><span class="op">(</span><span class="va">FOCUS_2006_L3</span><span class="op">)</span></pre></div>
 <div id="fit-multiple-models" class="section level2">
 <h2 class="hasAnchor">
 <a href="#fit-multiple-models" class="anchor"></a>Fit multiple models</h2>
 <p>As of mkin version 0.9-39 (June 2015), we can fit several models to one or more datasets in one call to the function <code>mmkin</code>. The datasets have to be passed in a list, in this case a named list holding only the L3 dataset prepared above.</p>
-<div class="sourceCode" id="cb23"><html><body><pre class="r"><span class="co"># Only use one core here, not to offend the CRAN checks</span>
-<span class="no">mm.L3</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../reference/mmkin.html">mmkin</a></span>(<span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>), <span class="kw">cores</span> <span class="kw">=</span> <span class="fl">1</span>,
-               <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="st">"FOCUS L3"</span> <span class="kw">=</span> <span class="no">FOCUS_2006_L3_mkin</span>), <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)
-<span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">mm.L3</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb23"><pre class="downlit">
+<span class="co"># Only use one core here, not to offend the CRAN checks</span>
+<span class="va">mm.L3</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mmkin.html">mmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span><span class="op">)</span>, cores <span class="op">=</span> <span class="fl">1</span>,
+               <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="st">"FOCUS L3"</span> <span class="op">=</span> <span class="va">FOCUS_2006_L3_mkin</span><span class="op">)</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>
+<span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">mm.L3</span><span class="op">)</span></pre></div>
 <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-12-1.png" width="700"></p>
 <p>The <span class="math inline">\(\chi^2\)</span> error level of 21% as well as the plot suggest that the SFO model does not fit very well. The FOMC model performs better, with an error level at which the <span class="math inline">\(\chi^2\)</span> test passes of 7%. Fitting the four parameter DFOP model further reduces the <span class="math inline">\(\chi^2\)</span> error level considerably.</p>
 </div>
@@ -511,11 +529,12 @@
 <a href="#accessing-mmkin-objects" class="anchor"></a>Accessing mmkin objects</h2>
 <p>The objects returned by mmkin are arranged like a matrix, with models as a row index and datasets as a column index.</p>
 <p>We can extract the summary and plot for <em>e.g.</em> the DFOP fit, using square brackets for indexing which will result in the use of the summary and plot functions working on mkinfit objects.</p>
-<div class="sourceCode" id="cb24"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">mm.L3</span><span class="kw">[[</span><span class="st">"DFOP"</span>, <span class="fl">1</span>]])</pre></body></html></div>
-<pre><code>## mkin version used for fitting:    0.9.50.2 
-## R version used for fitting:       4.0.0 
-## Date of fit:     Wed May 27 07:05:38 2020 
-## Date of summary: Wed May 27 07:05:38 2020 
+<div class="sourceCode" id="cb24"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span><span class="op">(</span><span class="va">mm.L3</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="fl">1</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></pre></div>
+<pre><code>## mkin version used for fitting:    0.9.50.3 
+## R version used for fitting:       4.0.3 
+## Date of fit:     Thu Oct 15 12:42:05 2020 
+## Date of summary: Thu Oct 15 12:42:05 2020 
 ## 
 ## Equations:
 ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -524,7 +543,7 @@
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 373 model solutions performed in 0.083 s
+## Fitted using 373 model solutions performed in 0.084 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -562,11 +581,11 @@
 ## 
 ## Parameter correlation:
 ##            parent_0     log_k1     log_k2      g_ilr      sigma
-## parent_0  1.000e+00  1.732e-01  2.282e-02  4.009e-01 -6.872e-07
-## log_k1    1.732e-01  1.000e+00  4.945e-01 -5.809e-01  3.200e-07
-## log_k2    2.282e-02  4.945e-01  1.000e+00 -6.812e-01  7.673e-07
-## g_ilr     4.009e-01 -5.809e-01 -6.812e-01  1.000e+00 -8.731e-07
-## sigma    -6.872e-07  3.200e-07  7.673e-07 -8.731e-07  1.000e+00
+## parent_0  1.000e+00  1.732e-01  2.282e-02  4.009e-01 -6.868e-07
+## log_k1    1.732e-01  1.000e+00  4.945e-01 -5.809e-01  3.175e-07
+## log_k2    2.282e-02  4.945e-01  1.000e+00 -6.812e-01  7.631e-07
+## g_ilr     4.009e-01 -5.809e-01 -6.812e-01  1.000e+00 -8.694e-07
+## sigma    -6.868e-07  3.175e-07  7.631e-07 -8.694e-07  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -585,8 +604,8 @@
 ## parent     2.225       4  4
 ## 
 ## Estimated disappearance times:
-##         DT50 DT90 DT50_k1 DT50_k2
-## parent 7.464  123   1.343   50.37
+##         DT50 DT90 DT50back DT50_k1 DT50_k2
+## parent 7.464  123    37.03   1.343   50.37
 ## 
 ## Data:
 ##  time variable observed predicted residual
@@ -598,7 +617,8 @@
 ##    60   parent     22.0     23.26 -1.25919
 ##    91   parent     15.0     15.18 -0.18181
 ##   120   parent     12.0     10.19  1.81395</code></pre>
-<div class="sourceCode" id="cb26"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">mm.L3</span><span class="kw">[[</span><span class="st">"DFOP"</span>, <span class="fl">1</span>]], <span class="kw">show_errmin</span> <span class="kw">=</span> <span class="fl">TRUE</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb26"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">mm.L3</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="fl">1</span><span class="op">]</span><span class="op">]</span>, show_errmin <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></pre></div>
 <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-13-1.png" width="700"></p>
 <p>Here, a look to the model plot, the confidence intervals of the parameters and the correlation matrix suggest that the parameter estimates are reliable, and the DFOP model can be used as the best-fit model based on the <span class="math inline">\(\chi^2\)</span> error level criterion for laboratory data L3.</p>
 <p>This is also an example where the standard t-test for the parameter <code>g_ilr</code> is misleading, as it tests for a significant difference from zero. In this case, zero appears to be the correct value for this parameter, and the confidence interval for the backtransformed parameter <code>g</code> is quite narrow.</p>
@@ -608,44 +628,47 @@
 <h1 class="hasAnchor">
 <a href="#laboratory-data-l4" class="anchor"></a>Laboratory Data L4</h1>
 <p>The following code defines example dataset L4 from the FOCUS kinetics report, p. 293:</p>
-<div class="sourceCode" id="cb27"><html><body><pre class="r"><span class="no">FOCUS_2006_L4</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html">data.frame</a></span>(
-  <span class="kw">t</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="fl">0</span>, <span class="fl">3</span>, <span class="fl">7</span>, <span class="fl">14</span>, <span class="fl">30</span>, <span class="fl">60</span>, <span class="fl">91</span>, <span class="fl">120</span>),
-  <span class="kw">parent</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="fl">96.6</span>, <span class="fl">96.3</span>, <span class="fl">94.3</span>, <span class="fl">88.8</span>, <span class="fl">74.9</span>, <span class="fl">59.9</span>, <span class="fl">53.5</span>, <span class="fl">49.0</span>))
-<span class="no">FOCUS_2006_L4_mkin</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span>(<span class="no">FOCUS_2006_L4</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb27"><pre class="downlit">
+<span class="va">FOCUS_2006_L4</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html">data.frame</a></span><span class="op">(</span>
+  t <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">3</span>, <span class="fl">7</span>, <span class="fl">14</span>, <span class="fl">30</span>, <span class="fl">60</span>, <span class="fl">91</span>, <span class="fl">120</span><span class="op">)</span>,
+  parent <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="fl">96.6</span>, <span class="fl">96.3</span>, <span class="fl">94.3</span>, <span class="fl">88.8</span>, <span class="fl">74.9</span>, <span class="fl">59.9</span>, <span class="fl">53.5</span>, <span class="fl">49.0</span><span class="op">)</span><span class="op">)</span>
+<span class="va">FOCUS_2006_L4_mkin</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span><span class="op">(</span><span class="va">FOCUS_2006_L4</span><span class="op">)</span></pre></div>
 <p>Fits of the SFO and FOMC models, plots and summaries are produced below:</p>
-<div class="sourceCode" id="cb28"><html><body><pre class="r"><span class="co"># Only use one core here, not to offend the CRAN checks</span>
-<span class="no">mm.L4</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../reference/mmkin.html">mmkin</a></span>(<span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="st">"SFO"</span>, <span class="st">"FOMC"</span>), <span class="kw">cores</span> <span class="kw">=</span> <span class="fl">1</span>,
-               <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="st">"FOCUS L4"</span> <span class="kw">=</span> <span class="no">FOCUS_2006_L4_mkin</span>),
-               <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)
-<span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">mm.L4</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb28"><pre class="downlit">
+<span class="co"># Only use one core here, not to offend the CRAN checks</span>
+<span class="va">mm.L4</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mmkin.html">mmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"FOMC"</span><span class="op">)</span>, cores <span class="op">=</span> <span class="fl">1</span>,
+               <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="st">"FOCUS L4"</span> <span class="op">=</span> <span class="va">FOCUS_2006_L4_mkin</span><span class="op">)</span>,
+               quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>
+<span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">mm.L4</span><span class="op">)</span></pre></div>
 <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-15-1.png" width="700"></p>
 <p>The <span class="math inline">\(\chi^2\)</span> error level of 3.3% as well as the plot suggest that the SFO model fits very well. The error level at which the <span class="math inline">\(\chi^2\)</span> test passes is slightly lower for the FOMC model. However, the difference appears negligible.</p>
-<div class="sourceCode" id="cb29"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">mm.L4</span><span class="kw">[[</span><span class="st">"SFO"</span>, <span class="fl">1</span>]], <span class="kw">data</span> <span class="kw">=</span> <span class="fl">FALSE</span>)</pre></body></html></div>
-<pre><code>## mkin version used for fitting:    0.9.50.2 
-## R version used for fitting:       4.0.0 
-## Date of fit:     Wed May 27 07:05:38 2020 
-## Date of summary: Wed May 27 07:05:38 2020 
+<div class="sourceCode" id="cb29"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span><span class="op">(</span><span class="va">mm.L4</span><span class="op">[[</span><span class="st">"SFO"</span>, <span class="fl">1</span><span class="op">]</span><span class="op">]</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></pre></div>
+<pre><code>## mkin version used for fitting:    0.9.50.3 
+## R version used for fitting:       4.0.3 
+## Date of fit:     Thu Oct 15 12:42:05 2020 
+## Date of summary: Thu Oct 15 12:42:06 2020 
 ## 
 ## Equations:
-## d_parent/dt = - k_parent_sink * parent
+## d_parent/dt = - k_parent * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 142 model solutions performed in 0.029 s
+## Fitted using 142 model solutions performed in 0.03 s
 ## 
 ## Error model: Constant variance 
 ## 
 ## Error model algorithm: OLS 
 ## 
 ## Starting values for parameters to be optimised:
-##               value   type
-## parent_0       96.6  state
-## k_parent_sink   0.1 deparm
+##          value   type
+## parent_0  96.6  state
+## k_parent   0.1 deparm
 ## 
 ## Starting values for the transformed parameters actually optimised:
-##                       value lower upper
-## parent_0          96.600000  -Inf   Inf
-## log_k_parent_sink -2.302585  -Inf   Inf
+##                  value lower upper
+## parent_0     96.600000  -Inf   Inf
+## log_k_parent -2.302585  -Inf   Inf
 ## 
 ## Fixed parameter values:
 ## None
@@ -656,25 +679,25 @@
 ##   47.12133 47.35966 -20.56067
 ## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
-##                   Estimate Std. Error  Lower   Upper
-## parent_0            96.440    1.69900 92.070 100.800
-## log_k_parent_sink   -5.030    0.07059 -5.211  -4.848
-## sigma                3.162    0.79050  1.130   5.194
+##              Estimate Std. Error  Lower   Upper
+## parent_0       96.440    1.69900 92.070 100.800
+## log_k_parent   -5.030    0.07059 -5.211  -4.848
+## sigma           3.162    0.79050  1.130   5.194
 ## 
 ## Parameter correlation:
-##                    parent_0 log_k_parent_sink     sigma
-## parent_0          1.000e+00         5.938e-01 3.440e-07
-## log_k_parent_sink 5.938e-01         1.000e+00 5.885e-07
-## sigma             3.440e-07         5.885e-07 1.000e+00
+##               parent_0 log_k_parent     sigma
+## parent_0     1.000e+00    5.938e-01 3.387e-07
+## log_k_parent 5.938e-01    1.000e+00 5.830e-07
+## sigma        3.387e-07    5.830e-07 1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
 ## t-test (unrealistically) based on the assumption of normal distribution
 ## for estimators of untransformed parameters.
-##                Estimate t value    Pr(&gt;t)     Lower     Upper
-## parent_0      96.440000   56.77 1.604e-08 92.070000 1.008e+02
-## k_parent_sink  0.006541   14.17 1.578e-05  0.005455 7.842e-03
-## sigma          3.162000    4.00 5.162e-03  1.130000 5.194e+00
+##           Estimate t value    Pr(&gt;t)     Lower     Upper
+## parent_0 96.440000   56.77 1.604e-08 92.070000 1.008e+02
+## k_parent  0.006541   14.17 1.578e-05  0.005455 7.842e-03
+## sigma     3.162000    4.00 5.162e-03  1.130000 5.194e+00
 ## 
 ## FOCUS Chi2 error levels in percent:
 ##          err.min n.optim df
@@ -684,18 +707,19 @@
 ## Estimated disappearance times:
 ##        DT50 DT90
 ## parent  106  352</code></pre>
-<div class="sourceCode" id="cb31"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">mm.L4</span><span class="kw">[[</span><span class="st">"FOMC"</span>, <span class="fl">1</span>]], <span class="kw">data</span> <span class="kw">=</span> <span class="fl">FALSE</span>)</pre></body></html></div>
-<pre><code>## mkin version used for fitting:    0.9.50.2 
-## R version used for fitting:       4.0.0 
-## Date of fit:     Wed May 27 07:05:38 2020 
-## Date of summary: Wed May 27 07:05:38 2020 
+<div class="sourceCode" id="cb31"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span><span class="op">(</span><span class="va">mm.L4</span><span class="op">[[</span><span class="st">"FOMC"</span>, <span class="fl">1</span><span class="op">]</span><span class="op">]</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></pre></div>
+<pre><code>## mkin version used for fitting:    0.9.50.3 
+## R version used for fitting:       4.0.3 
+## Date of fit:     Thu Oct 15 12:42:05 2020 
+## Date of summary: Thu Oct 15 12:42:06 2020 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 224 model solutions performed in 0.043 s
+## Fitted using 224 model solutions performed in 0.046 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -730,10 +754,10 @@
 ## 
 ## Parameter correlation:
 ##             parent_0  log_alpha   log_beta      sigma
-## parent_0   1.000e+00 -4.696e-01 -5.543e-01 -2.563e-07
-## log_alpha -4.696e-01  1.000e+00  9.889e-01  4.066e-08
-## log_beta  -5.543e-01  9.889e-01  1.000e+00  6.818e-08
-## sigma     -2.563e-07  4.066e-08  6.818e-08  1.000e+00
+## parent_0   1.000e+00 -4.696e-01 -5.543e-01 -2.456e-07
+## log_alpha -4.696e-01  1.000e+00  9.889e-01  2.169e-08
+## log_beta  -5.543e-01  9.889e-01  1.000e+00  4.910e-08
+## sigma     -2.456e-07  2.169e-08  4.910e-08  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -780,7 +804,7 @@
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-10-1.png b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-10-1.png
index 88d03d24..a5418249 100644
--- a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-10-1.png
+++ b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-10-1.png
diff --git a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-12-1.png b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-12-1.png
index f23a4c97..521c7079 100644
--- a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-12-1.png
+++ b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-12-1.png
diff --git a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-13-1.png b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-13-1.png
index ed6a781d..1aa97f8c 100644
--- a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-13-1.png
+++ b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-13-1.png
diff --git a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-15-1.png b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-15-1.png
index 2e5071d9..36e862f6 100644
--- a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-15-1.png
+++ b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-15-1.png
diff --git a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-4-1.png b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-4-1.png
index 04bee502..68b24b5e 100644
--- a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-4-1.png
+++ b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-4-1.png
diff --git a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-5-1.png b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-5-1.png
index 86af1cf9..e8f21107 100644
--- a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-5-1.png
+++ b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-5-1.png
diff --git a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-6-1.png b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-6-1.png
index 16235059..53e33b68 100644
--- a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-6-1.png
+++ b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-6-1.png
diff --git a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-8-1.png b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-8-1.png
index 8b39f0fc..47d5b335 100644
--- a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-8-1.png
+++ b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-8-1.png
diff --git a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-9-1.png b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-9-1.png
index 13019224..f644c299 100644
--- a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-9-1.png
+++ b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-9-1.png
diff --git a/docs/articles/index.html b/docs/articles/index.html
index 6f97722c..0ff8d97f 100644
--- a/docs/articles/index.html
+++ b/docs/articles/index.html
@@ -71,7 +71,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -108,6 +108,9 @@
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -116,7 +119,7 @@
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -154,7 +157,7 @@
         <dd></dt>
         <dt><a href="web_only/NAFTA_examples.html">Evaluation of example datasets from Attachment 1 to the US EPA SOP for the NAFTA guidance</a></dt>
         <dd></dt>
-        <dt><a href="web_only/benchmarks.html">Benchmark timings for mkin on various systems</a></dt>
+        <dt><a href="web_only/benchmarks.html">Benchmark timings for mkin</a></dt>
         <dd></dt>
         <dt><a href="web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a></dt>
         <dd></dt>
@@ -170,7 +173,7 @@
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/articles/mkin.html b/docs/articles/mkin.html
index 5f858d57..0c417f13 100644
--- a/docs/articles/mkin.html
+++ b/docs/articles/mkin.html
@@ -31,7 +31,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -68,6 +68,9 @@
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -76,7 +79,7 @@
       </ul>
 <ul class="nav navbar-nav navbar-right">
 <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -97,49 +100,50 @@
       <h1 data-toc-skip>Introduction to mkin</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2020-05-27</h4>
+            <h4 class="date">2020-10-15</h4>
       
-      <small class="dont-index">Source: <a href="http://github.com/jranke/mkin/blob/master/vignettes/mkin.Rmd"><code>vignettes/mkin.Rmd</code></a></small>
-      <div class="hidden name"><code>mkin.Rmd</code></div>
+      <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/master/vignettes/mkin.rmd"><code>vignettes/mkin.rmd</code></a></small>
+      <div class="hidden name"><code>mkin.rmd</code></div>
 
     </div>
 
     
     
-<p><a href="http://www.jrwb.de">Wissenschaftlicher Berater, Kronacher Str. 12, 79639 Grenzach-Wyhlen, Germany</a><br><a href="http://chem.uft.uni-bremen.de/ranke">Privatdozent at the University of Bremen</a></p>
+<p><a href="https://www.jrwb.de">Wissenschaftlicher Berater, Kronacher Str. 12, 79639 Grenzach-Wyhlen, Germany</a><br><a href="http://chem.uft.uni-bremen.de/ranke/">Privatdozent at the University of Bremen</a></p>
 <div id="abstract" class="section level1">
 <h1 class="hasAnchor">
 <a href="#abstract" class="anchor"></a>Abstract</h1>
 <p>In the regulatory evaluation of chemical substances like plant protection products (pesticides), biocides and other chemicals, degradation data play an important role. For the evaluation of pesticide degradation experiments, detailed guidance has been developed, based on nonlinear optimisation. The <code>R</code> add-on package <code>mkin</code> implements fitting some of the models recommended in this guidance from within R and calculates some statistical measures for data series within one or more compartments, for parent and metabolites.</p>
-<div class="sourceCode" id="cb1"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/library.html">library</a></span>(<span class="st">"mkin"</span>, <span class="kw">quietly</span> <span class="kw">=</span> <span class="fl">TRUE</span>)
+<div class="sourceCode" id="cb1"><pre class="downlit">
+<span class="kw"><a href="https://rdrr.io/r/base/library.html">library</a></span><span class="op">(</span><span class="st"><a href="https://pkgdown.jrwb.de/mkin/">"mkin"</a></span>, quietly <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>
 <span class="co"># Define the kinetic model</span>
-<span class="no">m_SFO_SFO_SFO</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../reference/mkinmod.html">mkinmod</a></span>(<span class="kw">parent</span> <span class="kw">=</span> <span class="fu"><a href="../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"M1"</span>),
-                         <span class="kw">M1</span> <span class="kw">=</span> <span class="fu"><a href="../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"M2"</span>),
-                         <span class="kw">M2</span> <span class="kw">=</span> <span class="fu"><a href="../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>),
-                         <span class="kw">use_of_ff</span> <span class="kw">=</span> <span class="st">"max"</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)
+<span class="va">m_SFO_SFO_SFO</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>parent <span class="op">=</span> <span class="fu"><a href="../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M1"</span><span class="op">)</span>,
+                         M1 <span class="op">=</span> <span class="fu"><a href="../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M2"</span><span class="op">)</span>,
+                         M2 <span class="op">=</span> <span class="fu"><a href="../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,
+                         use_of_ff <span class="op">=</span> <span class="st">"max"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>
 
 
 <span class="co"># Produce model predictions using some arbitrary parameters</span>
-<span class="no">sampling_times</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="fl">0</span>, <span class="fl">1</span>, <span class="fl">3</span>, <span class="fl">7</span>, <span class="fl">14</span>, <span class="fl">28</span>, <span class="fl">60</span>, <span class="fl">90</span>, <span class="fl">120</span>)
-<span class="no">d_SFO_SFO_SFO</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../reference/mkinpredict.html">mkinpredict</a></span>(<span class="no">m_SFO_SFO_SFO</span>,
-  <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="kw">k_parent</span> <span class="kw">=</span> <span class="fl">0.03</span>,
-    <span class="kw">f_parent_to_M1</span> <span class="kw">=</span> <span class="fl">0.5</span>, <span class="kw">k_M1</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/Log.html">log</a></span>(<span class="fl">2</span>)/<span class="fl">100</span>,
-    <span class="kw">f_M1_to_M2</span> <span class="kw">=</span> <span class="fl">0.9</span>, <span class="kw">k_M2</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/Log.html">log</a></span>(<span class="fl">2</span>)/<span class="fl">50</span>),
-  <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="kw">parent</span> <span class="kw">=</span> <span class="fl">100</span>, <span class="kw">M1</span> <span class="kw">=</span> <span class="fl">0</span>, <span class="kw">M2</span> <span class="kw">=</span> <span class="fl">0</span>),
-  <span class="no">sampling_times</span>)
+<span class="va">sampling_times</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">1</span>, <span class="fl">3</span>, <span class="fl">7</span>, <span class="fl">14</span>, <span class="fl">28</span>, <span class="fl">60</span>, <span class="fl">90</span>, <span class="fl">120</span><span class="op">)</span>
+<span class="va">d_SFO_SFO_SFO</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkinpredict.html">mkinpredict</a></span><span class="op">(</span><span class="va">m_SFO_SFO_SFO</span>,
+  <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span>k_parent <span class="op">=</span> <span class="fl">0.03</span>,
+    f_parent_to_M1 <span class="op">=</span> <span class="fl">0.5</span>, k_M1 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/Log.html">log</a></span><span class="op">(</span><span class="fl">2</span><span class="op">)</span><span class="op">/</span><span class="fl">100</span>,
+    f_M1_to_M2 <span class="op">=</span> <span class="fl">0.9</span>, k_M2 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/Log.html">log</a></span><span class="op">(</span><span class="fl">2</span><span class="op">)</span><span class="op">/</span><span class="fl">50</span><span class="op">)</span>,
+  <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span>parent <span class="op">=</span> <span class="fl">100</span>, M1 <span class="op">=</span> <span class="fl">0</span>, M2 <span class="op">=</span> <span class="fl">0</span><span class="op">)</span>,
+  <span class="va">sampling_times</span><span class="op">)</span>
 
 <span class="co"># Generate a dataset by adding normally distributed errors with</span>
 <span class="co"># standard deviation 3, for two replicates at each sampling time</span>
-<span class="no">d_SFO_SFO_SFO_err</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../reference/add_err.html">add_err</a></span>(<span class="no">d_SFO_SFO_SFO</span>, <span class="kw">reps</span> <span class="kw">=</span> <span class="fl">2</span>,
-                             <span class="kw">sdfunc</span> <span class="kw">=</span> <span class="kw">function</span>(<span class="no">x</span>) <span class="fl">3</span>,
-                             <span class="kw">n</span> <span class="kw">=</span> <span class="fl">1</span>, <span class="kw">seed</span> <span class="kw">=</span> <span class="fl">123456789</span> )
+<span class="va">d_SFO_SFO_SFO_err</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/add_err.html">add_err</a></span><span class="op">(</span><span class="va">d_SFO_SFO_SFO</span>, reps <span class="op">=</span> <span class="fl">2</span>,
+                             sdfunc <span class="op">=</span> <span class="kw">function</span><span class="op">(</span><span class="va">x</span><span class="op">)</span> <span class="fl">3</span>,
+                             n <span class="op">=</span> <span class="fl">1</span>, seed <span class="op">=</span> <span class="fl">123456789</span> <span class="op">)</span>
 
 <span class="co"># Fit the model to the dataset</span>
-<span class="no">f_SFO_SFO_SFO</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span>(<span class="no">m_SFO_SFO_SFO</span>, <span class="no">d_SFO_SFO_SFO_err</span><span class="kw">[[</span><span class="fl">1</span>]], <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)
+<span class="va">f_SFO_SFO_SFO</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">m_SFO_SFO_SFO</span>, <span class="va">d_SFO_SFO_SFO_err</span><span class="op">[[</span><span class="fl">1</span><span class="op">]</span><span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>
 
 <span class="co"># Plot the results separately for parent and metabolites</span>
-<span class="fu"><a href="../reference/plot.mkinfit.html">plot_sep</a></span>(<span class="no">f_SFO_SFO_SFO</span>, <span class="kw">lpos</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="st">"topright"</span>, <span class="st">"bottomright"</span>, <span class="st">"bottomright"</span>))</pre></body></html></div>
-<p><img src="../docs/articles/mkin_files/figure-html/unnamed-chunk-2-1.png" width="768"></p>
+<span class="fu"><a href="../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">f_SFO_SFO_SFO</span>, lpos <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="st">"topright"</span>, <span class="st">"bottomright"</span>, <span class="st">"bottomright"</span><span class="op">)</span><span class="op">)</span></pre></div>
+<p><img src="mkin_files/figure-html/unnamed-chunk-2-1.png" width="768"></p>
 </div>
 <div id="background" class="section level1">
 <h1 class="hasAnchor">
@@ -147,7 +151,7 @@
 <p>Many approaches are possible regarding the evaluation of chemical degradation data.</p>
 <p>The <code>mkin</code> package <span class="citation">(Ranke 2019)</span> implements the approach recommended in the kinetics report provided by the FOrum for Co-ordination of pesticide fate models and their USe <span class="citation">(FOCUS Work Group on Degradation Kinetics 2006, 2014)</span> for simple decline data series, data series with transformation products, commonly termed metabolites, and for data series for more than one compartment. It is also possible to include back reactions, so equilibrium reactions and equilibrium partitioning can be specified, although this oftentimes leads to an overparameterisation of the model.</p>
 <p>When the first <code>mkin</code> code was published in 2010, the most commonly used tools for fitting more complex kinetic degradation models to experimental data were KinGUI <span class="citation">(Schäfer et al. 2007)</span>, a MATLAB based tool with a graphical user interface that was specifically tailored to the task and included some output as proposed by the FOCUS Kinetics Workgroup, and ModelMaker, a general purpose compartment based tool providing infrastructure for fitting dynamic simulation models based on differential equations to data.</p>
-<p>The code was first uploaded to the BerliOS platform. When this was taken down, the version control history was imported into the R-Forge site (see <em>e.g.</em> <a href="http://cgit.jrwb.de/mkin/commit/?id=30cbb4092f6d2d3beff5800603374a0d009ad770">the initial commit on 11 May 2010</a>), where the code is still occasionally updated.</p>
+<p>The code was first uploaded to the BerliOS platform. When this was taken down, the version control history was imported into the R-Forge site (see <em>e.g.</em> <a href="https://cgit.jrwb.de/mkin/commit/?id=30cbb4092f6d2d3beff5800603374a0d009ad770">the initial commit on 11 May 2010</a>), where the code is still occasionally updated.</p>
 <p>At that time, the R package <code>FME</code> (Flexible Modelling Environment) <span class="citation">(Soetaert and Petzoldt 2010)</span> was already available, and provided a good basis for developing a package specifically tailored to the task. The remaining challenge was to make it as easy as possible for the users (including the author of this vignette) to specify the system of differential equations and to include the output requested by the FOCUS guidance, such as the relative standard deviation that has to be assumed for the residuals, such that the <span class="math inline">\(\chi^2\)</span> goodness-of-fit test as defined by the FOCUS kinetics workgroup would pass using an significance level <span class="math inline">\(\alpha\)</span> of 0.05. This relative error, expressed as a percentage, is often termed <span class="math inline">\(\chi^2\)</span> error level or similar.</p>
 <p>Also, <code>mkin</code> introduced using analytical solutions for parent only kinetics for improved optimization speed. Later, Eigenvalue based solutions were introduced to <code>mkin</code> for the case of linear differential equations (<em>i.e.</em> where the FOMC or DFOP models were not used for the parent compound), greatly improving the optimization speed for these cases. This, however, has become somehow obsolete, as the use of compiled code described below gives even smaller execution times.</p>
 <p>The possibility to specify back-reactions and a biphasic model (SFORB) for metabolites were present in <code>mkin</code> from the very beginning.</p>
@@ -157,7 +161,7 @@
 <p>Soon after the publication of <code>mkin</code>, two derived tools were published, namely KinGUII (available from Bayer Crop Science) and CAKE (commissioned to Tessella by Syngenta), which added a graphical user interface (GUI), and added fitting by iteratively reweighted least squares (IRLS) and characterisation of likely parameter distributions by Markov Chain Monte Carlo (MCMC) sampling.</p>
 <p>CAKE focuses on a smooth use experience, sacrificing some flexibility in the model definition, originally allowing only two primary metabolites in parallel. The current version 3.3 of CAKE release in March 2016 uses a basic scheme for up to six metabolites in a flexible arrangement, but does not support back-reactions (non-instantaneous equilibria) or biphasic kinetics for metabolites.</p>
 <p>KinGUI offers an even more flexible widget for specifying complex kinetic models. Back-reactions (non-instantaneous equilibria) were supported early on, but until 2014, only simple first-order models could be specified for transformation products. Starting with KinGUII version 2.1, biphasic modelling of metabolites was also available in KinGUII.</p>
-<p>A further graphical user interface (GUI) that has recently been brought to a decent degree of maturity is the browser based GUI named <code>gmkin</code>. Please see its <a href="https://pkgdown.jrwb.de/gmkin">documentation page</a> and <a href="https://pkgdown.jrwb.de/gmkin/articles/gmkin_manual.html">manual</a> for further information.</p>
+<p>A further graphical user interface (GUI) that has recently been brought to a decent degree of maturity is the browser based GUI named <code>gmkin</code>. Please see its <a href="https://pkgdown.jrwb.de/gmkin/">documentation page</a> and <a href="https://pkgdown.jrwb.de/gmkin/articles/gmkin_manual.html">manual</a> for further information.</p>
 <p>A comparison of scope, usability and numerical results obtained with these tools has been recently been published by <span class="citation">Ranke, Wöltjen, and Meinecke (2018)</span>.</p>
 </div>
 <div id="recent-developments" class="section level2">
@@ -223,7 +227,7 @@
 <p>Schäfer, D., B. Mikolasch, P. Rainbird, and B. Harvey. 2007. “KinGUI: A New Kinetic Software Tool for Evaluations According to FOCUS Degradation Kinetics.” In <em>Proceedings of the Xiii Symposium Pesticide Chemistry</em>, edited by Del Re A. A. M., Capri E., Fragoulis G., and Trevisan M., 916–23. Piacenza.</p>
 </div>
 <div id="ref-soetaert2010">
-<p>Soetaert, Karline, and Thomas Petzoldt. 2010. “Inverse Modelling, Sensitivity and Monte Carlo Analysis in R Using Package FME.” <em>Journal of Statistical Software</em> 33 (3): 1–28. <a href="http://www.jstatsoft.org/v33/i03/" class="uri">http://www.jstatsoft.org/v33/i03/</a>.</p>
+<p>Soetaert, Karline, and Thomas Petzoldt. 2010. “Inverse Modelling, Sensitivity and Monte Carlo Analysis in R Using Package FME.” <em>Journal of Statistical Software</em> 33 (3): 1–28. <a href="https://www.jstatsoft.org/v33/i03/" class="uri">https://www.jstatsoft.org/v33/i03/</a>.</p>
 </div>
 </div>
 </div>
@@ -244,7 +248,7 @@
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/articles/mkin_files/figure-html/unnamed-chunk-2-1.png b/docs/articles/mkin_files/figure-html/unnamed-chunk-2-1.png
new file mode 100644
index 00000000..2f3d7a46
--- /dev/null
+++ b/docs/articles/mkin_files/figure-html/unnamed-chunk-2-1.png
diff --git a/docs/articles/twa.html b/docs/articles/twa.html
index e70205f2..3f7820b4 100644
--- a/docs/articles/twa.html
+++ b/docs/articles/twa.html
@@ -31,7 +31,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -68,6 +68,9 @@
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -76,7 +79,7 @@
       </ul>
 <ul class="nav navbar-nav navbar-right">
 <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -97,10 +100,10 @@
       <h1 data-toc-skip>Calculation of time weighted average concentrations with mkin</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2020-05-27</h4>
+            <h4 class="date">2020-10-15</h4>
       
-      <small class="dont-index">Source: <a href="http://github.com/jranke/mkin/blob/master/vignettes/twa.Rmd"><code>vignettes/twa.Rmd</code></a></small>
-      <div class="hidden name"><code>twa.Rmd</code></div>
+      <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/master/vignettes/twa.rmd"><code>vignettes/twa.rmd</code></a></small>
+      <div class="hidden name"><code>twa.rmd</code></div>
 
     </div>
 
@@ -137,7 +140,7 @@
 <p><span class="math display">\[f_\textrm{twa} = \frac{1}{t} \left(
   \frac{1}{k_1} \left( 1 - e^{- k_1 t_b} \right) +
   \frac{e^{- k_1 t_b}}{k_2} \left( 1 - e^{- k_2 (t - t_b)} \right)  \right) \]</span></p>
-<p>Note that a method for calculating maximum moving window time weighted average concentrations for a model fitted by ‘mkinfit’ or from parent decline model parameters is included in the <code><a href="../reference/max_twa_parent.html">max_twa_parent()</a></code> function. If the same is needed for metabolites, the function <code><a href="https://rdrr.io/pkg/pfm/man/max_twa.html">pfm::max_twa()</a></code> from the ‘pfm’ package can be used.</p>
+<p>Note that a method for calculating maximum moving window time weighted average concentrations for a model fitted by ‘mkinfit’ or from parent decline model parameters is included in the <code><a href="../reference/max_twa_parent.html">max_twa_parent()</a></code> function. If the same is needed for metabolites, the function <code><a href="https://pkgdown.jrwb.de/pfm/reference/max_twa.html">pfm::max_twa()</a></code> from the ‘pfm’ package can be used.</p>
 <div id="refs" class="references">
 <div id="ref-FOCUSkinetics2014">
 <p>FOCUS Work Group on Degradation Kinetics. 2014. <em>Generic Guidance for Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in Eu Registration</em>. 1.1 ed. <a href="http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics" class="uri">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>.</p>
@@ -158,7 +161,7 @@
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/articles/web_only/FOCUS_Z.html b/docs/articles/web_only/FOCUS_Z.html
index ccbfcc86..b740b5ed 100644
--- a/docs/articles/web_only/FOCUS_Z.html
+++ b/docs/articles/web_only/FOCUS_Z.html
@@ -31,7 +31,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -68,6 +68,9 @@
     <li>
       <a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -76,7 +79,7 @@
       </ul>
 <ul class="nav navbar-nav navbar-right">
 <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -97,10 +100,10 @@
       <h1 data-toc-skip>Example evaluation of FOCUS dataset Z</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2020-05-27</h4>
+            <h4 class="date">2020-10-15</h4>
       
-      <small class="dont-index">Source: <a href="http://github.com/jranke/mkin/blob/master/vignettes/web_only/FOCUS_Z.Rmd"><code>vignettes/web_only/FOCUS_Z.Rmd</code></a></small>
-      <div class="hidden name"><code>FOCUS_Z.Rmd</code></div>
+      <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/master/vignettes/web_only/FOCUS_Z.rmd"><code>vignettes/web_only/FOCUS_Z.rmd</code></a></small>
+      <div class="hidden name"><code>FOCUS_Z.rmd</code></div>
 
     </div>
 
@@ -111,35 +114,40 @@
 <h1 class="hasAnchor">
 <a href="#the-data" class="anchor"></a>The data</h1>
 <p>The following code defines the example dataset from Appendix 7 to the FOCUS kinetics report <span class="citation">(FOCUS Work Group on Degradation Kinetics 2014, 354)</span>.</p>
-<div class="sourceCode" id="cb1"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/library.html">library</a></span>(<span class="no">mkin</span>, <span class="kw">quietly</span> <span class="kw">=</span> <span class="fl">TRUE</span>)
-<span class="no">LOD</span> <span class="kw">=</span> <span class="fl">0.5</span>
-<span class="no">FOCUS_2006_Z</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html">data.frame</a></span>(
-  <span class="kw">t</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="fl">0</span>, <span class="fl">0.04</span>, <span class="fl">0.125</span>, <span class="fl">0.29</span>, <span class="fl">0.54</span>, <span class="fl">1</span>, <span class="fl">2</span>, <span class="fl">3</span>, <span class="fl">4</span>, <span class="fl">7</span>, <span class="fl">10</span>, <span class="fl">14</span>, <span class="fl">21</span>,
-        <span class="fl">42</span>, <span class="fl">61</span>, <span class="fl">96</span>, <span class="fl">124</span>),
-  <span class="kw">Z0</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="fl">100</span>, <span class="fl">81.7</span>, <span class="fl">70.4</span>, <span class="fl">51.1</span>, <span class="fl">41.2</span>, <span class="fl">6.6</span>, <span class="fl">4.6</span>, <span class="fl">3.9</span>, <span class="fl">4.6</span>, <span class="fl">4.3</span>, <span class="fl">6.8</span>,
-         <span class="fl">2.9</span>, <span class="fl">3.5</span>, <span class="fl">5.3</span>, <span class="fl">4.4</span>, <span class="fl">1.2</span>, <span class="fl">0.7</span>),
-  <span class="kw">Z1</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="fl">0</span>, <span class="fl">18.3</span>, <span class="fl">29.6</span>, <span class="fl">46.3</span>, <span class="fl">55.1</span>, <span class="fl">65.7</span>, <span class="fl">39.1</span>, <span class="fl">36</span>, <span class="fl">15.3</span>, <span class="fl">5.6</span>, <span class="fl">1.1</span>,
-         <span class="fl">1.6</span>, <span class="fl">0.6</span>, <span class="fl">0.5</span> * <span class="no">LOD</span>, <span class="fl">NA</span>, <span class="fl">NA</span>, <span class="fl">NA</span>),
-  <span class="kw">Z2</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="fl">0</span>, <span class="fl">NA</span>, <span class="fl">0.5</span> * <span class="no">LOD</span>, <span class="fl">2.6</span>, <span class="fl">3.8</span>, <span class="fl">15.3</span>, <span class="fl">37.2</span>, <span class="fl">31.7</span>, <span class="fl">35.6</span>, <span class="fl">14.5</span>,
-         <span class="fl">0.8</span>, <span class="fl">2.1</span>, <span class="fl">1.9</span>, <span class="fl">0.5</span> * <span class="no">LOD</span>, <span class="fl">NA</span>, <span class="fl">NA</span>, <span class="fl">NA</span>),
-  <span class="kw">Z3</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="fl">0</span>, <span class="fl">NA</span>, <span class="fl">NA</span>, <span class="fl">NA</span>, <span class="fl">NA</span>, <span class="fl">0.5</span> * <span class="no">LOD</span>, <span class="fl">9.2</span>, <span class="fl">13.1</span>, <span class="fl">22.3</span>, <span class="fl">28.4</span>, <span class="fl">32.5</span>,
-         <span class="fl">25.2</span>, <span class="fl">17.2</span>, <span class="fl">4.8</span>, <span class="fl">4.5</span>, <span class="fl">2.8</span>, <span class="fl">4.4</span>))
+<div class="sourceCode" id="cb1"><pre class="downlit">
+<span class="kw"><a href="https://rdrr.io/r/base/library.html">library</a></span><span class="op">(</span><span class="va"><a href="https://pkgdown.jrwb.de/mkin/">mkin</a></span>, quietly <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>
+<span class="va">LOD</span> <span class="op">=</span> <span class="fl">0.5</span>
+<span class="va">FOCUS_2006_Z</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html">data.frame</a></span><span class="op">(</span>
+  t <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">0.04</span>, <span class="fl">0.125</span>, <span class="fl">0.29</span>, <span class="fl">0.54</span>, <span class="fl">1</span>, <span class="fl">2</span>, <span class="fl">3</span>, <span class="fl">4</span>, <span class="fl">7</span>, <span class="fl">10</span>, <span class="fl">14</span>, <span class="fl">21</span>,
+        <span class="fl">42</span>, <span class="fl">61</span>, <span class="fl">96</span>, <span class="fl">124</span><span class="op">)</span>,
+  Z0 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="fl">100</span>, <span class="fl">81.7</span>, <span class="fl">70.4</span>, <span class="fl">51.1</span>, <span class="fl">41.2</span>, <span class="fl">6.6</span>, <span class="fl">4.6</span>, <span class="fl">3.9</span>, <span class="fl">4.6</span>, <span class="fl">4.3</span>, <span class="fl">6.8</span>,
+         <span class="fl">2.9</span>, <span class="fl">3.5</span>, <span class="fl">5.3</span>, <span class="fl">4.4</span>, <span class="fl">1.2</span>, <span class="fl">0.7</span><span class="op">)</span>,
+  Z1 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">18.3</span>, <span class="fl">29.6</span>, <span class="fl">46.3</span>, <span class="fl">55.1</span>, <span class="fl">65.7</span>, <span class="fl">39.1</span>, <span class="fl">36</span>, <span class="fl">15.3</span>, <span class="fl">5.6</span>, <span class="fl">1.1</span>,
+         <span class="fl">1.6</span>, <span class="fl">0.6</span>, <span class="fl">0.5</span> <span class="op">*</span> <span class="va">LOD</span>, <span class="cn">NA</span>, <span class="cn">NA</span>, <span class="cn">NA</span><span class="op">)</span>,
+  Z2 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="cn">NA</span>, <span class="fl">0.5</span> <span class="op">*</span> <span class="va">LOD</span>, <span class="fl">2.6</span>, <span class="fl">3.8</span>, <span class="fl">15.3</span>, <span class="fl">37.2</span>, <span class="fl">31.7</span>, <span class="fl">35.6</span>, <span class="fl">14.5</span>,
+         <span class="fl">0.8</span>, <span class="fl">2.1</span>, <span class="fl">1.9</span>, <span class="fl">0.5</span> <span class="op">*</span> <span class="va">LOD</span>, <span class="cn">NA</span>, <span class="cn">NA</span>, <span class="cn">NA</span><span class="op">)</span>,
+  Z3 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="cn">NA</span>, <span class="cn">NA</span>, <span class="cn">NA</span>, <span class="cn">NA</span>, <span class="fl">0.5</span> <span class="op">*</span> <span class="va">LOD</span>, <span class="fl">9.2</span>, <span class="fl">13.1</span>, <span class="fl">22.3</span>, <span class="fl">28.4</span>, <span class="fl">32.5</span>,
+         <span class="fl">25.2</span>, <span class="fl">17.2</span>, <span class="fl">4.8</span>, <span class="fl">4.5</span>, <span class="fl">2.8</span>, <span class="fl">4.4</span><span class="op">)</span><span class="op">)</span>
 
-<span class="no">FOCUS_2006_Z_mkin</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span>(<span class="no">FOCUS_2006_Z</span>)</pre></body></html></div>
+<span class="va">FOCUS_2006_Z_mkin</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span><span class="op">(</span><span class="va">FOCUS_2006_Z</span><span class="op">)</span></pre></div>
 </div>
 <div id="parent-and-one-metabolite" class="section level1">
 <h1 class="hasAnchor">
 <a href="#parent-and-one-metabolite" class="anchor"></a>Parent and one metabolite</h1>
 <p>The next step is to set up the models used for the kinetic analysis. As the simultaneous fit of parent and the first metabolite is usually straightforward, Step 1 (SFO for parent only) is skipped here. We start with the model 2a, with formation and decline of metabolite Z1 and the pathway from parent directly to sink included (default in mkin).</p>
-<div class="sourceCode" id="cb2"><html><body><pre class="r"><span class="no">Z.2a</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="kw">Z0</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z1"</span>),
-                <span class="kw">Z1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>))</pre></body></html></div>
+<div class="sourceCode" id="cb2"><pre class="downlit">
+<span class="va">Z.2a</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z1"</span><span class="op">)</span>,
+                Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span><span class="op">)</span></pre></div>
 <pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
-<div class="sourceCode" id="cb4"><html><body><pre class="r"><span class="no">m.Z.2a</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">Z.2a</span>, <span class="no">FOCUS_2006_Z_mkin</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb4"><pre class="downlit">
+<span class="va">m.Z.2a</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.2a</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></pre></div>
 <pre><code>## Warning in mkinfit(Z.2a, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with
 ## value of zero were removed from the data</code></pre>
-<div class="sourceCode" id="cb6"><html><body><pre class="r"><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(<span class="no">m.Z.2a</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb6"><pre class="downlit">
+<span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.2a</span><span class="op">)</span></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png" width="700"></p>
-<div class="sourceCode" id="cb7"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">m.Z.2a</span>, <span class="kw">data</span> <span class="kw">=</span> <span class="fl">FALSE</span>)$<span class="no">bpar</span></pre></body></html></div>
+<div class="sourceCode" id="cb7"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span><span class="op">(</span><span class="va">m.Z.2a</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></pre></div>
 <pre><code>##            Estimate se_notrans t value     Pr(&gt;t)    Lower    Upper
 ## Z0_0       97.01488   3.301084 29.3888 3.2971e-21 91.66556 102.3642
 ## k_Z0        2.23601   0.207078 10.7979 3.3309e-11  1.95303   2.5600
@@ -148,16 +156,20 @@
 ## sigma       4.80411   0.635638  7.5579 3.2592e-08  3.52677   6.0815</code></pre>
 <p>As obvious from the parameter summary (the  component of the summary), the kinetic rate constant from parent compound Z to sink is very small and the t-test for this parameter suggests that it is not significantly different from zero. This suggests, in agreement with the analysis in the FOCUS kinetics report, to simplify the model by removing the pathway to sink.</p>
 <p>A similar result can be obtained when formation fractions are used in the model formulation:</p>
-<div class="sourceCode" id="cb9"><html><body><pre class="r"><span class="no">Z.2a.ff</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="kw">Z0</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z1"</span>),
-                   <span class="kw">Z1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>),
-                   <span class="kw">use_of_ff</span> <span class="kw">=</span> <span class="st">"max"</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb9"><pre class="downlit">
+<span class="va">Z.2a.ff</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z1"</span><span class="op">)</span>,
+                   Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,
+                   use_of_ff <span class="op">=</span> <span class="st">"max"</span><span class="op">)</span></pre></div>
 <pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
-<div class="sourceCode" id="cb11"><html><body><pre class="r"><span class="no">m.Z.2a.ff</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">Z.2a.ff</span>, <span class="no">FOCUS_2006_Z_mkin</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb11"><pre class="downlit">
+<span class="va">m.Z.2a.ff</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.2a.ff</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></pre></div>
 <pre><code>## Warning in mkinfit(Z.2a.ff, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with
 ## value of zero were removed from the data</code></pre>
-<div class="sourceCode" id="cb13"><html><body><pre class="r"><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(<span class="no">m.Z.2a.ff</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb13"><pre class="downlit">
+<span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.2a.ff</span><span class="op">)</span></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png" width="700"></p>
-<div class="sourceCode" id="cb14"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">m.Z.2a.ff</span>, <span class="kw">data</span> <span class="kw">=</span> <span class="fl">FALSE</span>)$<span class="no">bpar</span></pre></body></html></div>
+<div class="sourceCode" id="cb14"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span><span class="op">(</span><span class="va">m.Z.2a.ff</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></pre></div>
 <pre><code>##            Estimate se_notrans t value     Pr(&gt;t)    Lower    Upper
 ## Z0_0       97.01488   3.301084 29.3888 3.2971e-21 91.66556 102.3642
 ## k_Z0        2.23601   0.207078 10.7979 3.3309e-11  1.95303   2.5600
@@ -167,15 +179,19 @@
 <p>Here, the ilr transformed formation fraction fitted in the model takes a very large value, and the backtransformed formation fraction from parent Z to Z1 is practically unity. Here, the covariance matrix used for the calculation of confidence intervals is not returned as the model is overparameterised.</p>
 <p>A simplified model is obtained by removing the pathway to the sink. </p>
 <p>In the following, we use the parameterisation with formation fractions in order to be able to compare with the results in the FOCUS guidance, and as it makes it easier to use parameters obtained in a previous fit when adding a further metabolite.</p>
-<div class="sourceCode" id="cb16"><html><body><pre class="r"><span class="no">Z.3</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="kw">Z0</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z1"</span>, <span class="kw">sink</span> <span class="kw">=</span> <span class="fl">FALSE</span>),
-               <span class="kw">Z1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>), <span class="kw">use_of_ff</span> <span class="kw">=</span> <span class="st">"max"</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb16"><pre class="downlit">
+<span class="va">Z.3</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,
+               Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>, use_of_ff <span class="op">=</span> <span class="st">"max"</span><span class="op">)</span></pre></div>
 <pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
-<div class="sourceCode" id="cb18"><html><body><pre class="r"><span class="no">m.Z.3</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">Z.3</span>, <span class="no">FOCUS_2006_Z_mkin</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb18"><pre class="downlit">
+<span class="va">m.Z.3</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.3</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></pre></div>
 <pre><code>## Warning in mkinfit(Z.3, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with
 ## value of zero were removed from the data</code></pre>
-<div class="sourceCode" id="cb20"><html><body><pre class="r"><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(<span class="no">m.Z.3</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb20"><pre class="downlit">
+<span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.3</span><span class="op">)</span></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png" width="700"></p>
-<div class="sourceCode" id="cb21"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">m.Z.3</span>, <span class="kw">data</span> <span class="kw">=</span> <span class="fl">FALSE</span>)$<span class="no">bpar</span></pre></body></html></div>
+<div class="sourceCode" id="cb21"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span><span class="op">(</span><span class="va">m.Z.3</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></pre></div>
 <pre><code>##       Estimate se_notrans t value     Pr(&gt;t)    Lower    Upper
 ## Z0_0  97.01488   2.597342  37.352 2.0106e-24 91.67597 102.3538
 ## k_Z0   2.23601   0.146904  15.221 9.1477e-15  1.95354   2.5593
@@ -187,51 +203,59 @@
 <h1 class="hasAnchor">
 <a href="#metabolites-z2-and-z3" class="anchor"></a>Metabolites Z2 and Z3</h1>
 <p>As suggested in the FOCUS report, the pathway to sink was removed for metabolite Z1 as well in the next step. While this step appears questionable on the basis of the above results, it is followed here for the purpose of comparison. Also, in the FOCUS report, it is assumed that there is additional empirical evidence that Z1 quickly and exclusively hydrolyses to Z2.</p>
-<div class="sourceCode" id="cb23"><html><body><pre class="r"><span class="no">Z.5</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="kw">Z0</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z1"</span>, <span class="kw">sink</span> <span class="kw">=</span> <span class="fl">FALSE</span>),
-               <span class="kw">Z1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z2"</span>, <span class="kw">sink</span> <span class="kw">=</span> <span class="fl">FALSE</span>),
-               <span class="kw">Z2</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>), <span class="kw">use_of_ff</span> <span class="kw">=</span> <span class="st">"max"</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb23"><pre class="downlit">
+<span class="va">Z.5</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,
+               Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,
+               Z2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>, use_of_ff <span class="op">=</span> <span class="st">"max"</span><span class="op">)</span></pre></div>
 <pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
-<div class="sourceCode" id="cb25"><html><body><pre class="r"><span class="no">m.Z.5</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">Z.5</span>, <span class="no">FOCUS_2006_Z_mkin</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb25"><pre class="downlit">
+<span class="va">m.Z.5</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.5</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></pre></div>
 <pre><code>## Warning in mkinfit(Z.5, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with
 ## value of zero were removed from the data</code></pre>
-<div class="sourceCode" id="cb27"><html><body><pre class="r"><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(<span class="no">m.Z.5</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb27"><pre class="downlit">
+<span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.5</span><span class="op">)</span></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png" width="700"></p>
 <p>Finally, metabolite Z3 is added to the model. We use the optimised differential equation parameter values from the previous fit in order to accelerate the optimization.</p>
-<div class="sourceCode" id="cb28"><html><body><pre class="r"><span class="no">Z.FOCUS</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="kw">Z0</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z1"</span>, <span class="kw">sink</span> <span class="kw">=</span> <span class="fl">FALSE</span>),
-                   <span class="kw">Z1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z2"</span>, <span class="kw">sink</span> <span class="kw">=</span> <span class="fl">FALSE</span>),
-                   <span class="kw">Z2</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z3"</span>),
-                   <span class="kw">Z3</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>),
-                   <span class="kw">use_of_ff</span> <span class="kw">=</span> <span class="st">"max"</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb28"><pre class="downlit">
+<span class="va">Z.FOCUS</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,
+                   Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,
+                   Z2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z3"</span><span class="op">)</span>,
+                   Z3 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,
+                   use_of_ff <span class="op">=</span> <span class="st">"max"</span><span class="op">)</span></pre></div>
 <pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
-<div class="sourceCode" id="cb30"><html><body><pre class="r"><span class="no">m.Z.FOCUS</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">Z.FOCUS</span>, <span class="no">FOCUS_2006_Z_mkin</span>,
-                     <span class="kw">parms.ini</span> <span class="kw">=</span> <span class="no">m.Z.5</span>$<span class="no">bparms.ode</span>,
-                     <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb30"><pre class="downlit">
+<span class="va">m.Z.FOCUS</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.FOCUS</span>, <span class="va">FOCUS_2006_Z_mkin</span>,
+                     parms.ini <span class="op">=</span> <span class="va">m.Z.5</span><span class="op">$</span><span class="va">bparms.ode</span>,
+                     quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></pre></div>
 <pre><code>## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.5$bparms.ode, :
 ## Observations with value of zero were removed from the data</code></pre>
 <pre><code>## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.5$bparms.ode, : Optimisation did not converge:
 ## false convergence (8)</code></pre>
-<div class="sourceCode" id="cb33"><html><body><pre class="r"><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(<span class="no">m.Z.FOCUS</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb33"><pre class="downlit">
+<span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.FOCUS</span><span class="op">)</span></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png" width="700"></p>
-<div class="sourceCode" id="cb34"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">m.Z.FOCUS</span>, <span class="kw">data</span> <span class="kw">=</span> <span class="fl">FALSE</span>)$<span class="no">bpar</span></pre></body></html></div>
-<pre><code>##             Estimate se_notrans t value     Pr(&gt;t)     Lower     Upper
-## Z0_0       96.840695   1.994285 48.5591 4.0254e-42 92.828744 100.85265
-## k_Z0        2.215467   0.118463 18.7018 1.0417e-23  1.989524   2.46707
-## k_Z1        0.478325   0.028259 16.9265 6.2441e-22  0.424725   0.53869
-## k_Z2        0.451638   0.042139 10.7177 1.6309e-14  0.374346   0.54489
-## k_Z3        0.058692   0.015245  3.8498 1.7807e-04  0.034806   0.09897
-## f_Z2_to_Z3  0.471484   0.058348  8.0805 9.6599e-11  0.357736   0.58827
-## sigma       3.984431   0.383402 10.3923 4.5576e-14  3.213126   4.75574</code></pre>
-<div class="sourceCode" id="cb36"><html><body><pre class="r"><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span>(<span class="no">m.Z.FOCUS</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb34"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span><span class="op">(</span><span class="va">m.Z.FOCUS</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></pre></div>
+<pre><code>##             Estimate se_notrans t value     Pr(&gt;t)     Lower      Upper
+## Z0_0       96.838721   1.994275 48.5584 4.0283e-42 92.826878 100.850563
+## k_Z0        2.215400   0.118459 18.7019 1.0414e-23  1.989462   2.466998
+## k_Z1        0.478301   0.028257 16.9267 6.2411e-22  0.424705   0.538662
+## k_Z2        0.451623   0.042138 10.7176 1.6313e-14  0.374336   0.544867
+## k_Z3        0.058694   0.015246  3.8499 1.7804e-04  0.034809   0.098967
+## f_Z2_to_Z3  0.471510   0.058352  8.0804 9.6640e-11  0.357775   0.588283
+## sigma       3.984431   0.383402 10.3923 4.5575e-14  3.213126   4.755736</code></pre>
+<div class="sourceCode" id="cb36"><pre class="downlit">
+<span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">m.Z.FOCUS</span><span class="op">)</span></pre></div>
 <pre><code>## $ff
 ##   Z2_Z3 Z2_sink 
-## 0.47148 0.52852 
+## 0.47151 0.52849 
 ## 
 ## $distimes
 ##        DT50    DT90
-## Z0  0.31287  1.0393
-## Z1  1.44911  4.8138
-## Z2  1.53474  5.0983
-## Z3 11.80989 39.2316</code></pre>
+## Z0  0.31288  1.0394
+## Z1  1.44919  4.8141
+## Z2  1.53479  5.0985
+## Z3 11.80955 39.2305</code></pre>
 <p>This fit corresponds to the final result chosen in Appendix 7 of the FOCUS report. Confidence intervals returned by mkin are based on internally transformed parameters, however.</p>
 </div>
 <div id="using-the-sforb-model" class="section level1">
@@ -239,85 +263,108 @@
 <a href="#using-the-sforb-model" class="anchor"></a>Using the SFORB model</h1>
 <p>As the FOCUS report states, there is a certain tailing of the time course of metabolite Z3. Also, the time course of the parent compound is not fitted very well using the SFO model, as residues at a certain low level remain.</p>
 <p>Therefore, an additional model is offered here, using the single first-order reversible binding (SFORB) model for metabolite Z3. As expected, the <span class="math inline">\(\chi^2\)</span> error level is lower for metabolite Z3 using this model and the graphical fit for Z3 is improved. However, the covariance matrix is not returned.</p>
-<div class="sourceCode" id="cb38"><html><body><pre class="r"><span class="no">Z.mkin.1</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="kw">Z0</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z1"</span>, <span class="kw">sink</span> <span class="kw">=</span> <span class="fl">FALSE</span>),
-                    <span class="kw">Z1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z2"</span>, <span class="kw">sink</span> <span class="kw">=</span> <span class="fl">FALSE</span>),
-                    <span class="kw">Z2</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z3"</span>),
-                    <span class="kw">Z3</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFORB"</span>))</pre></body></html></div>
+<div class="sourceCode" id="cb38"><pre class="downlit">
+<span class="va">Z.mkin.1</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,
+                    Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,
+                    Z2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z3"</span><span class="op">)</span>,
+                    Z3 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span><span class="op">)</span><span class="op">)</span></pre></div>
 <pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
-<div class="sourceCode" id="cb40"><html><body><pre class="r"><span class="no">m.Z.mkin.1</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">Z.mkin.1</span>, <span class="no">FOCUS_2006_Z_mkin</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb40"><pre class="downlit">
+<span class="va">m.Z.mkin.1</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.mkin.1</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></pre></div>
 <pre><code>## Warning in mkinfit(Z.mkin.1, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with
 ## value of zero were removed from the data</code></pre>
-<div class="sourceCode" id="cb42"><html><body><pre class="r"><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(<span class="no">m.Z.mkin.1</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb42"><pre class="downlit">
+<span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.1</span><span class="op">)</span></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png" width="700"></p>
-<div class="sourceCode" id="cb43"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">m.Z.mkin.1</span>, <span class="kw">data</span> <span class="kw">=</span> <span class="fl">FALSE</span>)$<span class="no">cov.unscaled</span></pre></body></html></div>
+<div class="sourceCode" id="cb43"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span><span class="op">(</span><span class="va">m.Z.mkin.1</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">cov.unscaled</span></pre></div>
 <pre><code>## NULL</code></pre>
 <p>Therefore, a further stepwise model building is performed starting from the stage of parent and two metabolites, starting from the assumption that the model fit for the parent compound can be improved by using the SFORB model.</p>
-<div class="sourceCode" id="cb45"><html><body><pre class="r"><span class="no">Z.mkin.3</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="kw">Z0</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFORB"</span>, <span class="st">"Z1"</span>, <span class="kw">sink</span> <span class="kw">=</span> <span class="fl">FALSE</span>),
-                    <span class="kw">Z1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z2"</span>, <span class="kw">sink</span> <span class="kw">=</span> <span class="fl">FALSE</span>),
-                    <span class="kw">Z2</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>))</pre></body></html></div>
+<div class="sourceCode" id="cb45"><pre class="downlit">
+<span class="va">Z.mkin.3</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span>, <span class="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,
+                    Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,
+                    Z2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span><span class="op">)</span></pre></div>
 <pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
-<div class="sourceCode" id="cb47"><html><body><pre class="r"><span class="no">m.Z.mkin.3</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">Z.mkin.3</span>, <span class="no">FOCUS_2006_Z_mkin</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb47"><pre class="downlit">
+<span class="va">m.Z.mkin.3</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.mkin.3</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></pre></div>
 <pre><code>## Warning in mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with
 ## value of zero were removed from the data</code></pre>
-<div class="sourceCode" id="cb49"><html><body><pre class="r"><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(<span class="no">m.Z.mkin.3</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb49"><pre class="downlit">
+<span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.3</span><span class="op">)</span></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png" width="700"></p>
 <p>This results in a much better representation of the behaviour of the parent compound Z0.</p>
 <p>Finally, Z3 is added as well. These models appear overparameterised (no covariance matrix returned) if the sink for Z1 is left in the models.</p>
-<div class="sourceCode" id="cb50"><html><body><pre class="r"><span class="no">Z.mkin.4</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="kw">Z0</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFORB"</span>, <span class="st">"Z1"</span>, <span class="kw">sink</span> <span class="kw">=</span> <span class="fl">FALSE</span>),
-                    <span class="kw">Z1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z2"</span>, <span class="kw">sink</span> <span class="kw">=</span> <span class="fl">FALSE</span>),
-                    <span class="kw">Z2</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z3"</span>),
-                    <span class="kw">Z3</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>))</pre></body></html></div>
+<div class="sourceCode" id="cb50"><pre class="downlit">
+<span class="va">Z.mkin.4</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span>, <span class="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,
+                    Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,
+                    Z2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z3"</span><span class="op">)</span>,
+                    Z3 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span><span class="op">)</span></pre></div>
 <pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
-<div class="sourceCode" id="cb52"><html><body><pre class="r"><span class="no">m.Z.mkin.4</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">Z.mkin.4</span>, <span class="no">FOCUS_2006_Z_mkin</span>,
-                      <span class="kw">parms.ini</span> <span class="kw">=</span> <span class="no">m.Z.mkin.3</span>$<span class="no">bparms.ode</span>,
-                      <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb52"><pre class="downlit">
+<span class="va">m.Z.mkin.4</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.mkin.4</span>, <span class="va">FOCUS_2006_Z_mkin</span>,
+                      parms.ini <span class="op">=</span> <span class="va">m.Z.mkin.3</span><span class="op">$</span><span class="va">bparms.ode</span>,
+                      quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></pre></div>
 <pre><code>## Warning in mkinfit(Z.mkin.4, FOCUS_2006_Z_mkin, parms.ini = m.Z.mkin.
 ## 3$bparms.ode, : Observations with value of zero were removed from the data</code></pre>
-<div class="sourceCode" id="cb54"><html><body><pre class="r"><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(<span class="no">m.Z.mkin.4</span>)</pre></body></html></div>
+<pre><code>## Warning in mkinfit(Z.mkin.4, FOCUS_2006_Z_mkin, parms.ini = m.Z.mkin.
+## 3$bparms.ode, : Shapiro-Wilk test for standardized residuals: p = 0.0449</code></pre>
+<div class="sourceCode" id="cb55"><pre class="downlit">
+<span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.4</span><span class="op">)</span></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png" width="700"></p>
 <p>The error level of the fit, but especially of metabolite Z3, can be improved if the SFORB model is chosen for this metabolite, as this model is capable of representing the tailing of the metabolite decline phase.</p>
-<div class="sourceCode" id="cb55"><html><body><pre class="r"><span class="no">Z.mkin.5</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="kw">Z0</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFORB"</span>, <span class="st">"Z1"</span>, <span class="kw">sink</span> <span class="kw">=</span> <span class="fl">FALSE</span>),
-                    <span class="kw">Z1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z2"</span>, <span class="kw">sink</span> <span class="kw">=</span> <span class="fl">FALSE</span>),
-                    <span class="kw">Z2</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z3"</span>),
-                    <span class="kw">Z3</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFORB"</span>))</pre></body></html></div>
+<div class="sourceCode" id="cb56"><pre class="downlit">
+<span class="va">Z.mkin.5</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span>, <span class="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,
+                    Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,
+                    Z2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z3"</span><span class="op">)</span>,
+                    Z3 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span><span class="op">)</span><span class="op">)</span></pre></div>
 <pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
-<div class="sourceCode" id="cb57"><html><body><pre class="r"><span class="no">m.Z.mkin.5</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">Z.mkin.5</span>, <span class="no">FOCUS_2006_Z_mkin</span>,
-                      <span class="kw">parms.ini</span> <span class="kw">=</span> <span class="no">m.Z.mkin.4</span>$<span class="no">bparms.ode</span>[<span class="fl">1</span>:<span class="fl">4</span>],
-                      <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb58"><pre class="downlit">
+<span class="va">m.Z.mkin.5</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.mkin.5</span>, <span class="va">FOCUS_2006_Z_mkin</span>,
+                      parms.ini <span class="op">=</span> <span class="va">m.Z.mkin.4</span><span class="op">$</span><span class="va">bparms.ode</span><span class="op">[</span><span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span>,
+                      quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></pre></div>
 <pre><code>## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini = m.Z.mkin.
 ## 4$bparms.ode[1:4], : Observations with value of zero were removed from the data</code></pre>
-<div class="sourceCode" id="cb59"><html><body><pre class="r"><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(<span class="no">m.Z.mkin.5</span>)</pre></body></html></div>
+<pre><code>## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini = m.Z.mkin.
+## 4$bparms.ode[1:4], : Shapiro-Wilk test for standardized residuals: p = 0.00785</code></pre>
+<div class="sourceCode" id="cb61"><pre class="downlit">
+<span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.5</span><span class="op">)</span></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png" width="700"></p>
 <p>The summary view of the backtransformed parameters shows that we get no confidence intervals due to overparameterisation. As the optimized  is excessively small, it seems reasonable to fix it to zero.</p>
-<div class="sourceCode" id="cb60"><html><body><pre class="r"><span class="no">m.Z.mkin.5a</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">Z.mkin.5</span>, <span class="no">FOCUS_2006_Z_mkin</span>,
-                       <span class="kw">parms.ini</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="no">m.Z.mkin.5</span>$<span class="no">bparms.ode</span>[<span class="fl">1</span>:<span class="fl">7</span>],
-                                     <span class="kw">k_Z3_bound_free</span> <span class="kw">=</span> <span class="fl">0</span>),
-                       <span class="kw">fixed_parms</span> <span class="kw">=</span> <span class="st">"k_Z3_bound_free"</span>,
-                       <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb62"><pre class="downlit">
+<span class="va">m.Z.mkin.5a</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.mkin.5</span>, <span class="va">FOCUS_2006_Z_mkin</span>,
+                       parms.ini <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="va">m.Z.mkin.5</span><span class="op">$</span><span class="va">bparms.ode</span><span class="op">[</span><span class="fl">1</span><span class="op">:</span><span class="fl">7</span><span class="op">]</span>,
+                                     k_Z3_bound_free <span class="op">=</span> <span class="fl">0</span><span class="op">)</span>,
+                       fixed_parms <span class="op">=</span> <span class="st">"k_Z3_bound_free"</span>,
+                       quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></pre></div>
 <pre><code>## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini = c(m.Z.mkin.
 ## 5$bparms.ode[1:7], : Observations with value of zero were removed from the data</code></pre>
-<div class="sourceCode" id="cb62"><html><body><pre class="r"><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(<span class="no">m.Z.mkin.5a</span>)</pre></body></html></div>
+<pre><code>## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini = c(m.Z.mkin.
+## 5$bparms.ode[1:7], : Shapiro-Wilk test for standardized residuals: p = 0.00785</code></pre>
+<div class="sourceCode" id="cb65"><pre class="downlit">
+<span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.5a</span><span class="op">)</span></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png" width="700"></p>
 <p>As expected, the residual plots for Z0 and Z3 are more random than in the case of the all SFO model for which they were shown above. In conclusion, the model  is proposed as the best-fit model for the dataset from Appendix 7 of the FOCUS report.</p>
 <p>A graphical representation of the confidence intervals can finally be obtained.</p>
-<div class="sourceCode" id="cb63"><html><body><pre class="r"><span class="fu"><a href="../../reference/mkinparplot.html">mkinparplot</a></span>(<span class="no">m.Z.mkin.5a</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb66"><pre class="downlit">
+<span class="fu"><a href="../../reference/mkinparplot.html">mkinparplot</a></span><span class="op">(</span><span class="va">m.Z.mkin.5a</span><span class="op">)</span></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png" width="700"></p>
 <p>The endpoints obtained with this model are</p>
-<div class="sourceCode" id="cb64"><html><body><pre class="r"><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span>(<span class="no">m.Z.mkin.5a</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb67"><pre class="downlit">
+<span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">m.Z.mkin.5a</span><span class="op">)</span></pre></div>
 <pre><code>## $ff
 ## Z0_free   Z2_Z3 Z2_sink Z3_free 
 ## 1.00000 0.53656 0.46344 1.00000 
 ## 
 ## $SFORB
 ##     Z0_b1     Z0_b2     Z3_b1     Z3_b2 
-## 2.4471337 0.0075125 0.0800071 0.0000000 
+## 2.4471358 0.0075126 0.0800073 0.0000000 
 ## 
 ## $distimes
-##      DT50   DT90 DT50_Z0_b1 DT50_Z0_b2 DT50_Z3_b1 DT50_Z3_b2
-## Z0 0.3043 1.1848    0.28325     92.266         NA         NA
-## Z1 1.5148 5.0320         NA         NA         NA         NA
-## Z2 1.6414 5.4526         NA         NA         NA         NA
-## Z3     NA     NA         NA         NA     8.6636        Inf</code></pre>
+##      DT50   DT90 DT50back DT50_Z0_b1 DT50_Z0_b2 DT50_Z3_b1 DT50_Z3_b2
+## Z0 0.3043 1.1848  0.35666    0.28325     92.265         NA         NA
+## Z1 1.5148 5.0320       NA         NA         NA         NA         NA
+## Z2 1.6414 5.4526       NA         NA         NA         NA         NA
+## Z3     NA     NA       NA         NA         NA     8.6636        Inf</code></pre>
 <p>It is clear the degradation rate of Z3 towards the end of the experiment is very low as DT50_Z3_b2 (the second Eigenvalue of the system of two differential equations representing the SFORB system for Z3, corresponding to the slower rate constant of the DFOP model) is reported to be infinity. However, this appears to be a feature of the data.</p>
 </div>
 <div id="references" class="section level1">
@@ -347,7 +394,7 @@
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png
index 23d051ce..575def46 100644
--- a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png
+++ b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png
index 96738dd0..abdded73 100644
--- a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png
+++ b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png
index 4f3c2554..599f3226 100644
--- a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png
+++ b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png
index b8c3ed26..ce993d09 100644
--- a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png
+++ b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png
index 132a7317..4b71d7b8 100644
--- a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png
+++ b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png
index 23d051ce..575def46 100644
--- a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png
+++ b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png
index 6e9f4efa..98ce34a7 100644
--- a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png
+++ b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png
index 146acea9..d04a411e 100644
--- a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png
+++ b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png
index b25bf26a..0a9265f5 100644
--- a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png
+++ b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png
index 7db8b07d..0acfa2a4 100644
--- a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png
+++ b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png
index dd5d89cd..ca191b00 100644
--- a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png
+++ b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png
diff --git a/docs/articles/web_only/NAFTA_examples.html b/docs/articles/web_only/NAFTA_examples.html
index b91e7ee7..411d4bb8 100644
--- a/docs/articles/web_only/NAFTA_examples.html
+++ b/docs/articles/web_only/NAFTA_examples.html
@@ -31,7 +31,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -68,6 +68,9 @@
     <li>
       <a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -76,7 +79,7 @@
       </ul>
 <ul class="nav navbar-nav navbar-right">
 <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -97,10 +100,10 @@
       <h1 data-toc-skip>Evaluation of example datasets from Attachment 1 to the US EPA SOP for the NAFTA guidance</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2020-05-27</h4>
+            <h4 class="date">2020-10-15</h4>
       
-      <small class="dont-index">Source: <a href="http://github.com/jranke/mkin/blob/master/vignettes/web_only/NAFTA_examples.Rmd"><code>vignettes/web_only/NAFTA_examples.Rmd</code></a></small>
-      <div class="hidden name"><code>NAFTA_examples.Rmd</code></div>
+      <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/master/vignettes/web_only/NAFTA_examples.rmd"><code>vignettes/web_only/NAFTA_examples.rmd</code></a></small>
+      <div class="hidden name"><code>NAFTA_examples.rmd</code></div>
 
     </div>
 
@@ -119,12 +122,15 @@
 <div id="example-on-page-5-upper-panel" class="section level2">
 <h2 class="hasAnchor">
 <a href="#example-on-page-5-upper-panel" class="anchor"></a>Example on page 5, upper panel</h2>
-<div class="sourceCode" id="cb1"><html><body><pre class="r"><span class="no">p5a</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p5a"</span>]])</pre></body></html></div>
+<div class="sourceCode" id="cb1"><pre class="downlit">
+<span class="va">p5a</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p5a"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></pre></div>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb4"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p5a</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb4"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">p5a</span><span class="op">)</span></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p5a-1.png" width="700"></p>
-<div class="sourceCode" id="cb5"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p5a</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb5"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p5a</span><span class="op">)</span></pre></div>
 <pre><code>## Sums of squares:
 ##       SFO      IORE      DFOP 
 ## 465.21753  56.27506  32.06401 
@@ -134,23 +140,23 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(&gt;t)  Lower   Upper
-## parent_0       95.8401 4.67e-21 92.245 99.4357
-## k_parent_sink   0.0102 3.92e-12  0.009  0.0117
-## sigma           4.8230 3.81e-06  3.214  6.4318
+##          Estimate   Pr(&gt;t)  Lower   Upper
+## parent_0  95.8401 4.67e-21 92.245 99.4357
+## k_parent   0.0102 3.92e-12  0.009  0.0117
+## sigma      4.8230 3.81e-06  3.214  6.4318
 ## 
 ## $IORE
-##                     Estimate Pr(&gt;t)    Lower    Upper
-## parent_0            1.01e+02     NA 9.91e+01 1.02e+02
-## k__iore_parent_sink 1.54e-05     NA 4.08e-06 5.84e-05
-## N_parent            2.57e+00     NA 2.25e+00 2.89e+00
-## sigma               1.68e+00     NA 1.12e+00 2.24e+00
+##                Estimate Pr(&gt;t)    Lower    Upper
+## parent_0       1.01e+02     NA 9.91e+01 1.02e+02
+## k__iore_parent 1.54e-05     NA 4.08e-06 5.84e-05
+## N_parent       2.57e+00     NA 2.25e+00 2.89e+00
+## sigma          1.68e+00     NA 1.12e+00 2.24e+00
 ## 
 ## $DFOP
 ##          Estimate   Pr(&gt;t)   Lower    Upper
 ## parent_0 9.99e+01 1.41e-26 98.8116 101.0810
 ## k1       2.67e-02 5.05e-06  0.0243   0.0295
-## k2       2.86e-12 5.00e-01  0.0000      Inf
+## k2       2.17e-12 5.00e-01  0.0000      Inf
 ## g        6.47e-01 3.67e-06  0.6248   0.6677
 ## sigma    1.27e+00 8.91e-06  0.8395   1.6929
 ## 
@@ -159,7 +165,7 @@
 ##      DT50     DT90 DT50_rep
 ## SFO  67.7 2.25e+02 6.77e+01
 ## IORE 58.2 1.07e+03 3.22e+02
-## DFOP 55.5 4.42e+11 2.42e+11
+## DFOP 55.5 5.83e+11 3.20e+11
 ## 
 ## Representative half-life:
 ## [1] 321.51</code></pre>
@@ -167,12 +173,15 @@
 <div id="example-on-page-5-lower-panel" class="section level2">
 <h2 class="hasAnchor">
 <a href="#example-on-page-5-lower-panel" class="anchor"></a>Example on page 5, lower panel</h2>
-<div class="sourceCode" id="cb7"><html><body><pre class="r"><span class="no">p5b</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p5b"</span>]])</pre></body></html></div>
+<div class="sourceCode" id="cb7"><pre class="downlit">
+<span class="va">p5b</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p5b"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></pre></div>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb10"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p5b</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb10"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">p5b</span><span class="op">)</span></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p5b-1.png" width="700"></p>
-<div class="sourceCode" id="cb11"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p5b</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb11"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p5b</span><span class="op">)</span></pre></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 94.81123 10.10936  7.55871 
@@ -182,23 +191,23 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(&gt;t)    Lower    Upper
-## parent_0        96.497 2.32e-24 94.85271 98.14155
-## k_parent_sink    0.008 3.42e-14  0.00737  0.00869
-## sigma            2.295 1.22e-05  1.47976  3.11036
+##          Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0   96.497 2.32e-24 94.85271 98.14155
+## k_parent    0.008 3.42e-14  0.00737  0.00869
+## sigma       2.295 1.22e-05  1.47976  3.11036
 ## 
 ## $IORE
-##                     Estimate   Pr(&gt;t)    Lower    Upper
-## parent_0            9.85e+01 1.17e-28 9.79e+01 9.92e+01
-## k__iore_parent_sink 1.53e-04 6.50e-03 7.21e-05 3.26e-04
-## N_parent            1.94e+00 5.88e-13 1.76e+00 2.12e+00
-## sigma               7.49e-01 1.63e-05 4.82e-01 1.02e+00
+##                Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0       9.85e+01 1.17e-28 9.79e+01 9.92e+01
+## k__iore_parent 1.53e-04 6.50e-03 7.21e-05 3.26e-04
+## N_parent       1.94e+00 5.88e-13 1.76e+00 2.12e+00
+## sigma          7.49e-01 1.63e-05 4.82e-01 1.02e+00
 ## 
 ## $DFOP
 ##          Estimate   Pr(&gt;t)   Lower   Upper
 ## parent_0 9.84e+01 1.24e-27 97.8078 98.9187
 ## k1       1.55e-02 4.10e-04  0.0143  0.0167
-## k2       1.16e-11 5.00e-01  0.0000     Inf
+## k2       1.04e-11 5.00e-01  0.0000     Inf
 ## g        6.89e-01 2.92e-03  0.6626  0.7142
 ## sigma    6.48e-01 2.38e-05  0.4147  0.8813
 ## 
@@ -207,7 +216,7 @@
 ##      DT50     DT90 DT50_rep
 ## SFO  86.6 2.88e+02 8.66e+01
 ## IORE 85.5 7.17e+02 2.16e+02
-## DFOP 83.6 9.80e+10 5.98e+10
+## DFOP 83.6 1.09e+11 6.67e+10
 ## 
 ## Representative half-life:
 ## [1] 215.87</code></pre>
@@ -215,12 +224,15 @@
 <div id="example-on-page-6" class="section level2">
 <h2 class="hasAnchor">
 <a href="#example-on-page-6" class="anchor"></a>Example on page 6</h2>
-<div class="sourceCode" id="cb13"><html><body><pre class="r"><span class="no">p6</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p6"</span>]])</pre></body></html></div>
+<div class="sourceCode" id="cb13"><pre class="downlit">
+<span class="va">p6</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p6"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></pre></div>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb16"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p6</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb16"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">p6</span><span class="op">)</span></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p6-1.png" width="700"></p>
-<div class="sourceCode" id="cb17"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p6</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb17"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p6</span><span class="op">)</span></pre></div>
 <pre><code>## Sums of squares:
 ##       SFO      IORE      DFOP 
 ## 188.45361  51.00699  42.46931 
@@ -230,23 +242,23 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(&gt;t)   Lower   Upper
-## parent_0       94.7759 7.29e-24 92.3478 97.2039
-## k_parent_sink   0.0179 8.02e-16  0.0166  0.0194
-## sigma           3.0696 3.81e-06  2.0456  4.0936
+##          Estimate   Pr(&gt;t)   Lower   Upper
+## parent_0  94.7759 7.29e-24 92.3478 97.2039
+## k_parent   0.0179 8.02e-16  0.0166  0.0194
+## sigma      3.0696 3.81e-06  2.0456  4.0936
 ## 
 ## $IORE
-##                     Estimate   Pr(&gt;t)    Lower    Upper
-## parent_0            97.12446 2.63e-26 95.62461 98.62431
-## k__iore_parent_sink  0.00252 1.95e-03  0.00134  0.00472
-## N_parent             1.49587 4.07e-13  1.33896  1.65279
-## sigma                1.59698 5.05e-06  1.06169  2.13227
+##                Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0       97.12446 2.63e-26 95.62461 98.62431
+## k__iore_parent  0.00252 1.95e-03  0.00134  0.00472
+## N_parent        1.49587 4.07e-13  1.33896  1.65279
+## sigma           1.59698 5.05e-06  1.06169  2.13227
 ## 
 ## $DFOP
 ##          Estimate   Pr(&gt;t)   Lower   Upper
 ## parent_0 9.66e+01 1.57e-25 95.3476 97.8979
 ## k1       2.55e-02 7.33e-06  0.0233  0.0278
-## k2       4.90e-11 5.00e-01  0.0000     Inf
+## k2       3.88e-11 5.00e-01  0.0000     Inf
 ## g        8.61e-01 7.55e-06  0.8314  0.8867
 ## sigma    1.46e+00 6.93e-06  0.9661  1.9483
 ## 
@@ -255,7 +267,7 @@
 ##      DT50     DT90 DT50_rep
 ## SFO  38.6 1.28e+02 3.86e+01
 ## IORE 34.0 1.77e+02 5.32e+01
-## DFOP 34.1 6.66e+09 1.41e+10
+## DFOP 34.1 8.42e+09 1.79e+10
 ## 
 ## Representative half-life:
 ## [1] 53.17</code></pre>
@@ -263,12 +275,15 @@
 <div id="example-on-page-7" class="section level2">
 <h2 class="hasAnchor">
 <a href="#example-on-page-7" class="anchor"></a>Example on page 7</h2>
-<div class="sourceCode" id="cb19"><html><body><pre class="r"><span class="no">p7</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p7"</span>]])</pre></body></html></div>
+<div class="sourceCode" id="cb19"><pre class="downlit">
+<span class="va">p7</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p7"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></pre></div>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb22"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p7</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb22"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">p7</span><span class="op">)</span></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p7-1.png" width="700"></p>
-<div class="sourceCode" id="cb23"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p7</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb23"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p7</span><span class="op">)</span></pre></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 3661.661 3195.030 3174.145 
@@ -278,23 +293,23 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(&gt;t)    Lower    Upper
-## parent_0      96.41796 4.80e-53 93.32245 99.51347
-## k_parent_sink  0.00735 7.64e-21  0.00641  0.00843
-## sigma          7.94557 1.83e-15  6.46713  9.42401
+##          Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0 96.41796 4.80e-53 93.32245 99.51347
+## k_parent  0.00735 7.64e-21  0.00641  0.00843
+## sigma     7.94557 1.83e-15  6.46713  9.42401
 ## 
 ## $IORE
-##                     Estimate Pr(&gt;t)    Lower    Upper
-## parent_0            9.92e+01     NA 9.55e+01 1.03e+02
-## k__iore_parent_sink 1.60e-05     NA 1.45e-07 1.77e-03
-## N_parent            2.45e+00     NA 1.35e+00 3.54e+00
-## sigma               7.42e+00     NA 6.04e+00 8.80e+00
+##                Estimate Pr(&gt;t)    Lower    Upper
+## parent_0       9.92e+01     NA 9.55e+01 1.03e+02
+## k__iore_parent 1.60e-05     NA 1.45e-07 1.77e-03
+## N_parent       2.45e+00     NA 1.35e+00 3.54e+00
+## sigma          7.42e+00     NA 6.04e+00 8.80e+00
 ## 
 ## $DFOP
 ##          Estimate   Pr(&gt;t)   Lower    Upper
 ## parent_0 9.89e+01 9.44e-49 95.4640 102.2573
 ## k1       1.81e-02 1.75e-01  0.0116   0.0281
-## k2       1.97e-10 5.00e-01  0.0000      Inf
+## k2       2.30e-10 5.00e-01  0.0000      Inf
 ## g        6.06e-01 2.19e-01  0.4826   0.7178
 ## sigma    7.40e+00 2.97e-15  6.0201   8.7754
 ## 
@@ -303,7 +318,7 @@
 ##      DT50     DT90 DT50_rep
 ## SFO  94.3 3.13e+02 9.43e+01
 ## IORE 96.7 1.51e+03 4.55e+02
-## DFOP 96.4 6.97e+09 3.52e+09
+## DFOP 96.4 5.95e+09 3.01e+09
 ## 
 ## Representative half-life:
 ## [1] 454.55</code></pre>
@@ -316,12 +331,15 @@
 <h2 class="hasAnchor">
 <a href="#example-on-page-8" class="anchor"></a>Example on page 8</h2>
 <p>For this dataset, the IORE fit does not converge when the default starting values used by mkin for the IORE model are used. Therefore, a lower value for the rate constant is used here.</p>
-<div class="sourceCode" id="cb25"><html><body><pre class="r"><span class="no">p8</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p8"</span>]], <span class="kw">parms.ini</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="kw">k__iore_parent_sink</span> <span class="kw">=</span> <span class="fl">1e-3</span>))</pre></body></html></div>
+<div class="sourceCode" id="cb25"><pre class="downlit">
+<span class="va">p8</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p8"</span><span class="op">]</span><span class="op">]</span>, parms.ini <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span>k__iore_parent <span class="op">=</span> <span class="fl">1e-3</span><span class="op">)</span><span class="op">)</span></pre></div>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb28"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p8</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb28"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">p8</span><span class="op">)</span></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p8-1.png" width="700"></p>
-<div class="sourceCode" id="cb29"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p8</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb29"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p8</span><span class="op">)</span></pre></div>
 <pre><code>## Sums of squares:
 ##       SFO      IORE      DFOP 
 ## 1996.9408  444.9237  547.5616 
@@ -331,17 +349,17 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(&gt;t)    Lower    Upper
-## parent_0      88.16549 6.53e-29 83.37344 92.95754
-## k_parent_sink  0.00803 1.67e-13  0.00674  0.00957
-## sigma          7.44786 4.17e-10  5.66209  9.23363
+##          Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0 88.16549 6.53e-29 83.37344 92.95754
+## k_parent  0.00803 1.67e-13  0.00674  0.00957
+## sigma     7.44786 4.17e-10  5.66209  9.23363
 ## 
 ## $IORE
-##                     Estimate   Pr(&gt;t)    Lower    Upper
-## parent_0            9.77e+01 7.03e-35 9.44e+01 1.01e+02
-## k__iore_parent_sink 6.14e-05 3.20e-02 2.12e-05 1.78e-04
-## N_parent            2.27e+00 4.23e-18 2.00e+00 2.54e+00
-## sigma               3.52e+00 5.36e-10 2.67e+00 4.36e+00
+##                Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0       9.77e+01 7.03e-35 9.44e+01 1.01e+02
+## k__iore_parent 6.14e-05 3.20e-02 2.12e-05 1.78e-04
+## N_parent       2.27e+00 4.23e-18 2.00e+00 2.54e+00
+## sigma          3.52e+00 5.36e-10 2.67e+00 4.36e+00
 ## 
 ## $DFOP
 ##          Estimate   Pr(&gt;t)    Lower    Upper
@@ -368,12 +386,15 @@
 <div id="example-on-page-9-upper-panel" class="section level2">
 <h2 class="hasAnchor">
 <a href="#example-on-page-9-upper-panel" class="anchor"></a>Example on page 9, upper panel</h2>
-<div class="sourceCode" id="cb31"><html><body><pre class="r"><span class="no">p9a</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p9a"</span>]])</pre></body></html></div>
+<div class="sourceCode" id="cb31"><pre class="downlit">
+<span class="va">p9a</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p9a"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></pre></div>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb34"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p9a</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb34"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">p9a</span><span class="op">)</span></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p9a-1.png" width="700"></p>
-<div class="sourceCode" id="cb35"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p9a</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb35"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p9a</span><span class="op">)</span></pre></div>
 <pre><code>## Sums of squares:
 ##       SFO      IORE      DFOP 
 ## 839.35238  88.57064   9.93363 
@@ -383,23 +404,23 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(&gt;t)   Lower   Upper
-## parent_0       88.1933 3.06e-12 79.9447 96.4419
-## k_parent_sink   0.0409 2.07e-07  0.0324  0.0516
-## sigma           7.2429 3.92e-05  4.4768 10.0090
+##          Estimate   Pr(&gt;t)   Lower   Upper
+## parent_0  88.1933 3.06e-12 79.9447 96.4419
+## k_parent   0.0409 2.07e-07  0.0324  0.0516
+## sigma      7.2429 3.92e-05  4.4768 10.0090
 ## 
 ## $IORE
-##                     Estimate   Pr(&gt;t)    Lower    Upper
-## parent_0            9.89e+01 1.12e-16 9.54e+01 1.02e+02
-## k__iore_parent_sink 1.93e-05 1.13e-01 3.49e-06 1.06e-04
-## N_parent            2.91e+00 1.45e-09 2.50e+00 3.32e+00
-## sigma               2.35e+00 5.31e-05 1.45e+00 3.26e+00
+##                Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0       9.89e+01 1.12e-16 9.54e+01 1.02e+02
+## k__iore_parent 1.93e-05 1.13e-01 3.49e-06 1.06e-04
+## N_parent       2.91e+00 1.45e-09 2.50e+00 3.32e+00
+## sigma          2.35e+00 5.31e-05 1.45e+00 3.26e+00
 ## 
 ## $DFOP
 ##          Estimate   Pr(&gt;t)  Lower  Upper
 ## parent_0 9.85e+01 2.54e-20 97.390 99.672
 ## k1       1.38e-01 3.52e-05  0.131  0.146
-## k2       6.02e-13 5.00e-01  0.000    Inf
+## k2       6.69e-13 5.00e-01  0.000    Inf
 ## g        6.52e-01 8.13e-06  0.642  0.661
 ## sigma    7.88e-01 6.13e-02  0.481  1.095
 ## 
@@ -408,7 +429,7 @@
 ##      DT50     DT90 DT50_rep
 ## SFO  16.9 5.63e+01 1.69e+01
 ## IORE 11.6 3.37e+02 1.01e+02
-## DFOP 10.5 2.07e+12 1.15e+12
+## DFOP 10.5 1.86e+12 1.04e+12
 ## 
 ## Representative half-life:
 ## [1] 101.43</code></pre>
@@ -417,17 +438,15 @@
 <div id="example-on-page-9-lower-panel" class="section level2">
 <h2 class="hasAnchor">
 <a href="#example-on-page-9-lower-panel" class="anchor"></a>Example on page 9, lower panel</h2>
-<div class="sourceCode" id="cb37"><html><body><pre class="r"><span class="no">p9b</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p9b"</span>]])</pre></body></html></div>
-<pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
-<pre><code>## Warning in sqrt(diag(covar_notrans)): NaNs produced</code></pre>
-<pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
-<pre><code>## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
-## doubtful</code></pre>
+<div class="sourceCode" id="cb37"><pre class="downlit">
+<span class="va">p9b</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p9b"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></pre></div>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb44"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p9b</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb40"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">p9b</span><span class="op">)</span></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p9b-1.png" width="700"></p>
-<div class="sourceCode" id="cb45"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p9b</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb41"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p9b</span><span class="op">)</span></pre></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 35.64867 23.22334 35.64867 
@@ -437,24 +456,24 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(&gt;t)  Lower   Upper
-## parent_0       94.7123 2.15e-19 93.178 96.2464
-## k_parent_sink   0.0389 4.47e-14  0.037  0.0408
-## sigma           1.5957 1.28e-04  0.932  2.2595
+##          Estimate   Pr(&gt;t)  Lower   Upper
+## parent_0  94.7123 2.15e-19 93.178 96.2464
+## k_parent   0.0389 4.47e-14  0.037  0.0408
+## sigma      1.5957 1.28e-04  0.932  2.2595
 ## 
 ## $IORE
-##                     Estimate   Pr(&gt;t)   Lower  Upper
-## parent_0              93.863 2.32e-18 92.4565 95.269
-## k__iore_parent_sink    0.127 1.85e-02  0.0504  0.321
-## N_parent               0.711 1.88e-05  0.4843  0.937
-## sigma                  1.288 1.76e-04  0.7456  1.830
+##                Estimate   Pr(&gt;t)   Lower  Upper
+## parent_0         93.863 2.32e-18 92.4565 95.269
+## k__iore_parent    0.127 1.85e-02  0.0504  0.321
+## N_parent          0.711 1.88e-05  0.4843  0.937
+## sigma             1.288 1.76e-04  0.7456  1.830
 ## 
 ## $DFOP
 ##          Estimate   Pr(&gt;t)   Lower   Upper
 ## parent_0  94.7123 1.61e-16 93.1355 96.2891
 ## k1         0.0389 1.43e-06  0.0312  0.0485
 ## k2         0.0389 6.67e-03  0.0186  0.0812
-## g          0.7742      NaN      NA      NA
+## g          0.7742 5.00e-01  0.0000  1.0000
 ## sigma      1.5957 2.50e-04  0.9135  2.2779
 ## 
 ## 
@@ -471,12 +490,15 @@
 <div id="example-on-page-10" class="section level2">
 <h2 class="hasAnchor">
 <a href="#example-on-page-10" class="anchor"></a>Example on page 10</h2>
-<div class="sourceCode" id="cb47"><html><body><pre class="r"><span class="no">p10</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p10"</span>]])</pre></body></html></div>
+<div class="sourceCode" id="cb43"><pre class="downlit">
+<span class="va">p10</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p10"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></pre></div>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb50"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p10</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb46"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">p10</span><span class="op">)</span></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p10-1.png" width="700"></p>
-<div class="sourceCode" id="cb51"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p10</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb47"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p10</span><span class="op">)</span></pre></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 899.4089 336.4348 899.4089 
@@ -486,25 +508,25 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(&gt;t)   Lower    Upper
-## parent_0      101.7315 6.42e-11 91.9259 111.5371
-## k_parent_sink   0.0495 1.70e-07  0.0404   0.0607
-## sigma           8.0152 1.28e-04  4.6813  11.3491
+##          Estimate   Pr(&gt;t)   Lower    Upper
+## parent_0 101.7315 6.42e-11 91.9259 111.5371
+## k_parent   0.0495 1.70e-07  0.0404   0.0607
+## sigma      8.0152 1.28e-04  4.6813  11.3491
 ## 
 ## $IORE
-##                     Estimate   Pr(&gt;t)  Lower   Upper
-## parent_0               96.86 3.32e-12 90.848 102.863
-## k__iore_parent_sink     2.96 7.91e-02  0.687  12.761
-## N_parent                0.00 5.00e-01 -0.372   0.372
-## sigma                   4.90 1.77e-04  2.837   6.968
+##                Estimate   Pr(&gt;t)  Lower   Upper
+## parent_0          96.86 3.32e-12 90.848 102.863
+## k__iore_parent     2.96 7.91e-02  0.687  12.761
+## N_parent           0.00 5.00e-01 -0.372   0.372
+## sigma              4.90 1.77e-04  2.837   6.968
 ## 
 ## $DFOP
-##          Estimate   Pr(&gt;t)   Lower    Upper
-## parent_0 101.7315 1.41e-09 91.6534 111.8097
-## k1         0.0495 6.42e-04  0.0301   0.0814
-## k2         0.0495 1.66e-02  0.0200   0.1225
-## g          0.6634 5.00e-01  0.0000   1.0000
-## sigma      8.0152 2.50e-04  4.5886  11.4418
+##          Estimate   Pr(&gt;t)   Lower   Upper
+## parent_0 101.7315 1.41e-09 91.6534 111.810
+## k1         0.0495 6.48e-04  0.0303   0.081
+## k2         0.0495 1.67e-02  0.0201   0.122
+## g          0.6634 5.00e-01  0.0000   1.000
+## sigma      8.0152 2.50e-04  4.5886  11.442
 ## 
 ## 
 ## DTx values:
@@ -524,12 +546,15 @@
 <div id="example-on-page-11" class="section level2">
 <h2 class="hasAnchor">
 <a href="#example-on-page-11" class="anchor"></a>Example on page 11</h2>
-<div class="sourceCode" id="cb53"><html><body><pre class="r"><span class="no">p11</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p11"</span>]])</pre></body></html></div>
+<div class="sourceCode" id="cb49"><pre class="downlit">
+<span class="va">p11</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p11"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></pre></div>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb56"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p11</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb52"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">p11</span><span class="op">)</span></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p11-1.png" width="700"></p>
-<div class="sourceCode" id="cb57"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p11</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb53"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p11</span><span class="op">)</span></pre></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 579.6805 204.7932 144.7783 
@@ -539,17 +564,17 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(&gt;t)    Lower    Upper
-## parent_0      96.15820 4.83e-13 90.24934 1.02e+02
-## k_parent_sink  0.00321 4.71e-05  0.00222 4.64e-03
-## sigma          6.43473 1.28e-04  3.75822 9.11e+00
+##          Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0 96.15820 4.83e-13 90.24934 1.02e+02
+## k_parent  0.00321 4.71e-05  0.00222 4.64e-03
+## sigma     6.43473 1.28e-04  3.75822 9.11e+00
 ## 
 ## $IORE
-##                     Estimate Pr(&gt;t)    Lower    Upper
-## parent_0            1.05e+02     NA 9.90e+01 1.10e+02
-## k__iore_parent_sink 3.11e-17     NA 1.35e-20 7.18e-14
-## N_parent            8.36e+00     NA 6.62e+00 1.01e+01
-## sigma               3.82e+00     NA 2.21e+00 5.44e+00
+##                Estimate Pr(&gt;t)    Lower    Upper
+## parent_0       1.05e+02     NA 9.90e+01 1.10e+02
+## k__iore_parent 3.11e-17     NA 1.35e-20 7.18e-14
+## N_parent       8.36e+00     NA 6.62e+00 1.01e+01
+## sigma          3.82e+00     NA 2.21e+00 5.44e+00
 ## 
 ## $DFOP
 ##          Estimate   Pr(&gt;t)    Lower    Upper
@@ -567,7 +592,7 @@
 ## DFOP 4.21e+11 2.64e+12 9.56e+11
 ## 
 ## Representative half-life:
-## [1] 41148169</code></pre>
+## [1] 41148171</code></pre>
 <p>In this case, the DFOP fit reported for PestDF resulted in a negative value for the slower rate constant, which is not possible in mkin. The other results are in agreement.</p>
 </div>
 </div>
@@ -578,14 +603,17 @@
 <div id="example-on-page-12-upper-panel" class="section level2">
 <h2 class="hasAnchor">
 <a href="#example-on-page-12-upper-panel" class="anchor"></a>Example on page 12, upper panel</h2>
-<div class="sourceCode" id="cb59"><html><body><pre class="r"><span class="no">p12a</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p12a"</span>]])</pre></body></html></div>
+<div class="sourceCode" id="cb55"><pre class="downlit">
+<span class="va">p12a</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p12a"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></pre></div>
 <pre><code>## Warning in summary.mkinfit(x): Could not calculate correlation; no covariance
 ## matrix</code></pre>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb63"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p12a</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb59"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">p12a</span><span class="op">)</span></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p12a-1.png" width="700"></p>
-<div class="sourceCode" id="cb64"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p12a</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb60"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p12a</span><span class="op">)</span></pre></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 695.4440 220.0685 695.4440 
@@ -595,23 +623,23 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(&gt;t)  Lower   Upper
-## parent_0       100.521 8.75e-12 92.461 108.581
-## k_parent_sink    0.124 3.61e-08  0.104   0.148
-## sigma            7.048 1.28e-04  4.116   9.980
+##          Estimate   Pr(&gt;t)  Lower   Upper
+## parent_0  100.521 8.75e-12 92.461 108.581
+## k_parent    0.124 3.61e-08  0.104   0.148
+## sigma       7.048 1.28e-04  4.116   9.980
 ## 
 ## $IORE
-##                     Estimate Pr(&gt;t) Lower Upper
-## parent_0              96.823     NA    NA    NA
-## k__iore_parent_sink    2.436     NA    NA    NA
-## N_parent               0.263     NA    NA    NA
-## sigma                  3.965     NA    NA    NA
+##                Estimate Pr(&gt;t) Lower Upper
+## parent_0         96.823     NA    NA    NA
+## k__iore_parent    2.436     NA    NA    NA
+## N_parent          0.263     NA    NA    NA
+## sigma             3.965     NA    NA    NA
 ## 
 ## $DFOP
 ##          Estimate   Pr(&gt;t)   Lower   Upper
 ## parent_0  100.521 2.74e-10 92.2366 108.805
-## k1          0.124 5.74e-06  0.0958   0.161
-## k2          0.124 6.61e-02  0.0319   0.484
+## k1          0.124 5.75e-06  0.0958   0.161
+## k2          0.124 6.72e-02  0.0319   0.484
 ## g           0.877 5.00e-01  0.0000   1.000
 ## sigma       7.048 2.50e-04  4.0349  10.061
 ## 
@@ -628,7 +656,8 @@
 <div id="example-on-page-12-lower-panel" class="section level2">
 <h2 class="hasAnchor">
 <a href="#example-on-page-12-lower-panel" class="anchor"></a>Example on page 12, lower panel</h2>
-<div class="sourceCode" id="cb66"><html><body><pre class="r"><span class="no">p12b</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p12b"</span>]])</pre></body></html></div>
+<div class="sourceCode" id="cb62"><pre class="downlit">
+<span class="va">p12b</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p12b"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></pre></div>
 <pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
 <pre><code>## Warning in qt(alpha/2, rdf): NaNs produced</code></pre>
 <pre><code>## Warning in qt(1 - alpha/2, rdf): NaNs produced</code></pre>
@@ -639,9 +668,11 @@
 ## doubtful</code></pre>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb76"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p12b</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb72"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">p12b</span><span class="op">)</span></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p12b-1.png" width="700"></p>
-<div class="sourceCode" id="cb77"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p12b</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb73"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p12b</span><span class="op">)</span></pre></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 58.90242 19.06353 58.90242 
@@ -651,17 +682,17 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate  Pr(&gt;t)   Lower    Upper
-## parent_0       97.6840 0.00039 85.9388 109.4292
-## k_parent_sink   0.0589 0.00261  0.0431   0.0805
-## sigma           3.4323 0.04356 -1.2377   8.1023
+##          Estimate  Pr(&gt;t)   Lower    Upper
+## parent_0  97.6840 0.00039 85.9388 109.4292
+## k_parent   0.0589 0.00261  0.0431   0.0805
+## sigma      3.4323 0.04356 -1.2377   8.1023
 ## 
 ## $IORE
-##                     Estimate Pr(&gt;t)     Lower  Upper
-## parent_0              95.523 0.0055 74.539157 116.51
-## k__iore_parent_sink    0.333 0.1433  0.000717 154.57
-## N_parent               0.568 0.0677 -0.989464   2.13
-## sigma                  1.953 0.0975 -5.893100   9.80
+##                Estimate Pr(&gt;t)     Lower  Upper
+## parent_0         95.523 0.0055 74.539157 116.51
+## k__iore_parent    0.333 0.1433  0.000717 154.57
+## N_parent          0.568 0.0677 -0.989464   2.13
+## sigma             1.953 0.0975 -5.893100   9.80
 ## 
 ## $DFOP
 ##          Estimate Pr(&gt;t) Lower Upper
@@ -684,16 +715,15 @@
 <div id="example-on-page-13" class="section level2">
 <h2 class="hasAnchor">
 <a href="#example-on-page-13" class="anchor"></a>Example on page 13</h2>
-<div class="sourceCode" id="cb79"><html><body><pre class="r"><span class="no">p13</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p13"</span>]])</pre></body></html></div>
-<pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
-<pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
-<pre><code>## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
-## doubtful</code></pre>
+<div class="sourceCode" id="cb75"><pre class="downlit">
+<span class="va">p13</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p13"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></pre></div>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb85"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p13</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb78"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">p13</span><span class="op">)</span></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p13-1.png" width="700"></p>
-<div class="sourceCode" id="cb86"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p13</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb79"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p13</span><span class="op">)</span></pre></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 174.5971 142.3951 174.5971 
@@ -703,24 +733,24 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(&gt;t)    Lower    Upper
-## parent_0      92.73500 5.99e-17 89.61936 95.85065
-## k_parent_sink  0.00258 2.42e-09  0.00223  0.00299
-## sigma          3.41172 7.07e-05  2.05455  4.76888
+##          Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0 92.73500 5.99e-17 89.61936 95.85065
+## k_parent  0.00258 2.42e-09  0.00223  0.00299
+## sigma     3.41172 7.07e-05  2.05455  4.76888
 ## 
 ## $IORE
-##                     Estimate   Pr(&gt;t)    Lower  Upper
-## parent_0             91.6016 6.34e-16 88.53086 94.672
-## k__iore_parent_sink   0.0396 2.36e-01  0.00207  0.759
-## N_parent              0.3541 1.46e-01 -0.35153  1.060
-## sigma                 3.0811 9.64e-05  1.84296  4.319
+##                Estimate   Pr(&gt;t)    Lower  Upper
+## parent_0        91.6016 6.34e-16 88.53086 94.672
+## k__iore_parent   0.0396 2.36e-01  0.00207  0.759
+## N_parent         0.3541 1.46e-01 -0.35153  1.060
+## sigma            3.0811 9.64e-05  1.84296  4.319
 ## 
 ## $DFOP
 ##          Estimate   Pr(&gt;t)    Lower    Upper
 ## parent_0 92.73500 9.25e-15 8.95e+01 9.59e+01
-## k1        0.00258 4.28e-01 1.70e-08 3.92e+02
+## k1        0.00258 4.28e-01 1.45e-08 4.61e+02
 ## k2        0.00258 3.69e-08 2.20e-03 3.03e-03
-## g         0.00442 5.00e-01       NA       NA
+## g         0.00442 5.00e-01 0.00e+00 1.00e+00
 ## sigma     3.41172 1.35e-04 2.02e+00 4.80e+00
 ## 
 ## 
@@ -737,16 +767,19 @@
 <div id="dt50-not-observed-in-the-study-and-dfop-problems-in-pestdf" class="section level1">
 <h1 class="hasAnchor">
 <a href="#dt50-not-observed-in-the-study-and-dfop-problems-in-pestdf" class="anchor"></a>DT50 not observed in the study and DFOP problems in PestDF</h1>
-<div class="sourceCode" id="cb88"><html><body><pre class="r"><span class="no">p14</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p14"</span>]])</pre></body></html></div>
+<div class="sourceCode" id="cb81"><pre class="downlit">
+<span class="va">p14</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p14"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></pre></div>
 <pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
 <pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
 <pre><code>## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
 ## doubtful</code></pre>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb94"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p14</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb87"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">p14</span><span class="op">)</span></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p14-1.png" width="700"></p>
-<div class="sourceCode" id="cb95"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p14</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb88"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p14</span><span class="op">)</span></pre></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 48.43249 28.67746 27.26248 
@@ -756,23 +789,23 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(&gt;t)    Lower    Upper
-## parent_0      99.47124 2.06e-30 98.42254 1.01e+02
-## k_parent_sink  0.00279 3.75e-15  0.00256 3.04e-03
-## sigma          1.55616 3.81e-06  1.03704 2.08e+00
+##          Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0 99.47124 2.06e-30 98.42254 1.01e+02
+## k_parent  0.00279 3.75e-15  0.00256 3.04e-03
+## sigma     1.55616 3.81e-06  1.03704 2.08e+00
 ## 
 ## $IORE
-##                     Estimate Pr(&gt;t) Lower Upper
-## parent_0            1.00e+02     NA   NaN   NaN
-## k__iore_parent_sink 9.44e-08     NA   NaN   NaN
-## N_parent            3.31e+00     NA   NaN   NaN
-## sigma               1.20e+00     NA 0.796   1.6
+##                Estimate Pr(&gt;t) Lower Upper
+## parent_0       1.00e+02     NA   NaN   NaN
+## k__iore_parent 9.44e-08     NA   NaN   NaN
+## N_parent       3.31e+00     NA   NaN   NaN
+## sigma          1.20e+00     NA 0.796   1.6
 ## 
 ## $DFOP
 ##          Estimate   Pr(&gt;t)    Lower    Upper
 ## parent_0 1.00e+02 2.96e-28 99.40280 101.2768
 ## k1       9.53e-03 1.20e-01  0.00638   0.0143
-## k2       7.29e-12 5.00e-01  0.00000      Inf
+## k2       7.70e-12 5.00e-01  0.00000      Inf
 ## g        3.98e-01 2.19e-01  0.30481   0.4998
 ## sigma    1.17e+00 7.68e-06  0.77406   1.5610
 ## 
@@ -781,7 +814,7 @@
 ##          DT50     DT90 DT50_rep
 ## SFO  2.48e+02 8.25e+02 2.48e+02
 ## IORE 4.34e+02 2.22e+04 6.70e+03
-## DFOP 2.54e+10 2.46e+11 9.51e+10
+## DFOP 2.41e+10 2.33e+11 9.00e+10
 ## 
 ## Representative half-life:
 ## [1] 6697.44</code></pre>
@@ -790,17 +823,19 @@
 <div id="n-is-less-than-1-and-dfop-fraction-parameter-is-below-zero" class="section level1">
 <h1 class="hasAnchor">
 <a href="#n-is-less-than-1-and-dfop-fraction-parameter-is-below-zero" class="anchor"></a>N is less than 1 and DFOP fraction parameter is below zero</h1>
-<div class="sourceCode" id="cb97"><html><body><pre class="r"><span class="no">p15a</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p15a"</span>]])</pre></body></html></div>
+<div class="sourceCode" id="cb90"><pre class="downlit">
+<span class="va">p15a</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p15a"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></pre></div>
 <pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
-<pre><code>## Warning in sqrt(diag(covar_notrans)): NaNs produced</code></pre>
 <pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
 <pre><code>## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
 ## doubtful</code></pre>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb104"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p15a</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb96"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">p15a</span><span class="op">)</span></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p15a-1.png" width="700"></p>
-<div class="sourceCode" id="cb105"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p15a</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb97"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p15a</span><span class="op">)</span></pre></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 245.5248 135.0132 245.5248 
@@ -810,25 +845,25 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(&gt;t)    Lower   Upper
-## parent_0      97.96751 2.00e-15 94.32049 101.615
-## k_parent_sink  0.00952 4.93e-09  0.00824   0.011
-## sigma          4.18778 1.28e-04  2.44588   5.930
+##          Estimate   Pr(&gt;t)    Lower   Upper
+## parent_0 97.96751 2.00e-15 94.32049 101.615
+## k_parent  0.00952 4.93e-09  0.00824   0.011
+## sigma     4.18778 1.28e-04  2.44588   5.930
 ## 
 ## $IORE
-##                     Estimate   Pr(&gt;t)  Lower  Upper
-## parent_0              95.874 2.94e-15 92.937 98.811
-## k__iore_parent_sink    0.629 2.11e-01  0.044  8.982
-## N_parent               0.000 5.00e-01 -0.642  0.642
-## sigma                  3.105 1.78e-04  1.795  4.416
+##                Estimate   Pr(&gt;t)  Lower  Upper
+## parent_0         95.874 2.94e-15 92.937 98.811
+## k__iore_parent    0.629 2.11e-01  0.044  8.982
+## N_parent          0.000 5.00e-01 -0.642  0.642
+## sigma             3.105 1.78e-04  1.795  4.416
 ## 
 ## $DFOP
-##          Estimate   Pr(&gt;t)    Lower    Upper
-## parent_0 97.96752 2.85e-13 94.21914 101.7159
-## k1        0.00952 6.80e-02  0.00277   0.0327
-## k2        0.00952 3.82e-06  0.00902   0.0100
-## g         0.17247      NaN       NA       NA
-## sigma     4.18778 2.50e-04  2.39747   5.9781
+##          Estimate Pr(&gt;t)    Lower    Upper
+## parent_0 97.96752     NA 94.21914 101.7159
+## k1        0.00952     NA  0.00241   0.0377
+## k2        0.00952     NA  0.00747   0.0121
+## g         0.17247     NA       NA       NA
+## sigma     4.18778     NA  2.39747   5.9781
 ## 
 ## 
 ## DTx values:
@@ -839,16 +874,19 @@
 ## 
 ## Representative half-life:
 ## [1] 41.33</code></pre>
-<div class="sourceCode" id="cb107"><html><body><pre class="r"><span class="no">p15b</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p15b"</span>]])</pre></body></html></div>
+<div class="sourceCode" id="cb99"><pre class="downlit">
+<span class="va">p15b</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p15b"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></pre></div>
 <pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
 <pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
 <pre><code>## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
 ## doubtful</code></pre>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb113"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p15b</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb105"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">p15b</span><span class="op">)</span></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p15b-1.png" width="700"></p>
-<div class="sourceCode" id="cb114"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p15b</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb106"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p15b</span><span class="op">)</span></pre></div>
 <pre><code>## Sums of squares:
 ##       SFO      IORE      DFOP 
 ## 106.91629  68.55574 106.91629 
@@ -858,25 +896,25 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(&gt;t)    Lower    Upper
-## parent_0      1.01e+02 3.06e-17 98.31594 1.03e+02
-## k_parent_sink 4.86e-03 2.48e-10  0.00435 5.42e-03
-## sigma         2.76e+00 1.28e-04  1.61402 3.91e+00
+##          Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0 1.01e+02 3.06e-17 98.31594 1.03e+02
+## k_parent 4.86e-03 2.48e-10  0.00435 5.42e-03
+## sigma    2.76e+00 1.28e-04  1.61402 3.91e+00
 ## 
 ## $IORE
-##                     Estimate   Pr(&gt;t)    Lower  Upper
-## parent_0               99.83 1.81e-16 97.51349 102.14
-## k__iore_parent_sink     0.38 3.22e-01  0.00352  41.05
-## N_parent                0.00 5.00e-01 -1.07695   1.08
-## sigma                   2.21 2.57e-04  1.23245   3.19
+##                Estimate   Pr(&gt;t)    Lower  Upper
+## parent_0          99.83 1.81e-16 97.51348 102.14
+## k__iore_parent     0.38 3.22e-01  0.00352  41.05
+## N_parent           0.00 5.00e-01 -1.07696   1.08
+## sigma              2.21 2.57e-04  1.23245   3.19
 ## 
 ## $DFOP
 ##          Estimate Pr(&gt;t)    Lower    Upper
-## parent_0 1.01e+02     NA 9.82e+01 1.04e+02
-## k1       4.86e-03     NA 6.75e-04 3.49e-02
-## k2       4.86e-03     NA 3.37e-03 6.99e-03
+## parent_0 1.01e+02     NA 98.24464 1.04e+02
+## k1       4.86e-03     NA  0.00068 3.47e-02
+## k2       4.86e-03     NA  0.00338 6.99e-03
 ## g        1.50e-01     NA       NA       NA
-## sigma    2.76e+00     NA 1.58e+00 3.94e+00
+## sigma    2.76e+00     NA  1.58208 3.94e+00
 ## 
 ## 
 ## DTx values:
@@ -892,14 +930,17 @@
 <div id="the-dfop-fraction-parameter-is-greater-than-1" class="section level1">
 <h1 class="hasAnchor">
 <a href="#the-dfop-fraction-parameter-is-greater-than-1" class="anchor"></a>The DFOP fraction parameter is greater than 1</h1>
-<div class="sourceCode" id="cb116"><html><body><pre class="r"><span class="no">p16</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p16"</span>]])</pre></body></html></div>
+<div class="sourceCode" id="cb108"><pre class="downlit">
+<span class="va">p16</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p16"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></pre></div>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The representative half-life of the IORE model is longer than the one corresponding</code></pre>
 <pre><code>## to the terminal degradation rate found with the DFOP model.</code></pre>
 <pre><code>## The representative half-life obtained from the DFOP model may be used</code></pre>
-<div class="sourceCode" id="cb121"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p16</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb113"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">p16</span><span class="op">)</span></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p16-1.png" width="700"></p>
-<div class="sourceCode" id="cb122"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p16</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb114"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p16</span><span class="op">)</span></pre></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 3831.804 2062.008 1550.980 
@@ -909,22 +950,22 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(&gt;t)  Lower Upper
-## parent_0        71.953 2.33e-13 60.509 83.40
-## k_parent_sink    0.159 4.86e-05  0.102  0.25
-## sigma           11.302 1.25e-08  8.308 14.30
+##          Estimate   Pr(&gt;t)  Lower Upper
+## parent_0   71.953 2.33e-13 60.509 83.40
+## k_parent    0.159 4.86e-05  0.102  0.25
+## sigma      11.302 1.25e-08  8.308 14.30
 ## 
 ## $IORE
-##                     Estimate   Pr(&gt;t)    Lower    Upper
-## parent_0            8.74e+01 2.48e-16 7.72e+01 97.52972
-## k__iore_parent_sink 4.55e-04 2.16e-01 3.48e-05  0.00595
-## N_parent            2.70e+00 1.21e-08 1.99e+00  3.40046
-## sigma               8.29e+00 1.61e-08 6.09e+00 10.49062
+##                Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0       8.74e+01 2.48e-16 7.72e+01 97.52972
+## k__iore_parent 4.55e-04 2.16e-01 3.48e-05  0.00595
+## N_parent       2.70e+00 1.21e-08 1.99e+00  3.40046
+## sigma          8.29e+00 1.61e-08 6.09e+00 10.49062
 ## 
 ## $DFOP
 ##          Estimate   Pr(&gt;t)   Lower  Upper
 ## parent_0  88.5333 7.40e-18 79.9836 97.083
-## k1        18.5561 5.00e-01  0.0000    Inf
+## k1        18.5560 5.00e-01  0.0000    Inf
 ## k2         0.0776 1.41e-05  0.0518  0.116
 ## g          0.4733 1.41e-09  0.3674  0.582
 ## sigma      7.1902 2.11e-08  5.2785  9.102
@@ -972,7 +1013,7 @@
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p10-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p10-1.png
index 291b48e1..3e9c743f 100644
--- a/docs/articles/web_only/NAFTA_examples_files/figure-html/p10-1.png
+++ b/docs/articles/web_only/NAFTA_examples_files/figure-html/p10-1.png
diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p11-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p11-1.png
index 149cf24c..77463495 100644
--- a/docs/articles/web_only/NAFTA_examples_files/figure-html/p11-1.png
+++ b/docs/articles/web_only/NAFTA_examples_files/figure-html/p11-1.png
diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p12a-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p12a-1.png
index 85ea5f4e..ccf8f77a 100644
--- a/docs/articles/web_only/NAFTA_examples_files/figure-html/p12a-1.png
+++ b/docs/articles/web_only/NAFTA_examples_files/figure-html/p12a-1.png
diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p12b-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p12b-1.png
index 0ae354c4..6b0dcaf2 100644
--- a/docs/articles/web_only/NAFTA_examples_files/figure-html/p12b-1.png
+++ b/docs/articles/web_only/NAFTA_examples_files/figure-html/p12b-1.png
diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p13-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p13-1.png
index d0f89858..029e6a17 100644
--- a/docs/articles/web_only/NAFTA_examples_files/figure-html/p13-1.png
+++ b/docs/articles/web_only/NAFTA_examples_files/figure-html/p13-1.png
diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p14-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p14-1.png
index 84b53d01..f2f59ff7 100644
--- a/docs/articles/web_only/NAFTA_examples_files/figure-html/p14-1.png
+++ b/docs/articles/web_only/NAFTA_examples_files/figure-html/p14-1.png
diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p15a-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p15a-1.png
index a09b2e3d..24cb27d8 100644
--- a/docs/articles/web_only/NAFTA_examples_files/figure-html/p15a-1.png
+++ b/docs/articles/web_only/NAFTA_examples_files/figure-html/p15a-1.png
diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p15b-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p15b-1.png
index 5a51714c..3640ea68 100644
--- a/docs/articles/web_only/NAFTA_examples_files/figure-html/p15b-1.png
+++ b/docs/articles/web_only/NAFTA_examples_files/figure-html/p15b-1.png
diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p16-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p16-1.png
index 36999356..f3fa460e 100644
--- a/docs/articles/web_only/NAFTA_examples_files/figure-html/p16-1.png
+++ b/docs/articles/web_only/NAFTA_examples_files/figure-html/p16-1.png
diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p5a-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p5a-1.png
index 596a33b2..8d38b89c 100644
--- a/docs/articles/web_only/NAFTA_examples_files/figure-html/p5a-1.png
+++ b/docs/articles/web_only/NAFTA_examples_files/figure-html/p5a-1.png
diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p5b-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p5b-1.png
index e6f9716e..3f2da285 100644
--- a/docs/articles/web_only/NAFTA_examples_files/figure-html/p5b-1.png
+++ b/docs/articles/web_only/NAFTA_examples_files/figure-html/p5b-1.png
diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p6-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p6-1.png
index f8576168..37274769 100644
--- a/docs/articles/web_only/NAFTA_examples_files/figure-html/p6-1.png
+++ b/docs/articles/web_only/NAFTA_examples_files/figure-html/p6-1.png
diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p7-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p7-1.png
index 218a790f..d6ae1fa4 100644
--- a/docs/articles/web_only/NAFTA_examples_files/figure-html/p7-1.png
+++ b/docs/articles/web_only/NAFTA_examples_files/figure-html/p7-1.png
diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p8-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p8-1.png
index fa8621e7..ebcc326c 100644
--- a/docs/articles/web_only/NAFTA_examples_files/figure-html/p8-1.png
+++ b/docs/articles/web_only/NAFTA_examples_files/figure-html/p8-1.png
diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p9a-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p9a-1.png
index aac3600b..a6f4e763 100644
--- a/docs/articles/web_only/NAFTA_examples_files/figure-html/p9a-1.png
+++ b/docs/articles/web_only/NAFTA_examples_files/figure-html/p9a-1.png
diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p9b-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p9b-1.png
index cb52aecd..2a8cf947 100644
--- a/docs/articles/web_only/NAFTA_examples_files/figure-html/p9b-1.png
+++ b/docs/articles/web_only/NAFTA_examples_files/figure-html/p9b-1.png
diff --git a/docs/articles/web_only/benchmarks.html b/docs/articles/web_only/benchmarks.html
index 0698baf6..28a3b68a 100644
--- a/docs/articles/web_only/benchmarks.html
+++ b/docs/articles/web_only/benchmarks.html
@@ -5,13 +5,13 @@
 <meta charset="utf-8">
 <meta http-equiv="X-UA-Compatible" content="IE=edge">
 <meta name="viewport" content="width=device-width, initial-scale=1.0">
-<title>Benchmark timings for mkin on various systems • mkin</title>
+<title>Benchmark timings for mkin • mkin</title>
 <!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous">
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-<script src="../../pkgdown.js"></script><meta property="og:title" content="Benchmark timings for mkin on various systems">
+<script src="../../pkgdown.js"></script><meta property="og:title" content="Benchmark timings for mkin">
 <meta property="og:description" content="mkin">
 <!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
 <script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script>
@@ -31,7 +31,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -68,6 +68,9 @@
     <li>
       <a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -76,7 +79,7 @@
       </ul>
 <ul class="nav navbar-nav navbar-right">
 <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -94,148 +97,282 @@
       </header><div class="row">
   <div class="col-md-9 contents">
     <div class="page-header toc-ignore">
-      <h1 data-toc-skip>Benchmark timings for mkin on various systems</h1>
+      <h1 data-toc-skip>Benchmark timings for mkin</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2020-05-27</h4>
+            <h4 class="date">2020-10-15</h4>
       
-      <small class="dont-index">Source: <a href="http://github.com/jranke/mkin/blob/master/vignettes/web_only/benchmarks.Rmd"><code>vignettes/web_only/benchmarks.Rmd</code></a></small>
-      <div class="hidden name"><code>benchmarks.Rmd</code></div>
+      <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/master/vignettes/web_only/benchmarks.rmd"><code>vignettes/web_only/benchmarks.rmd</code></a></small>
+      <div class="hidden name"><code>benchmarks.rmd</code></div>
 
     </div>
 
     
     
-<div id="systems" class="section level2">
+<p>Each system is characterized by its CPU type, the operating system type and the mkin version. Currently only values for one system are available. A compiler was available, so if no analytical solution was available, compiled ODE models are used.</p>
+<div id="test-cases" class="section level2">
 <h2 class="hasAnchor">
-<a href="#systems" class="anchor"></a>Systems</h2>
-<p>Each system is characterized by its CPU type, the operating system type and the mkin version.</p>
-<div class="sourceCode" id="cb1"><html><body><pre class="r"><span class="no">cpu_model</span> <span class="kw">&lt;-</span> <span class="kw pkg">benchmarkme</span><span class="kw ns">::</span><span class="fu"><a href="https://rdrr.io/pkg/benchmarkme/man/get_cpu.html">get_cpu</a></span>()$<span class="no">model_name</span>
-<span class="no">operating_system</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/Sys.info.html">Sys.info</a></span>()<span class="kw">[[</span><span class="st">"sysname"</span>]]
-<span class="no">mkin_version</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/character.html">as.character</a></span>(<span class="fu"><a href="https://rdrr.io/r/utils/packageDescription.html">packageVersion</a></span>(<span class="st">"mkin"</span>))
-<span class="no">system_string</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html">paste0</a></span>(<span class="no">operating_system</span>, <span class="st">", "</span>, <span class="no">cpu_model</span>, <span class="st">", mkin version "</span>, <span class="no">mkin_version</span>)
-<span class="fu"><a href="https://rdrr.io/r/base/load.html">load</a></span>(<span class="st">"~/git/mkin/vignettes/web_only/mkin_benchmarks.rda"</span>)
-<span class="no">mkin_benchmarks</span>[<span class="no">system_string</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="st">"CPU"</span>, <span class="st">"OS"</span>, <span class="st">"mkin"</span>)] <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="no">cpu_model</span>, <span class="no">operating_system</span>, <span class="no">mkin_version</span>)
-
-<span class="kw">if</span> (<span class="no">mkin_version</span> <span class="kw">&gt;</span> <span class="st">"0.9.48.1"</span>) {
-  <span class="no">mmkin_bench</span> <span class="kw">&lt;-</span> <span class="kw">function</span>(<span class="no">models</span>, <span class="no">datasets</span>, <span class="no">error_model</span> <span class="kw">=</span> <span class="st">"const"</span>) <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span>(<span class="no">models</span>, <span class="no">datasets</span>, <span class="kw">error_model</span> <span class="kw">=</span> <span class="no">error_model</span>, <span class="kw">cores</span> <span class="kw">=</span> <span class="fl">1</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)
-} <span class="kw">else</span> {
-  <span class="no">mmkin_bench</span> <span class="kw">&lt;-</span> <span class="kw">function</span>(<span class="no">models</span>, <span class="no">datasets</span>, <span class="no">error_model</span> <span class="kw">=</span> <span class="kw">NULL</span>) <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span>(<span class="no">models</span>, <span class="no">datasets</span>, <span class="kw">reweight.method</span> <span class="kw">=</span> <span class="no">error_model</span>, <span class="kw">cores</span> <span class="kw">=</span> <span class="fl">1</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)
-}</pre></body></html></div>
-<div class="sourceCode" id="cb2"><html><body><pre class="r"><span class="no">FOCUS_C</span> <span class="kw">&lt;-</span> <span class="no">FOCUS_2006_C</span>
-<span class="no">FOCUS_D</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/subset.html">subset</a></span>(<span class="no">FOCUS_2006_D</span>, <span class="no">value</span> <span class="kw">!=</span> <span class="fl">0</span>)
-<span class="co"># Parent only</span>
-<span class="no">t1</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>, <span class="st">"HS"</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">FOCUS_C</span>, <span class="no">FOCUS_D</span>)))<span class="kw">[[</span><span class="st">"elapsed"</span>]]
-<span class="no">t2</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>, <span class="st">"HS"</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">FOCUS_C</span>, <span class="no">FOCUS_D</span>), <span class="kw">error_model</span> <span class="kw">=</span> <span class="st">"tc"</span>))<span class="kw">[[</span><span class="st">"elapsed"</span>]]</pre></body></html></div>
-<pre><code>## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...): Optimisation did not converge:
-## iteration limit reached without convergence (10)</code></pre>
-<div class="sourceCode" id="cb4"><html><body><pre class="r"><span class="co"># One metabolite</span>
-<span class="no">SFO_SFO</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(
-  <span class="kw">parent</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"m1"</span>),
-  <span class="kw">m1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>))</pre></body></html></div>
-<pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
-<div class="sourceCode" id="cb6"><html><body><pre class="r"><span class="no">FOMC_SFO</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(
-  <span class="kw">parent</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"FOMC"</span>, <span class="st">"m1"</span>),
-  <span class="kw">m1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>))</pre></body></html></div>
-<pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
-<div class="sourceCode" id="cb8"><html><body><pre class="r"><span class="no">DFOP_SFO</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(
-  <span class="kw">parent</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"FOMC"</span>, <span class="st">"m1"</span>),
-  <span class="kw">m1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>))</pre></body></html></div>
-<pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
-<div class="sourceCode" id="cb10"><html><body><pre class="r"><span class="no">t3</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">SFO_SFO</span>, <span class="no">FOMC_SFO</span>, <span class="no">DFOP_SFO</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">FOCUS_D</span>)))<span class="kw">[[</span><span class="st">"elapsed"</span>]]
-<span class="no">t4</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">SFO_SFO</span>, <span class="no">FOMC_SFO</span>, <span class="no">DFOP_SFO</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">FOCUS_D</span>), <span class="kw">error_model</span> <span class="kw">=</span> <span class="st">"tc"</span>))<span class="kw">[[</span><span class="st">"elapsed"</span>]]
-<span class="no">t5</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">SFO_SFO</span>, <span class="no">FOMC_SFO</span>, <span class="no">DFOP_SFO</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">FOCUS_D</span>), <span class="kw">error_model</span> <span class="kw">=</span> <span class="st">"obs"</span>))<span class="kw">[[</span><span class="st">"elapsed"</span>]]
+<a href="#test-cases" class="anchor"></a>Test cases</h2>
+<p>Parent only:</p>
+<div class="sourceCode" id="cb1"><pre class="downlit">
+<span class="va">FOCUS_C</span> <span class="op">&lt;-</span> <span class="va">FOCUS_2006_C</span>
+<span class="va">FOCUS_D</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/subset.html">subset</a></span><span class="op">(</span><span class="va">FOCUS_2006_D</span>, <span class="va">value</span> <span class="op">!=</span> <span class="fl">0</span><span class="op">)</span>
+<span class="va">parent_datasets</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">FOCUS_C</span>, <span class="va">FOCUS_D</span><span class="op">)</span>
 
-<span class="co"># Two metabolites, synthetic data</span>
-<span class="no">m_synth_SFO_lin</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="kw">parent</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"M1"</span>),
-                           <span class="kw">M1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"M2"</span>),
-                           <span class="kw">M2</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>),
-                           <span class="kw">use_of_ff</span> <span class="kw">=</span> <span class="st">"max"</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)
+<span class="va">t1</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>, <span class="st">"HS"</span><span class="op">)</span>, <span class="va">parent_datasets</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span>
+<span class="va">t2</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>, <span class="st">"HS"</span><span class="op">)</span>, <span class="va">parent_datasets</span>,
+    error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></pre></div>
+<p>One metabolite:</p>
+<div class="sourceCode" id="cb2"><pre class="downlit">
+<span class="va">SFO_SFO</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>
+  parent <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"m1"</span><span class="op">)</span>,
+  m1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span><span class="op">)</span>
+<span class="va">FOMC_SFO</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>
+  parent <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"FOMC"</span>, <span class="st">"m1"</span><span class="op">)</span>,
+  m1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span><span class="op">)</span>
+<span class="va">DFOP_SFO</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>
+  parent <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"FOMC"</span>, <span class="st">"m1"</span><span class="op">)</span>,
+  m1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span><span class="op">)</span>
+<span class="va">t3</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOMC_SFO</span>, <span class="va">DFOP_SFO</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">FOCUS_D</span><span class="op">)</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></pre></div>
+<pre><code>## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...):
+## Shapiro-Wilk test for standardized residuals: p = 0.0165</code></pre>
+<pre><code>## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...):
+## Shapiro-Wilk test for standardized residuals: p = 0.0499
 
-<span class="no">m_synth_DFOP_par</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="kw">parent</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"DFOP"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="st">"M1"</span>, <span class="st">"M2"</span>)),
-                           <span class="kw">M1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>),
-                           <span class="kw">M2</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>),
-                           <span class="kw">use_of_ff</span> <span class="kw">=</span> <span class="st">"max"</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)
+## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...):
+## Shapiro-Wilk test for standardized residuals: p = 0.0499</code></pre>
+<div class="sourceCode" id="cb5"><pre class="downlit">
+<span class="va">t4</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOMC_SFO</span>, <span class="va">DFOP_SFO</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">FOCUS_D</span><span class="op">)</span>,
+    error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span>
+<span class="va">t5</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOMC_SFO</span>, <span class="va">DFOP_SFO</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">FOCUS_D</span><span class="op">)</span>,
+    error_model <span class="op">=</span> <span class="st">"obs"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></pre></div>
+<p>Two metabolites, synthetic data:</p>
+<div class="sourceCode" id="cb6"><pre class="downlit">
+<span class="va">m_synth_SFO_lin</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>parent <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M1"</span><span class="op">)</span>,
+                           M1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M2"</span><span class="op">)</span>,
+                           M2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,
+                           use_of_ff <span class="op">=</span> <span class="st">"max"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>
 
-<span class="no">SFO_lin_a</span> <span class="kw">&lt;-</span> <span class="no">synthetic_data_for_UBA_2014</span><span class="kw">[[</span><span class="fl">1</span>]]$<span class="no">data</span>
+<span class="va">m_synth_DFOP_par</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>parent <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"DFOP"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="st">"M1"</span>, <span class="st">"M2"</span><span class="op">)</span><span class="op">)</span>,
+                           M1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,
+                           M2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,
+                           use_of_ff <span class="op">=</span> <span class="st">"max"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>
 
-<span class="no">DFOP_par_c</span> <span class="kw">&lt;-</span> <span class="no">synthetic_data_for_UBA_2014</span><span class="kw">[[</span><span class="fl">12</span>]]$<span class="no">data</span>
+<span class="va">SFO_lin_a</span> <span class="op">&lt;-</span> <span class="va">synthetic_data_for_UBA_2014</span><span class="op">[[</span><span class="fl">1</span><span class="op">]</span><span class="op">]</span><span class="op">$</span><span class="va">data</span>
 
-<span class="no">t6</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">m_synth_SFO_lin</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">SFO_lin_a</span>)))[<span class="st">"elapsed"</span>]
-<span class="no">t7</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">m_synth_DFOP_par</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">DFOP_par_c</span>)))[<span class="st">"elapsed"</span>]
+<span class="va">DFOP_par_c</span> <span class="op">&lt;-</span> <span class="va">synthetic_data_for_UBA_2014</span><span class="op">[[</span><span class="fl">12</span><span class="op">]</span><span class="op">]</span><span class="op">$</span><span class="va">data</span>
 
-<span class="no">t8</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">m_synth_SFO_lin</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">SFO_lin_a</span>), <span class="kw">error_model</span> <span class="kw">=</span> <span class="st">"tc"</span>))[<span class="st">"elapsed"</span>]
-<span class="no">t9</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">m_synth_DFOP_par</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">DFOP_par_c</span>), <span class="kw">error_model</span> <span class="kw">=</span> <span class="st">"tc"</span>))[<span class="st">"elapsed"</span>]
+<span class="va">t6</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">m_synth_SFO_lin</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">SFO_lin_a</span><span class="op">)</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span>
+<span class="va">t7</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">m_synth_DFOP_par</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">DFOP_par_c</span><span class="op">)</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></pre></div>
+<pre><code>## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...):
+## Shapiro-Wilk test for standardized residuals: p = 0.000174</code></pre>
+<div class="sourceCode" id="cb8"><pre class="downlit">
+<span class="va">t8</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">m_synth_SFO_lin</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">SFO_lin_a</span><span class="op">)</span>,
+    error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span>
+<span class="va">t9</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">m_synth_DFOP_par</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">DFOP_par_c</span><span class="op">)</span>,
+    error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span>
 
-<span class="no">t10</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">m_synth_SFO_lin</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">SFO_lin_a</span>), <span class="kw">error_model</span> <span class="kw">=</span> <span class="st">"obs"</span>))[<span class="st">"elapsed"</span>]
-<span class="no">t11</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">m_synth_DFOP_par</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">DFOP_par_c</span>), <span class="kw">error_model</span> <span class="kw">=</span> <span class="st">"obs"</span>))[<span class="st">"elapsed"</span>]
-
-<span class="no">mkin_benchmarks</span>[<span class="no">system_string</span>, <span class="fu"><a href="https://rdrr.io/r/base/paste.html">paste0</a></span>(<span class="st">"t"</span>, <span class="fl">1</span>:<span class="fl">11</span>)] <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="no">t1</span>, <span class="no">t2</span>, <span class="no">t3</span>, <span class="no">t4</span>, <span class="no">t5</span>, <span class="no">t6</span>, <span class="no">t7</span>, <span class="no">t8</span>, <span class="no">t9</span>, <span class="no">t10</span>, <span class="no">t11</span>)
-<span class="no">mkin_benchmarks</span>[, -<span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="fl">1</span>:<span class="fl">3</span>)]</pre></body></html></div>
-<pre><code>##                                                                        t1
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 3.610
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 8.184
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 7.064
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 7.296
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 5.936
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.50.2 1.679
-##                                                                         t2
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 11.019
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 22.889
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 12.558
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 21.239
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 20.545
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.50.2  3.613
-##                                                                        t3
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 3.764
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 4.649
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 4.786
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 4.510
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 4.446
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.50.2 1.366
-##                                                                         t4
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 14.347
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 13.789
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2  8.461
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 13.805
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 15.335
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.50.2  6.545
-##                                                                        t5    t6
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 9.495 2.623
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 6.395 2.542
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 5.675 2.723
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 7.386 2.643
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 6.002 2.635
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.50.2 2.709 0.752
-##                                                                        t7    t8
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 4.587 7.525
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 4.128 4.632
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 4.478 4.862
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 4.374  7.02
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 4.259 4.737
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.50.2 1.214 1.455
-##                                                                         t9
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 16.621
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1  8.171
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2  7.618
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 11.124
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4  7.763
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.50.2  4.196
-##                                                                       t10
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 8.576
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 3.676
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 3.579
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 5.388
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 3.427
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.50.2 1.996
-##                                                                        t11
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 31.267
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1  5.636
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2  5.574
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3  7.365
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4  5.626
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.50.2    3.1</code></pre>
-<div class="sourceCode" id="cb12"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/save.html">save</a></span>(<span class="no">mkin_benchmarks</span>, <span class="kw">file</span> <span class="kw">=</span> <span class="st">"~/git/mkin/vignettes/mkin_benchmarks.rda"</span>)</pre></body></html></div>
+<span class="va">t10</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">m_synth_SFO_lin</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">SFO_lin_a</span><span class="op">)</span>,
+    error_model <span class="op">=</span> <span class="st">"obs"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span>
+<span class="va">t11</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">m_synth_DFOP_par</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">DFOP_par_c</span><span class="op">)</span>,
+    error_model <span class="op">=</span> <span class="st">"obs"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></pre></div>
+<div class="sourceCode" id="cb9"><pre class="downlit">
+<span class="va">mkin_benchmarks</span><span class="op">[</span><span class="va">system_string</span>, <span class="fu"><a href="https://rdrr.io/r/base/paste.html">paste0</a></span><span class="op">(</span><span class="st">"t"</span>, <span class="fl">1</span><span class="op">:</span><span class="fl">11</span><span class="op">)</span><span class="op">]</span> <span class="op">&lt;-</span>
+  <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="va">t1</span>, <span class="va">t2</span>, <span class="va">t3</span>, <span class="va">t4</span>, <span class="va">t5</span>, <span class="va">t6</span>, <span class="va">t7</span>, <span class="va">t8</span>, <span class="va">t9</span>, <span class="va">t10</span>, <span class="va">t11</span><span class="op">)</span>
+<span class="fu"><a href="https://rdrr.io/r/base/save.html">save</a></span><span class="op">(</span><span class="va">mkin_benchmarks</span>, file <span class="op">=</span> <span class="st">"~/git/mkin/vignettes/web_only/mkin_benchmarks.rda"</span><span class="op">)</span></pre></div>
+</div>
+<div id="results" class="section level2">
+<h2 class="hasAnchor">
+<a href="#results" class="anchor"></a>Results</h2>
+<p>Currently, we only have benchmark information on one system, therefore only the mkin version is shown with the results below. Timings are in seconds, shorter is better. All results were obtained by serial, i.e. not using multiple computing cores.</p>
+<p>Benchmarks for all available error models are shown.</p>
+<div id="parent-only" class="section level3">
+<h3 class="hasAnchor">
+<a href="#parent-only" class="anchor"></a>Parent only</h3>
+<p>Constant variance (t1) and two-component error model (t2) for four models fitted to two datasets, i.e. eight fits for each test.</p>
+<table class="table">
+<thead><tr class="header">
+<th align="left">mkin version</th>
+<th align="right">t1 [s]</th>
+<th align="right">t2 [s]</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">0.9.48.1</td>
+<td align="right">3.610</td>
+<td align="right">11.019</td>
+</tr>
+<tr class="even">
+<td align="left">0.9.49.1</td>
+<td align="right">8.184</td>
+<td align="right">22.889</td>
+</tr>
+<tr class="odd">
+<td align="left">0.9.49.2</td>
+<td align="right">7.064</td>
+<td align="right">12.558</td>
+</tr>
+<tr class="even">
+<td align="left">0.9.49.3</td>
+<td align="right">7.296</td>
+<td align="right">21.239</td>
+</tr>
+<tr class="odd">
+<td align="left">0.9.49.4</td>
+<td align="right">5.936</td>
+<td align="right">20.545</td>
+</tr>
+<tr class="even">
+<td align="left">0.9.50.2</td>
+<td align="right">1.714</td>
+<td align="right">3.971</td>
+</tr>
+<tr class="odd">
+<td align="left">0.9.50.3</td>
+<td align="right">1.752</td>
+<td align="right">4.156</td>
+</tr>
+</tbody>
+</table>
+</div>
+<div id="one-metabolite" class="section level3">
+<h3 class="hasAnchor">
+<a href="#one-metabolite" class="anchor"></a>One metabolite</h3>
+<p>Constant variance (t3), two-component error model (t4), and variance by variable (t5) for three models fitted to one dataset, i.e. three fits for each test.</p>
+<table class="table">
+<thead><tr class="header">
+<th align="left">mkin version</th>
+<th align="right">t3 [s]</th>
+<th align="right">t4 [s]</th>
+<th align="right">t5 [s]</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">0.9.48.1</td>
+<td align="right">3.764</td>
+<td align="right">14.347</td>
+<td align="right">9.495</td>
+</tr>
+<tr class="even">
+<td align="left">0.9.49.1</td>
+<td align="right">4.649</td>
+<td align="right">13.789</td>
+<td align="right">6.395</td>
+</tr>
+<tr class="odd">
+<td align="left">0.9.49.2</td>
+<td align="right">4.786</td>
+<td align="right">8.461</td>
+<td align="right">5.675</td>
+</tr>
+<tr class="even">
+<td align="left">0.9.49.3</td>
+<td align="right">4.510</td>
+<td align="right">13.805</td>
+<td align="right">7.386</td>
+</tr>
+<tr class="odd">
+<td align="left">0.9.49.4</td>
+<td align="right">4.446</td>
+<td align="right">15.335</td>
+<td align="right">6.002</td>
+</tr>
+<tr class="even">
+<td align="left">0.9.50.2</td>
+<td align="right">1.402</td>
+<td align="right">6.174</td>
+<td align="right">2.764</td>
+</tr>
+<tr class="odd">
+<td align="left">0.9.50.3</td>
+<td align="right">1.430</td>
+<td align="right">6.615</td>
+<td align="right">2.878</td>
+</tr>
+</tbody>
+</table>
+</div>
+<div id="two-metabolites" class="section level3">
+<h3 class="hasAnchor">
+<a href="#two-metabolites" class="anchor"></a>Two metabolites</h3>
+<p>Constant variance (t6 and t7), two-component error model (t8 and t9), and variance by variable (t10 and t11) for one model fitted to one dataset, i.e. one fit for each test.</p>
+<table class="table">
+<thead><tr class="header">
+<th align="left">mkin version</th>
+<th align="right">t6 [s]</th>
+<th align="right">t7 [s]</th>
+<th align="right">t8 [s]</th>
+<th align="right">t9 [s]</th>
+<th align="right">t10 [s]</th>
+<th align="right">t11 [s]</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">0.9.48.1</td>
+<td align="right">2.623</td>
+<td align="right">4.587</td>
+<td align="right">7.525</td>
+<td align="right">16.621</td>
+<td align="right">8.576</td>
+<td align="right">31.267</td>
+</tr>
+<tr class="even">
+<td align="left">0.9.49.1</td>
+<td align="right">2.542</td>
+<td align="right">4.128</td>
+<td align="right">4.632</td>
+<td align="right">8.171</td>
+<td align="right">3.676</td>
+<td align="right">5.636</td>
+</tr>
+<tr class="odd">
+<td align="left">0.9.49.2</td>
+<td align="right">2.723</td>
+<td align="right">4.478</td>
+<td align="right">4.862</td>
+<td align="right">7.618</td>
+<td align="right">3.579</td>
+<td align="right">5.574</td>
+</tr>
+<tr class="even">
+<td align="left">0.9.49.3</td>
+<td align="right">2.643</td>
+<td align="right">4.374</td>
+<td align="right">7.020</td>
+<td align="right">11.124</td>
+<td align="right">5.388</td>
+<td align="right">7.365</td>
+</tr>
+<tr class="odd">
+<td align="left">0.9.49.4</td>
+<td align="right">2.635</td>
+<td align="right">4.259</td>
+<td align="right">4.737</td>
+<td align="right">7.763</td>
+<td align="right">3.427</td>
+<td align="right">5.626</td>
+</tr>
+<tr class="even">
+<td align="left">0.9.50.2</td>
+<td align="right">0.777</td>
+<td align="right">1.236</td>
+<td align="right">1.332</td>
+<td align="right">2.872</td>
+<td align="right">2.069</td>
+<td align="right">2.987</td>
+</tr>
+<tr class="odd">
+<td align="left">0.9.50.3</td>
+<td align="right">0.858</td>
+<td align="right">1.264</td>
+<td align="right">1.333</td>
+<td align="right">2.984</td>
+<td align="right">2.113</td>
+<td align="right">3.073</td>
+</tr>
+</tbody>
+</table>
+</div>
 </div>
   </div>
 
@@ -254,7 +391,7 @@
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/articles/web_only/compiled_models.html b/docs/articles/web_only/compiled_models.html
index 5aaa09bc..c2964762 100644
--- a/docs/articles/web_only/compiled_models.html
+++ b/docs/articles/web_only/compiled_models.html
@@ -31,7 +31,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -68,6 +68,9 @@
     <li>
       <a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -76,7 +79,7 @@
       </ul>
 <ul class="nav navbar-nav navbar-right">
 <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -97,10 +100,10 @@
       <h1 data-toc-skip>Performance benefit by using compiled model definitions in mkin</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2020-05-27</h4>
+            <h4 class="date">2020-10-15</h4>
       
-      <small class="dont-index">Source: <a href="http://github.com/jranke/mkin/blob/master/vignettes/web_only/compiled_models.Rmd"><code>vignettes/web_only/compiled_models.Rmd</code></a></small>
-      <div class="hidden name"><code>compiled_models.Rmd</code></div>
+      <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/master/vignettes/web_only/compiled_models.rmd"><code>vignettes/web_only/compiled_models.rmd</code></a></small>
+      <div class="hidden name"><code>compiled_models.rmd</code></div>
 
     </div>
 
@@ -110,81 +113,86 @@
 <h2 class="hasAnchor">
 <a href="#how-to-benefit-from-compiled-models" class="anchor"></a>How to benefit from compiled models</h2>
 <p>When using an mkin version equal to or greater than 0.9-36 and a C compiler is available, you will see a message that the model is being compiled from autogenerated C code when defining a model using mkinmod. Starting from version 0.9.49.9, the <code><a href="../../reference/mkinmod.html">mkinmod()</a></code> function checks for presence of a compiler using</p>
-<div class="sourceCode" id="cb1"><html><body><pre class="r"><span class="kw pkg">pkgbuild</span><span class="kw ns">::</span><span class="fu"><a href="https://rdrr.io/pkg/pkgbuild/man/has_compiler.html">has_compiler</a></span>()</pre></body></html></div>
+<div class="sourceCode" id="cb1"><pre class="downlit">
+<span class="fu">pkgbuild</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/pkgbuild/man/has_compiler.html">has_compiler</a></span><span class="op">(</span><span class="op">)</span></pre></div>
 <p>In previous versions, it used <code><a href="https://rdrr.io/r/base/Sys.which.html">Sys.which("gcc")</a></code> for this check.</p>
 <p>On Linux, you need to have the essential build tools like make and gcc or clang installed. On Debian based linux distributions, these will be pulled in by installing the build-essential package.</p>
 <p>On MacOS, which I do not use personally, I have had reports that a compiler is available by default.</p>
 <p>On Windows, you need to install Rtools and have the path to its bin directory in your PATH variable. You do not need to modify the PATH variable when installing Rtools. Instead, I would recommend to put the line</p>
-<div class="sourceCode" id="cb2"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/Sys.setenv.html">Sys.setenv</a></span>(<span class="kw">PATH</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html">paste</a></span>(<span class="st">"C:/Rtools/bin"</span>, <span class="fu"><a href="https://rdrr.io/r/base/Sys.getenv.html">Sys.getenv</a></span>(<span class="st">"PATH"</span>), <span class="kw">sep</span><span class="kw">=</span><span class="st">";"</span>))</pre></body></html></div>
+<div class="sourceCode" id="cb2"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/base/Sys.setenv.html">Sys.setenv</a></span><span class="op">(</span>PATH <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html">paste</a></span><span class="op">(</span><span class="st">"C:/Rtools/bin"</span>, <span class="fu"><a href="https://rdrr.io/r/base/Sys.getenv.html">Sys.getenv</a></span><span class="op">(</span><span class="st">"PATH"</span><span class="op">)</span>, sep<span class="op">=</span><span class="st">";"</span><span class="op">)</span><span class="op">)</span></pre></div>
 <p>into your .Rprofile startup file. This is just a text file with some R code that is executed when your R session starts. It has to be named .Rprofile and has to be located in your home directory, which will generally be your Documents folder. You can check the location of the home directory used by R by issuing</p>
-<div class="sourceCode" id="cb3"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/Sys.getenv.html">Sys.getenv</a></span>(<span class="st">"HOME"</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb3"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/base/Sys.getenv.html">Sys.getenv</a></span><span class="op">(</span><span class="st">"HOME"</span><span class="op">)</span></pre></div>
 </div>
-<div id="comparison-with-eigenvalue-based-solutions" class="section level2">
+<div id="comparison-with-other-solution-methods" class="section level2">
 <h2 class="hasAnchor">
-<a href="#comparison-with-eigenvalue-based-solutions" class="anchor"></a>Comparison with Eigenvalue based solutions</h2>
-<p>First, we build a simple degradation model for a parent compound with one metabolite.</p>
-<div class="sourceCode" id="cb4"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/library.html">library</a></span>(<span class="st">"mkin"</span>, <span class="kw">quietly</span> <span class="kw">=</span> <span class="fl">TRUE</span>)
-<span class="no">SFO_SFO</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(
-  <span class="kw">parent</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"m1"</span>),
-  <span class="kw">m1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>))</pre></body></html></div>
+<a href="#comparison-with-other-solution-methods" class="anchor"></a>Comparison with other solution methods</h2>
+<p>First, we build a simple degradation model for a parent compound with one metabolite, and we remove zero values from the dataset.</p>
+<div class="sourceCode" id="cb4"><pre class="downlit">
+<span class="kw"><a href="https://rdrr.io/r/base/library.html">library</a></span><span class="op">(</span><span class="st"><a href="https://pkgdown.jrwb.de/mkin/">"mkin"</a></span>, quietly <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>
+<span class="va">SFO_SFO</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>
+  parent <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"m1"</span><span class="op">)</span>,
+  m1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span><span class="op">)</span></pre></div>
 <pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
-<p>We can compare the performance of the Eigenvalue based solution against the compiled version and the R implementation of the differential equations using the benchmark package. In the output of below code, the warnings about zero being removed from the FOCUS D dataset are suppressed.</p>
-<div class="sourceCode" id="cb6"><html><body><pre class="r"><span class="kw">if</span> (<span class="fu"><a href="https://rdrr.io/r/base/library.html">require</a></span>(<span class="no">rbenchmark</span>)) {
-  <span class="no">b.1</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/rbenchmark/man/benchmark.html">benchmark</a></span>(
-    <span class="st">"deSolve, not compiled"</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">SFO_SFO</span>, <span class="no">FOCUS_2006_D</span>,
-                                      <span class="kw">solution_type</span> <span class="kw">=</span> <span class="st">"deSolve"</span>,
-                                      <span class="kw">use_compiled</span> <span class="kw">=</span> <span class="fl">FALSE</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>),
-    <span class="st">"Eigenvalue based"</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">SFO_SFO</span>, <span class="no">FOCUS_2006_D</span>,
-                                 <span class="kw">solution_type</span> <span class="kw">=</span> <span class="st">"eigen"</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>),
-    <span class="st">"deSolve, compiled"</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">SFO_SFO</span>, <span class="no">FOCUS_2006_D</span>,
-                                  <span class="kw">solution_type</span> <span class="kw">=</span> <span class="st">"deSolve"</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>),
-    <span class="kw">replications</span> <span class="kw">=</span> <span class="fl">3</span>)
-  <span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">b.1</span>)
-  <span class="no">factor_SFO_SFO</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/Round.html">round</a></span>(<span class="no">b.1</span>[<span class="st">"1"</span>, <span class="st">"relative"</span>])
-} <span class="kw">else</span> {
-  <span class="no">factor_SFO_SFO</span> <span class="kw">&lt;-</span> <span class="fl">NA</span>
-  <span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="st">"R package rbenchmark is not available"</span>)
-}</pre></body></html></div>
-<pre><code>##                    test replications elapsed relative user.self sys.self
-## 3     deSolve, compiled            3   0.997    1.000     0.997    0.000
-## 1 deSolve, not compiled            3  24.417   24.490    24.405    0.001
-## 2      Eigenvalue based            3   1.159    1.162     1.159    0.000
-##   user.child sys.child
-## 3          0         0
-## 1          0         0
-## 2          0         0</code></pre>
-<p>We see that using the compiled model is by a factor of around 24 faster than using the R version with the default ode solver, and it is even faster than the Eigenvalue based solution implemented in R which does not need iterative solution of the ODEs.</p>
+<div class="sourceCode" id="cb6"><pre class="downlit">
+<span class="va">FOCUS_D</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/subset.html">subset</a></span><span class="op">(</span><span class="va">FOCUS_2006_D</span>, <span class="va">value</span> <span class="op">!=</span> <span class="fl">0</span><span class="op">)</span></pre></div>
+<p>We can compare the performance of the Eigenvalue based solution against the compiled version and the R implementation of the differential equations using the benchmark package. In the output of below code, the warnings about zero being removed from the FOCUS D dataset are suppressed. Since mkin version 0.9.49.11, an analytical solution is also implemented, which is included in the tests below.</p>
+<div class="sourceCode" id="cb7"><pre class="downlit">
+<span class="kw">if</span> <span class="op">(</span><span class="kw"><a href="https://rdrr.io/r/base/library.html">require</a></span><span class="op">(</span><span class="va"><a href="http://rbenchmark.googlecode.com">rbenchmark</a></span><span class="op">)</span><span class="op">)</span> <span class="op">{</span>
+  <span class="va">b.1</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/rbenchmark/man/benchmark.html">benchmark</a></span><span class="op">(</span>
+    <span class="st">"deSolve, not compiled"</span> <span class="op">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOCUS_D</span>,
+       solution_type <span class="op">=</span> <span class="st">"deSolve"</span>,
+       use_compiled <span class="op">=</span> <span class="cn">FALSE</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,
+    <span class="st">"Eigenvalue based"</span> <span class="op">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOCUS_D</span>,
+       solution_type <span class="op">=</span> <span class="st">"eigen"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,
+    <span class="st">"deSolve, compiled"</span> <span class="op">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOCUS_D</span>,
+       solution_type <span class="op">=</span> <span class="st">"deSolve"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,
+    <span class="st">"analytical"</span> <span class="op">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOCUS_D</span>,
+       solution_type <span class="op">=</span> <span class="st">"analytical"</span>,
+       use_compiled <span class="op">=</span> <span class="cn">FALSE</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,
+    replications <span class="op">=</span> <span class="fl">1</span>, order <span class="op">=</span> <span class="st">"relative"</span>,
+    columns <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="st">"test"</span>, <span class="st">"replications"</span>, <span class="st">"relative"</span>, <span class="st">"elapsed"</span><span class="op">)</span><span class="op">)</span>
+  <span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">b.1</span><span class="op">)</span>
+<span class="op">}</span> <span class="kw">else</span> <span class="op">{</span>
+  <span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="st">"R package rbenchmark is not available"</span><span class="op">)</span>
+<span class="op">}</span></pre></div>
+<pre><code>##                    test replications relative elapsed
+## 4            analytical            1    1.000   0.200
+## 3     deSolve, compiled            1    1.745   0.349
+## 2      Eigenvalue based            1    2.040   0.408
+## 1 deSolve, not compiled            1   42.235   8.447</code></pre>
+<p>We see that using the compiled model is by more than a factor of 10 faster than using deSolve without compiled code.</p>
 </div>
-<div id="model-that-can-not-be-solved-with-eigenvalues" class="section level2">
+<div id="model-without-analytical-solution" class="section level2">
 <h2 class="hasAnchor">
-<a href="#model-that-can-not-be-solved-with-eigenvalues" class="anchor"></a>Model that can not be solved with Eigenvalues</h2>
-<p>This evaluation is also taken from the example section of mkinfit.</p>
-<div class="sourceCode" id="cb8"><html><body><pre class="r"><span class="kw">if</span> (<span class="fu"><a href="https://rdrr.io/r/base/library.html">require</a></span>(<span class="no">rbenchmark</span>)) {
-  <span class="no">FOMC_SFO</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(
-    <span class="kw">parent</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"FOMC"</span>, <span class="st">"m1"</span>),
-    <span class="kw">m1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>( <span class="st">"SFO"</span>))
-
-  <span class="no">b.2</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/rbenchmark/man/benchmark.html">benchmark</a></span>(
-    <span class="st">"deSolve, not compiled"</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">FOMC_SFO</span>, <span class="no">FOCUS_2006_D</span>,
-                                      <span class="kw">use_compiled</span> <span class="kw">=</span> <span class="fl">FALSE</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>),
-    <span class="st">"deSolve, compiled"</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">FOMC_SFO</span>, <span class="no">FOCUS_2006_D</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>),
-    <span class="kw">replications</span> <span class="kw">=</span> <span class="fl">3</span>)
-  <span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">b.2</span>)
-  <span class="no">factor_FOMC_SFO</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/Round.html">round</a></span>(<span class="no">b.2</span>[<span class="st">"1"</span>, <span class="st">"relative"</span>])
-} <span class="kw">else</span> {
-  <span class="no">factor_FOMC_SFO</span> <span class="kw">&lt;-</span> <span class="fl">NA</span>
-  <span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="st">"R package benchmark is not available"</span>)
-}</pre></body></html></div>
+<a href="#model-without-analytical-solution" class="anchor"></a>Model without analytical solution</h2>
+<p>This evaluation is also taken from the example section of mkinfit. No analytical solution is available for this system, and now Eigenvalue based solution is possible, so only deSolve using with or without compiled code is available.</p>
+<div class="sourceCode" id="cb9"><pre class="downlit">
+<span class="kw">if</span> <span class="op">(</span><span class="kw"><a href="https://rdrr.io/r/base/library.html">require</a></span><span class="op">(</span><span class="va"><a href="http://rbenchmark.googlecode.com">rbenchmark</a></span><span class="op">)</span><span class="op">)</span> <span class="op">{</span>
+  <span class="va">FOMC_SFO</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>
+    parent <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span><span class="st">"FOMC"</span>, <span class="st">"m1"</span><span class="op">)</span>,
+    m1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span><span class="op">(</span> <span class="st">"SFO"</span><span class="op">)</span><span class="op">)</span>
+
+  <span class="va">b.2</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/rbenchmark/man/benchmark.html">benchmark</a></span><span class="op">(</span>
+    <span class="st">"deSolve, not compiled"</span> <span class="op">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">FOMC_SFO</span>, <span class="va">FOCUS_D</span>,
+                                      use_compiled <span class="op">=</span> <span class="cn">FALSE</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,
+    <span class="st">"deSolve, compiled"</span> <span class="op">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">FOMC_SFO</span>, <span class="va">FOCUS_D</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,
+    replications <span class="op">=</span> <span class="fl">1</span>, order <span class="op">=</span> <span class="st">"relative"</span>,
+    columns <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="st">"test"</span>, <span class="st">"replications"</span>, <span class="st">"relative"</span>, <span class="st">"elapsed"</span><span class="op">)</span><span class="op">)</span>
+  <span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">b.2</span><span class="op">)</span>
+  <span class="va">factor_FOMC_SFO</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/Round.html">round</a></span><span class="op">(</span><span class="va">b.2</span><span class="op">[</span><span class="st">"1"</span>, <span class="st">"relative"</span><span class="op">]</span><span class="op">)</span>
+<span class="op">}</span> <span class="kw">else</span> <span class="op">{</span>
+  <span class="va">factor_FOMC_SFO</span> <span class="op">&lt;-</span> <span class="cn">NA</span>
+  <span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="st">"R package benchmark is not available"</span><span class="op">)</span>
+<span class="op">}</span></pre></div>
 <pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
-<pre><code>##                    test replications elapsed relative user.self sys.self
-## 2     deSolve, compiled            3   1.392    1.000     1.391        0
-## 1 deSolve, not compiled            3  43.021   30.906    43.002        0
-##   user.child sys.child
-## 2          0         0
-## 1          0         0</code></pre>
-<p>Here we get a performance benefit of a factor of 31 using the version of the differential equation model compiled from C code!</p>
-<p>This vignette was built with mkin 0.9.50.2 on</p>
-<pre><code>## R version 4.0.0 (2020-04-24)
+<pre><code>##                    test replications relative elapsed
+## 2     deSolve, compiled            1    1.000   0.483
+## 1 deSolve, not compiled            1   30.451  14.708</code></pre>
+<p>Here we get a performance benefit of a factor of 30 using the version of the differential equation model compiled from C code!</p>
+<p>This vignette was built with mkin 0.9.50.3 on</p>
+<pre><code>## R version 4.0.3 (2020-10-10)
 ## Platform: x86_64-pc-linux-gnu (64-bit)
 ## Running under: Debian GNU/Linux 10 (buster)</code></pre>
 <pre><code>## CPU model: AMD Ryzen 7 1700 Eight-Core Processor</code></pre>
@@ -206,7 +214,7 @@
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/authors.html b/docs/authors.html
index c445f8dc..90293671 100644
--- a/docs/authors.html
+++ b/docs/authors.html
@@ -71,7 +71,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -108,6 +108,9 @@
     <li>
       <a href="articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -116,7 +119,7 @@
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -168,7 +171,7 @@
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/index.html b/docs/index.html
index ce5d6a9a..42084fc0 100644
--- a/docs/index.html
+++ b/docs/index.html
@@ -37,7 +37,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -74,6 +74,9 @@
     <li>
       <a href="articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -82,7 +85,7 @@
       </ul>
 <ul class="nav navbar-nav navbar-right">
 <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -103,12 +106,13 @@
 <div class="page-header"><h1 class="hasAnchor">
 <a href="#mkin" class="anchor"></a>mkin</h1></div>
 
-<p>The R package <strong>mkin</strong> provides calculation routines for the analysis of chemical degradation data, including <b>m</b>ulticompartment <b>kin</b>etics as needed for modelling the formation and decline of transformation products, or if several compartments are involved.</p>
+<p>The R package <strong>mkin</strong> provides calculation routines for the analysis of chemical degradation data, including <b>m</b>ulticompartment <b>kin</b>etics as needed for modelling the formation and decline of transformation products, or if several degradation compartments are involved.</p>
 <div id="installation" class="section level2">
 <h2 class="hasAnchor">
 <a href="#installation" class="anchor"></a>Installation</h2>
 <p>You can install the latest released version from <a href="https://cran.r-project.org/package=mkin">CRAN</a> from within R:</p>
-<div class="sourceCode" id="cb1"><pre class="r"><span class="fu"><a href="https://rdrr.io/r/utils/install.packages.html">install.packages</a></span>(<span class="st">"mkin"</span>)</pre></div>
+<div class="sourceCode" id="cb1"><pre class="downlit">
+<span class="fu"><a href="https://rdrr.io/r/utils/install.packages.html">install.packages</a></span><span class="op">(</span><span class="st">"mkin"</span><span class="op">)</span></pre></div>
 </div>
 <div id="background" class="section level2">
 <h2 class="hasAnchor">
@@ -123,7 +127,7 @@
 <div id="documentation" class="section level2">
 <h2 class="hasAnchor">
 <a href="#documentation" class="anchor"></a>Documentation</h2>
-<p>The HTML documentation is available at <a href="https://pkgdown.jrwb.de/mkin">jrwb.de</a>, at <a href="http://jranke.github.io/mkin">github</a> and at <a href="http://kinfit.r-forge.r-project.org/mkin_static/index.html">R-Forge</a>.</p>
+<p>The HTML documentation of the latest version released to CRAN is available at <a href="https://pkgdown.jrwb.de/mkin/">jrwb.de</a> and <a href="https://jranke.github.io/mkin/">github</a>. Documentation of the development version is found in the <a href="https://pkgdown.jrwb.de/mkin/dev/">‘dev’ subdirectory</a>.</p>
 </div>
 <div id="features" class="section level2">
 <h2 class="hasAnchor">
@@ -148,7 +152,7 @@
 <div id="gui" class="section level2">
 <h2 class="hasAnchor">
 <a href="#gui" class="anchor"></a>GUI</h2>
-<p>There is a graphical user interface that may be useful. Please refer to its <a href="http://kinfit.r-forge.r-project.org/gmkin_static">documentation page</a> for installation instructions and a manual.</p>
+<p>There is a graphical user interface that may be useful. Please refer to its <a href="https://pkgdown.jrwb.de/gmkin/">documentation page</a> for installation instructions and a manual.</p>
 </div>
 <div id="news" class="section level2">
 <h2 class="hasAnchor">
@@ -162,10 +166,10 @@
 <p><code>mkin</code> could not have been written without me being introduced to regulatory fate modelling of pesticides by Adrian Gurney during my time at Harlan Laboratories Ltd (formerly RCC Ltd). <code>mkin</code> greatly profits from and largely follows the work done by the <a href="http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics">FOCUS Degradation Kinetics Workgroup</a>, as detailed in their guidance document from 2006, slightly updated in 2011 and in 2014.</p>
 <p>Also, it was inspired by the first version of KinGUI developed by BayerCropScience, which is based on the MatLab runtime environment.</p>
 <p>The companion package <a href="http://kinfit.r-forge.r-project.org/kinfit_static/index.html">kinfit</a> (now deprecated) was <a href="https://r-forge.r-project.org/scm/viewvc.php?view=rev&amp;root=kinfit&amp;revision=2">started in 2008</a> and <a href="https://cran.r-project.org/src/contrib/Archive/kinfit/">first published</a> on CRAN on 01 May 2010.</p>
-<p>The first <code>mkin</code> code was <a href="https://r-forge.r-project.org/scm/viewvc.php?view=rev&amp;root=kinfit&amp;revision=8">published on 11 May 2010</a> and the <a href="https://cran.r-project.org/src/contrib/Archive/mkin">first CRAN version</a> on 18 May 2010.</p>
+<p>The first <code>mkin</code> code was <a href="https://r-forge.r-project.org/scm/viewvc.php?view=rev&amp;root=kinfit&amp;revision=8">published on 11 May 2010</a> and the <a href="https://cran.r-project.org/src/contrib/Archive/mkin/">first CRAN version</a> on 18 May 2010.</p>
 <p>In 2011, Bayer Crop Science started to distribute an R based successor to KinGUI named KinGUII whose R code is based on <code>mkin</code>, but which added, among other refinements, a closed source graphical user interface (GUI), iteratively reweighted least squares (IRLS) optimisation of the variance for each of the observed variables, and Markov Chain Monte Carlo (MCMC) simulation functionality, similar to what is available e.g. in the <code>FME</code> package.</p>
 <p>Somewhat in parallel, Syngenta has sponsored the development of an <code>mkin</code> and KinGUII based GUI application called CAKE, which also adds IRLS and MCMC, is more limited in the model formulation, but puts more weight on usability. CAKE is available for download from the <a href="https://www.tessella.com/showcase/computer-assisted-kinetic-evaluation">CAKE website</a>, where you can also find a zip archive of the R scripts derived from <code>mkin</code>, published under the GPL license.</p>
-<p>Finally, there is <a href="http://github.com/zhenglei-gao/KineticEval">KineticEval</a>, which contains a further development of the scripts used for KinGUII, so the different tools will hopefully be able to learn from each other in the future as well.</p>
+<p>Finally, there is <a href="https://github.com/zhenglei-gao/KineticEval">KineticEval</a>, which contains a further development of the scripts used for KinGUII, so the different tools will hopefully be able to learn from each other in the future as well.</p>
 </div>
 <div id="references" class="section level2">
 <h2 class="hasAnchor">
@@ -197,9 +201,9 @@ Ranke J, Wöltjen J, Meinecke S (2018) Comparison of software tools for kinetic
 <ul class="list-unstyled">
 <li>Download from CRAN at <br><a href="https://cloud.r-project.org/package=mkin">https://cloud.r-project.org/package=mkin</a>
 </li>
-<li>Browse source code at <br><a href="http://github.com/jranke/mkin/">http://github.com/jranke/mkin/</a>
+<li>Browse source code at <br><a href="https://github.com/jranke/mkin/">https://github.com/jranke/mkin/</a>
 </li>
-<li>Report a bug at <br><a href="http://github.com/jranke/mkin/issues">http://github.com/jranke/mkin/issues</a>
+<li>Report a bug at <br><a href="https://github.com/jranke/mkin/issues/">https://github.com/jranke/mkin/issues/</a>
 </li>
 </ul>
 </div>
@@ -234,7 +238,7 @@ Ranke J, Wöltjen J, Meinecke S (2018) Comparison of software tools for kinetic
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/news/index.html b/docs/news/index.html
index d61e532a..6b6fd2c4 100644
--- a/docs/news/index.html
+++ b/docs/news/index.html
@@ -71,7 +71,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -108,6 +108,9 @@
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -116,7 +119,7 @@
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -135,9 +138,25 @@
   <div class="col-md-9 contents">
     <div class="page-header">
       <h1 data-toc-skip>Changelog <small></small></h1>
-      <small>Source: <a href='http://github.com/jranke/mkin/blob/master/NEWS.md'><code>NEWS.md</code></a></small>
+      <small>Source: <a href='https://github.com/jranke/mkin/blob/master/NEWS.md'><code>NEWS.md</code></a></small>
     </div>
 
+    <div id="mkin-0-9-50-3" class="section level1">
+<h1 class="page-header" data-toc-text="0.9.50.3">
+<a href="#mkin-0-9-50-3" class="anchor"></a>mkin 0.9.50.3<small> 2020-10-08 </small>
+</h1>
+<ul>
+<li><p>‘parms’: Add a method for mmkin objects</p></li>
+<li><p>‘mmkin’ and ‘confint(method = ’profile’): Use all cores detected by parallel::detectCores() per default</p></li>
+<li><p>‘confint(method = ’profile’): Choose accuracy based on ‘rel_tol’ argument, relative to the bounds obtained by the quadratic approximation</p></li>
+<li><p>‘mkinfit’: Make ‘use_of_ff’ = “max” also the default for models specified using short names like “SFO” or “FOMC”</p></li>
+<li><p>‘mkinfit’: Run ‘stats::shapiro.test()’ on standardized residuals and warn if p &lt; 0.05</p></li>
+<li><p>‘mkinfit’: ‘error_model_algorithm’ = ‘d_3’ does not fail if direct fitting fails, but reports that the results for the threestep algorithm are returned</p></li>
+<li><p>‘mmkin’: Do not fail any more if one of the fits fails, but assign the try-error to the respective position in the mmkin object</p></li>
+<li><p>‘mkinfit’: Ignore components of state.ini that do not correspond to state variables in the model</p></li>
+<li><p>‘endpoints’: Back-calculate DT50 value from DT90 also for the biphasic models DFOP, HS and SFORB</p></li>
+</ul>
+</div>
     <div id="mkin-0-9-50-2-2020-05-12" class="section level1">
 <h1 class="page-header" data-toc-text="0.9.50.2">
 <a href="#mkin-0-9-50-2-2020-05-12" class="anchor"></a>mkin 0.9.50.2 (2020-05-12)<small> 2020-05-12 </small>
@@ -751,7 +770,7 @@
 <a href="#mkin-0-9-27-2014-05-10" class="anchor"></a>mkin 0.9-27 (2014-05-10)<small> 2014-05-10 </small>
 </h1>
 <ul>
-<li><p>Fork the GUI into a separate package <a href="http://github.com/jranke/gmkin">gmkin</a></p></li>
+<li><p>Fork the GUI into a separate package <a href="https://github.com/jranke/gmkin">gmkin</a></p></li>
 <li><p>DESCRIPTION, NAMESPACE, TODO: Adapt and add copyright information</p></li>
 <li><p>Remove files belonging to the GUI</p></li>
 <li><p>Possibility to fit without parameter transformations, using bounds as implemented in FME</p></li>
@@ -816,7 +835,7 @@
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/pkgdown.css b/docs/pkgdown.css
index c01e5923..1273238d 100644
--- a/docs/pkgdown.css
+++ b/docs/pkgdown.css
@@ -244,14 +244,14 @@ nav[data-toggle='toc'] .nav .nav > .active:focus > a {
 
 .ref-index th {font-weight: normal;}
 
-.ref-index td {vertical-align: top;}
+.ref-index td {vertical-align: top; min-width: 100px}
 .ref-index .icon {width: 40px;}
 .ref-index .alias {width: 40%;}
 .ref-index-icons .alias {width: calc(40% - 40px);}
 .ref-index .title {width: 60%;}
 
 .ref-arguments th {text-align: right; padding-right: 10px;}
-.ref-arguments th, .ref-arguments td {vertical-align: top;}
+.ref-arguments th, .ref-arguments td {vertical-align: top; min-width: 100px}
 .ref-arguments .name {width: 20%;}
 .ref-arguments .desc {width: 80%;}
 
diff --git a/docs/pkgdown.yml b/docs/pkgdown.yml
index 20a0b7d3..f9babf0b 100644
--- a/docs/pkgdown.yml
+++ b/docs/pkgdown.yml
@@ -1,16 +1,16 @@
 pandoc: 2.2.1
-pkgdown: 1.5.1
+pkgdown: 1.6.1
 pkgdown_sha: ~
 articles:
   FOCUS_D: FOCUS_D.html
   FOCUS_L: FOCUS_L.html
   mkin: mkin.html
   twa: twa.html
-  FOCUS_Z: web_only/FOCUS_Z.html
-  NAFTA_examples: web_only/NAFTA_examples.html
-  benchmarks: web_only/benchmarks.html
-  compiled_models: web_only/compiled_models.html
-last_built: 2020-05-27T05:02Z
+  web_only/FOCUS_Z: FOCUS_Z.html
+  web_only/NAFTA_examples: NAFTA_examples.html
+  web_only/benchmarks: benchmarks.html
+  web_only/compiled_models: compiled_models.html
+last_built: 2020-10-15T10:39Z
 urls:
   reference: https://pkgdown.jrwb.de/mkin/reference
   article: https://pkgdown.jrwb.de/mkin/articles
diff --git a/docs/reference/AIC.mmkin.html b/docs/reference/AIC.mmkin.html
index 58590f52..26a880e3 100644
--- a/docs/reference/AIC.mmkin.html
+++ b/docs/reference/AIC.mmkin.html
@@ -73,7 +73,7 @@ same dataset." />
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -110,6 +110,9 @@ same dataset." />
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -118,7 +121,7 @@ same dataset." />
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -137,7 +140,7 @@ same dataset." />
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>Calculate the AIC for a column of an mmkin object</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/AIC.mmkin.R'><code>R/AIC.mmkin.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/AIC.mmkin.R'><code>R/AIC.mmkin.R</code></a></small>
     <div class="hidden name"><code>AIC.mmkin.Rd</code></div>
     </div>
 
@@ -147,10 +150,10 @@ same dataset.</p>
     </div>
 
     <pre class="usage"><span class='co'># S3 method for mmkin</span>
-<span class='fu'><a href='https://rdrr.io/r/stats/AIC.html'>AIC</a></span>(<span class='no'>object</span>, <span class='no'>...</span>, <span class='kw'>k</span> <span class='kw'>=</span> <span class='fl'>2</span>)
+<span class='fu'><a href='https://rdrr.io/r/stats/AIC.html'>AIC</a></span><span class='op'>(</span><span class='va'>object</span>, <span class='va'>...</span>, k <span class='op'>=</span> <span class='fl'>2</span><span class='op'>)</span>
 
 <span class='co'># S3 method for mmkin</span>
-<span class='fu'><a href='https://rdrr.io/r/stats/AIC.html'>BIC</a></span>(<span class='no'>object</span>, <span class='no'>...</span>)</pre>
+<span class='fu'><a href='https://rdrr.io/r/stats/AIC.html'>BIC</a></span><span class='op'>(</span><span class='va'>object</span>, <span class='va'>...</span><span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
@@ -174,34 +177,45 @@ column.</p></td>
 
     <p>As in the generic method (a numeric value for single fits, or a
 dataframe if there are several fits in the column).</p>
+    <h2 class="hasAnchor" id="author"><a class="anchor" href="#author"></a>Author</h2>
+
+    <p>Johannes Ranke</p>
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
     <pre class="examples"><div class='input'>
    <span class='co'># skip, as it takes &gt; 10 s on winbuilder</span>
-  <span class='no'>f</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mmkin.html'>mmkin</a></span>(<span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"SFO"</span>, <span class='st'>"FOMC"</span>, <span class='st'>"DFOP"</span>),
-    <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='st'>"FOCUS A"</span> <span class='kw'>=</span> <span class='no'>FOCUS_2006_A</span>,
-         <span class='st'>"FOCUS C"</span> <span class='kw'>=</span> <span class='no'>FOCUS_2006_C</span>), <span class='kw'>cores</span> <span class='kw'>=</span> <span class='fl'>1</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#&gt; <span class='warning'>Warning: Optimisation did not converge:</span>
+  <span class='va'>f</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mmkin.html'>mmkin</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='st'>"FOMC"</span>, <span class='st'>"DFOP"</span><span class='op'>)</span>,
+    <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span><span class='st'>"FOCUS A"</span> <span class='op'>=</span> <span class='va'>FOCUS_2006_A</span>,
+         <span class='st'>"FOCUS C"</span> <span class='op'>=</span> <span class='va'>FOCUS_2006_C</span><span class='op'>)</span>, cores <span class='op'>=</span> <span class='fl'>1</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='warning'>Warning: Optimisation did not converge:</span>
 #&gt; <span class='warning'>false convergence (8)</span></div><div class='input'>  <span class='co'># We get a warning because the FOMC model does not converge for the</span>
   <span class='co'># FOCUS A dataset, as it is well described by SFO</span>
 
-  <span class='fu'><a href='https://rdrr.io/r/stats/AIC.html'>AIC</a></span>(<span class='no'>f</span>[<span class='st'>"SFO"</span>, <span class='st'>"FOCUS A"</span>]) <span class='co'># We get a single number for a single fit</span></div><div class='output co'>#&gt; [1] 55.28197</div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/stats/AIC.html'>AIC</a></span>(<span class='no'>f</span><span class='kw'>[[</span><span class='st'>"SFO"</span>, <span class='st'>"FOCUS A"</span>]]) <span class='co'># or when extracting an mkinfit object</span></div><div class='output co'>#&gt; [1] 55.28197</div><div class='input'>
+  <span class='fu'><a href='https://rdrr.io/r/stats/AIC.html'>AIC</a></span><span class='op'>(</span><span class='va'>f</span><span class='op'>[</span><span class='st'>"SFO"</span>, <span class='st'>"FOCUS A"</span><span class='op'>]</span><span class='op'>)</span> <span class='co'># We get a single number for a single fit</span>
+</div><div class='output co'>#&gt; [1] 55.28197</div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/stats/AIC.html'>AIC</a></span><span class='op'>(</span><span class='va'>f</span><span class='op'>[[</span><span class='st'>"SFO"</span>, <span class='st'>"FOCUS A"</span><span class='op'>]</span><span class='op'>]</span><span class='op'>)</span> <span class='co'># or when extracting an mkinfit object</span>
+</div><div class='output co'>#&gt; [1] 55.28197</div><div class='input'>
   <span class='co'># For FOCUS A, the models fit almost equally well, so the higher the number</span>
   <span class='co'># of parameters, the higher (worse) the AIC</span>
-  <span class='fu'><a href='https://rdrr.io/r/stats/AIC.html'>AIC</a></span>(<span class='no'>f</span>[, <span class='st'>"FOCUS A"</span>])</div><div class='output co'>#&gt;      df      AIC
+  <span class='fu'><a href='https://rdrr.io/r/stats/AIC.html'>AIC</a></span><span class='op'>(</span><span class='va'>f</span><span class='op'>[</span>, <span class='st'>"FOCUS A"</span><span class='op'>]</span><span class='op'>)</span>
+</div><div class='output co'>#&gt;      df      AIC
 #&gt; SFO   3 55.28197
-#&gt; FOMC  4 57.28202
-#&gt; DFOP  5 59.28197</div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/stats/AIC.html'>AIC</a></span>(<span class='no'>f</span>[, <span class='st'>"FOCUS A"</span>], <span class='kw'>k</span> <span class='kw'>=</span> <span class='fl'>0</span>) <span class='co'># If we do not penalize additional parameters, we get nearly the same</span></div><div class='output co'>#&gt;      df      AIC
+#&gt; FOMC  4 57.28211
+#&gt; DFOP  5 59.28197</div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/stats/AIC.html'>AIC</a></span><span class='op'>(</span><span class='va'>f</span><span class='op'>[</span>, <span class='st'>"FOCUS A"</span><span class='op'>]</span>, k <span class='op'>=</span> <span class='fl'>0</span><span class='op'>)</span> <span class='co'># If we do not penalize additional parameters, we get nearly the same</span>
+</div><div class='output co'>#&gt;      df      AIC
 #&gt; SFO   3 49.28197
-#&gt; FOMC  4 49.28202
-#&gt; DFOP  5 49.28197</div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/stats/AIC.html'>BIC</a></span>(<span class='no'>f</span>[, <span class='st'>"FOCUS A"</span>])        <span class='co'># Comparing the BIC gives a very similar picture</span></div><div class='output co'>#&gt;      df      BIC
+#&gt; FOMC  4 49.28211
+#&gt; DFOP  5 49.28197</div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/stats/AIC.html'>BIC</a></span><span class='op'>(</span><span class='va'>f</span><span class='op'>[</span>, <span class='st'>"FOCUS A"</span><span class='op'>]</span><span class='op'>)</span>        <span class='co'># Comparing the BIC gives a very similar picture</span>
+</div><div class='output co'>#&gt;      df      BIC
 #&gt; SFO   3 55.52030
-#&gt; FOMC  4 57.59979
+#&gt; FOMC  4 57.59987
 #&gt; DFOP  5 59.67918</div><div class='input'>
   <span class='co'># For FOCUS C, the more complex models fit better</span>
-  <span class='fu'><a href='https://rdrr.io/r/stats/AIC.html'>AIC</a></span>(<span class='no'>f</span>[, <span class='st'>"FOCUS C"</span>])</div><div class='output co'>#&gt;      df      AIC
+  <span class='fu'><a href='https://rdrr.io/r/stats/AIC.html'>AIC</a></span><span class='op'>(</span><span class='va'>f</span><span class='op'>[</span>, <span class='st'>"FOCUS C"</span><span class='op'>]</span><span class='op'>)</span>
+</div><div class='output co'>#&gt;      df      AIC
 #&gt; SFO   3 59.29336
 #&gt; FOMC  4 44.68652
-#&gt; DFOP  5 29.02372</div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/stats/AIC.html'>BIC</a></span>(<span class='no'>f</span>[, <span class='st'>"FOCUS C"</span>])</div><div class='output co'>#&gt;      df      BIC
+#&gt; DFOP  5 29.02372</div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/stats/AIC.html'>BIC</a></span><span class='op'>(</span><span class='va'>f</span><span class='op'>[</span>, <span class='st'>"FOCUS C"</span><span class='op'>]</span><span class='op'>)</span>
+</div><div class='output co'>#&gt;      df      BIC
 #&gt; SFO   3 59.88504
 #&gt; FOMC  4 45.47542
 #&gt; DFOP  5 30.00984</div><div class='input'>  
@@ -222,7 +236,7 @@ dataframe if there are several fits in the column).</p>
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/DFOP.solution-1.png b/docs/reference/DFOP.solution-1.png
index a2d75ccc..616e19d5 100644
--- a/docs/reference/DFOP.solution-1.png
+++ b/docs/reference/DFOP.solution-1.png
diff --git a/docs/reference/DFOP.solution.html b/docs/reference/DFOP.solution.html
index 3c1fff89..2bc1ee96 100644
--- a/docs/reference/DFOP.solution.html
+++ b/docs/reference/DFOP.solution.html
@@ -73,7 +73,7 @@ two exponential decline functions." />
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -110,6 +110,9 @@ two exponential decline functions." />
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -118,7 +121,7 @@ two exponential decline functions." />
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -137,7 +140,7 @@ two exponential decline functions." />
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>Double First-Order in Parallel kinetics</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/parent_solutions.R'><code>R/parent_solutions.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/parent_solutions.R'><code>R/parent_solutions.R</code></a></small>
     <div class="hidden name"><code>DFOP.solution.Rd</code></div>
     </div>
 
@@ -146,7 +149,7 @@ two exponential decline functions." />
 two exponential decline functions.</p>
     </div>
 
-    <pre class="usage"><span class='fu'>DFOP.solution</span>(<span class='no'>t</span>, <span class='no'>parent_0</span>, <span class='no'>k1</span>, <span class='no'>k2</span>, <span class='no'>g</span>)</pre>
+    <pre class="usage"><span class='fu'>DFOP.solution</span><span class='op'>(</span><span class='va'>t</span>, <span class='va'>parent_0</span>, <span class='va'>k1</span>, <span class='va'>k2</span>, <span class='va'>g</span><span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
@@ -201,7 +204,8 @@ Version 1.1, 18 December 2014
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
     <pre class="examples"><div class='input'>
-  <span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='kw'>function</span>(<span class='no'>x</span>) <span class='fu'>DFOP.solution</span>(<span class='no'>x</span>, <span class='fl'>100</span>, <span class='fl'>5</span>, <span class='fl'>0.5</span>, <span class='fl'>0.3</span>), <span class='fl'>0</span>, <span class='fl'>4</span>, <span class='kw'>ylim</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='fl'>0</span>,<span class='fl'>100</span>))</div><div class='img'><img src='DFOP.solution-1.png' alt='' width='700' height='433' /></div><div class='input'>
+  <span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='kw'>function</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span> <span class='fu'>DFOP.solution</span><span class='op'>(</span><span class='va'>x</span>, <span class='fl'>100</span>, <span class='fl'>5</span>, <span class='fl'>0.5</span>, <span class='fl'>0.3</span><span class='op'>)</span>, <span class='fl'>0</span>, <span class='fl'>4</span>, ylim <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>0</span>,<span class='fl'>100</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='img'><img src='DFOP.solution-1.png' alt='' width='700' height='433' /></div><div class='input'>
 </div></pre>
   </div>
   <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
@@ -218,7 +222,7 @@ Version 1.1, 18 December 2014
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/FOMC.solution-1.png b/docs/reference/FOMC.solution-1.png
index aa41a253..1d32355a 100644
--- a/docs/reference/FOMC.solution-1.png
+++ b/docs/reference/FOMC.solution-1.png
diff --git a/docs/reference/FOMC.solution.html b/docs/reference/FOMC.solution.html
index a7236844..d279f32f 100644
--- a/docs/reference/FOMC.solution.html
+++ b/docs/reference/FOMC.solution.html
@@ -73,7 +73,7 @@ a decreasing rate constant." />
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -110,6 +110,9 @@ a decreasing rate constant." />
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -118,7 +121,7 @@ a decreasing rate constant." />
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -137,7 +140,7 @@ a decreasing rate constant." />
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>First-Order Multi-Compartment kinetics</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/parent_solutions.R'><code>R/parent_solutions.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/parent_solutions.R'><code>R/parent_solutions.R</code></a></small>
     <div class="hidden name"><code>FOMC.solution.Rd</code></div>
     </div>
 
@@ -146,7 +149,7 @@ a decreasing rate constant." />
 a decreasing rate constant.</p>
     </div>
 
-    <pre class="usage"><span class='fu'>FOMC.solution</span>(<span class='no'>t</span>, <span class='no'>parent_0</span>, <span class='no'>alpha</span>, <span class='no'>beta</span>)</pre>
+    <pre class="usage"><span class='fu'>FOMC.solution</span><span class='op'>(</span><span class='va'>t</span>, <span class='va'>parent_0</span>, <span class='va'>alpha</span>, <span class='va'>beta</span><span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
@@ -210,7 +213,8 @@ Technology</em> <b>24</b>, 1032-1038</p>
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
     <pre class="examples"><div class='input'>
-  <span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='kw'>function</span>(<span class='no'>x</span>) <span class='fu'>FOMC.solution</span>(<span class='no'>x</span>, <span class='fl'>100</span>, <span class='fl'>10</span>, <span class='fl'>2</span>), <span class='fl'>0</span>, <span class='fl'>2</span>, <span class='kw'>ylim</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='fl'>0</span>, <span class='fl'>100</span>))</div><div class='img'><img src='FOMC.solution-1.png' alt='' width='700' height='433' /></div><div class='input'>
+  <span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='kw'>function</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span> <span class='fu'>FOMC.solution</span><span class='op'>(</span><span class='va'>x</span>, <span class='fl'>100</span>, <span class='fl'>10</span>, <span class='fl'>2</span><span class='op'>)</span>, <span class='fl'>0</span>, <span class='fl'>2</span>, ylim <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>0</span>, <span class='fl'>100</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='img'><img src='FOMC.solution-1.png' alt='' width='700' height='433' /></div><div class='input'>
 </div></pre>
   </div>
   <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
@@ -227,7 +231,7 @@ Technology</em> <b>24</b>, 1032-1038</p>
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/HS.solution-1.png b/docs/reference/HS.solution-1.png
index ae056d9b..32d04b2d 100644
--- a/docs/reference/HS.solution-1.png
+++ b/docs/reference/HS.solution-1.png
diff --git a/docs/reference/HS.solution.html b/docs/reference/HS.solution.html
index 2c4eebe3..0f5915c3 100644
--- a/docs/reference/HS.solution.html
+++ b/docs/reference/HS.solution.html
@@ -73,7 +73,7 @@ between them." />
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -110,6 +110,9 @@ between them." />
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -118,7 +121,7 @@ between them." />
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -137,7 +140,7 @@ between them." />
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>Hockey-Stick kinetics</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/parent_solutions.R'><code>R/parent_solutions.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/parent_solutions.R'><code>R/parent_solutions.R</code></a></small>
     <div class="hidden name"><code>HS.solution.Rd</code></div>
     </div>
 
@@ -146,7 +149,7 @@ between them." />
 between them.</p>
     </div>
 
-    <pre class="usage"><span class='fu'>HS.solution</span>(<span class='no'>t</span>, <span class='no'>parent_0</span>, <span class='no'>k1</span>, <span class='no'>k2</span>, <span class='no'>tb</span>)</pre>
+    <pre class="usage"><span class='fu'>HS.solution</span><span class='op'>(</span><span class='va'>t</span>, <span class='va'>parent_0</span>, <span class='va'>k1</span>, <span class='va'>k2</span>, <span class='va'>tb</span><span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
@@ -202,7 +205,8 @@ Version 1.1, 18 December 2014
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
     <pre class="examples"><div class='input'>
-  <span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='kw'>function</span>(<span class='no'>x</span>) <span class='fu'>HS.solution</span>(<span class='no'>x</span>, <span class='fl'>100</span>, <span class='fl'>2</span>, <span class='fl'>0.3</span>, <span class='fl'>0.5</span>), <span class='fl'>0</span>, <span class='fl'>2</span>, <span class='kw'>ylim</span><span class='kw'>=</span><span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='fl'>0</span>,<span class='fl'>100</span>))</div><div class='img'><img src='HS.solution-1.png' alt='' width='700' height='433' /></div><div class='input'>
+  <span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='kw'>function</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span> <span class='fu'>HS.solution</span><span class='op'>(</span><span class='va'>x</span>, <span class='fl'>100</span>, <span class='fl'>2</span>, <span class='fl'>0.3</span>, <span class='fl'>0.5</span><span class='op'>)</span>, <span class='fl'>0</span>, <span class='fl'>2</span>, ylim<span class='op'>=</span><span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>0</span>,<span class='fl'>100</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='img'><img src='HS.solution-1.png' alt='' width='700' height='433' /></div><div class='input'>
 </div></pre>
   </div>
   <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
@@ -219,7 +223,7 @@ Version 1.1, 18 December 2014
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/IORE.solution-1.png b/docs/reference/IORE.solution-1.png
index 00e28460..42643a58 100644
--- a/docs/reference/IORE.solution-1.png
+++ b/docs/reference/IORE.solution-1.png
diff --git a/docs/reference/IORE.solution.html b/docs/reference/IORE.solution.html
index 9c8df9b3..be326cff 100644
--- a/docs/reference/IORE.solution.html
+++ b/docs/reference/IORE.solution.html
@@ -73,7 +73,7 @@ a concentration dependent rate constant." />
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -110,6 +110,9 @@ a concentration dependent rate constant." />
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -118,7 +121,7 @@ a concentration dependent rate constant." />
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -137,7 +140,7 @@ a concentration dependent rate constant." />
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>Indeterminate order rate equation kinetics</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/parent_solutions.R'><code>R/parent_solutions.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/parent_solutions.R'><code>R/parent_solutions.R</code></a></small>
     <div class="hidden name"><code>IORE.solution.Rd</code></div>
     </div>
 
@@ -146,7 +149,7 @@ a concentration dependent rate constant." />
 a concentration dependent rate constant.</p>
     </div>
 
-    <pre class="usage"><span class='fu'>IORE.solution</span>(<span class='no'>t</span>, <span class='no'>parent_0</span>, <span class='no'>k__iore</span>, <span class='no'>N</span>)</pre>
+    <pre class="usage"><span class='fu'>IORE.solution</span><span class='op'>(</span><span class='va'>t</span>, <span class='va'>parent_0</span>, <span class='va'>k__iore</span>, <span class='va'>N</span><span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
@@ -195,21 +198,24 @@ for Evaluating and Calculating Degradation Kinetics in Environmental Media</p>
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
     <pre class="examples"><div class='input'>
-  <span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='kw'>function</span>(<span class='no'>x</span>) <span class='fu'>IORE.solution</span>(<span class='no'>x</span>, <span class='fl'>100</span>, <span class='fl'>0.2</span>, <span class='fl'>1.3</span>), <span class='fl'>0</span>, <span class='fl'>2</span>, <span class='kw'>ylim</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='fl'>0</span>, <span class='fl'>100</span>))</div><div class='img'><img src='IORE.solution-1.png' alt='' width='700' height='433' /></div><div class='input'>  <span class='co'># \dontrun{</span>
-    <span class='no'>fit.fomc</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='st'>"FOMC"</span>, <span class='no'>FOCUS_2006_C</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-    <span class='no'>fit.iore</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='st'>"IORE"</span>, <span class='no'>FOCUS_2006_C</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-    <span class='no'>fit.iore.deS</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='st'>"IORE"</span>, <span class='no'>FOCUS_2006_C</span>, <span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='st'>"deSolve"</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-
-    <span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span>(<span class='fu'><a href='https://rdrr.io/r/base/data.frame.html'>data.frame</a></span>(<span class='no'>fit.fomc</span>$<span class='no'>par</span>, <span class='no'>fit.iore</span>$<span class='no'>par</span>, <span class='no'>fit.iore.deS</span>$<span class='no'>par</span>,
-                     <span class='kw'>row.names</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/paste.html'>paste</a></span>(<span class='st'>"model par"</span>, <span class='fl'>1</span>:<span class='fl'>4</span>)))</div><div class='output co'>#&gt;             fit.fomc.par fit.iore.par fit.iore.deS.par
+  <span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='kw'>function</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span> <span class='fu'>IORE.solution</span><span class='op'>(</span><span class='va'>x</span>, <span class='fl'>100</span>, <span class='fl'>0.2</span>, <span class='fl'>1.3</span><span class='op'>)</span>, <span class='fl'>0</span>, <span class='fl'>2</span>, ylim <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>0</span>, <span class='fl'>100</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='img'><img src='IORE.solution-1.png' alt='' width='700' height='433' /></div><div class='input'>  <span class='co'># \dontrun{</span>
+    <span class='va'>fit.fomc</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='st'>"FOMC"</span>, <span class='va'>FOCUS_2006_C</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+    <span class='va'>fit.iore</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='st'>"IORE"</span>, <span class='va'>FOCUS_2006_C</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+    <span class='va'>fit.iore.deS</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='st'>"IORE"</span>, <span class='va'>FOCUS_2006_C</span>, solution_type <span class='op'>=</span> <span class='st'>"deSolve"</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+
+    <span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/data.frame.html'>data.frame</a></span><span class='op'>(</span><span class='va'>fit.fomc</span><span class='op'>$</span><span class='va'>par</span>, <span class='va'>fit.iore</span><span class='op'>$</span><span class='va'>par</span>, <span class='va'>fit.iore.deS</span><span class='op'>$</span><span class='va'>par</span>, 
+                     row.names <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/paste.html'>paste</a></span><span class='op'>(</span><span class='st'>"model par"</span>, <span class='fl'>1</span><span class='op'>:</span><span class='fl'>4</span><span class='op'>)</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='output co'>#&gt;             fit.fomc.par fit.iore.par fit.iore.deS.par
 #&gt; model par 1  85.87489063    85.874890        85.874890
 #&gt; model par 2   0.05192238    -4.826631        -4.826631
 #&gt; model par 3   0.65096665     1.949403         1.949403
-#&gt; model par 4   1.85744396     1.857444         1.857444</div><div class='input'>    <span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span>(<span class='fu'><a href='https://rdrr.io/r/base/cbind.html'>rbind</a></span>(<span class='kw'>fomc</span> <span class='kw'>=</span> <span class='fu'><a href='endpoints.html'>endpoints</a></span>(<span class='no'>fit.fomc</span>)$<span class='no'>distimes</span>, <span class='kw'>iore</span> <span class='kw'>=</span> <span class='fu'><a href='endpoints.html'>endpoints</a></span>(<span class='no'>fit.iore</span>)$<span class='no'>distimes</span>,
-                <span class='kw'>iore.deS</span> <span class='kw'>=</span> <span class='fu'><a href='endpoints.html'>endpoints</a></span>(<span class='no'>fit.iore</span>)$<span class='no'>distimes</span>))</div><div class='output co'>#&gt;              DT50    DT90 DT50back
+#&gt; model par 4   1.85744396     1.857444         1.857444</div><div class='input'>    <span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/cbind.html'>rbind</a></span><span class='op'>(</span>fomc <span class='op'>=</span> <span class='fu'><a href='endpoints.html'>endpoints</a></span><span class='op'>(</span><span class='va'>fit.fomc</span><span class='op'>)</span><span class='op'>$</span><span class='va'>distimes</span>, iore <span class='op'>=</span> <span class='fu'><a href='endpoints.html'>endpoints</a></span><span class='op'>(</span><span class='va'>fit.iore</span><span class='op'>)</span><span class='op'>$</span><span class='va'>distimes</span>, 
+                iore.deS <span class='op'>=</span> <span class='fu'><a href='endpoints.html'>endpoints</a></span><span class='op'>(</span><span class='va'>fit.iore</span><span class='op'>)</span><span class='op'>$</span><span class='va'>distimes</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='output co'>#&gt;              DT50    DT90 DT50back
 #&gt; fomc     1.785233 15.1479 4.559973
 #&gt; iore     1.785233 15.1479 4.559973
-#&gt; iore.deS 1.785233 15.1479 4.559973</div><div class='input'>  # }
+#&gt; iore.deS 1.785233 15.1479 4.559973</div><div class='input'>  <span class='co'># }</span>
 
 </div></pre>
   </div>
@@ -227,7 +233,7 @@ for Evaluating and Calculating Degradation Kinetics in Environmental Media</p>
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/Rplot001.png b/docs/reference/Rplot001.png
new file mode 100644
index 00000000..17a35806
--- /dev/null
+++ b/docs/reference/Rplot001.png
diff --git a/docs/reference/Rplot002.png b/docs/reference/Rplot002.png
new file mode 100644
index 00000000..aec326c7
--- /dev/null
+++ b/docs/reference/Rplot002.png
diff --git a/docs/reference/Rplot003.png b/docs/reference/Rplot003.png
new file mode 100644
index 00000000..fe53157f
--- /dev/null
+++ b/docs/reference/Rplot003.png
diff --git a/docs/reference/Rplot004.png b/docs/reference/Rplot004.png
new file mode 100644
index 00000000..e3ebe97b
--- /dev/null
+++ b/docs/reference/Rplot004.png
diff --git a/docs/reference/Rplot005.png b/docs/reference/Rplot005.png
new file mode 100644
index 00000000..962cfd2d
--- /dev/null
+++ b/docs/reference/Rplot005.png
diff --git a/docs/reference/Rplot006.png b/docs/reference/Rplot006.png
new file mode 100644
index 00000000..dbd9a00b
--- /dev/null
+++ b/docs/reference/Rplot006.png
diff --git a/docs/reference/Rplot007.png b/docs/reference/Rplot007.png
new file mode 100644
index 00000000..fcca232c
--- /dev/null
+++ b/docs/reference/Rplot007.png
diff --git a/docs/reference/SFO.solution-1.png b/docs/reference/SFO.solution-1.png
index b0b854bb..56d27ef6 100644
--- a/docs/reference/SFO.solution-1.png
+++ b/docs/reference/SFO.solution-1.png
diff --git a/docs/reference/SFO.solution.html b/docs/reference/SFO.solution.html
index 05332377..9f6fd80b 100644
--- a/docs/reference/SFO.solution.html
+++ b/docs/reference/SFO.solution.html
@@ -72,7 +72,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -109,6 +109,9 @@
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -117,7 +120,7 @@
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -136,7 +139,7 @@
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>Single First-Order kinetics</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/parent_solutions.R'><code>R/parent_solutions.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/parent_solutions.R'><code>R/parent_solutions.R</code></a></small>
     <div class="hidden name"><code>SFO.solution.Rd</code></div>
     </div>
 
@@ -144,7 +147,7 @@
     <p>Function describing exponential decline from a defined starting value.</p>
     </div>
 
-    <pre class="usage"><span class='fu'>SFO.solution</span>(<span class='no'>t</span>, <span class='no'>parent_0</span>, <span class='no'>k</span>)</pre>
+    <pre class="usage"><span class='fu'>SFO.solution</span><span class='op'>(</span><span class='va'>t</span>, <span class='va'>parent_0</span>, <span class='va'>k</span><span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
@@ -190,7 +193,8 @@ Version 1.1, 18 December 2014
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
     <pre class="examples"><div class='input'>
-  <span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='kw'>function</span>(<span class='no'>x</span>) <span class='fu'>SFO.solution</span>(<span class='no'>x</span>, <span class='fl'>100</span>, <span class='fl'>3</span>), <span class='fl'>0</span>, <span class='fl'>2</span>)</div><div class='img'><img src='SFO.solution-1.png' alt='' width='700' height='433' /></div><div class='input'>
+  <span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='kw'>function</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span> <span class='fu'>SFO.solution</span><span class='op'>(</span><span class='va'>x</span>, <span class='fl'>100</span>, <span class='fl'>3</span><span class='op'>)</span>, <span class='fl'>0</span>, <span class='fl'>2</span><span class='op'>)</span>
+</div><div class='img'><img src='SFO.solution-1.png' alt='' width='700' height='433' /></div><div class='input'>
 </div></pre>
   </div>
   <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
@@ -207,7 +211,7 @@ Version 1.1, 18 December 2014
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/SFORB.solution-1.png b/docs/reference/SFORB.solution-1.png
index cd58caec..4eeb0d41 100644
--- a/docs/reference/SFORB.solution-1.png
+++ b/docs/reference/SFORB.solution-1.png
diff --git a/docs/reference/SFORB.solution.html b/docs/reference/SFORB.solution.html
index e4c84edd..d6a3ea91 100644
--- a/docs/reference/SFORB.solution.html
+++ b/docs/reference/SFORB.solution.html
@@ -76,7 +76,7 @@ and no substance in the bound fraction." />
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -113,6 +113,9 @@ and no substance in the bound fraction." />
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -121,7 +124,7 @@ and no substance in the bound fraction." />
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -140,7 +143,7 @@ and no substance in the bound fraction." />
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>Single First-Order Reversible Binding kinetics</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/parent_solutions.R'><code>R/parent_solutions.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/parent_solutions.R'><code>R/parent_solutions.R</code></a></small>
     <div class="hidden name"><code>SFORB.solution.Rd</code></div>
     </div>
 
@@ -152,7 +155,7 @@ fraction.  The initial condition is a defined amount in the free fraction
 and no substance in the bound fraction.</p>
     </div>
 
-    <pre class="usage"><span class='fu'>SFORB.solution</span>(<span class='no'>t</span>, <span class='no'>parent_0</span>, <span class='no'>k_12</span>, <span class='no'>k_21</span>, <span class='no'>k_1output</span>)</pre>
+    <pre class="usage"><span class='fu'>SFORB.solution</span><span class='op'>(</span><span class='va'>t</span>, <span class='va'>parent_0</span>, <span class='va'>k_12</span>, <span class='va'>k_21</span>, <span class='va'>k_1output</span><span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
@@ -208,7 +211,8 @@ Version 1.1, 18 December 2014
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
     <pre class="examples"><div class='input'>
-  <span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='kw'>function</span>(<span class='no'>x</span>) <span class='fu'>SFORB.solution</span>(<span class='no'>x</span>, <span class='fl'>100</span>, <span class='fl'>0.5</span>, <span class='fl'>2</span>, <span class='fl'>3</span>), <span class='fl'>0</span>, <span class='fl'>2</span>)</div><div class='img'><img src='SFORB.solution-1.png' alt='' width='700' height='433' /></div><div class='input'>
+  <span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='kw'>function</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span> <span class='fu'>SFORB.solution</span><span class='op'>(</span><span class='va'>x</span>, <span class='fl'>100</span>, <span class='fl'>0.5</span>, <span class='fl'>2</span>, <span class='fl'>3</span><span class='op'>)</span>, <span class='fl'>0</span>, <span class='fl'>2</span><span class='op'>)</span>
+</div><div class='img'><img src='SFORB.solution-1.png' alt='' width='700' height='433' /></div><div class='input'>
 </div></pre>
   </div>
   <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
@@ -225,7 +229,7 @@ Version 1.1, 18 December 2014
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/add_err-1.png b/docs/reference/add_err-1.png
index 88806d7b..f5686754 100644
--- a/docs/reference/add_err-1.png
+++ b/docs/reference/add_err-1.png
diff --git a/docs/reference/add_err-2.png b/docs/reference/add_err-2.png
index 6a806c2d..ac220c9e 100644
--- a/docs/reference/add_err-2.png
+++ b/docs/reference/add_err-2.png
diff --git a/docs/reference/add_err-3.png b/docs/reference/add_err-3.png
index 1919a566..40465b71 100644
--- a/docs/reference/add_err-3.png
+++ b/docs/reference/add_err-3.png
diff --git a/docs/reference/add_err.html b/docs/reference/add_err.html
index 7c420146..8adc1fa6 100644
--- a/docs/reference/add_err.html
+++ b/docs/reference/add_err.html
@@ -74,7 +74,7 @@ may depend on the predicted value and is specified as a standard deviation." />
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -111,6 +111,9 @@ may depend on the predicted value and is specified as a standard deviation." />
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -119,7 +122,7 @@ may depend on the predicted value and is specified as a standard deviation." />
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -138,7 +141,7 @@ may depend on the predicted value and is specified as a standard deviation." />
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>Add normally distributed errors to simulated kinetic degradation data</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/add_err.R'><code>R/add_err.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/add_err.R'><code>R/add_err.R</code></a></small>
     <div class="hidden name"><code>add_err.Rd</code></div>
     </div>
 
@@ -148,16 +151,16 @@ degradation model using <code><a href='mkinpredict.html'>mkinpredict</a></code>.
 may depend on the predicted value and is specified as a standard deviation.</p>
     </div>
 
-    <pre class="usage"><span class='fu'>add_err</span>(
-  <span class='no'>prediction</span>,
-  <span class='no'>sdfunc</span>,
-  <span class='kw'>secondary</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"M1"</span>, <span class='st'>"M2"</span>),
-  <span class='kw'>n</span> <span class='kw'>=</span> <span class='fl'>1000</span>,
-  <span class='kw'>LOD</span> <span class='kw'>=</span> <span class='fl'>0.1</span>,
-  <span class='kw'>reps</span> <span class='kw'>=</span> <span class='fl'>2</span>,
-  <span class='kw'>digits</span> <span class='kw'>=</span> <span class='fl'>1</span>,
-  <span class='kw'>seed</span> <span class='kw'>=</span> <span class='fl'>NA</span>
-)</pre>
+    <pre class="usage"><span class='fu'>add_err</span><span class='op'>(</span>
+  <span class='va'>prediction</span>,
+  <span class='va'>sdfunc</span>,
+  secondary <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"M1"</span>, <span class='st'>"M2"</span><span class='op'>)</span>,
+  n <span class='op'>=</span> <span class='fl'>1000</span>,
+  LOD <span class='op'>=</span> <span class='fl'>0.1</span>,
+  reps <span class='op'>=</span> <span class='fl'>2</span>,
+  digits <span class='op'>=</span> <span class='fl'>1</span>,
+  seed <span class='op'>=</span> <span class='cn'>NA</span>
+<span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
@@ -212,46 +215,53 @@ components of the list are datasets compatible with <code><a href='mkinfit.html'
 the question. XV Symposium on Pesticide Chemistry 2-4 September 2015,
 Piacenza, Italy
 https://jrwb.de/posters/piacenza_2015.pdf</p>
+    <h2 class="hasAnchor" id="author"><a class="anchor" href="#author"></a>Author</h2>
+
+    <p>Johannes Ranke</p>
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
     <pre class="examples"><div class='input'>
 <span class='co'># The kinetic model</span>
-<span class='no'>m_SFO_SFO</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>, <span class='st'>"M1"</span>),
-                     <span class='kw'>M1</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>), <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"max"</span>)</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>
+<span class='va'>m_SFO_SFO</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='st'>"M1"</span><span class='op'>)</span>,
+                     M1 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span>, use_of_ff <span class='op'>=</span> <span class='st'>"max"</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>
 <span class='co'># Generate a prediction for a specific set of parameters</span>
-<span class='no'>sampling_times</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='fl'>0</span>, <span class='fl'>1</span>, <span class='fl'>3</span>, <span class='fl'>7</span>, <span class='fl'>14</span>, <span class='fl'>28</span>, <span class='fl'>60</span>, <span class='fl'>90</span>, <span class='fl'>120</span>)
+<span class='va'>sampling_times</span> <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>0</span>, <span class='fl'>1</span>, <span class='fl'>3</span>, <span class='fl'>7</span>, <span class='fl'>14</span>, <span class='fl'>28</span>, <span class='fl'>60</span>, <span class='fl'>90</span>, <span class='fl'>120</span><span class='op'>)</span>
 
 <span class='co'># This is the prediction used for the "Type 2 datasets" on the Piacenza poster</span>
 <span class='co'># from 2015</span>
-<span class='no'>d_SFO_SFO</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinpredict.html'>mkinpredict</a></span>(<span class='no'>m_SFO_SFO</span>,
-                         <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>k_parent</span> <span class='kw'>=</span> <span class='fl'>0.1</span>, <span class='kw'>f_parent_to_M1</span> <span class='kw'>=</span> <span class='fl'>0.5</span>,
-                           <span class='kw'>k_M1</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/Log.html'>log</a></span>(<span class='fl'>2</span>)/<span class='fl'>1000</span>),
-                         <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fl'>100</span>, <span class='kw'>M1</span> <span class='kw'>=</span> <span class='fl'>0</span>),
-                         <span class='no'>sampling_times</span>)
+<span class='va'>d_SFO_SFO</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinpredict.html'>mkinpredict</a></span><span class='op'>(</span><span class='va'>m_SFO_SFO</span>,
+                         <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>k_parent <span class='op'>=</span> <span class='fl'>0.1</span>, f_parent_to_M1 <span class='op'>=</span> <span class='fl'>0.5</span>,
+                           k_M1 <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/Log.html'>log</a></span><span class='op'>(</span><span class='fl'>2</span><span class='op'>)</span><span class='op'>/</span><span class='fl'>1000</span><span class='op'>)</span>,
+                         <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fl'>100</span>, M1 <span class='op'>=</span> <span class='fl'>0</span><span class='op'>)</span>,
+                         <span class='va'>sampling_times</span><span class='op'>)</span>
 
 <span class='co'># Add an error term with a constant (independent of the value) standard deviation</span>
 <span class='co'># of 10, and generate three datasets</span>
-<span class='no'>d_SFO_SFO_err</span> <span class='kw'>&lt;-</span> <span class='fu'>add_err</span>(<span class='no'>d_SFO_SFO</span>, <span class='kw'>function</span>(<span class='no'>x</span>) <span class='fl'>10</span>, <span class='kw'>n</span> <span class='kw'>=</span> <span class='fl'>3</span>, <span class='kw'>seed</span> <span class='kw'>=</span> <span class='fl'>123456789</span> )
+<span class='va'>d_SFO_SFO_err</span> <span class='op'>&lt;-</span> <span class='fu'>add_err</span><span class='op'>(</span><span class='va'>d_SFO_SFO</span>, <span class='kw'>function</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span> <span class='fl'>10</span>, n <span class='op'>=</span> <span class='fl'>3</span>, seed <span class='op'>=</span> <span class='fl'>123456789</span> <span class='op'>)</span>
 
 <span class='co'># Name the datasets for nicer plotting</span>
-<span class='fu'><a href='https://rdrr.io/r/base/names.html'>names</a></span>(<span class='no'>d_SFO_SFO_err</span>) <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/paste.html'>paste</a></span>(<span class='st'>"Dataset"</span>, <span class='fl'>1</span>:<span class='fl'>3</span>)
+<span class='fu'><a href='https://rdrr.io/r/base/names.html'>names</a></span><span class='op'>(</span><span class='va'>d_SFO_SFO_err</span><span class='op'>)</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/paste.html'>paste</a></span><span class='op'>(</span><span class='st'>"Dataset"</span>, <span class='fl'>1</span><span class='op'>:</span><span class='fl'>3</span><span class='op'>)</span>
 
 <span class='co'># Name the model in the list of models (with only one member in this case) for</span>
 <span class='co'># nicer plotting later on.  Be quiet and use only one core not to offend CRAN</span>
 <span class='co'># checks</span>
 <span class='co'># \dontrun{</span>
-<span class='no'>f_SFO_SFO</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mmkin.html'>mmkin</a></span>(<span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='st'>"SFO-SFO"</span> <span class='kw'>=</span> <span class='no'>m_SFO_SFO</span>),
-                   <span class='no'>d_SFO_SFO_err</span>, <span class='kw'>cores</span> <span class='kw'>=</span> <span class='fl'>1</span>,
-                   <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
+<span class='va'>f_SFO_SFO</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mmkin.html'>mmkin</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span><span class='st'>"SFO-SFO"</span> <span class='op'>=</span> <span class='va'>m_SFO_SFO</span><span class='op'>)</span>,
+                   <span class='va'>d_SFO_SFO_err</span>, cores <span class='op'>=</span> <span class='fl'>1</span>,
+                   quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
 
-<span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='no'>f_SFO_SFO</span>)</div><div class='img'><img src='add_err-1.png' alt='' width='700' height='433' /></div><div class='input'>
+<span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>f_SFO_SFO</span><span class='op'>)</span>
+</div><div class='img'><img src='add_err-1.png' alt='' width='700' height='433' /></div><div class='input'>
 <span class='co'># We would like to inspect the fit for dataset 3 more closely</span>
 <span class='co'># Using double brackets makes the returned object an mkinfit object</span>
 <span class='co'># instead of a list of mkinfit objects, so plot.mkinfit is used</span>
-<span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='no'>f_SFO_SFO</span><span class='kw'>[[</span><span class='fl'>3</span>]], <span class='kw'>show_residuals</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='img'><img src='add_err-2.png' alt='' width='700' height='433' /></div><div class='input'>
+<span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>f_SFO_SFO</span><span class='op'>[[</span><span class='fl'>3</span><span class='op'>]</span><span class='op'>]</span>, show_residuals <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+</div><div class='img'><img src='add_err-2.png' alt='' width='700' height='433' /></div><div class='input'>
 <span class='co'># If we use single brackets, we should give two indices (model and dataset),</span>
 <span class='co'># and plot.mmkin is used</span>
-<span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='no'>f_SFO_SFO</span>[<span class='fl'>1</span>, <span class='fl'>3</span>])</div><div class='img'><img src='add_err-3.png' alt='' width='700' height='433' /></div><div class='input'># }
+<span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>f_SFO_SFO</span><span class='op'>[</span><span class='fl'>1</span>, <span class='fl'>3</span><span class='op'>]</span><span class='op'>)</span>
+</div><div class='img'><img src='add_err-3.png' alt='' width='700' height='433' /></div><div class='input'><span class='co'># }</span>
 
 </div></pre>
   </div>
@@ -269,7 +279,7 @@ https://jrwb.de/posters/piacenza_2015.pdf</p>
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/confint.mkinfit.html b/docs/reference/confint.mkinfit.html
index a9080c39..b9e58e8f 100644
--- a/docs/reference/confint.mkinfit.html
+++ b/docs/reference/confint.mkinfit.html
@@ -79,7 +79,7 @@ method of Venzon and Moolgavkar (1988)." />
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -116,6 +116,9 @@ method of Venzon and Moolgavkar (1988)." />
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -124,7 +127,7 @@ method of Venzon and Moolgavkar (1988)." />
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -143,7 +146,7 @@ method of Venzon and Moolgavkar (1988)." />
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>Confidence intervals for parameters of mkinfit objects</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/confint.mkinfit.R'><code>R/confint.mkinfit.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/confint.mkinfit.R'><code>R/confint.mkinfit.R</code></a></small>
     <div class="hidden name"><code>confint.mkinfit.Rd</code></div>
     </div>
 
@@ -159,19 +162,20 @@ method of Venzon and Moolgavkar (1988).</p>
     </div>
 
     <pre class="usage"><span class='co'># S3 method for mkinfit</span>
-<span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span>(
-  <span class='no'>object</span>,
-  <span class='no'>parm</span>,
-  <span class='kw'>level</span> <span class='kw'>=</span> <span class='fl'>0.95</span>,
-  <span class='kw'>alpha</span> <span class='kw'>=</span> <span class='fl'>1</span> - <span class='no'>level</span>,
-  <span class='no'>cutoff</span>,
-  <span class='kw'>method</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"quadratic"</span>, <span class='st'>"profile"</span>),
-  <span class='kw'>transformed</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>,
-  <span class='kw'>backtransform</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>,
-  <span class='kw'>cores</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/Round.html'>round</a></span>(<span class='fu'>detectCores</span>()/<span class='fl'>2</span>),
-  <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>,
-  <span class='no'>...</span>
-)</pre>
+<span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span><span class='op'>(</span>
+  <span class='va'>object</span>,
+  <span class='va'>parm</span>,
+  level <span class='op'>=</span> <span class='fl'>0.95</span>,
+  alpha <span class='op'>=</span> <span class='fl'>1</span> <span class='op'>-</span> <span class='va'>level</span>,
+  <span class='va'>cutoff</span>,
+  method <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"quadratic"</span>, <span class='st'>"profile"</span><span class='op'>)</span>,
+  transformed <span class='op'>=</span> <span class='cn'>TRUE</span>,
+  backtransform <span class='op'>=</span> <span class='cn'>TRUE</span>,
+  cores <span class='op'>=</span> <span class='fu'>parallel</span><span class='fu'>::</span><span class='fu'><a href='https://rdrr.io/r/parallel/detectCores.html'>detectCores</a></span><span class='op'>(</span><span class='op'>)</span>,
+  rel_tol <span class='op'>=</span> <span class='fl'>0.01</span>,
+  quiet <span class='op'>=</span> <span class='cn'>FALSE</span>,
+  <span class='va'>...</span>
+<span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
@@ -224,6 +228,12 @@ their confidence intervals?</p></td>
 On Windows machines, cores &gt; 1 is currently not supported.</p></td>
     </tr>
     <tr>
+      <th>rel_tol</th>
+      <td><p>If the method is 'profile', what should be the accuracy
+of the lower and upper bounds, relative to the estimate obtained from
+the quadratic method?</p></td>
+    </tr>
+    <tr>
       <th>quiet</th>
       <td><p>Should we suppress the message "Profiling the likelihood"</p></td>
     </tr>
@@ -247,69 +257,79 @@ Profile-Likelihood Based Confidence Intervals, Applied Statistics, 37,
 87–94.</p>
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
-    <pre class="examples"><div class='input'><span class='no'>f</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='st'>"SFO"</span>, <span class='no'>FOCUS_2006_C</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-<span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span>(<span class='no'>f</span>, <span class='kw'>method</span> <span class='kw'>=</span> <span class='st'>"quadratic"</span>)</div><div class='output co'>#&gt;                     2.5%      97.5%
-#&gt; parent_0      71.8242430 93.1600766
-#&gt; k_parent_sink  0.2109541  0.4440528
-#&gt; sigma          1.9778868  7.3681380</div><div class='input'>
+    <pre class="examples"><div class='input'><span class='va'>f</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='va'>FOCUS_2006_C</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+<span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span><span class='op'>(</span><span class='va'>f</span>, method <span class='op'>=</span> <span class='st'>"quadratic"</span><span class='op'>)</span>
+</div><div class='output co'>#&gt;                2.5%      97.5%
+#&gt; parent_0 71.8242430 93.1600766
+#&gt; k_parent  0.2109541  0.4440528
+#&gt; sigma     1.9778868  7.3681380</div><div class='input'>
 <span class='co'># \dontrun{</span>
-<span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span>(<span class='no'>f</span>, <span class='kw'>method</span> <span class='kw'>=</span> <span class='st'>"profile"</span>)</div><div class='output co'>#&gt; <span class='message'>Profiling the likelihood</span></div><div class='output co'>#&gt;                     2.5%      97.5%
-#&gt; parent_0      73.0641834 92.1392181
-#&gt; k_parent_sink  0.2170293  0.4235348
-#&gt; sigma          3.1307772  8.0628314</div><div class='input'>
+<span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span><span class='op'>(</span><span class='va'>f</span>, method <span class='op'>=</span> <span class='st'>"profile"</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='message'>Profiling the likelihood</span></div><div class='output co'>#&gt;                2.5%      97.5%
+#&gt; parent_0 73.0641834 92.1392181
+#&gt; k_parent  0.2170293  0.4235348
+#&gt; sigma     3.1307772  8.0628314</div><div class='input'>
 <span class='co'># Set the number of cores for the profiling method for further examples</span>
-<span class='kw'>if</span> (<span class='fu'><a href='https://rdrr.io/r/base/identical.html'>identical</a></span>(<span class='fu'><a href='https://rdrr.io/r/base/Sys.getenv.html'>Sys.getenv</a></span>(<span class='st'>"NOT_CRAN"</span>), <span class='st'>"true"</span>)) {
-  <span class='no'>n_cores</span> <span class='kw'>&lt;-</span> <span class='kw pkg'>parallel</span><span class='kw ns'>::</span><span class='fu'><a href='https://rdrr.io/r/parallel/detectCores.html'>detectCores</a></span>() - <span class='fl'>1</span>
-} <span class='kw'>else</span> {
- <span class='no'>n_cores</span> <span class='kw'>&lt;-</span> <span class='fl'>1</span>
-}
-<span class='kw'>if</span> (<span class='fu'><a href='https://rdrr.io/r/base/Sys.getenv.html'>Sys.getenv</a></span>(<span class='st'>"TRAVIS"</span>) <span class='kw'>!=</span> <span class='st'>""</span>) <span class='no'>n_cores</span> <span class='kw'>=</span> <span class='fl'>1</span>
-<span class='kw'>if</span> (<span class='fu'><a href='https://rdrr.io/r/base/Sys.info.html'>Sys.info</a></span>()[<span class='st'>"sysname"</span>] <span class='kw'>==</span> <span class='st'>"Windows"</span>) <span class='no'>n_cores</span> <span class='kw'>=</span> <span class='fl'>1</span>
-
-<span class='no'>SFO_SFO</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>, <span class='st'>"m1"</span>), <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>), <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-<span class='no'>SFO_SFO.ff</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>, <span class='st'>"m1"</span>), <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>),
-  <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"max"</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-<span class='no'>f_d_1</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>SFO_SFO</span>, <span class='fu'><a href='https://rdrr.io/r/base/subset.html'>subset</a></span>(<span class='no'>FOCUS_2006_D</span>, <span class='no'>value</span> <span class='kw'>!=</span> <span class='fl'>0</span>), <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-<span class='fu'><a href='https://rdrr.io/r/base/system.time.html'>system.time</a></span>(<span class='no'>ci_profile</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span>(<span class='no'>f_d_1</span>, <span class='kw'>method</span> <span class='kw'>=</span> <span class='st'>"profile"</span>, <span class='kw'>cores</span> <span class='kw'>=</span> <span class='fl'>1</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>))</div><div class='output co'>#&gt;    user  system elapsed 
-#&gt;   3.430   0.000   3.432 </div><div class='input'><span class='co'># Using more cores does not save much time here, as parent_0 takes up most of the time</span>
+<span class='kw'>if</span> <span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/identical.html'>identical</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/Sys.getenv.html'>Sys.getenv</a></span><span class='op'>(</span><span class='st'>"NOT_CRAN"</span><span class='op'>)</span>, <span class='st'>"true"</span><span class='op'>)</span><span class='op'>)</span> <span class='op'>{</span>
+  <span class='va'>n_cores</span> <span class='op'>&lt;-</span> <span class='fu'>parallel</span><span class='fu'>::</span><span class='fu'><a href='https://rdrr.io/r/parallel/detectCores.html'>detectCores</a></span><span class='op'>(</span><span class='op'>)</span> <span class='op'>-</span> <span class='fl'>1</span>
+<span class='op'>}</span> <span class='kw'>else</span> <span class='op'>{</span>
+ <span class='va'>n_cores</span> <span class='op'>&lt;-</span> <span class='fl'>1</span>
+<span class='op'>}</span>
+<span class='kw'>if</span> <span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/Sys.getenv.html'>Sys.getenv</a></span><span class='op'>(</span><span class='st'>"TRAVIS"</span><span class='op'>)</span> <span class='op'>!=</span> <span class='st'>""</span><span class='op'>)</span> <span class='va'>n_cores</span> <span class='op'>=</span> <span class='fl'>1</span>
+<span class='kw'>if</span> <span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/Sys.info.html'>Sys.info</a></span><span class='op'>(</span><span class='op'>)</span><span class='op'>[</span><span class='st'>"sysname"</span><span class='op'>]</span> <span class='op'>==</span> <span class='st'>"Windows"</span><span class='op'>)</span> <span class='va'>n_cores</span> <span class='op'>=</span> <span class='fl'>1</span>
+
+<span class='va'>SFO_SFO</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='st'>"m1"</span><span class='op'>)</span>, m1 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+<span class='va'>SFO_SFO.ff</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='st'>"m1"</span><span class='op'>)</span>, m1 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span>,
+  use_of_ff <span class='op'>=</span> <span class='st'>"max"</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+<span class='va'>f_d_1</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='va'>SFO_SFO</span>, <span class='fu'><a href='https://rdrr.io/r/base/subset.html'>subset</a></span><span class='op'>(</span><span class='va'>FOCUS_2006_D</span>, <span class='va'>value</span> <span class='op'>!=</span> <span class='fl'>0</span><span class='op'>)</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.0165</span></div><div class='input'><span class='fu'><a href='https://rdrr.io/r/base/system.time.html'>system.time</a></span><span class='op'>(</span><span class='va'>ci_profile</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span><span class='op'>(</span><span class='va'>f_d_1</span>, method <span class='op'>=</span> <span class='st'>"profile"</span>, cores <span class='op'>=</span> <span class='fl'>1</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='output co'>#&gt;    user  system elapsed 
+#&gt;   3.770   1.035   3.460 </div><div class='input'><span class='co'># Using more cores does not save much time here, as parent_0 takes up most of the time</span>
 <span class='co'># If we additionally exclude parent_0 (the confidence of which is often of</span>
 <span class='co'># minor interest), we get a nice performance improvement from about 50</span>
 <span class='co'># seconds to about 12 seconds if we use at least four cores</span>
-<span class='fu'><a href='https://rdrr.io/r/base/system.time.html'>system.time</a></span>(<span class='no'>ci_profile_no_parent_0</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span>(<span class='no'>f_d_1</span>, <span class='kw'>method</span> <span class='kw'>=</span> <span class='st'>"profile"</span>,
-  <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"k_parent_sink"</span>, <span class='st'>"k_parent_m1"</span>, <span class='st'>"k_m1_sink"</span>, <span class='st'>"sigma"</span>), <span class='kw'>cores</span> <span class='kw'>=</span> <span class='no'>n_cores</span>))</div><div class='output co'>#&gt; <span class='message'>Profiling the likelihood</span></div><div class='output co'>#&gt; <span class='warning'>Warning: scheduled cores 1, 2, 3 encountered errors in user code, all values of the jobs will be affected</span></div><div class='output co'>#&gt; <span class='error'>Error in dimnames(x) &lt;- dn: length of 'dimnames' [2] not equal to array extent</span></div><div class='output co'>#&gt; <span class='message'>Timing stopped at: 0.012 0.042 0.211</span></div><div class='input'><span class='no'>ci_profile</span></div><div class='output co'>#&gt;                        2.5%        97.5%
+<span class='fu'><a href='https://rdrr.io/r/base/system.time.html'>system.time</a></span><span class='op'>(</span><span class='va'>ci_profile_no_parent_0</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span><span class='op'>(</span><span class='va'>f_d_1</span>, method <span class='op'>=</span> <span class='st'>"profile"</span>,
+  <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"k_parent_sink"</span>, <span class='st'>"k_parent_m1"</span>, <span class='st'>"k_m1_sink"</span>, <span class='st'>"sigma"</span><span class='op'>)</span>, cores <span class='op'>=</span> <span class='va'>n_cores</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='message'>Profiling the likelihood</span></div><div class='output co'>#&gt; <span class='warning'>Warning: scheduled cores 3, 2, 1 encountered errors in user code, all values of the jobs will be affected</span></div><div class='output co'>#&gt; <span class='error'>Error in dimnames(x) &lt;- dn: length of 'dimnames' [2] not equal to array extent</span></div><div class='output co'>#&gt; <span class='message'>Timing stopped at: 0.014 0.027 0.196</span></div><div class='input'><span class='va'>ci_profile</span>
+</div><div class='output co'>#&gt;                        2.5%        97.5%
 #&gt; parent_0       96.456003640 1.027703e+02
 #&gt; k_parent        0.090911032 1.071578e-01
 #&gt; k_m1            0.003892605 6.702778e-03
 #&gt; f_parent_to_m1  0.471328495 5.611550e-01
-#&gt; sigma           2.535612399 3.985263e+00</div><div class='input'><span class='no'>ci_quadratic_transformed</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span>(<span class='no'>f_d_1</span>, <span class='kw'>method</span> <span class='kw'>=</span> <span class='st'>"quadratic"</span>)
-<span class='no'>ci_quadratic_transformed</span></div><div class='output co'>#&gt;                        2.5%        97.5%
-#&gt; parent_0       96.403839476 1.027931e+02
+#&gt; sigma           2.535612399 3.985263e+00</div><div class='input'><span class='va'>ci_quadratic_transformed</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span><span class='op'>(</span><span class='va'>f_d_1</span>, method <span class='op'>=</span> <span class='st'>"quadratic"</span><span class='op'>)</span>
+<span class='va'>ci_quadratic_transformed</span>
+</div><div class='output co'>#&gt;                        2.5%        97.5%
+#&gt; parent_0       96.403839460 1.027931e+02
 #&gt; k_parent        0.090823790 1.072543e-01
 #&gt; k_m1            0.004012216 6.897547e-03
 #&gt; f_parent_to_m1  0.469118713 5.595960e-01
-#&gt; sigma           2.396089689 3.854918e+00</div><div class='input'><span class='no'>ci_quadratic_untransformed</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span>(<span class='no'>f_d_1</span>, <span class='kw'>method</span> <span class='kw'>=</span> <span class='st'>"quadratic"</span>, <span class='kw'>transformed</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>)
-<span class='no'>ci_quadratic_untransformed</span></div><div class='output co'>#&gt;                        2.5%        97.5%
-#&gt; parent_0       96.403839429 1.027931e+02
+#&gt; sigma           2.396089689 3.854918e+00</div><div class='input'><span class='va'>ci_quadratic_untransformed</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span><span class='op'>(</span><span class='va'>f_d_1</span>, method <span class='op'>=</span> <span class='st'>"quadratic"</span>, transformed <span class='op'>=</span> <span class='cn'>FALSE</span><span class='op'>)</span>
+<span class='va'>ci_quadratic_untransformed</span>
+</div><div class='output co'>#&gt;                        2.5%        97.5%
+#&gt; parent_0       96.403839413 1.027931e+02
 #&gt; k_parent        0.090491931 1.069035e-01
 #&gt; k_m1            0.003835483 6.685819e-03
-#&gt; f_parent_to_m1  0.469113364 5.598386e-01
+#&gt; f_parent_to_m1  0.469113365 5.598386e-01
 #&gt; sigma           2.396089689 3.854918e+00</div><div class='input'><span class='co'># Against the expectation based on Bates and Watts (1988), the confidence</span>
 <span class='co'># intervals based on the internal parameter transformation are less</span>
 <span class='co'># congruent with the likelihood based intervals. Note the superiority of the</span>
 <span class='co'># interval based on the untransformed fit for k_m1_sink</span>
-<span class='no'>rel_diffs_transformed</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/MathFun.html'>abs</a></span>((<span class='no'>ci_quadratic_transformed</span> - <span class='no'>ci_profile</span>)/<span class='no'>ci_profile</span>)
-<span class='no'>rel_diffs_untransformed</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/MathFun.html'>abs</a></span>((<span class='no'>ci_quadratic_untransformed</span> - <span class='no'>ci_profile</span>)/<span class='no'>ci_profile</span>)
-<span class='no'>rel_diffs_transformed</span> <span class='kw'>&lt;</span> <span class='no'>rel_diffs_untransformed</span></div><div class='output co'>#&gt;                 2.5% 97.5%
+<span class='va'>rel_diffs_transformed</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/MathFun.html'>abs</a></span><span class='op'>(</span><span class='op'>(</span><span class='va'>ci_quadratic_transformed</span> <span class='op'>-</span> <span class='va'>ci_profile</span><span class='op'>)</span><span class='op'>/</span><span class='va'>ci_profile</span><span class='op'>)</span>
+<span class='va'>rel_diffs_untransformed</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/MathFun.html'>abs</a></span><span class='op'>(</span><span class='op'>(</span><span class='va'>ci_quadratic_untransformed</span> <span class='op'>-</span> <span class='va'>ci_profile</span><span class='op'>)</span><span class='op'>/</span><span class='va'>ci_profile</span><span class='op'>)</span>
+<span class='va'>rel_diffs_transformed</span> <span class='op'>&lt;</span> <span class='va'>rel_diffs_untransformed</span>
+</div><div class='output co'>#&gt;                 2.5% 97.5%
 #&gt; parent_0        TRUE  TRUE
 #&gt; k_parent        TRUE  TRUE
 #&gt; k_m1           FALSE FALSE
 #&gt; f_parent_to_m1  TRUE FALSE
-#&gt; sigma          FALSE  TRUE</div><div class='input'><span class='fu'><a href='https://rdrr.io/r/base/Round.html'>signif</a></span>(<span class='no'>rel_diffs_transformed</span>, <span class='fl'>3</span>)</div><div class='output co'>#&gt;                    2.5%    97.5%
+#&gt; sigma          FALSE FALSE</div><div class='input'><span class='fu'><a href='https://rdrr.io/r/base/Round.html'>signif</a></span><span class='op'>(</span><span class='va'>rel_diffs_transformed</span>, <span class='fl'>3</span><span class='op'>)</span>
+</div><div class='output co'>#&gt;                    2.5%    97.5%
 #&gt; parent_0       0.000541 0.000222
 #&gt; k_parent       0.000960 0.000900
 #&gt; k_m1           0.030700 0.029100
 #&gt; f_parent_to_m1 0.004690 0.002780
-#&gt; sigma          0.055000 0.032700</div><div class='input'><span class='fu'><a href='https://rdrr.io/r/base/Round.html'>signif</a></span>(<span class='no'>rel_diffs_untransformed</span>, <span class='fl'>3</span>)</div><div class='output co'>#&gt;                    2.5%    97.5%
+#&gt; sigma          0.055000 0.032700</div><div class='input'><span class='fu'><a href='https://rdrr.io/r/base/Round.html'>signif</a></span><span class='op'>(</span><span class='va'>rel_diffs_untransformed</span>, <span class='fl'>3</span><span class='op'>)</span>
+</div><div class='output co'>#&gt;                    2.5%    97.5%
 #&gt; parent_0       0.000541 0.000222
 #&gt; k_parent       0.004610 0.002370
 #&gt; k_m1           0.014700 0.002530
@@ -317,67 +337,76 @@ Profile-Likelihood Based Confidence Intervals, Applied Statistics, 37,
 #&gt; sigma          0.055000 0.032700</div><div class='input'>
 
 <span class='co'># Investigate a case with formation fractions</span>
-<span class='no'>f_d_2</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>SFO_SFO.ff</span>, <span class='fu'><a href='https://rdrr.io/r/base/subset.html'>subset</a></span>(<span class='no'>FOCUS_2006_D</span>, <span class='no'>value</span> <span class='kw'>!=</span> <span class='fl'>0</span>), <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-<span class='no'>ci_profile_ff</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span>(<span class='no'>f_d_2</span>, <span class='kw'>method</span> <span class='kw'>=</span> <span class='st'>"profile"</span>, <span class='kw'>cores</span> <span class='kw'>=</span> <span class='no'>n_cores</span>)</div><div class='output co'>#&gt; <span class='message'>Profiling the likelihood</span></div><div class='input'><span class='no'>ci_profile_ff</span></div><div class='output co'>#&gt;                        2.5%        97.5%
+<span class='va'>f_d_2</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='va'>SFO_SFO.ff</span>, <span class='fu'><a href='https://rdrr.io/r/base/subset.html'>subset</a></span><span class='op'>(</span><span class='va'>FOCUS_2006_D</span>, <span class='va'>value</span> <span class='op'>!=</span> <span class='fl'>0</span><span class='op'>)</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.0165</span></div><div class='input'><span class='va'>ci_profile_ff</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span><span class='op'>(</span><span class='va'>f_d_2</span>, method <span class='op'>=</span> <span class='st'>"profile"</span>, cores <span class='op'>=</span> <span class='va'>n_cores</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='message'>Profiling the likelihood</span></div><div class='input'><span class='va'>ci_profile_ff</span>
+</div><div class='output co'>#&gt;                        2.5%        97.5%
 #&gt; parent_0       96.456003640 1.027703e+02
 #&gt; k_parent        0.090911032 1.071578e-01
 #&gt; k_m1            0.003892605 6.702778e-03
 #&gt; f_parent_to_m1  0.471328495 5.611550e-01
-#&gt; sigma           2.535612399 3.985263e+00</div><div class='input'><span class='no'>ci_quadratic_transformed_ff</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span>(<span class='no'>f_d_2</span>, <span class='kw'>method</span> <span class='kw'>=</span> <span class='st'>"quadratic"</span>)
-<span class='no'>ci_quadratic_transformed_ff</span></div><div class='output co'>#&gt;                        2.5%        97.5%
-#&gt; parent_0       96.403839476 1.027931e+02
+#&gt; sigma           2.535612399 3.985263e+00</div><div class='input'><span class='va'>ci_quadratic_transformed_ff</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span><span class='op'>(</span><span class='va'>f_d_2</span>, method <span class='op'>=</span> <span class='st'>"quadratic"</span><span class='op'>)</span>
+<span class='va'>ci_quadratic_transformed_ff</span>
+</div><div class='output co'>#&gt;                        2.5%        97.5%
+#&gt; parent_0       96.403839460 1.027931e+02
 #&gt; k_parent        0.090823790 1.072543e-01
 #&gt; k_m1            0.004012216 6.897547e-03
 #&gt; f_parent_to_m1  0.469118713 5.595960e-01
-#&gt; sigma           2.396089689 3.854918e+00</div><div class='input'><span class='no'>ci_quadratic_untransformed_ff</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span>(<span class='no'>f_d_2</span>, <span class='kw'>method</span> <span class='kw'>=</span> <span class='st'>"quadratic"</span>, <span class='kw'>transformed</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>)
-<span class='no'>ci_quadratic_untransformed_ff</span></div><div class='output co'>#&gt;                        2.5%        97.5%
-#&gt; parent_0       96.403839429 1.027931e+02
+#&gt; sigma           2.396089689 3.854918e+00</div><div class='input'><span class='va'>ci_quadratic_untransformed_ff</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span><span class='op'>(</span><span class='va'>f_d_2</span>, method <span class='op'>=</span> <span class='st'>"quadratic"</span>, transformed <span class='op'>=</span> <span class='cn'>FALSE</span><span class='op'>)</span>
+<span class='va'>ci_quadratic_untransformed_ff</span>
+</div><div class='output co'>#&gt;                        2.5%        97.5%
+#&gt; parent_0       96.403839413 1.027931e+02
 #&gt; k_parent        0.090491931 1.069035e-01
 #&gt; k_m1            0.003835483 6.685819e-03
-#&gt; f_parent_to_m1  0.469113364 5.598386e-01
-#&gt; sigma           2.396089689 3.854918e+00</div><div class='input'><span class='no'>rel_diffs_transformed_ff</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/MathFun.html'>abs</a></span>((<span class='no'>ci_quadratic_transformed_ff</span> - <span class='no'>ci_profile_ff</span>)/<span class='no'>ci_profile_ff</span>)
-<span class='no'>rel_diffs_untransformed_ff</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/MathFun.html'>abs</a></span>((<span class='no'>ci_quadratic_untransformed_ff</span> - <span class='no'>ci_profile_ff</span>)/<span class='no'>ci_profile_ff</span>)
+#&gt; f_parent_to_m1  0.469113365 5.598386e-01
+#&gt; sigma           2.396089689 3.854918e+00</div><div class='input'><span class='va'>rel_diffs_transformed_ff</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/MathFun.html'>abs</a></span><span class='op'>(</span><span class='op'>(</span><span class='va'>ci_quadratic_transformed_ff</span> <span class='op'>-</span> <span class='va'>ci_profile_ff</span><span class='op'>)</span><span class='op'>/</span><span class='va'>ci_profile_ff</span><span class='op'>)</span>
+<span class='va'>rel_diffs_untransformed_ff</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/MathFun.html'>abs</a></span><span class='op'>(</span><span class='op'>(</span><span class='va'>ci_quadratic_untransformed_ff</span> <span class='op'>-</span> <span class='va'>ci_profile_ff</span><span class='op'>)</span><span class='op'>/</span><span class='va'>ci_profile_ff</span><span class='op'>)</span>
 <span class='co'># While the confidence interval for the parent rate constant is closer to</span>
 <span class='co'># the profile based interval when using the internal parameter</span>
 <span class='co'># transformation, the interval for the metabolite rate constant is 'better</span>
 <span class='co'># without internal parameter transformation.</span>
-<span class='no'>rel_diffs_transformed_ff</span> <span class='kw'>&lt;</span> <span class='no'>rel_diffs_untransformed_ff</span></div><div class='output co'>#&gt;                 2.5% 97.5%
+<span class='va'>rel_diffs_transformed_ff</span> <span class='op'>&lt;</span> <span class='va'>rel_diffs_untransformed_ff</span>
+</div><div class='output co'>#&gt;                 2.5% 97.5%
 #&gt; parent_0        TRUE  TRUE
 #&gt; k_parent        TRUE  TRUE
 #&gt; k_m1           FALSE FALSE
 #&gt; f_parent_to_m1  TRUE FALSE
-#&gt; sigma          FALSE  TRUE</div><div class='input'><span class='no'>rel_diffs_transformed_ff</span></div><div class='output co'>#&gt;                        2.5%        97.5%
-#&gt; parent_0       0.0005408078 0.0002217796
+#&gt; sigma          FALSE FALSE</div><div class='input'><span class='va'>rel_diffs_transformed_ff</span>
+</div><div class='output co'>#&gt;                        2.5%        97.5%
+#&gt; parent_0       0.0005408080 0.0002217794
 #&gt; k_parent       0.0009596417 0.0009003876
-#&gt; k_m1           0.0307277372 0.0290579184
-#&gt; f_parent_to_m1 0.0046884131 0.0027782558
-#&gt; sigma          0.0550252516 0.0327066836</div><div class='input'><span class='no'>rel_diffs_untransformed_ff</span></div><div class='output co'>#&gt;                        2.5%       97.5%
-#&gt; parent_0       0.0005408083 0.000221780
-#&gt; k_parent       0.0046100096 0.002373023
-#&gt; k_m1           0.0146746467 0.002530101
-#&gt; f_parent_to_m1 0.0046997600 0.002346022
-#&gt; sigma          0.0550252516 0.032706684</div><div class='input'>
+#&gt; k_m1           0.0307277370 0.0290579182
+#&gt; f_parent_to_m1 0.0046884130 0.0027782556
+#&gt; sigma          0.0550252516 0.0327066836</div><div class='input'><span class='va'>rel_diffs_untransformed_ff</span>
+</div><div class='output co'>#&gt;                        2.5%        97.5%
+#&gt; parent_0       0.0005408085 0.0002217799
+#&gt; k_parent       0.0046100096 0.0023730229
+#&gt; k_m1           0.0146746469 0.0025301011
+#&gt; f_parent_to_m1 0.0046997599 0.0023460223
+#&gt; sigma          0.0550252516 0.0327066836</div><div class='input'>
 <span class='co'># The profiling for the following fit does not finish in a reasonable time,</span>
 <span class='co'># therefore we use the quadratic approximation</span>
-<span class='no'>m_synth_DFOP_par</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"DFOP"</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"M1"</span>, <span class='st'>"M2"</span>)),
-  <span class='kw'>M1</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>),
-  <span class='kw'>M2</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>),
-  <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"max"</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-<span class='no'>DFOP_par_c</span> <span class='kw'>&lt;-</span> <span class='no'>synthetic_data_for_UBA_2014</span><span class='kw'>[[</span><span class='fl'>12</span>]]$<span class='no'>data</span>
-<span class='no'>f_tc_2</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>m_synth_DFOP_par</span>, <span class='no'>DFOP_par_c</span>, <span class='kw'>error_model</span> <span class='kw'>=</span> <span class='st'>"tc"</span>,
-  <span class='kw'>error_model_algorithm</span> <span class='kw'>=</span> <span class='st'>"direct"</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#&gt; <span class='warning'>Warning: Optimisation did not converge:</span>
-#&gt; <span class='warning'>iteration limit reached without convergence (10)</span></div><div class='input'><span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span>(<span class='no'>f_tc_2</span>, <span class='kw'>method</span> <span class='kw'>=</span> <span class='st'>"quadratic"</span>)</div><div class='output co'>#&gt;                        2.5%        97.5%
-#&gt; parent_0       95.654015524 105.79279749
-#&gt; k_M1            0.037723773   0.04447598
-#&gt; k_M2            0.008586438   0.01078076
-#&gt; f_parent_to_M1  0.230403596   0.61953014
-#&gt; f_parent_to_M2  0.162909765   0.38019017
-#&gt; k1              0.275434628   0.33331386
-#&gt; k2              0.018602188   0.02249211
-#&gt; g               0.675149759   0.73520889
-#&gt; sigma_low       0.251416929   0.84272023
-#&gt; rsd_high        0.040371818   0.07666540</div><div class='input'><span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span>(<span class='no'>f_tc_2</span>, <span class='st'>"parent_0"</span>, <span class='kw'>method</span> <span class='kw'>=</span> <span class='st'>"quadratic"</span>)</div><div class='output co'>#&gt;              2.5%    97.5%
-#&gt; parent_0 95.65402 105.7928</div><div class='input'># }
+<span class='va'>m_synth_DFOP_par</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"DFOP"</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"M1"</span>, <span class='st'>"M2"</span><span class='op'>)</span><span class='op'>)</span>,
+  M1 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span>,
+  M2 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span>,
+  use_of_ff <span class='op'>=</span> <span class='st'>"max"</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+<span class='va'>DFOP_par_c</span> <span class='op'>&lt;-</span> <span class='va'>synthetic_data_for_UBA_2014</span><span class='op'>[[</span><span class='fl'>12</span><span class='op'>]</span><span class='op'>]</span><span class='op'>$</span><span class='va'>data</span>
+<span class='va'>f_tc_2</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='va'>m_synth_DFOP_par</span>, <span class='va'>DFOP_par_c</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span>,
+  error_model_algorithm <span class='op'>=</span> <span class='st'>"direct"</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+<span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span><span class='op'>(</span><span class='va'>f_tc_2</span>, method <span class='op'>=</span> <span class='st'>"quadratic"</span><span class='op'>)</span>
+</div><div class='output co'>#&gt;                       2.5%        97.5%
+#&gt; parent_0       94.59613833 106.19939215
+#&gt; k_M1            0.03760542   0.04490759
+#&gt; k_M2            0.00856874   0.01087675
+#&gt; f_parent_to_M1  0.02146166   0.62023888
+#&gt; f_parent_to_M2  0.01516502   0.37975343
+#&gt; k1              0.27389751   0.33388078
+#&gt; k2              0.01861456   0.02250379
+#&gt; g               0.67194349   0.73583256
+#&gt; sigma_low       0.25128383   0.83992146
+#&gt; rsd_high        0.04041100   0.07662001</div><div class='input'><span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span><span class='op'>(</span><span class='va'>f_tc_2</span>, <span class='st'>"parent_0"</span>, method <span class='op'>=</span> <span class='st'>"quadratic"</span><span class='op'>)</span>
+</div><div class='output co'>#&gt;              2.5%    97.5%
+#&gt; parent_0 94.59614 106.1994</div><div class='input'><span class='co'># }</span>
 </div></pre>
   </div>
   <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
@@ -394,7 +423,7 @@ Profile-Likelihood Based Confidence Intervals, Applied Statistics, 37,
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/create_deg_func.html b/docs/reference/create_deg_func.html
index 3bb512cd..6b8f3e83 100644
--- a/docs/reference/create_deg_func.html
+++ b/docs/reference/create_deg_func.html
@@ -72,7 +72,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -109,6 +109,9 @@
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -117,7 +120,7 @@
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -136,7 +139,7 @@
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>Create degradation functions for known analytical solutions</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/create_deg_func.R'><code>R/create_deg_func.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/create_deg_func.R'><code>R/create_deg_func.R</code></a></small>
     <div class="hidden name"><code>create_deg_func.Rd</code></div>
     </div>
 
@@ -144,7 +147,7 @@
     <p>Create degradation functions for known analytical solutions</p>
     </div>
 
-    <pre class="usage"><span class='fu'>create_deg_func</span>(<span class='no'>spec</span>, <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"min"</span>, <span class='st'>"max"</span>))</pre>
+    <pre class="usage"><span class='fu'>create_deg_func</span><span class='op'>(</span><span class='va'>spec</span>, use_of_ff <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"min"</span>, <span class='st'>"max"</span><span class='op'>)</span><span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
@@ -165,32 +168,36 @@
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
     <pre class="examples"><div class='input'>
-<span class='no'>SFO_SFO</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(
-  <span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>, <span class='st'>"m1"</span>),
-  <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>))</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'><span class='no'>FOCUS_D</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/subset.html'>subset</a></span>(<span class='no'>FOCUS_2006_D</span>, <span class='no'>value</span> <span class='kw'>!=</span> <span class='fl'>0</span>) <span class='co'># to avoid warnings</span>
-<span class='no'>fit_1</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>SFO_SFO</span>, <span class='no'>FOCUS_D</span>, <span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='st'>"analytical"</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-<span class='no'>fit_2</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>SFO_SFO</span>, <span class='no'>FOCUS_D</span>, <span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='st'>"deSolve"</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-<span class='co'># \dontrun{</span>
-<span class='kw'>if</span> (<span class='fu'><a href='https://rdrr.io/r/base/library.html'>require</a></span>(<span class='no'>rbenchmark</span>))
-  <span class='fu'><a href='https://rdrr.io/pkg/rbenchmark/man/benchmark.html'>benchmark</a></span>(
-    <span class='kw'>analytical</span> <span class='kw'>=</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>SFO_SFO</span>, <span class='no'>FOCUS_D</span>, <span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='st'>"analytical"</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>),
-    <span class='kw'>deSolve</span> <span class='kw'>=</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>SFO_SFO</span>, <span class='no'>FOCUS_D</span>, <span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='st'>"deSolve"</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>),
-    <span class='kw'>replications</span> <span class='kw'>=</span> <span class='fl'>2</span>)</div><div class='output co'>#&gt; <span class='message'>Loading required package: rbenchmark</span></div><div class='output co'>#&gt;         test replications elapsed relative user.self sys.self user.child
-#&gt; 1 analytical            2   0.407    1.000     0.407        0          0
-#&gt; 2    deSolve            2   0.699    1.717     0.698        0          0
+<span class='va'>SFO_SFO</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>
+  parent <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='st'>"m1"</span><span class='op'>)</span>,
+  m1 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'><span class='va'>FOCUS_D</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/subset.html'>subset</a></span><span class='op'>(</span><span class='va'>FOCUS_2006_D</span>, <span class='va'>value</span> <span class='op'>!=</span> <span class='fl'>0</span><span class='op'>)</span> <span class='co'># to avoid warnings</span>
+<span class='va'>fit_1</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='va'>SFO_SFO</span>, <span class='va'>FOCUS_D</span>, solution_type <span class='op'>=</span> <span class='st'>"analytical"</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.0165</span></div><div class='input'><span class='va'>fit_2</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='va'>SFO_SFO</span>, <span class='va'>FOCUS_D</span>, solution_type <span class='op'>=</span> <span class='st'>"deSolve"</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.0165</span></div><div class='input'><span class='co'># \dontrun{</span>
+<span class='kw'>if</span> <span class='op'>(</span><span class='kw'><a href='https://rdrr.io/r/base/library.html'>require</a></span><span class='op'>(</span><span class='va'><a href='http://rbenchmark.googlecode.com'>rbenchmark</a></span><span class='op'>)</span><span class='op'>)</span>
+  <span class='fu'><a href='https://rdrr.io/pkg/rbenchmark/man/benchmark.html'>benchmark</a></span><span class='op'>(</span>
+    analytical <span class='op'>=</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='va'>SFO_SFO</span>, <span class='va'>FOCUS_D</span>, solution_type <span class='op'>=</span> <span class='st'>"analytical"</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>,
+    deSolve <span class='op'>=</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='va'>SFO_SFO</span>, <span class='va'>FOCUS_D</span>, solution_type <span class='op'>=</span> <span class='st'>"deSolve"</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>,
+    replications <span class='op'>=</span> <span class='fl'>2</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='message'>Loading required package: rbenchmark</span></div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.0165</span></div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.0165</span></div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.0165</span></div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.0165</span></div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.0165</span></div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.0165</span></div><div class='output co'>#&gt;         test replications elapsed relative user.self sys.self user.child
+#&gt; 1 analytical            2   0.416    1.000     0.416        0          0
+#&gt; 2    deSolve            2   0.715    1.719     0.715        0          0
 #&gt;   sys.child
 #&gt; 1         0
-#&gt; 2         0</div><div class='input'>  <span class='no'>DFOP_SFO</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(
-    <span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"DFOP"</span>, <span class='st'>"m1"</span>),
-    <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>))</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>  <span class='fu'><a href='https://rdrr.io/pkg/rbenchmark/man/benchmark.html'>benchmark</a></span>(
-    <span class='kw'>analytical</span> <span class='kw'>=</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>DFOP_SFO</span>, <span class='no'>FOCUS_D</span>, <span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='st'>"analytical"</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>),
-    <span class='kw'>deSolve</span> <span class='kw'>=</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>DFOP_SFO</span>, <span class='no'>FOCUS_D</span>, <span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='st'>"deSolve"</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>),
-    <span class='kw'>replications</span> <span class='kw'>=</span> <span class='fl'>2</span>)</div><div class='output co'>#&gt;         test replications elapsed relative user.self sys.self user.child
-#&gt; 1 analytical            2   0.887    1.000     0.886        0          0
-#&gt; 2    deSolve            2   1.639    1.848     1.638        0          0
+#&gt; 2         0</div><div class='input'>  <span class='va'>DFOP_SFO</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>
+    parent <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"DFOP"</span>, <span class='st'>"m1"</span><span class='op'>)</span>,
+    m1 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>  <span class='fu'><a href='https://rdrr.io/pkg/rbenchmark/man/benchmark.html'>benchmark</a></span><span class='op'>(</span>
+    analytical <span class='op'>=</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='va'>DFOP_SFO</span>, <span class='va'>FOCUS_D</span>, solution_type <span class='op'>=</span> <span class='st'>"analytical"</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>,
+    deSolve <span class='op'>=</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='va'>DFOP_SFO</span>, <span class='va'>FOCUS_D</span>, solution_type <span class='op'>=</span> <span class='st'>"deSolve"</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>,
+    replications <span class='op'>=</span> <span class='fl'>2</span><span class='op'>)</span>
+</div><div class='output co'>#&gt;         test replications elapsed relative user.self sys.self user.child
+#&gt; 1 analytical            2   0.912     1.00     0.912    0.001          0
+#&gt; 2    deSolve            2   1.724     1.89     1.723    0.000          0
 #&gt;   sys.child
 #&gt; 1         0
-#&gt; 2         0</div><div class='input'># }
+#&gt; 2         0</div><div class='input'><span class='co'># }</span>
 </div></pre>
   </div>
   <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
@@ -207,7 +214,7 @@
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/endpoints.html b/docs/reference/endpoints.html
index d9c43f84..376a263e 100644
--- a/docs/reference/endpoints.html
+++ b/docs/reference/endpoints.html
@@ -78,7 +78,7 @@ advantage that the SFORB model can also be used for metabolites." />
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -115,6 +115,9 @@ advantage that the SFORB model can also be used for metabolites." />
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -123,7 +126,7 @@ advantage that the SFORB model can also be used for metabolites." />
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -143,7 +146,7 @@ advantage that the SFORB model can also be used for metabolites." />
     <div class="page-header">
     <h1>Function to calculate endpoints for further use from kinetic models fitted
 with mkinfit</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/endpoints.R'><code>R/endpoints.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/endpoints.R'><code>R/endpoints.R</code></a></small>
     <div class="hidden name"><code>endpoints.Rd</code></div>
     </div>
 
@@ -155,7 +158,7 @@ are equivalent to the rate constants of the DFOP model, but with the
 advantage that the SFORB model can also be used for metabolites.</p>
     </div>
 
-    <pre class="usage"><span class='fu'>endpoints</span>(<span class='no'>fit</span>)</pre>
+    <pre class="usage"><span class='fu'>endpoints</span><span class='op'>(</span><span class='va'>fit</span><span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
@@ -176,27 +179,37 @@ of these SFORB models, equivalent to DFOP rate constants</p>
     <h2 class="hasAnchor" id="note"><a class="anchor" href="#note"></a>Note</h2>
 
     <p>The function is used internally by <code><a href='summary.mkinfit.html'>summary.mkinfit</a></code>.</p>
+    <h2 class="hasAnchor" id="author"><a class="anchor" href="#author"></a>Author</h2>
+
+    <p>Johannes Ranke</p>
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
     <pre class="examples"><div class='input'>
-  <span class='no'>fit</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='st'>"FOMC"</span>, <span class='no'>FOCUS_2006_C</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-  <span class='fu'>endpoints</span>(<span class='no'>fit</span>)</div><div class='output co'>#&gt; $distimes
+  <span class='va'>fit</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='st'>"FOMC"</span>, <span class='va'>FOCUS_2006_C</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+  <span class='fu'>endpoints</span><span class='op'>(</span><span class='va'>fit</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; $distimes
 #&gt;            DT50    DT90 DT50back
 #&gt; parent 1.785233 15.1479 4.559973
 #&gt; </div><div class='input'>  <span class='co'># \dontrun{</span>
-    <span class='no'>fit_2</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='st'>"SFORB"</span>, <span class='no'>FOCUS_2006_C</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-    <span class='fu'>endpoints</span>(<span class='no'>fit_2</span>)</div><div class='output co'>#&gt; $ff
-#&gt; parent_free_sink 
-#&gt;                1 
+    <span class='va'>fit_2</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='st'>"DFOP"</span>, <span class='va'>FOCUS_2006_C</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+    <span class='fu'>endpoints</span><span class='op'>(</span><span class='va'>fit_2</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; $distimes
+#&gt;            DT50     DT90 DT50back  DT50_k1  DT50_k2
+#&gt; parent 1.886925 21.25106 6.397207 1.508293 38.83438
+#&gt; </div><div class='input'>    <span class='va'>fit_3</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='st'>"SFORB"</span>, <span class='va'>FOCUS_2006_C</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+    <span class='fu'>endpoints</span><span class='op'>(</span><span class='va'>fit_3</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; $ff
+#&gt; parent_free 
+#&gt;           1 
 #&gt; 
 #&gt; $SFORB
 #&gt; parent_b1 parent_b2 
 #&gt; 0.4595574 0.0178488 
 #&gt; 
 #&gt; $distimes
-#&gt;            DT50     DT90 DT50_parent_b1 DT50_parent_b2
-#&gt; parent 1.886925 21.25106       1.508293       38.83438
-#&gt; </div><div class='input'>  # }
+#&gt;            DT50     DT90 DT50back DT50_parent_b1 DT50_parent_b2
+#&gt; parent 1.886925 21.25106 6.397208       1.508293       38.83438
+#&gt; </div><div class='input'>  <span class='co'># }</span>
 
 </div></pre>
   </div>
@@ -214,7 +227,7 @@ of these SFORB models, equivalent to DFOP rate constants</p>
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/get_deg_func.html b/docs/reference/get_deg_func.html
index 812b25d7..a8e289a6 100644
--- a/docs/reference/get_deg_func.html
+++ b/docs/reference/get_deg_func.html
@@ -72,7 +72,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -109,6 +109,9 @@
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -117,7 +120,7 @@
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -136,7 +139,7 @@
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>Retrieve a degradation function from the mmkin namespace</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/nlme.mmkin.R'><code>R/nlme.mmkin.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/nlme.mmkin.R'><code>R/nlme.mmkin.R</code></a></small>
     <div class="hidden name"><code>get_deg_func.Rd</code></div>
     </div>
 
@@ -144,7 +147,7 @@
     <p>Retrieve a degradation function from the mmkin namespace</p>
     </div>
 
-    <pre class="usage"><span class='fu'>get_deg_func</span>()</pre>
+    <pre class="usage"><span class='fu'>get_deg_func</span><span class='op'>(</span><span class='op'>)</span></pre>
 
 
     <h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>
@@ -167,7 +170,7 @@ nlme.mmkin</p>
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/ilr.html b/docs/reference/ilr.html
index 30be0a73..485fcaf0 100644
--- a/docs/reference/ilr.html
+++ b/docs/reference/ilr.html
@@ -73,7 +73,7 @@ transformations." />
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -110,6 +110,9 @@ transformations." />
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -118,7 +121,7 @@ transformations." />
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -137,7 +140,7 @@ transformations." />
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>Function to perform isometric log-ratio transformation</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/ilr.R'><code>R/ilr.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/ilr.R'><code>R/ilr.R</code></a></small>
     <div class="hidden name"><code>ilr.Rd</code></div>
     </div>
 
@@ -146,9 +149,9 @@ transformations." />
 transformations.</p>
     </div>
 
-    <pre class="usage"><span class='fu'>ilr</span>(<span class='no'>x</span>)
+    <pre class="usage"><span class='fu'>ilr</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span>
 
-<span class='fu'>invilr</span>(<span class='no'>x</span>)</pre>
+<span class='fu'>invilr</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
@@ -173,19 +176,33 @@ Compositional Data Using Robust Methods. Math Geosci 40 233-248</p>
 
     <div class='dont-index'><p>Another implementation can be found in R package
 <code>robCompositions</code>.</p></div>
+    <h2 class="hasAnchor" id="author"><a class="anchor" href="#author"></a>Author</h2>
+
+    <p>René Lehmann and Johannes Ranke</p>
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
     <pre class="examples"><div class='input'>
 <span class='co'># Order matters</span>
-<span class='fu'>ilr</span>(<span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='fl'>0.1</span>, <span class='fl'>1</span>, <span class='fl'>10</span>))</div><div class='output co'>#&gt; [1] -1.628174 -2.820079</div><div class='input'><span class='fu'>ilr</span>(<span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='fl'>10</span>, <span class='fl'>1</span>, <span class='fl'>0.1</span>))</div><div class='output co'>#&gt; [1] 1.628174 2.820079</div><div class='input'><span class='co'># Equal entries give ilr transformations with zeros as elements</span>
-<span class='fu'>ilr</span>(<span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='fl'>3</span>, <span class='fl'>3</span>, <span class='fl'>3</span>))</div><div class='output co'>#&gt; [1] 0 0</div><div class='input'><span class='co'># Almost equal entries give small numbers</span>
-<span class='fu'>ilr</span>(<span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='fl'>0.3</span>, <span class='fl'>0.4</span>, <span class='fl'>0.3</span>))</div><div class='output co'>#&gt; [1] -0.2034219  0.1174457</div><div class='input'><span class='co'># Only the ratio between the numbers counts, not their sum</span>
-<span class='fu'>invilr</span>(<span class='fu'>ilr</span>(<span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='fl'>0.7</span>, <span class='fl'>0.29</span>, <span class='fl'>0.01</span>)))</div><div class='output co'>#&gt; [1] 0.70 0.29 0.01</div><div class='input'><span class='fu'>invilr</span>(<span class='fu'>ilr</span>(<span class='fl'>2.1</span> * <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='fl'>0.7</span>, <span class='fl'>0.29</span>, <span class='fl'>0.01</span>)))</div><div class='output co'>#&gt; [1] 0.70 0.29 0.01</div><div class='input'><span class='co'># Inverse transformation of larger numbers gives unequal elements</span>
-<span class='fu'>invilr</span>(-<span class='fl'>10</span>)</div><div class='output co'>#&gt; [1] 7.213536e-07 9.999993e-01</div><div class='input'><span class='fu'>invilr</span>(<span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(-<span class='fl'>10</span>, <span class='fl'>0</span>))</div><div class='output co'>#&gt; [1] 7.207415e-07 9.991507e-01 8.486044e-04</div><div class='input'><span class='co'># The sum of the elements of the inverse ilr is 1</span>
-<span class='fu'><a href='https://rdrr.io/r/base/sum.html'>sum</a></span>(<span class='fu'>invilr</span>(<span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(-<span class='fl'>10</span>, <span class='fl'>0</span>)))</div><div class='output co'>#&gt; [1] 1</div><div class='input'><span class='co'># This is why we do not need all elements of the inverse transformation to go back:</span>
-<span class='no'>a</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='fl'>0.1</span>, <span class='fl'>0.3</span>, <span class='fl'>0.5</span>)
-<span class='no'>b</span> <span class='kw'>&lt;-</span> <span class='fu'>invilr</span>(<span class='no'>a</span>)
-<span class='fu'><a href='https://rdrr.io/r/base/length.html'>length</a></span>(<span class='no'>b</span>) <span class='co'># Four elements</span></div><div class='output co'>#&gt; [1] 4</div><div class='input'><span class='fu'>ilr</span>(<span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='no'>b</span>[<span class='fl'>1</span>:<span class='fl'>3</span>], <span class='fl'>1</span> - <span class='fu'><a href='https://rdrr.io/r/base/sum.html'>sum</a></span>(<span class='no'>b</span>[<span class='fl'>1</span>:<span class='fl'>3</span>]))) <span class='co'># Gives c(0.1, 0.3, 0.5)</span></div><div class='output co'>#&gt; [1] 0.1 0.3 0.5</div><div class='input'>
+<span class='fu'>ilr</span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>0.1</span>, <span class='fl'>1</span>, <span class='fl'>10</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; [1] -1.628174 -2.820079</div><div class='input'><span class='fu'>ilr</span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>10</span>, <span class='fl'>1</span>, <span class='fl'>0.1</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; [1] 1.628174 2.820079</div><div class='input'><span class='co'># Equal entries give ilr transformations with zeros as elements</span>
+<span class='fu'>ilr</span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>3</span>, <span class='fl'>3</span>, <span class='fl'>3</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; [1] 0 0</div><div class='input'><span class='co'># Almost equal entries give small numbers</span>
+<span class='fu'>ilr</span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>0.3</span>, <span class='fl'>0.4</span>, <span class='fl'>0.3</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; [1] -0.2034219  0.1174457</div><div class='input'><span class='co'># Only the ratio between the numbers counts, not their sum</span>
+<span class='fu'>invilr</span><span class='op'>(</span><span class='fu'>ilr</span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>0.7</span>, <span class='fl'>0.29</span>, <span class='fl'>0.01</span><span class='op'>)</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; [1] 0.70 0.29 0.01</div><div class='input'><span class='fu'>invilr</span><span class='op'>(</span><span class='fu'>ilr</span><span class='op'>(</span><span class='fl'>2.1</span> <span class='op'>*</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>0.7</span>, <span class='fl'>0.29</span>, <span class='fl'>0.01</span><span class='op'>)</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; [1] 0.70 0.29 0.01</div><div class='input'><span class='co'># Inverse transformation of larger numbers gives unequal elements</span>
+<span class='fu'>invilr</span><span class='op'>(</span><span class='op'>-</span><span class='fl'>10</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; [1] 7.213536e-07 9.999993e-01</div><div class='input'><span class='fu'>invilr</span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='op'>-</span><span class='fl'>10</span>, <span class='fl'>0</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; [1] 7.207415e-07 9.991507e-01 8.486044e-04</div><div class='input'><span class='co'># The sum of the elements of the inverse ilr is 1</span>
+<span class='fu'><a href='https://rdrr.io/r/base/sum.html'>sum</a></span><span class='op'>(</span><span class='fu'>invilr</span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='op'>-</span><span class='fl'>10</span>, <span class='fl'>0</span><span class='op'>)</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; [1] 1</div><div class='input'><span class='co'># This is why we do not need all elements of the inverse transformation to go back:</span>
+<span class='va'>a</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>0.1</span>, <span class='fl'>0.3</span>, <span class='fl'>0.5</span><span class='op'>)</span>
+<span class='va'>b</span> <span class='op'>&lt;-</span> <span class='fu'>invilr</span><span class='op'>(</span><span class='va'>a</span><span class='op'>)</span>
+<span class='fu'><a href='https://rdrr.io/r/base/length.html'>length</a></span><span class='op'>(</span><span class='va'>b</span><span class='op'>)</span> <span class='co'># Four elements</span>
+</div><div class='output co'>#&gt; [1] 4</div><div class='input'><span class='fu'>ilr</span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='va'>b</span><span class='op'>[</span><span class='fl'>1</span><span class='op'>:</span><span class='fl'>3</span><span class='op'>]</span>, <span class='fl'>1</span> <span class='op'>-</span> <span class='fu'><a href='https://rdrr.io/r/base/sum.html'>sum</a></span><span class='op'>(</span><span class='va'>b</span><span class='op'>[</span><span class='fl'>1</span><span class='op'>:</span><span class='fl'>3</span><span class='op'>]</span><span class='op'>)</span><span class='op'>)</span><span class='op'>)</span> <span class='co'># Gives c(0.1, 0.3, 0.5)</span>
+</div><div class='output co'>#&gt; [1] 0.1 0.3 0.5</div><div class='input'>
 </div></pre>
   </div>
   <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
@@ -202,7 +219,7 @@ Compositional Data Using Robust Methods. Math Geosci 40 233-248</p>
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/index.html b/docs/reference/index.html
index 961352e0..e0d34e8f 100644
--- a/docs/reference/index.html
+++ b/docs/reference/index.html
@@ -71,7 +71,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -108,6 +108,9 @@
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -116,7 +119,7 @@
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -675,7 +678,7 @@ kinetic models fitted with mkinfit</p></td>
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/logLik.mkinfit.html b/docs/reference/logLik.mkinfit.html
index 22561d8a..2b87c95f 100644
--- a/docs/reference/logLik.mkinfit.html
+++ b/docs/reference/logLik.mkinfit.html
@@ -76,7 +76,7 @@ the error model." />
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -113,6 +113,9 @@ the error model." />
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -121,7 +124,7 @@ the error model." />
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -140,7 +143,7 @@ the error model." />
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>Calculated the log-likelihood of a fitted mkinfit object</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/logLik.mkinfit.R'><code>R/logLik.mkinfit.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/logLik.mkinfit.R'><code>R/logLik.mkinfit.R</code></a></small>
     <div class="hidden name"><code>logLik.mkinfit.Rd</code></div>
     </div>
 
@@ -153,7 +156,7 @@ the error model.</p>
     </div>
 
     <pre class="usage"><span class='co'># S3 method for mkinfit</span>
-<span class='fu'><a href='https://rdrr.io/r/stats/logLik.html'>logLik</a></span>(<span class='no'>object</span>, <span class='no'>...</span>)</pre>
+<span class='fu'><a href='https://rdrr.io/r/stats/logLik.html'>logLik</a></span><span class='op'>(</span><span class='va'>object</span>, <span class='va'>...</span><span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
@@ -182,18 +185,26 @@ and the fitted error model parameters.</p>
 
     <div class='dont-index'><p>Compare the AIC of columns of <code><a href='mmkin.html'>mmkin</a></code> objects using
 <code><a href='AIC.mmkin.html'>AIC.mmkin</a></code>.</p></div>
+    <h2 class="hasAnchor" id="author"><a class="anchor" href="#author"></a>Author</h2>
+
+    <p>Johannes Ranke</p>
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
     <pre class="examples"><div class='input'>
   <span class='co'># \dontrun{</span>
-  <span class='no'>sfo_sfo</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(
-    <span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='st'>"m1"</span>),
-    <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>)
-  )</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>  <span class='no'>d_t</span> <span class='kw'>&lt;-</span> <span class='no'>FOCUS_2006_D</span>
-  <span class='no'>f_nw</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>sfo_sfo</span>, <span class='no'>d_t</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>) <span class='co'># no weighting (weights are unity)</span></div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'>  <span class='no'>f_obs</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>sfo_sfo</span>, <span class='no'>d_t</span>, <span class='kw'>error_model</span> <span class='kw'>=</span> <span class='st'>"obs"</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'>  <span class='no'>f_tc</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>sfo_sfo</span>, <span class='no'>d_t</span>, <span class='kw'>error_model</span> <span class='kw'>=</span> <span class='st'>"tc"</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/stats/AIC.html'>AIC</a></span>(<span class='no'>f_nw</span>, <span class='no'>f_obs</span>, <span class='no'>f_tc</span>)</div><div class='output co'>#&gt;       df      AIC
+  <span class='va'>sfo_sfo</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>
+    parent <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, to <span class='op'>=</span> <span class='st'>"m1"</span><span class='op'>)</span>,
+    m1 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span>
+  <span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>  <span class='va'>d_t</span> <span class='op'>&lt;-</span> <span class='va'>FOCUS_2006_D</span>
+  <span class='va'>f_nw</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='va'>sfo_sfo</span>, <span class='va'>d_t</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span> <span class='co'># no weighting (weights are unity)</span>
+</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.0165</span></div><div class='input'>  <span class='va'>f_obs</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='va'>sfo_sfo</span>, <span class='va'>d_t</span>, error_model <span class='op'>=</span> <span class='st'>"obs"</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'>  <span class='va'>f_tc</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='va'>sfo_sfo</span>, <span class='va'>d_t</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/stats/AIC.html'>AIC</a></span><span class='op'>(</span><span class='va'>f_nw</span>, <span class='va'>f_obs</span>, <span class='va'>f_tc</span><span class='op'>)</span>
+</div><div class='output co'>#&gt;       df      AIC
 #&gt; f_nw   5 204.4486
 #&gt; f_obs  6 205.8727
-#&gt; f_tc   6 141.9656</div><div class='input'>  # }
+#&gt; f_tc   6 141.9656</div><div class='input'>  <span class='co'># }</span>
 
 </div></pre>
   </div>
@@ -211,7 +222,7 @@ and the fitted error model parameters.</p>
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/logistic.solution-1.png b/docs/reference/logistic.solution-1.png
index fd11d0c0..84d8e722 100644
--- a/docs/reference/logistic.solution-1.png
+++ b/docs/reference/logistic.solution-1.png
diff --git a/docs/reference/logistic.solution-2.png b/docs/reference/logistic.solution-2.png
index 78a31f93..764996df 100644
--- a/docs/reference/logistic.solution-2.png
+++ b/docs/reference/logistic.solution-2.png
diff --git a/docs/reference/logistic.solution.html b/docs/reference/logistic.solution.html
index 87dc78a9..97c98a4a 100644
--- a/docs/reference/logistic.solution.html
+++ b/docs/reference/logistic.solution.html
@@ -73,7 +73,7 @@ an increasing rate constant, supposedly caused by microbial growth" />
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -110,6 +110,9 @@ an increasing rate constant, supposedly caused by microbial growth" />
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -118,7 +121,7 @@ an increasing rate constant, supposedly caused by microbial growth" />
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -137,7 +140,7 @@ an increasing rate constant, supposedly caused by microbial growth" />
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>Logistic kinetics</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/parent_solutions.R'><code>R/parent_solutions.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/parent_solutions.R'><code>R/parent_solutions.R</code></a></small>
     <div class="hidden name"><code>logistic.solution.Rd</code></div>
     </div>
 
@@ -146,7 +149,7 @@ an increasing rate constant, supposedly caused by microbial growth" />
 an increasing rate constant, supposedly caused by microbial growth</p>
     </div>
 
-    <pre class="usage"><span class='fu'>logistic.solution</span>(<span class='no'>t</span>, <span class='no'>parent_0</span>, <span class='no'>kmax</span>, <span class='no'>k0</span>, <span class='no'>r</span>)</pre>
+    <pre class="usage"><span class='fu'>logistic.solution</span><span class='op'>(</span><span class='va'>t</span>, <span class='va'>parent_0</span>, <span class='va'>kmax</span>, <span class='va'>k0</span>, <span class='va'>r</span><span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
@@ -205,42 +208,51 @@ Version 1.1, 18 December 2014
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
     <pre class="examples"><div class='input'>
   <span class='co'># Reproduce the plot on page 57 of FOCUS (2014)</span>
-  <span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='kw'>function</span>(<span class='no'>x</span>) <span class='fu'>logistic.solution</span>(<span class='no'>x</span>, <span class='fl'>100</span>, <span class='fl'>0.08</span>, <span class='fl'>0.0001</span>, <span class='fl'>0.2</span>),
-       <span class='kw'>from</span> <span class='kw'>=</span> <span class='fl'>0</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='fl'>100</span>, <span class='kw'>ylim</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='fl'>0</span>, <span class='fl'>100</span>),
-       <span class='kw'>xlab</span> <span class='kw'>=</span> <span class='st'>"Time"</span>, <span class='kw'>ylab</span> <span class='kw'>=</span> <span class='st'>"Residue"</span>)</div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='kw'>function</span>(<span class='no'>x</span>) <span class='fu'>logistic.solution</span>(<span class='no'>x</span>, <span class='fl'>100</span>, <span class='fl'>0.08</span>, <span class='fl'>0.0001</span>, <span class='fl'>0.4</span>),
-       <span class='kw'>from</span> <span class='kw'>=</span> <span class='fl'>0</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='fl'>100</span>, <span class='kw'>add</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>lty</span> <span class='kw'>=</span> <span class='fl'>2</span>, <span class='kw'>col</span> <span class='kw'>=</span> <span class='fl'>2</span>)</div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='kw'>function</span>(<span class='no'>x</span>) <span class='fu'>logistic.solution</span>(<span class='no'>x</span>, <span class='fl'>100</span>, <span class='fl'>0.08</span>, <span class='fl'>0.0001</span>, <span class='fl'>0.8</span>),
-       <span class='kw'>from</span> <span class='kw'>=</span> <span class='fl'>0</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='fl'>100</span>, <span class='kw'>add</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>lty</span> <span class='kw'>=</span> <span class='fl'>3</span>, <span class='kw'>col</span> <span class='kw'>=</span> <span class='fl'>3</span>)</div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='kw'>function</span>(<span class='no'>x</span>) <span class='fu'>logistic.solution</span>(<span class='no'>x</span>, <span class='fl'>100</span>, <span class='fl'>0.08</span>, <span class='fl'>0.001</span>, <span class='fl'>0.2</span>),
-       <span class='kw'>from</span> <span class='kw'>=</span> <span class='fl'>0</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='fl'>100</span>, <span class='kw'>add</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>lty</span> <span class='kw'>=</span> <span class='fl'>4</span>, <span class='kw'>col</span> <span class='kw'>=</span> <span class='fl'>4</span>)</div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='kw'>function</span>(<span class='no'>x</span>) <span class='fu'>logistic.solution</span>(<span class='no'>x</span>, <span class='fl'>100</span>, <span class='fl'>0.08</span>, <span class='fl'>0.08</span>, <span class='fl'>0.2</span>),
-       <span class='kw'>from</span> <span class='kw'>=</span> <span class='fl'>0</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='fl'>100</span>, <span class='kw'>add</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>lty</span> <span class='kw'>=</span> <span class='fl'>5</span>, <span class='kw'>col</span> <span class='kw'>=</span> <span class='fl'>5</span>)</div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/graphics/legend.html'>legend</a></span>(<span class='st'>"topright"</span>, <span class='kw'>inset</span> <span class='kw'>=</span> <span class='fl'>0.05</span>,
-         <span class='kw'>legend</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/paste.html'>paste0</a></span>(<span class='st'>"k0 = "</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='fl'>0.0001</span>, <span class='fl'>0.0001</span>, <span class='fl'>0.0001</span>, <span class='fl'>0.001</span>, <span class='fl'>0.08</span>),
-                         <span class='st'>", r = "</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='fl'>0.2</span>, <span class='fl'>0.4</span>, <span class='fl'>0.8</span>, <span class='fl'>0.2</span>, <span class='fl'>0.2</span>)),
-         <span class='kw'>lty</span> <span class='kw'>=</span> <span class='fl'>1</span>:<span class='fl'>5</span>, <span class='kw'>col</span> <span class='kw'>=</span> <span class='fl'>1</span>:<span class='fl'>5</span>)</div><div class='img'><img src='logistic.solution-1.png' alt='' width='700' height='433' /></div><div class='input'>
+  <span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='kw'>function</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span> <span class='fu'>logistic.solution</span><span class='op'>(</span><span class='va'>x</span>, <span class='fl'>100</span>, <span class='fl'>0.08</span>, <span class='fl'>0.0001</span>, <span class='fl'>0.2</span><span class='op'>)</span>,
+       from <span class='op'>=</span> <span class='fl'>0</span>, to <span class='op'>=</span> <span class='fl'>100</span>, ylim <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>0</span>, <span class='fl'>100</span><span class='op'>)</span>,
+       xlab <span class='op'>=</span> <span class='st'>"Time"</span>, ylab <span class='op'>=</span> <span class='st'>"Residue"</span><span class='op'>)</span>
+</div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='kw'>function</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span> <span class='fu'>logistic.solution</span><span class='op'>(</span><span class='va'>x</span>, <span class='fl'>100</span>, <span class='fl'>0.08</span>, <span class='fl'>0.0001</span>, <span class='fl'>0.4</span><span class='op'>)</span>,
+       from <span class='op'>=</span> <span class='fl'>0</span>, to <span class='op'>=</span> <span class='fl'>100</span>, add <span class='op'>=</span> <span class='cn'>TRUE</span>, lty <span class='op'>=</span> <span class='fl'>2</span>, col <span class='op'>=</span> <span class='fl'>2</span><span class='op'>)</span>
+</div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='kw'>function</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span> <span class='fu'>logistic.solution</span><span class='op'>(</span><span class='va'>x</span>, <span class='fl'>100</span>, <span class='fl'>0.08</span>, <span class='fl'>0.0001</span>, <span class='fl'>0.8</span><span class='op'>)</span>,
+       from <span class='op'>=</span> <span class='fl'>0</span>, to <span class='op'>=</span> <span class='fl'>100</span>, add <span class='op'>=</span> <span class='cn'>TRUE</span>, lty <span class='op'>=</span> <span class='fl'>3</span>, col <span class='op'>=</span> <span class='fl'>3</span><span class='op'>)</span>
+</div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='kw'>function</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span> <span class='fu'>logistic.solution</span><span class='op'>(</span><span class='va'>x</span>, <span class='fl'>100</span>, <span class='fl'>0.08</span>, <span class='fl'>0.001</span>, <span class='fl'>0.2</span><span class='op'>)</span>,
+       from <span class='op'>=</span> <span class='fl'>0</span>, to <span class='op'>=</span> <span class='fl'>100</span>, add <span class='op'>=</span> <span class='cn'>TRUE</span>, lty <span class='op'>=</span> <span class='fl'>4</span>, col <span class='op'>=</span> <span class='fl'>4</span><span class='op'>)</span>
+</div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='kw'>function</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span> <span class='fu'>logistic.solution</span><span class='op'>(</span><span class='va'>x</span>, <span class='fl'>100</span>, <span class='fl'>0.08</span>, <span class='fl'>0.08</span>, <span class='fl'>0.2</span><span class='op'>)</span>,
+       from <span class='op'>=</span> <span class='fl'>0</span>, to <span class='op'>=</span> <span class='fl'>100</span>, add <span class='op'>=</span> <span class='cn'>TRUE</span>, lty <span class='op'>=</span> <span class='fl'>5</span>, col <span class='op'>=</span> <span class='fl'>5</span><span class='op'>)</span>
+</div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/graphics/legend.html'>legend</a></span><span class='op'>(</span><span class='st'>"topright"</span>, inset <span class='op'>=</span> <span class='fl'>0.05</span>,
+         legend <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/paste.html'>paste0</a></span><span class='op'>(</span><span class='st'>"k0 = "</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>0.0001</span>, <span class='fl'>0.0001</span>, <span class='fl'>0.0001</span>, <span class='fl'>0.001</span>, <span class='fl'>0.08</span><span class='op'>)</span>,
+                         <span class='st'>", r = "</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>0.2</span>, <span class='fl'>0.4</span>, <span class='fl'>0.8</span>, <span class='fl'>0.2</span>, <span class='fl'>0.2</span><span class='op'>)</span><span class='op'>)</span>,
+         lty <span class='op'>=</span> <span class='fl'>1</span><span class='op'>:</span><span class='fl'>5</span>, col <span class='op'>=</span> <span class='fl'>1</span><span class='op'>:</span><span class='fl'>5</span><span class='op'>)</span>
+</div><div class='img'><img src='logistic.solution-1.png' alt='' width='700' height='433' /></div><div class='input'>
   <span class='co'># Fit with synthetic data</span>
-  <span class='no'>logistic</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"logistic"</span>))
-
-  <span class='no'>sampling_times</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='fl'>0</span>, <span class='fl'>1</span>, <span class='fl'>3</span>, <span class='fl'>7</span>, <span class='fl'>14</span>, <span class='fl'>28</span>, <span class='fl'>60</span>, <span class='fl'>90</span>, <span class='fl'>120</span>)
-  <span class='no'>parms_logistic</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>kmax</span> <span class='kw'>=</span> <span class='fl'>0.08</span>, <span class='kw'>k0</span> <span class='kw'>=</span> <span class='fl'>0.0001</span>, <span class='kw'>r</span> <span class='kw'>=</span> <span class='fl'>0.2</span>)
-  <span class='no'>d_logistic</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinpredict.html'>mkinpredict</a></span>(<span class='no'>logistic</span>,
-    <span class='no'>parms_logistic</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fl'>100</span>),
-    <span class='no'>sampling_times</span>)
-  <span class='no'>d_2_1</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='add_err.html'>add_err</a></span>(<span class='no'>d_logistic</span>,
-    <span class='kw'>sdfunc</span> <span class='kw'>=</span> <span class='kw'>function</span>(<span class='no'>x</span>) <span class='fu'><a href='sigma_twocomp.html'>sigma_twocomp</a></span>(<span class='no'>x</span>, <span class='fl'>0.5</span>, <span class='fl'>0.07</span>),
-    <span class='kw'>n</span> <span class='kw'>=</span> <span class='fl'>1</span>, <span class='kw'>reps</span> <span class='kw'>=</span> <span class='fl'>2</span>, <span class='kw'>digits</span> <span class='kw'>=</span> <span class='fl'>5</span>, <span class='kw'>LOD</span> <span class='kw'>=</span> <span class='fl'>0.1</span>, <span class='kw'>seed</span> <span class='kw'>=</span> <span class='fl'>123456</span>)<span class='kw'>[[</span><span class='fl'>1</span>]]
-
-  <span class='no'>m</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='st'>"logistic"</span>, <span class='no'>d_2_1</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-  <span class='fu'><a href='plot.mkinfit.html'>plot_sep</a></span>(<span class='no'>m</span>)</div><div class='img'><img src='logistic.solution-2.png' alt='' width='700' height='433' /></div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span>(<span class='no'>m</span>)$<span class='no'>bpar</span></div><div class='output co'>#&gt;              Estimate   se_notrans   t value       Pr(&gt;t)        Lower
-#&gt; parent_0 1.057896e+02 1.9023449649 55.610120 3.768361e-16 1.016451e+02
-#&gt; kmax     6.398190e-02 0.0143201029  4.467978 3.841828e-04 3.929235e-02
-#&gt; k0       1.612775e-04 0.0005866813  0.274898 3.940351e-01 5.846685e-08
-#&gt; r        2.263946e-01 0.1718110773  1.317695 1.061044e-01 4.335843e-02
+  <span class='va'>logistic</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"logistic"</span><span class='op'>)</span><span class='op'>)</span>
+
+  <span class='va'>sampling_times</span> <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>0</span>, <span class='fl'>1</span>, <span class='fl'>3</span>, <span class='fl'>7</span>, <span class='fl'>14</span>, <span class='fl'>28</span>, <span class='fl'>60</span>, <span class='fl'>90</span>, <span class='fl'>120</span><span class='op'>)</span>
+  <span class='va'>parms_logistic</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>kmax <span class='op'>=</span> <span class='fl'>0.08</span>, k0 <span class='op'>=</span> <span class='fl'>0.0001</span>, r <span class='op'>=</span> <span class='fl'>0.2</span><span class='op'>)</span>
+  <span class='va'>d_logistic</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinpredict.html'>mkinpredict</a></span><span class='op'>(</span><span class='va'>logistic</span>,
+    <span class='va'>parms_logistic</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fl'>100</span><span class='op'>)</span>,
+    <span class='va'>sampling_times</span><span class='op'>)</span>
+  <span class='va'>d_2_1</span> <span class='op'>&lt;-</span> <span class='fu'><a href='add_err.html'>add_err</a></span><span class='op'>(</span><span class='va'>d_logistic</span>,
+    sdfunc <span class='op'>=</span> <span class='kw'>function</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span> <span class='fu'><a href='sigma_twocomp.html'>sigma_twocomp</a></span><span class='op'>(</span><span class='va'>x</span>, <span class='fl'>0.5</span>, <span class='fl'>0.07</span><span class='op'>)</span>,
+    n <span class='op'>=</span> <span class='fl'>1</span>, reps <span class='op'>=</span> <span class='fl'>2</span>, digits <span class='op'>=</span> <span class='fl'>5</span>, LOD <span class='op'>=</span> <span class='fl'>0.1</span>, seed <span class='op'>=</span> <span class='fl'>123456</span><span class='op'>)</span><span class='op'>[[</span><span class='fl'>1</span><span class='op'>]</span><span class='op'>]</span>
+
+  <span class='va'>m</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='st'>"logistic"</span>, <span class='va'>d_2_1</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+  <span class='fu'><a href='plot.mkinfit.html'>plot_sep</a></span><span class='op'>(</span><span class='va'>m</span><span class='op'>)</span>
+</div><div class='img'><img src='logistic.solution-2.png' alt='' width='700' height='433' /></div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span><span class='op'>(</span><span class='va'>m</span><span class='op'>)</span><span class='op'>$</span><span class='va'>bpar</span>
+</div><div class='output co'>#&gt;              Estimate   se_notrans   t value       Pr(&gt;t)        Lower
+#&gt; parent_0 1.057896e+02 1.9023449703 55.610119 3.768361e-16 1.016451e+02
+#&gt; kmax     6.398190e-02 0.0143201031  4.467978 3.841829e-04 3.929235e-02
+#&gt; k0       1.612775e-04 0.0005866813  0.274898 3.940351e-01 5.846688e-08
+#&gt; r        2.263946e-01 0.1718110715  1.317695 1.061044e-01 4.335843e-02
 #&gt; sigma    5.332935e+00 0.9145907310  5.830952 4.036926e-05 3.340213e+00
 #&gt;                Upper
 #&gt; parent_0 109.9341588
 #&gt; kmax       0.1041853
-#&gt; k0         0.4448750
-#&gt; r          1.1821121
-#&gt; sigma      7.3256566</div><div class='input'>  <span class='fu'><a href='endpoints.html'>endpoints</a></span>(<span class='no'>m</span>)$<span class='no'>distimes</span></div><div class='output co'>#&gt;            DT50     DT90  DT50_k0 DT50_kmax
-#&gt; parent 36.86533 62.41511 4297.854  10.83349</div><div class='input'>
+#&gt; k0         0.4448749
+#&gt; r          1.1821120
+#&gt; sigma      7.3256566</div><div class='input'>  <span class='fu'><a href='endpoints.html'>endpoints</a></span><span class='op'>(</span><span class='va'>m</span><span class='op'>)</span><span class='op'>$</span><span class='va'>distimes</span>
+</div><div class='output co'>#&gt;            DT50     DT90  DT50_k0 DT50_kmax
+#&gt; parent 36.86533 62.41511 4297.853  10.83349</div><div class='input'>
 </div></pre>
   </div>
   <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
@@ -257,7 +269,7 @@ Version 1.1, 18 December 2014
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/max_twa_parent.html b/docs/reference/max_twa_parent.html
index ada54cba..8e584375 100644
--- a/docs/reference/max_twa_parent.html
+++ b/docs/reference/max_twa_parent.html
@@ -78,7 +78,7 @@ soil section of the FOCUS guidance." />
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -115,6 +115,9 @@ soil section of the FOCUS guidance." />
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -123,7 +126,7 @@ soil section of the FOCUS guidance." />
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -143,7 +146,7 @@ soil section of the FOCUS guidance." />
     <div class="page-header">
     <h1>Function to calculate maximum time weighted average concentrations from
 kinetic models fitted with mkinfit</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/max_twa_parent.R'><code>R/max_twa_parent.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/max_twa_parent.R'><code>R/max_twa_parent.R</code></a></small>
     <div class="hidden name"><code>max_twa_parent.Rd</code></div>
     </div>
 
@@ -155,15 +158,15 @@ FOMC, DFOP and HS models, using the analytical formulas given in the PEC
 soil section of the FOCUS guidance.</p>
     </div>
 
-    <pre class="usage"><span class='fu'>max_twa_parent</span>(<span class='no'>fit</span>, <span class='no'>windows</span>)
+    <pre class="usage"><span class='fu'>max_twa_parent</span><span class='op'>(</span><span class='va'>fit</span>, <span class='va'>windows</span><span class='op'>)</span>
 
-<span class='fu'>max_twa_sfo</span>(<span class='kw'>M0</span> <span class='kw'>=</span> <span class='fl'>1</span>, <span class='no'>k</span>, <span class='no'>t</span>)
+<span class='fu'>max_twa_sfo</span><span class='op'>(</span>M0 <span class='op'>=</span> <span class='fl'>1</span>, <span class='va'>k</span>, <span class='va'>t</span><span class='op'>)</span>
 
-<span class='fu'>max_twa_fomc</span>(<span class='kw'>M0</span> <span class='kw'>=</span> <span class='fl'>1</span>, <span class='no'>alpha</span>, <span class='no'>beta</span>, <span class='no'>t</span>)
+<span class='fu'>max_twa_fomc</span><span class='op'>(</span>M0 <span class='op'>=</span> <span class='fl'>1</span>, <span class='va'>alpha</span>, <span class='va'>beta</span>, <span class='va'>t</span><span class='op'>)</span>
 
-<span class='fu'>max_twa_dfop</span>(<span class='kw'>M0</span> <span class='kw'>=</span> <span class='fl'>1</span>, <span class='no'>k1</span>, <span class='no'>k2</span>, <span class='no'>g</span>, <span class='no'>t</span>)
+<span class='fu'>max_twa_dfop</span><span class='op'>(</span>M0 <span class='op'>=</span> <span class='fl'>1</span>, <span class='va'>k1</span>, <span class='va'>k2</span>, <span class='va'>g</span>, <span class='va'>t</span><span class='op'>)</span>
 
-<span class='fu'>max_twa_hs</span>(<span class='kw'>M0</span> <span class='kw'>=</span> <span class='fl'>1</span>, <span class='no'>k1</span>, <span class='no'>k2</span>, <span class='no'>tb</span>, <span class='no'>t</span>)</pre>
+<span class='fu'>max_twa_hs</span><span class='op'>(</span>M0 <span class='op'>=</span> <span class='fl'>1</span>, <span class='va'>k1</span>, <span class='va'>k2</span>, <span class='va'>tb</span>, <span class='va'>t</span><span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
@@ -230,11 +233,15 @@ and Degradation Kinetics from Environmental Fate Studies on Pesticides in
 EU Registration&#8221; Report of the FOCUS Work Group on Degradation Kinetics,
 EC Document Reference Sanco/10058/2005 version 2.0, 434 pp,
 <a href='http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics'>http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a></p>
+    <h2 class="hasAnchor" id="author"><a class="anchor" href="#author"></a>Author</h2>
+
+    <p>Johannes Ranke</p>
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
     <pre class="examples"><div class='input'>
-  <span class='no'>fit</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='st'>"FOMC"</span>, <span class='no'>FOCUS_2006_C</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-  <span class='fu'>max_twa_parent</span>(<span class='no'>fit</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='fl'>7</span>, <span class='fl'>21</span>))</div><div class='output co'>#&gt;        7       21 
+  <span class='va'>fit</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='st'>"FOMC"</span>, <span class='va'>FOCUS_2006_C</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+  <span class='fu'>max_twa_parent</span><span class='op'>(</span><span class='va'>fit</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>7</span>, <span class='fl'>21</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='output co'>#&gt;        7       21 
 #&gt; 34.71343 18.22124 </div><div class='input'>
 </div></pre>
   </div>
@@ -252,7 +259,7 @@ EC Document Reference Sanco/10058/2005 version 2.0, 434 pp,
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/mccall81_245T.html b/docs/reference/mccall81_245T.html
index b2402e04..b8adde34 100644
--- a/docs/reference/mccall81_245T.html
+++ b/docs/reference/mccall81_245T.html
@@ -74,7 +74,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -111,6 +111,9 @@
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -119,7 +122,7 @@
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -148,12 +151,12 @@
  extracts.</p>
     </div>
 
-    <pre class="usage"><span class='no'>mccall81_245T</span></pre>
+    <pre class="usage"><span class='va'>mccall81_245T</span></pre>
 
 
     <h2 class="hasAnchor" id="format"><a class="anchor" href="#format"></a>Format</h2>
 
-    <p>A dataframe containing the following variables.</p><dl'>
+    <p>A dataframe containing the following variables.</p><dl>
     <dt><code>name</code></dt><dd><p>the name of the compound observed. Note that T245 is used as
                        an acronym for 2,4,5-T. T245 is a legitimate object name
                        in R, which is necessary for specifying models using
@@ -171,27 +174,31 @@
   <a href='http://dx.doi.org/10.1021/jf00103a026'>http://dx.doi.org/10.1021/jf00103a026</a></p>
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
-    <pre class="examples"><div class='input'>  <span class='no'>SFO_SFO_SFO</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>T245</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='st'>"phenol"</span>),
-                         <span class='kw'>phenol</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='st'>"anisole"</span>),
-                         <span class='kw'>anisole</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>))</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>  <span class='co'># \dontrun{</span>
-    <span class='no'>fit.1</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>SFO_SFO_SFO</span>, <span class='fu'><a href='https://rdrr.io/r/base/subset.html'>subset</a></span>(<span class='no'>mccall81_245T</span>, <span class='no'>soil</span> <span class='kw'>==</span> <span class='st'>"Commerce"</span>), <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'>    <span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span>(<span class='no'>fit.1</span>)$<span class='no'>bpar</span></div><div class='output co'>#&gt;                         Estimate  se_notrans   t value       Pr(&gt;t)
-#&gt; T245_0              1.038550e+02 2.184707509 47.537272 4.472189e-18
+    <pre class="examples"><div class='input'>  <span class='va'>SFO_SFO_SFO</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>T245 <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>type <span class='op'>=</span> <span class='st'>"SFO"</span>, to <span class='op'>=</span> <span class='st'>"phenol"</span><span class='op'>)</span>,
+                         phenol <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>type <span class='op'>=</span> <span class='st'>"SFO"</span>, to <span class='op'>=</span> <span class='st'>"anisole"</span><span class='op'>)</span>,
+                         anisole <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>type <span class='op'>=</span> <span class='st'>"SFO"</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>  <span class='co'># \dontrun{</span>
+    <span class='va'>fit.1</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='va'>SFO_SFO_SFO</span>, <span class='fu'><a href='https://rdrr.io/r/base/subset.html'>subset</a></span><span class='op'>(</span><span class='va'>mccall81_245T</span>, <span class='va'>soil</span> <span class='op'>==</span> <span class='st'>"Commerce"</span><span class='op'>)</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'>    <span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span><span class='op'>(</span><span class='va'>fit.1</span><span class='op'>)</span><span class='op'>$</span><span class='va'>bpar</span>
+</div><div class='output co'>#&gt;                         Estimate  se_notrans   t value       Pr(&gt;t)
+#&gt; T245_0              1.038550e+02 2.184707514 47.537272 4.472189e-18
 #&gt; k_T245              4.337042e-02 0.001898397 22.845818 2.276912e-13
-#&gt; k_phenol            4.050581e-01 0.298699410  1.356073 9.756993e-02
+#&gt; k_phenol            4.050581e-01 0.298699428  1.356073 9.756994e-02
 #&gt; k_anisole           6.678742e-03 0.000802144  8.326114 2.623179e-07
-#&gt; f_T245_to_phenol    6.227599e-01 0.398534147  1.562626 6.949418e-02
-#&gt; f_phenol_to_anisole 1.000000e+00 0.671844135  1.488440 7.867793e-02
-#&gt; sigma               2.514628e+00 0.490755933  5.123989 6.233163e-05
+#&gt; f_T245_to_phenol    6.227599e-01 0.398534167  1.562626 6.949418e-02
+#&gt; f_phenol_to_anisole 1.000000e+00 0.671844168  1.488440 7.867794e-02
+#&gt; sigma               2.514628e+00 0.490755943  5.123989 6.233164e-05
 #&gt;                            Lower        Upper
-#&gt; T245_0              99.246061427 1.084640e+02
+#&gt; T245_0              99.246061371 1.084640e+02
 #&gt; k_T245               0.039631621 4.746194e-02
 #&gt; k_phenol             0.218013878 7.525762e-01
 #&gt; k_anisole            0.005370739 8.305299e-03
 #&gt; f_T245_to_phenol     0.547559082 6.924813e-01
 #&gt; f_phenol_to_anisole  0.000000000 1.000000e+00
-#&gt; sigma                1.706607296 3.322649e+00</div><div class='input'>    <span class='fu'><a href='endpoints.html'>endpoints</a></span>(<span class='no'>fit.1</span>)</div><div class='output co'>#&gt; $ff
+#&gt; sigma                1.706607296 3.322649e+00</div><div class='input'>    <span class='fu'><a href='endpoints.html'>endpoints</a></span><span class='op'>(</span><span class='va'>fit.1</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; $ff
 #&gt;    T245_phenol      T245_sink phenol_anisole    phenol_sink 
-#&gt;   6.227599e-01   3.772401e-01   1.000000e+00   1.005127e-10 
+#&gt;   6.227599e-01   3.772401e-01   1.000000e+00   1.748047e-10 
 #&gt; 
 #&gt; $distimes
 #&gt;               DT50      DT90
@@ -199,18 +206,22 @@
 #&gt; phenol    1.711229   5.68458
 #&gt; anisole 103.784092 344.76329
 #&gt; </div><div class='input'>    <span class='co'># k_phenol_sink is really small, therefore fix it to zero</span>
-    <span class='no'>fit.2</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>SFO_SFO_SFO</span>, <span class='fu'><a href='https://rdrr.io/r/base/subset.html'>subset</a></span>(<span class='no'>mccall81_245T</span>, <span class='no'>soil</span> <span class='kw'>==</span> <span class='st'>"Commerce"</span>),
-                   <span class='kw'>parms.ini</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>k_phenol_sink</span> <span class='kw'>=</span> <span class='fl'>0</span>),
-                   <span class='kw'>fixed_parms</span> <span class='kw'>=</span> <span class='st'>"k_phenol_sink"</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='output co'>#&gt; <span class='warning'>Warning: Initial parameter(s) k_phenol_sink not used in the model</span></div><div class='output co'>#&gt; <span class='error'>Error in data.frame(value = c(state.ini.fixed, parms.fixed)): row names contain missing values</span></div><div class='input'>    <span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span>(<span class='no'>fit.2</span>)$<span class='no'>bpar</span></div><div class='output co'>#&gt; <span class='error'>Error in summary(fit.2): object 'fit.2' not found</span></div><div class='input'>    <span class='fu'><a href='endpoints.html'>endpoints</a></span>(<span class='no'>fit.1</span>)</div><div class='output co'>#&gt; $ff
+    <span class='va'>fit.2</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='va'>SFO_SFO_SFO</span>, <span class='fu'><a href='https://rdrr.io/r/base/subset.html'>subset</a></span><span class='op'>(</span><span class='va'>mccall81_245T</span>, <span class='va'>soil</span> <span class='op'>==</span> <span class='st'>"Commerce"</span><span class='op'>)</span>,
+                   parms.ini <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>k_phenol_sink <span class='op'>=</span> <span class='fl'>0</span><span class='op'>)</span>,
+                   fixed_parms <span class='op'>=</span> <span class='st'>"k_phenol_sink"</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='output co'>#&gt; <span class='warning'>Warning: Initial parameter(s) k_phenol_sink not used in the model</span></div><div class='output co'>#&gt; <span class='error'>Error in data.frame(value = c(state.ini.fixed, parms.fixed)): row names contain missing values</span></div><div class='input'>    <span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span><span class='op'>(</span><span class='va'>fit.2</span><span class='op'>)</span><span class='op'>$</span><span class='va'>bpar</span>
+</div><div class='output co'>#&gt; <span class='error'>Error in summary(fit.2): object 'fit.2' not found</span></div><div class='input'>    <span class='fu'><a href='endpoints.html'>endpoints</a></span><span class='op'>(</span><span class='va'>fit.1</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; $ff
 #&gt;    T245_phenol      T245_sink phenol_anisole    phenol_sink 
-#&gt;   6.227599e-01   3.772401e-01   1.000000e+00   1.005127e-10 
+#&gt;   6.227599e-01   3.772401e-01   1.000000e+00   1.748047e-10 
 #&gt; 
 #&gt; $distimes
 #&gt;               DT50      DT90
 #&gt; T245     15.982025  53.09114
 #&gt; phenol    1.711229   5.68458
 #&gt; anisole 103.784092 344.76329
-#&gt; </div><div class='input'>    <span class='fu'><a href='plot.mkinfit.html'>plot_sep</a></span>(<span class='no'>fit.2</span>)</div><div class='output co'>#&gt; <span class='error'>Error in identical(fit$err_mod, "const"): object 'fit.2' not found</span></div><div class='input'>  # }
+#&gt; </div><div class='input'>    <span class='fu'><a href='plot.mkinfit.html'>plot_sep</a></span><span class='op'>(</span><span class='va'>fit.2</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='error'>Error in identical(fit$err_mod, "const"): object 'fit.2' not found</span></div><div class='input'>  <span class='co'># }</span>
 </div></pre>
   </div>
   <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
@@ -227,7 +238,7 @@
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/mkinds.html b/docs/reference/mkinds.html
index 2e52a95d..1fa1bca5 100644
--- a/docs/reference/mkinds.html
+++ b/docs/reference/mkinds.html
@@ -75,7 +75,7 @@ provided by this package come as mkinds objects nevertheless." />
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -112,6 +112,9 @@ provided by this package come as mkinds objects nevertheless." />
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -120,7 +123,7 @@ provided by this package come as mkinds objects nevertheless." />
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -139,7 +142,7 @@ provided by this package come as mkinds objects nevertheless." />
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>A dataset class for mkin</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/mkinds.R'><code>R/mkinds.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/mkinds.R'><code>R/mkinds.R</code></a></small>
     <div class="hidden name"><code>mkinds.Rd</code></div>
     </div>
 
@@ -157,7 +160,7 @@ provided by this package come as mkinds objects nevertheless.</p>
     <div class='dont-index'><p>The S3 printing method <code><a href='print.mkinds.html'>print.mkinds</a></code></p></div>
     <h2 class="hasAnchor" id="public-fields"><a class="anchor" href="#public-fields"></a>Public fields</h2>
 
-    <p><div class="r6-fields"></p><dl'>
+    <p><div class="r6-fields"></p><dl>
 <dt><code>title</code></dt><dd><p>A full title for the dataset</p></dd>
 
 <dt><code>sampling_times</code></dt><dd><p>The sampling times</p></dd>
@@ -177,19 +180,19 @@ and value in order to be compatible with mkinfit</p></dd>
     <h2 class="hasAnchor" id="methods"><a class="anchor" href="#methods"></a>Methods</h2>
 
     
-<h3>Public methods</h3>
+<h3 class='hasAnchor' id='arguments'><a class='anchor' href='#arguments'></a>Public methods</h3>
 
 <ul>
 <li><p><a href='#method-new'><code>mkinds$new()</code></a></p></li>
 <li><p><a href='#method-clone'><code>mkinds$clone()</code></a></p></li>
 </ul>
 <p><hr>
-<a id="method-new"></a></p><h3>Method <code>new()</code></h3>
-<p>Create a new mkinds object</p><h3>Usage</h3>
-<p><div class="r"></p><pre><span class='no'>mkinds</span>$<span class='fu'>new</span>(<span class='kw'>title</span> <span class='kw'>=</span> <span class='st'>""</span>, <span class='no'>data</span>, <span class='kw'>time_unit</span> <span class='kw'>=</span> <span class='fl'>NA</span>, <span class='kw'>unit</span> <span class='kw'>=</span> <span class='fl'>NA</span>)</pre><p></div></p>
+<a id="method-new"></a></p><h3 class='hasAnchor' id='arguments'><a class='anchor' href='#arguments'></a>Method <code>new()</code></h3>
+<p>Create a new mkinds object</p><h4 class='hasAnchor' id='arguments'><a class='anchor' href='#arguments'></a>Usage</h4>
+<p><div class="r"></p><pre><span class='va'>mkinds</span><span class='op'>$</span><span class='fu'>new</span><span class='op'>(</span>title <span class='op'>=</span> <span class='st'>""</span>, <span class='va'>data</span>, time_unit <span class='op'>=</span> <span class='cn'>NA</span>, unit <span class='op'>=</span> <span class='cn'>NA</span><span class='op'>)</span></pre><p></div></p>
 
-<h3>Arguments</h3>
-<p><div class="arguments"></p><dl'>
+<h4 class='hasAnchor' id='arguments'><a class='anchor' href='#arguments'></a>Arguments</h4>
+<p><div class="arguments"></p><dl>
 <dt><code>title</code></dt><dd><p>The dataset title</p></dd>
 
 <dt><code>data</code></dt><dd><p>The data</p></dd>
@@ -200,12 +203,12 @@ and value in order to be compatible with mkinfit</p></dd>
 
 </dl><p></div></p>
 <p><hr>
-<a id="method-clone"></a></p><h3>Method <code>clone()</code></h3>
-<p>The objects of this class are cloneable with this method.</p><h3>Usage</h3>
-<p><div class="r"></p><pre><span class='no'>mkinds</span>$<span class='fu'>clone</span>(<span class='kw'>deep</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>)</pre><p></div></p>
+<a id="method-clone"></a></p><h3 class='hasAnchor' id='arguments'><a class='anchor' href='#arguments'></a>Method <code>clone()</code></h3>
+<p>The objects of this class are cloneable with this method.</p><h4 class='hasAnchor' id='arguments'><a class='anchor' href='#arguments'></a>Usage</h4>
+<p><div class="r"></p><pre><span class='va'>mkinds</span><span class='op'>$</span><span class='fu'>clone</span><span class='op'>(</span>deep <span class='op'>=</span> <span class='cn'>FALSE</span><span class='op'>)</span></pre><p></div></p>
 
-<h3>Arguments</h3>
-<p><div class="arguments"></p><dl'>
+<h4 class='hasAnchor' id='arguments'><a class='anchor' href='#arguments'></a>Arguments</h4>
+<p><div class="arguments"></p><dl>
 <dt><code>deep</code></dt><dd><p>Whether to make a deep clone.</p></dd>
 
 </dl><p></div></p>
@@ -214,8 +217,9 @@ and value in order to be compatible with mkinfit</p></dd>
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
     <pre class="examples"><div class='input'>
-<span class='no'>mds</span> <span class='kw'>&lt;-</span> <span class='no'>mkinds</span>$<span class='fu'>new</span>(<span class='st'>"FOCUS A"</span>, <span class='no'>FOCUS_2006_A</span>)
-<span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span>(<span class='no'>mds</span>)</div><div class='output co'>#&gt; &lt;mkinds&gt; with $title:  FOCUS A 
+<span class='va'>mds</span> <span class='op'>&lt;-</span> <span class='va'>mkinds</span><span class='op'>$</span><span class='fu'>new</span><span class='op'>(</span><span class='st'>"FOCUS A"</span>, <span class='va'>FOCUS_2006_A</span><span class='op'>)</span>
+<span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span><span class='op'>(</span><span class='va'>mds</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; &lt;mkinds&gt; with $title:  FOCUS A 
 #&gt; Observed compounds $observed:  parent 
 #&gt; Sampling times $sampling_times:  0, 3, 7, 14, 30, 62, 90, 118 
 #&gt; With a maximum of  1  replicates</div><div class='input'>
@@ -235,7 +239,7 @@ and value in order to be compatible with mkinfit</p></dd>
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/mkinerrplot-1.png b/docs/reference/mkinerrplot-1.png
index c5d3495f..8b3240de 100644
--- a/docs/reference/mkinerrplot-1.png
+++ b/docs/reference/mkinerrplot-1.png
diff --git a/docs/reference/mkinerrplot.html b/docs/reference/mkinerrplot.html
index c2be5abf..dfbd88be 100644
--- a/docs/reference/mkinerrplot.html
+++ b/docs/reference/mkinerrplot.html
@@ -76,7 +76,7 @@ using the argument show_errplot = TRUE." />
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -113,6 +113,9 @@ using the argument show_errplot = TRUE." />
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -121,7 +124,7 @@ using the argument show_errplot = TRUE." />
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -140,7 +143,7 @@ using the argument show_errplot = TRUE." />
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>Function to plot squared residuals and the error model for an mkin object</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/mkinerrplot.R'><code>R/mkinerrplot.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/mkinerrplot.R'><code>R/mkinerrplot.R</code></a></small>
     <div class="hidden name"><code>mkinerrplot.Rd</code></div>
     </div>
 
@@ -152,20 +155,20 @@ and this error model plot can be obtained with <code><a href='plot.mkinfit.html'
 using the argument <code>show_errplot = TRUE</code>.</p>
     </div>
 
-    <pre class="usage"><span class='fu'>mkinerrplot</span>(
-  <span class='no'>object</span>,
-  <span class='kw'>obs_vars</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/names.html'>names</a></span>(<span class='no'>object</span>$<span class='no'>mkinmod</span>$<span class='no'>map</span>),
-  <span class='kw'>xlim</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='fl'>0</span>, <span class='fl'>1.1</span> * <span class='fu'><a href='https://rdrr.io/r/base/Extremes.html'>max</a></span>(<span class='no'>object</span>$<span class='no'>data</span>$<span class='no'>predicted</span>)),
-  <span class='kw'>xlab</span> <span class='kw'>=</span> <span class='st'>"Predicted"</span>,
-  <span class='kw'>ylab</span> <span class='kw'>=</span> <span class='st'>"Squared residual"</span>,
-  <span class='kw'>maxy</span> <span class='kw'>=</span> <span class='st'>"auto"</span>,
-  <span class='kw'>legend</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>,
-  <span class='kw'>lpos</span> <span class='kw'>=</span> <span class='st'>"topright"</span>,
-  <span class='kw'>col_obs</span> <span class='kw'>=</span> <span class='st'>"auto"</span>,
-  <span class='kw'>pch_obs</span> <span class='kw'>=</span> <span class='st'>"auto"</span>,
-  <span class='kw'>frame</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>,
-  <span class='no'>...</span>
-)</pre>
+    <pre class="usage"><span class='fu'>mkinerrplot</span><span class='op'>(</span>
+  <span class='va'>object</span>,
+  obs_vars <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/names.html'>names</a></span><span class='op'>(</span><span class='va'>object</span><span class='op'>$</span><span class='va'>mkinmod</span><span class='op'>$</span><span class='va'>map</span><span class='op'>)</span>,
+  xlim <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>0</span>, <span class='fl'>1.1</span> <span class='op'>*</span> <span class='fu'><a href='https://rdrr.io/r/base/Extremes.html'>max</a></span><span class='op'>(</span><span class='va'>object</span><span class='op'>$</span><span class='va'>data</span><span class='op'>$</span><span class='va'>predicted</span><span class='op'>)</span><span class='op'>)</span>,
+  xlab <span class='op'>=</span> <span class='st'>"Predicted"</span>,
+  ylab <span class='op'>=</span> <span class='st'>"Squared residual"</span>,
+  maxy <span class='op'>=</span> <span class='st'>"auto"</span>,
+  legend <span class='op'>=</span> <span class='cn'>TRUE</span>,
+  lpos <span class='op'>=</span> <span class='st'>"topright"</span>,
+  col_obs <span class='op'>=</span> <span class='st'>"auto"</span>,
+  pch_obs <span class='op'>=</span> <span class='st'>"auto"</span>,
+  frame <span class='op'>=</span> <span class='cn'>TRUE</span>,
+  <span class='va'>...</span>
+<span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
@@ -220,7 +223,7 @@ be passed on to <code><a href='https://rdrr.io/r/graphics/legend.html'>legend</a
     </tr>
     <tr>
       <th>...</th>
-      <td><p>further arguments passed to <code><a href='https://rdrr.io/r/base/plot.html'>plot</a></code>.</p></td>
+      <td><p>further arguments passed to <code><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></code>.</p></td>
     </tr>
     </table>
 
@@ -232,11 +235,17 @@ effect, namely to produce a plot.</p>
 
     <div class='dont-index'><p><code><a href='mkinplot.html'>mkinplot</a></code>, for a way to plot the data and the fitted
 lines of the mkinfit object.</p></div>
+    <h2 class="hasAnchor" id="author"><a class="anchor" href="#author"></a>Author</h2>
+
+    <p>Johannes Ranke</p>
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
     <pre class="examples"><div class='input'>
 <span class='co'># \dontrun{</span>
-<span class='no'>model</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>, <span class='st'>"m1"</span>), <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>))</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'><span class='no'>fit</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>model</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>error_model</span> <span class='kw'>=</span> <span class='st'>"tc"</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'><span class='fu'>mkinerrplot</span>(<span class='no'>fit</span>)</div><div class='img'><img src='mkinerrplot-1.png' alt='' width='700' height='433' /></div><div class='input'># }
+<span class='va'>model</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='st'>"m1"</span><span class='op'>)</span>, m1 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'><span class='va'>fit</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='va'>model</span>, <span class='va'>FOCUS_2006_D</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'><span class='fu'>mkinerrplot</span><span class='op'>(</span><span class='va'>fit</span><span class='op'>)</span>
+</div><div class='img'><img src='mkinerrplot-1.png' alt='' width='700' height='433' /></div><div class='input'><span class='co'># }</span>
 
 </div></pre>
   </div>
@@ -254,7 +263,7 @@ lines of the mkinfit object.</p></div>
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/mkinfit.html b/docs/reference/mkinfit.html
index c38c5cca..872b9ab5 100644
--- a/docs/reference/mkinfit.html
+++ b/docs/reference/mkinfit.html
@@ -41,9 +41,11 @@
 
 <meta property="og:title" content="Fit a kinetic model to data with one or more state variables — mkinfit" />
 <meta property="og:description" content="This function maximises the likelihood of the observed data using the Port
-algorithm nlminb, and the specified initial or fixed
+algorithm stats::nlminb(), and the specified initial or fixed
 parameters and starting values.  In each step of the optimisation, the
-kinetic model is solved using the function mkinpredict. The
+kinetic model is solved using the function mkinpredict(), except
+if an analytical solution is implemented, in which case the model is solved
+using the degradation function in the mkinmod object. The
 parameters of the selected error model are fitted simultaneously with the
 degradation model parameters, as both of them are arguments of the
 likelihood function." />
@@ -78,7 +80,7 @@ likelihood function." />
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -115,6 +117,9 @@ likelihood function." />
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -123,7 +128,7 @@ likelihood function." />
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -142,53 +147,55 @@ likelihood function." />
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>Fit a kinetic model to data with one or more state variables</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/mkinfit.R'><code>R/mkinfit.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/mkinfit.R'><code>R/mkinfit.R</code></a></small>
     <div class="hidden name"><code>mkinfit.Rd</code></div>
     </div>
 
     <div class="ref-description">
     <p>This function maximises the likelihood of the observed data using the Port
-algorithm <code><a href='https://rdrr.io/r/stats/nlminb.html'>nlminb</a></code>, and the specified initial or fixed
+algorithm <code><a href='https://rdrr.io/r/stats/nlminb.html'>stats::nlminb()</a></code>, and the specified initial or fixed
 parameters and starting values.  In each step of the optimisation, the
-kinetic model is solved using the function <code><a href='mkinpredict.html'>mkinpredict</a></code>. The
+kinetic model is solved using the function <code><a href='mkinpredict.html'>mkinpredict()</a></code>, except
+if an analytical solution is implemented, in which case the model is solved
+using the degradation function in the <a href='mkinmod.html'>mkinmod</a> object. The
 parameters of the selected error model are fitted simultaneously with the
 degradation model parameters, as both of them are arguments of the
 likelihood function.</p>
     </div>
 
-    <pre class="usage"><span class='fu'>mkinfit</span>(
-  <span class='no'>mkinmod</span>,
-  <span class='no'>observed</span>,
-  <span class='kw'>parms.ini</span> <span class='kw'>=</span> <span class='st'>"auto"</span>,
-  <span class='kw'>state.ini</span> <span class='kw'>=</span> <span class='st'>"auto"</span>,
-  <span class='kw'>err.ini</span> <span class='kw'>=</span> <span class='st'>"auto"</span>,
-  <span class='kw'>fixed_parms</span> <span class='kw'>=</span> <span class='kw'>NULL</span>,
-  <span class='kw'>fixed_initials</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/names.html'>names</a></span>(<span class='no'>mkinmod</span>$<span class='no'>diffs</span>)[-<span class='fl'>1</span>],
-  <span class='kw'>from_max_mean</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>,
-  <span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"auto"</span>, <span class='st'>"analytical"</span>, <span class='st'>"eigen"</span>, <span class='st'>"deSolve"</span>),
-  <span class='kw'>method.ode</span> <span class='kw'>=</span> <span class='st'>"lsoda"</span>,
-  <span class='kw'>use_compiled</span> <span class='kw'>=</span> <span class='st'>"auto"</span>,
-  <span class='kw'>control</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>eval.max</span> <span class='kw'>=</span> <span class='fl'>300</span>, <span class='kw'>iter.max</span> <span class='kw'>=</span> <span class='fl'>200</span>),
-  <span class='kw'>transform_rates</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>,
-  <span class='kw'>transform_fractions</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>,
-  <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>,
-  <span class='kw'>atol</span> <span class='kw'>=</span> <span class='fl'>1e-08</span>,
-  <span class='kw'>rtol</span> <span class='kw'>=</span> <span class='fl'>1e-10</span>,
-  <span class='kw'>error_model</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"const"</span>, <span class='st'>"obs"</span>, <span class='st'>"tc"</span>),
-  <span class='kw'>error_model_algorithm</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"auto"</span>, <span class='st'>"d_3"</span>, <span class='st'>"direct"</span>, <span class='st'>"twostep"</span>, <span class='st'>"threestep"</span>,
-    <span class='st'>"fourstep"</span>, <span class='st'>"IRLS"</span>, <span class='st'>"OLS"</span>),
-  <span class='kw'>reweight.tol</span> <span class='kw'>=</span> <span class='fl'>1e-08</span>,
-  <span class='kw'>reweight.max.iter</span> <span class='kw'>=</span> <span class='fl'>10</span>,
-  <span class='kw'>trace_parms</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>,
-  <span class='no'>...</span>
-)</pre>
+    <pre class="usage"><span class='fu'>mkinfit</span><span class='op'>(</span>
+  <span class='va'>mkinmod</span>,
+  <span class='va'>observed</span>,
+  parms.ini <span class='op'>=</span> <span class='st'>"auto"</span>,
+  state.ini <span class='op'>=</span> <span class='st'>"auto"</span>,
+  err.ini <span class='op'>=</span> <span class='st'>"auto"</span>,
+  fixed_parms <span class='op'>=</span> <span class='cn'>NULL</span>,
+  fixed_initials <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/names.html'>names</a></span><span class='op'>(</span><span class='va'>mkinmod</span><span class='op'>$</span><span class='va'>diffs</span><span class='op'>)</span><span class='op'>[</span><span class='op'>-</span><span class='fl'>1</span><span class='op'>]</span>,
+  from_max_mean <span class='op'>=</span> <span class='cn'>FALSE</span>,
+  solution_type <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"auto"</span>, <span class='st'>"analytical"</span>, <span class='st'>"eigen"</span>, <span class='st'>"deSolve"</span><span class='op'>)</span>,
+  method.ode <span class='op'>=</span> <span class='st'>"lsoda"</span>,
+  use_compiled <span class='op'>=</span> <span class='st'>"auto"</span>,
+  control <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>eval.max <span class='op'>=</span> <span class='fl'>300</span>, iter.max <span class='op'>=</span> <span class='fl'>200</span><span class='op'>)</span>,
+  transform_rates <span class='op'>=</span> <span class='cn'>TRUE</span>,
+  transform_fractions <span class='op'>=</span> <span class='cn'>TRUE</span>,
+  quiet <span class='op'>=</span> <span class='cn'>FALSE</span>,
+  atol <span class='op'>=</span> <span class='fl'>1e-08</span>,
+  rtol <span class='op'>=</span> <span class='fl'>1e-10</span>,
+  error_model <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"const"</span>, <span class='st'>"obs"</span>, <span class='st'>"tc"</span><span class='op'>)</span>,
+  error_model_algorithm <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"auto"</span>, <span class='st'>"d_3"</span>, <span class='st'>"direct"</span>, <span class='st'>"twostep"</span>, <span class='st'>"threestep"</span>,
+    <span class='st'>"fourstep"</span>, <span class='st'>"IRLS"</span>, <span class='st'>"OLS"</span><span class='op'>)</span>,
+  reweight.tol <span class='op'>=</span> <span class='fl'>1e-08</span>,
+  reweight.max.iter <span class='op'>=</span> <span class='fl'>10</span>,
+  trace_parms <span class='op'>=</span> <span class='cn'>FALSE</span>,
+  <span class='va'>...</span>
+<span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
     <colgroup><col class="name" /><col class="desc" /></colgroup>
     <tr>
       <th>mkinmod</th>
-      <td><p>A list of class <code><a href='mkinmod.html'>mkinmod</a></code>, containing the kinetic
+      <td><p>A list of class <a href='mkinmod.html'>mkinmod</a>, containing the kinetic
 model to be fitted to the data, or one of the shorthand names ("SFO",
 "FOMC", "DFOP", "HS", "SFORB", "IORE"). If a shorthand name is given, a
 parent only degradation model is generated for the variable with the
@@ -224,7 +231,7 @@ given below.</p></td>
       <td><p>A named vector of initial values for the state variables of
 the model. In case the observed variables are represented by more than one
 model variable, the names will differ from the names of the observed
-variables (see <code>map</code> component of <code><a href='mkinmod.html'>mkinmod</a></code>). The default
+variables (see <code>map</code> component of <a href='mkinmod.html'>mkinmod</a>). The default
 is to set the initial value of the first model variable to the mean of the
 time zero values for the variable with the maximum observed value, and all
 others to 0.  If this variable has no time zero observations, its initial
@@ -263,30 +270,28 @@ observed mean value is the new time zero.</p></td>
       <td><p>If set to "eigen", the solution of the system of
 differential equations is based on the spectral decomposition of the
 coefficient matrix in cases that this is possible. If set to "deSolve", a
-numerical ode solver from package <code>deSolve</code> is used. If set to
-"analytical", an analytical solution of the model is used. This is only
-implemented for simple degradation experiments with only one state
-variable, i.e. with no metabolites. The default is "auto", which uses
-"analytical" if possible, otherwise "deSolve" if a compiler is present,
-and "eigen" if no compiler is present and the model can be expressed using
-eigenvalues and eigenvectors.  This argument is passed on to the helper
-function <code><a href='mkinpredict.html'>mkinpredict</a></code>.</p></td>
+numerical <a href='https://rdrr.io/pkg/deSolve/man/ode.html'>ode solver from package deSolve</a> is used. If
+set to "analytical", an analytical solution of the model is used. This is
+only implemented for relatively simple degradation models.  The default is
+"auto", which uses "analytical" if possible, otherwise "deSolve" if a
+compiler is present, and "eigen" if no compiler is present and the model
+can be expressed using eigenvalues and eigenvectors.</p></td>
     </tr>
     <tr>
       <th>method.ode</th>
-      <td><p>The solution method passed via <code><a href='mkinpredict.html'>mkinpredict</a></code>
-to <code>ode</code> in case the solution type is "deSolve". The default
+      <td><p>The solution method passed via <code><a href='mkinpredict.html'>mkinpredict()</a></code>
+to <code><a href='https://rdrr.io/pkg/deSolve/man/ode.html'>deSolve::ode()</a></code> in case the solution type is "deSolve". The default
 "lsoda" is performant, but sometimes fails to converge.</p></td>
     </tr>
     <tr>
       <th>use_compiled</th>
       <td><p>If set to <code>FALSE</code>, no compiled version of the
-<code><a href='mkinmod.html'>mkinmod</a></code> model is used in the calls to
-<code><a href='mkinpredict.html'>mkinpredict</a></code> even if a compiled version is present.</p></td>
+<a href='mkinmod.html'>mkinmod</a> model is used in the calls to <code><a href='mkinpredict.html'>mkinpredict()</a></code> even if a compiled
+version is present.</p></td>
     </tr>
     <tr>
       <th>control</th>
-      <td><p>A list of control arguments passed to <code><a href='https://rdrr.io/r/stats/nlminb.html'>nlminb</a></code>.</p></td>
+      <td><p>A list of control arguments passed to <code><a href='https://rdrr.io/r/stats/nlminb.html'>stats::nlminb()</a></code>.</p></td>
     </tr>
     <tr>
       <th>transform_rates</th>
@@ -306,7 +311,7 @@ fitting for better compliance with the assumption of normal distribution
 of the estimator. The default (TRUE) is to do transformations. If TRUE,
 the g parameter of the DFOP and HS models are also transformed, as they
 can also be seen as compositional data. The transformation used for these
-transformations is the <code><a href='ilr.html'>ilr</a></code> transformation.</p></td>
+transformations is the <code><a href='ilr.html'>ilr()</a></code> transformation.</p></td>
     </tr>
     <tr>
       <th>quiet</th>
@@ -315,13 +320,14 @@ log-likelihood after each improvement?</p></td>
     </tr>
     <tr>
       <th>atol</th>
-      <td><p>Absolute error tolerance, passed to <code>ode</code>. Default
-is 1e-8, lower than in <code>lsoda</code>.</p></td>
+      <td><p>Absolute error tolerance, passed to <code><a href='https://rdrr.io/pkg/deSolve/man/ode.html'>deSolve::ode()</a></code>. Default
+is 1e-8, which is lower than the default in the <code><a href='https://rdrr.io/pkg/deSolve/man/lsoda.html'>deSolve::lsoda()</a></code>
+function which is used per default.</p></td>
     </tr>
     <tr>
       <th>rtol</th>
-      <td><p>Absolute error tolerance, passed to <code>ode</code>. Default
-is 1e-10, much lower than in <code>lsoda</code>.</p></td>
+      <td><p>Absolute error tolerance, passed to <code><a href='https://rdrr.io/pkg/deSolve/man/ode.html'>deSolve::ode()</a></code>. Default
+is 1e-10, much lower than in <code><a href='https://rdrr.io/pkg/deSolve/man/lsoda.html'>deSolve::lsoda()</a></code>.</p></td>
     </tr>
     <tr>
       <th>error_model</th>
@@ -342,11 +348,9 @@ normal distribution as assumed by this method.</p></td>
 the error model.  If the error model is "const", unweighted nonlinear
 least squares fitting ("OLS") is selected. If the error model is "obs", or
 "tc", the "d_3" algorithm is selected.</p>
-<p>The algorithm "d_3" will directly minimize the negative log-likelihood and</p><ul>
-<li><p>independently - also use the three step algorithm described below. The
-fit with the higher likelihood is returned.</p></li>
-</ul>
-
+<p>The algorithm "d_3" will directly minimize the negative log-likelihood
+and independently also use the three step algorithm described below.
+The fit with the higher likelihood is returned.</p>
 <p>The algorithm "direct" will directly minimize the negative log-likelihood.</p>
 <p>The algorithm "twostep" will minimize the negative log-likelihood after an
 initial unweighted least squares optimisation step.</p>
@@ -381,14 +385,13 @@ the error model parameters in IRLS fits.</p></td>
     <tr>
       <th>...</th>
       <td><p>Further arguments that will be passed on to
-<code>deSolve</code>.</p></td>
+<code><a href='https://rdrr.io/pkg/deSolve/man/ode.html'>deSolve::ode()</a></code>.</p></td>
     </tr>
     </table>
 
     <h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>
 
-    <p>A list with "mkinfit" in the class attribute.  A summary can be
-obtained by <code><a href='summary.mkinfit.html'>summary.mkinfit</a></code>.</p>
+    <p>A list with "mkinfit" in the class attribute.</p>
     <h2 class="hasAnchor" id="details"><a class="anchor" href="#details"></a>Details</h2>
 
     <p>Per default, parameters in the kinetic models are internally transformed in
@@ -409,28 +412,31 @@ Degradation Data. <em>Environments</em> 6(12) 124
 <a href='https://doi.org/10.3390/environments6120124'>doi:10.3390/environments6120124</a>.</p>
     <h2 class="hasAnchor" id="see-also"><a class="anchor" href="#see-also"></a>See also</h2>
 
-    <div class='dont-index'><p>Plotting methods <code><a href='plot.mkinfit.html'>plot.mkinfit</a></code> and
-<code><a href='mkinparplot.html'>mkinparplot</a></code>.</p>
+    <div class='dont-index'><p><a href='summary.mkinfit.html'>summary.mkinfit</a>, <a href='plot.mkinfit.html'>plot.mkinfit</a>, <a href='parms.html'>parms</a> and <a href='https://rdrr.io/pkg/lmtest/man/lrtest.html'>lrtest</a>.</p>
 <p>Comparisons of models fitted to the same data can be made using
 <code><a href='https://rdrr.io/r/stats/AIC.html'>AIC</a></code> by virtue of the method <code><a href='logLik.mkinfit.html'>logLik.mkinfit</a></code>.</p>
 <p>Fitting of several models to several datasets in a single call to
 <code><a href='mmkin.html'>mmkin</a></code>.</p></div>
+    <h2 class="hasAnchor" id="author"><a class="anchor" href="#author"></a>Author</h2>
+
+    <p>Johannes Ranke</p>
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
     <pre class="examples"><div class='input'>
 <span class='co'># Use shorthand notation for parent only degradation</span>
-<span class='no'>fit</span> <span class='kw'>&lt;-</span> <span class='fu'>mkinfit</span>(<span class='st'>"FOMC"</span>, <span class='no'>FOCUS_2006_C</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-<span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span>(<span class='no'>fit</span>)</div><div class='output co'>#&gt; mkin version used for fitting:    0.9.50.2 
-#&gt; R version used for fitting:       4.0.0 
-#&gt; Date of fit:     Wed May 27 07:03:45 2020 
-#&gt; Date of summary: Wed May 27 07:03:45 2020 
+<span class='va'>fit</span> <span class='op'>&lt;-</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='st'>"FOMC"</span>, <span class='va'>FOCUS_2006_C</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+<span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span><span class='op'>(</span><span class='va'>fit</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; mkin version used for fitting:    0.9.50.3 
+#&gt; R version used for fitting:       4.0.3 
+#&gt; Date of fit:     Thu Oct 15 12:40:10 2020 
+#&gt; Date of summary: Thu Oct 15 12:40:10 2020 
 #&gt; 
 #&gt; Equations:
 #&gt; d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 #&gt; 
 #&gt; Model predictions using solution type analytical 
 #&gt; 
-#&gt; Fitted using 222 model solutions performed in 0.043 s
+#&gt; Fitted using 222 model solutions performed in 0.045 s
 #&gt; 
 #&gt; Error model: Constant variance 
 #&gt; 
@@ -465,10 +471,10 @@ Degradation Data. <em>Environments</em> 6(12) 124
 #&gt; 
 #&gt; Parameter correlation:
 #&gt;             parent_0  log_alpha   log_beta     sigma
-#&gt; parent_0   1.000e+00 -1.565e-01 -3.142e-01 4.770e-08
-#&gt; log_alpha -1.565e-01  1.000e+00  9.564e-01 9.974e-08
-#&gt; log_beta  -3.142e-01  9.564e-01  1.000e+00 8.468e-08
-#&gt; sigma      4.770e-08  9.974e-08  8.468e-08 1.000e+00
+#&gt; parent_0   1.000e+00 -1.565e-01 -3.142e-01 4.758e-08
+#&gt; log_alpha -1.565e-01  1.000e+00  9.564e-01 1.007e-07
+#&gt; log_beta  -3.142e-01  9.564e-01  1.000e+00 8.568e-08
+#&gt; sigma      4.758e-08  1.007e-07  8.568e-08 1.000e+00
 #&gt; 
 #&gt; Backtransformed parameters:
 #&gt; Confidence intervals for internally transformed parameters are asymmetric.
@@ -501,426 +507,129 @@ Degradation Data. <em>Environments</em> 6(12) 124
 #&gt;    91   parent      3.9     1.441   2.4590
 #&gt;   119   parent      0.6     1.092  -0.4919</div><div class='input'>
 <span class='co'># One parent compound, one metabolite, both single first order.</span>
+<span class='co'># We remove zero values from FOCUS dataset D in order to avoid warnings</span>
+<span class='va'>FOCUS_D</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/subset.html'>subset</a></span><span class='op'>(</span><span class='va'>FOCUS_2006_D</span>, <span class='va'>value</span> <span class='op'>!=</span> <span class='fl'>0</span><span class='op'>)</span>
 <span class='co'># Use mkinsub for convenience in model formulation. Pathway to sink included per default.</span>
-<span class='no'>SFO_SFO</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(
-  <span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>, <span class='st'>"m1"</span>),
-  <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>))</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'><span class='co'># Fit the model to the FOCUS example dataset D using defaults</span>
-<span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span>(<span class='fu'><a href='https://rdrr.io/r/base/system.time.html'>system.time</a></span>(<span class='no'>fit</span> <span class='kw'>&lt;-</span> <span class='fu'>mkinfit</span>(<span class='no'>SFO_SFO</span>, <span class='no'>FOCUS_2006_D</span>,
-                           <span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='st'>"eigen"</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)))</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='output co'>#&gt;    user  system elapsed 
-#&gt;   0.400   0.004   0.404 </div><div class='input'><span class='fu'><a href='parms.html'>parms</a></span>(<span class='no'>fit</span>)</div><div class='output co'>#&gt;       parent_0       k_parent           k_m1 f_parent_to_m1          sigma 
-#&gt;   99.598481046    0.098697740    0.005260651    0.514475962    3.125503875 </div><div class='input'><span class='fu'><a href='endpoints.html'>endpoints</a></span>(<span class='no'>fit</span>)</div><div class='output co'>#&gt; $ff
-#&gt;   parent_m1 parent_sink 
-#&gt;    0.514476    0.485524 
-#&gt; 
-#&gt; $distimes
-#&gt;              DT50      DT90
-#&gt; parent   7.022929  23.32966
-#&gt; m1     131.760724 437.69965
-#&gt; </div><div class='input'><span class='co'># \dontrun{</span>
-<span class='co'># deSolve is slower when no C compiler (gcc) was available during model generation</span>
-<span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span>(<span class='fu'><a href='https://rdrr.io/r/base/system.time.html'>system.time</a></span>(<span class='no'>fit.deSolve</span> <span class='kw'>&lt;-</span> <span class='fu'>mkinfit</span>(<span class='no'>SFO_SFO</span>, <span class='no'>FOCUS_2006_D</span>,
-                           <span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='st'>"deSolve"</span>)))</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='output co'>#&gt; <span class='message'>Ordinary least squares optimisation</span></div><div class='output co'>#&gt; Sum of squared residuals at call 1: 15156.12
-#&gt; Sum of squared residuals at call 2: 15156.12
-#&gt; Sum of squared residuals at call 6: 8243.645
-#&gt; Sum of squared residuals at call 12: 6290.712
-#&gt; Sum of squared residuals at call 13: 6290.683
-#&gt; Sum of squared residuals at call 15: 6290.452
-#&gt; Sum of squared residuals at call 18: 1700.749
-#&gt; Sum of squared residuals at call 20: 1700.611
-#&gt; Sum of squared residuals at call 24: 1190.923
-#&gt; Sum of squared residuals at call 26: 1190.922
-#&gt; Sum of squared residuals at call 29: 1017.417
-#&gt; Sum of squared residuals at call 31: 1017.417
-#&gt; Sum of squared residuals at call 33: 1017.416
-#&gt; Sum of squared residuals at call 34: 644.0472
-#&gt; Sum of squared residuals at call 36: 644.047
-#&gt; Sum of squared residuals at call 38: 644.047
-#&gt; Sum of squared residuals at call 39: 590.5025
-#&gt; Sum of squared residuals at call 41: 590.5022
-#&gt; Sum of squared residuals at call 43: 590.5016
-#&gt; Sum of squared residuals at call 44: 543.2196
-#&gt; Sum of squared residuals at call 45: 543.2193
-#&gt; Sum of squared residuals at call 46: 543.2192
-#&gt; Sum of squared residuals at call 50: 391.348
-#&gt; Sum of squared residuals at call 51: 391.3479
-#&gt; Sum of squared residuals at call 56: 386.479
-#&gt; Sum of squared residuals at call 58: 386.479
-#&gt; Sum of squared residuals at call 60: 386.4779
-#&gt; Sum of squared residuals at call 61: 384.0686
-#&gt; Sum of squared residuals at call 63: 384.0686
-#&gt; Sum of squared residuals at call 66: 382.7813
-#&gt; Sum of squared residuals at call 68: 382.7813
-#&gt; Sum of squared residuals at call 70: 382.7813
-#&gt; Sum of squared residuals at call 71: 378.9273
-#&gt; Sum of squared residuals at call 73: 378.9273
-#&gt; Sum of squared residuals at call 75: 378.9272
-#&gt; Sum of squared residuals at call 76: 377.4847
-#&gt; Sum of squared residuals at call 78: 377.4846
-#&gt; Sum of squared residuals at call 81: 375.9738
-#&gt; Sum of squared residuals at call 83: 375.9738
-#&gt; Sum of squared residuals at call 86: 375.3387
-#&gt; Sum of squared residuals at call 88: 375.3387
-#&gt; Sum of squared residuals at call 91: 374.5774
-#&gt; Sum of squared residuals at call 93: 374.5774
-#&gt; Sum of squared residuals at call 95: 374.5774
-#&gt; Sum of squared residuals at call 96: 373.5438
-#&gt; Sum of squared residuals at call 100: 373.5438
-#&gt; Sum of squared residuals at call 102: 373.265
-#&gt; Sum of squared residuals at call 104: 373.265
-#&gt; Sum of squared residuals at call 107: 372.6825
-#&gt; Sum of squared residuals at call 111: 372.6825
-#&gt; Sum of squared residuals at call 114: 372.6356
-#&gt; Sum of squared residuals at call 116: 372.6356
-#&gt; Sum of squared residuals at call 119: 372.6199
-#&gt; Sum of squared residuals at call 121: 372.6199
-#&gt; Sum of squared residuals at call 123: 372.6199
-#&gt; Sum of squared residuals at call 124: 372.5881
-#&gt; Sum of squared residuals at call 126: 372.5881
-#&gt; Sum of squared residuals at call 129: 372.5418
-#&gt; Sum of squared residuals at call 130: 372.4866
-#&gt; Sum of squared residuals at call 131: 372.2242
-#&gt; Sum of squared residuals at call 132: 371.5237
-#&gt; Sum of squared residuals at call 134: 371.5237
-#&gt; Sum of squared residuals at call 137: 371.292
-#&gt; Sum of squared residuals at call 139: 371.292
-#&gt; Sum of squared residuals at call 143: 371.2256
-#&gt; Sum of squared residuals at call 144: 371.2256
-#&gt; Sum of squared residuals at call 146: 371.2256
-#&gt; Sum of squared residuals at call 149: 371.2194
-#&gt; Sum of squared residuals at call 150: 371.2147
-#&gt; Sum of squared residuals at call 153: 371.2147
-#&gt; Sum of squared residuals at call 155: 371.2137
-#&gt; Sum of squared residuals at call 156: 371.2137
-#&gt; Sum of squared residuals at call 157: 371.2137
-#&gt; Sum of squared residuals at call 160: 371.2134
-#&gt; Sum of squared residuals at call 164: 371.2134
-#&gt; Sum of squared residuals at call 165: 371.2134
-#&gt; Sum of squared residuals at call 167: 371.2134
-#&gt; Negative log-likelihood at call 177: 97.22429</div><div class='output co'>#&gt; <span class='message'>Optimisation successfully terminated.</span></div><div class='output co'>#&gt;    user  system elapsed 
-#&gt;   0.360   0.000   0.361 </div><div class='input'><span class='fu'><a href='parms.html'>parms</a></span>(<span class='no'>fit.deSolve</span>)</div><div class='output co'>#&gt;       parent_0       k_parent           k_m1 f_parent_to_m1          sigma 
-#&gt;   99.598480300    0.098697739    0.005260651    0.514475968    3.125503874 </div><div class='input'><span class='fu'><a href='endpoints.html'>endpoints</a></span>(<span class='no'>fit.deSolve</span>)</div><div class='output co'>#&gt; $ff
+<span class='va'>SFO_SFO</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>
+  parent <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='st'>"m1"</span><span class='op'>)</span>,
+  m1 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>
+<span class='co'># Fit the model quietly to the FOCUS example dataset D using defaults</span>
+<span class='va'>fit</span> <span class='op'>&lt;-</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='va'>SFO_SFO</span>, <span class='va'>FOCUS_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.0165</span></div><div class='input'><span class='co'># Since mkin 0.9.50.3, we get a warning about non-normality of residuals,</span>
+<span class='co'># so we try an alternative error model</span>
+<span class='va'>fit.tc</span> <span class='op'>&lt;-</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='va'>SFO_SFO</span>, <span class='va'>FOCUS_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span><span class='op'>)</span>
+<span class='co'># This avoids the warning, and the likelihood ratio test confirms it is preferable</span>
+<span class='fu'><a href='https://rdrr.io/pkg/lmtest/man/lrtest.html'>lrtest</a></span><span class='op'>(</span><span class='va'>fit.tc</span>, <span class='va'>fit</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; Likelihood ratio test
+#&gt; 
+#&gt; Model 1: SFO_SFO with error model tc and fixed parameter(s) m1_0
+#&gt; Model 2: SFO_SFO with error model const and fixed parameter(s) m1_0
+#&gt;   #Df  LogLik Df  Chisq Pr(&gt;Chisq)    
+#&gt; 1   6 -64.983                         
+#&gt; 2   5 -97.224 -1 64.483  9.737e-16 ***
+#&gt; ---
+#&gt; Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1</div><div class='input'><span class='co'># We can also allow for different variances of parent and metabolite as error model</span>
+<span class='va'>fit.obs</span> <span class='op'>&lt;-</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='va'>SFO_SFO</span>, <span class='va'>FOCUS_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, error_model <span class='op'>=</span> <span class='st'>"obs"</span><span class='op'>)</span>
+<span class='co'># This also avoids the warning about non-normality, but the two-component error model</span>
+<span class='co'># has significantly higher likelihood</span>
+<span class='fu'><a href='https://rdrr.io/pkg/lmtest/man/lrtest.html'>lrtest</a></span><span class='op'>(</span><span class='va'>fit.obs</span>, <span class='va'>fit.tc</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; Likelihood ratio test
+#&gt; 
+#&gt; Model 1: SFO_SFO with error model tc and fixed parameter(s) m1_0
+#&gt; Model 2: SFO_SFO with error model obs and fixed parameter(s) m1_0
+#&gt;   #Df  LogLik Df  Chisq Pr(&gt;Chisq)    
+#&gt; 1   6 -64.983                         
+#&gt; 2   6 -96.936  0 63.907  &lt; 2.2e-16 ***
+#&gt; ---
+#&gt; Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1</div><div class='input'><span class='fu'><a href='parms.html'>parms</a></span><span class='op'>(</span><span class='va'>fit.tc</span><span class='op'>)</span>
+</div><div class='output co'>#&gt;       parent_0       k_parent           k_m1 f_parent_to_m1      sigma_low 
+#&gt;   1.007343e+02   1.005562e-01   5.166712e-03   5.083933e-01   3.049891e-03 
+#&gt;       rsd_high 
+#&gt;   7.928117e-02 </div><div class='input'><span class='fu'><a href='endpoints.html'>endpoints</a></span><span class='op'>(</span><span class='va'>fit.tc</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; $ff
 #&gt;   parent_m1 parent_sink 
-#&gt;    0.514476    0.485524 
+#&gt;   0.5083933   0.4916067 
 #&gt; 
 #&gt; $distimes
-#&gt;              DT50      DT90
-#&gt; parent   7.022929  23.32966
-#&gt; m1     131.760721 437.69964
-#&gt; </div><div class='input'><span class='co'># }</span>
-
-<span class='co'># Use stepwise fitting, using optimised parameters from parent only fit, FOMC</span>
+#&gt;             DT50      DT90
+#&gt; parent   6.89313  22.89848
+#&gt; m1     134.15635 445.65776
+#&gt; </div><div class='input'>
+<span class='co'># We can show a quick (only one replication) benchmark for this case, as we</span>
+<span class='co'># have several alternative solution methods for the model. We skip</span>
+<span class='co'># uncompiled deSolve, as it is so slow. More benchmarks are found in the</span>
+<span class='co'># benchmark vignette</span>
 <span class='co'># \dontrun{</span>
-<span class='no'>FOMC_SFO</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(
-  <span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"FOMC"</span>, <span class='st'>"m1"</span>),
-  <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>))</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'><span class='co'># Fit the model to the FOCUS example dataset D using defaults</span>
-<span class='no'>fit.FOMC_SFO</span> <span class='kw'>&lt;-</span> <span class='fu'>mkinfit</span>(<span class='no'>FOMC_SFO</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'><span class='co'># Use starting parameters from parent only FOMC fit</span>
-<span class='no'>fit.FOMC</span> <span class='kw'>=</span> <span class='fu'>mkinfit</span>(<span class='st'>"FOMC"</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-<span class='no'>fit.FOMC_SFO</span> <span class='kw'>&lt;-</span> <span class='fu'>mkinfit</span>(<span class='no'>FOMC_SFO</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>,
-  <span class='kw'>parms.ini</span> <span class='kw'>=</span> <span class='no'>fit.FOMC</span>$<span class='no'>bparms.ode</span>)</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'>
-<span class='co'># Use stepwise fitting, using optimised parameters from parent only fit, SFORB</span>
-<span class='no'>SFORB_SFO</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(
-  <span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFORB"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='st'>"m1"</span>, <span class='kw'>sink</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>),
-  <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>))</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'><span class='co'># Fit the model to the FOCUS example dataset D using defaults</span>
-<span class='no'>fit.SFORB_SFO</span> <span class='kw'>&lt;-</span> <span class='fu'>mkinfit</span>(<span class='no'>SFORB_SFO</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'><span class='no'>fit.SFORB_SFO.deSolve</span> <span class='kw'>&lt;-</span> <span class='fu'>mkinfit</span>(<span class='no'>SFORB_SFO</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='st'>"deSolve"</span>,
-                                 <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'><span class='co'># Use starting parameters from parent only SFORB fit (not really needed in this case)</span>
-<span class='no'>fit.SFORB</span> <span class='kw'>=</span> <span class='fu'>mkinfit</span>(<span class='st'>"SFORB"</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-<span class='no'>fit.SFORB_SFO</span> <span class='kw'>&lt;-</span> <span class='fu'>mkinfit</span>(<span class='no'>SFORB_SFO</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>parms.ini</span> <span class='kw'>=</span> <span class='no'>fit.SFORB</span>$<span class='no'>bparms.ode</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='output co'>#&gt; <span class='warning'>Warning: Initial parameter(s) k_parent_free_sink not used in the model</span></div><div class='input'><span class='co'># }</span>
-
+<span class='kw'>if</span><span class='op'>(</span><span class='kw'><a href='https://rdrr.io/r/base/library.html'>require</a></span><span class='op'>(</span><span class='va'><a href='http://rbenchmark.googlecode.com'>rbenchmark</a></span><span class='op'>)</span><span class='op'>)</span> <span class='op'>{</span>
+  <span class='fu'><a href='https://rdrr.io/pkg/rbenchmark/man/benchmark.html'>benchmark</a></span><span class='op'>(</span>replications <span class='op'>=</span> <span class='fl'>1</span>, order <span class='op'>=</span> <span class='st'>"relative"</span>, columns <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"test"</span>, <span class='st'>"relative"</span>, <span class='st'>"elapsed"</span><span class='op'>)</span>,
+    deSolve_compiled <span class='op'>=</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='va'>SFO_SFO</span>, <span class='va'>FOCUS_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span>,
+      solution_type <span class='op'>=</span> <span class='st'>"deSolve"</span>, use_compiled <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>,
+    eigen <span class='op'>=</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='va'>SFO_SFO</span>, <span class='va'>FOCUS_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span>,
+      solution_type <span class='op'>=</span> <span class='st'>"eigen"</span><span class='op'>)</span>,
+    analytical <span class='op'>=</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='va'>SFO_SFO</span>, <span class='va'>FOCUS_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span>,
+      solution_type <span class='op'>=</span> <span class='st'>"analytical"</span><span class='op'>)</span><span class='op'>)</span>
+<span class='op'>}</span>
+</div><div class='output co'>#&gt;               test relative elapsed
+#&gt; 3       analytical    1.000   0.752
+#&gt; 1 deSolve_compiled    2.294   1.725
+#&gt; 2            eigen    2.727   2.051</div><div class='input'><span class='co'># }</span>
+
+<span class='co'># Use stepwise fitting, using optimised parameters from parent only fit, FOMC-SFO</span>
 <span class='co'># \dontrun{</span>
-<span class='co'># Weighted fits, including IRLS (error_model = "obs")</span>
-<span class='no'>SFO_SFO.ff</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>, <span class='st'>"m1"</span>),
-                      <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>), <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"max"</span>)</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'><span class='no'>f.noweight</span> <span class='kw'>&lt;-</span> <span class='fu'>mkinfit</span>(<span class='no'>SFO_SFO.ff</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'><span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span>(<span class='no'>f.noweight</span>)</div><div class='output co'>#&gt; mkin version used for fitting:    0.9.50.2 
-#&gt; R version used for fitting:       4.0.0 
-#&gt; Date of fit:     Wed May 27 07:03:50 2020 
-#&gt; Date of summary: Wed May 27 07:03:50 2020 
-#&gt; 
-#&gt; Equations:
-#&gt; d_parent/dt = - k_parent * parent
-#&gt; d_m1/dt = + f_parent_to_m1 * k_parent * parent - k_m1 * m1
-#&gt; 
-#&gt; Model predictions using solution type analytical 
-#&gt; 
-#&gt; Fitted using 421 model solutions performed in 0.129 s
-#&gt; 
-#&gt; Error model: Constant variance 
-#&gt; 
-#&gt; Error model algorithm: OLS 
-#&gt; 
-#&gt; Starting values for parameters to be optimised:
-#&gt;                   value   type
-#&gt; parent_0       100.7500  state
-#&gt; k_parent         0.1000 deparm
-#&gt; k_m1             0.1001 deparm
-#&gt; f_parent_to_m1   0.5000 deparm
-#&gt; 
-#&gt; Starting values for the transformed parameters actually optimised:
-#&gt;                     value lower upper
-#&gt; parent_0       100.750000  -Inf   Inf
-#&gt; log_k_parent    -2.302585  -Inf   Inf
-#&gt; log_k_m1        -2.301586  -Inf   Inf
-#&gt; f_parent_ilr_1   0.000000  -Inf   Inf
-#&gt; 
-#&gt; Fixed parameter values:
-#&gt;      value  type
-#&gt; m1_0     0 state
-#&gt; 
-#&gt; Results:
-#&gt; 
-#&gt;        AIC      BIC    logLik
-#&gt;   204.4486 212.6365 -97.22429
-#&gt; 
-#&gt; Optimised, transformed parameters with symmetric confidence intervals:
-#&gt;                Estimate Std. Error    Lower    Upper
-#&gt; parent_0       99.60000    1.57000 96.40000 102.8000
-#&gt; log_k_parent   -2.31600    0.04087 -2.39900  -2.2330
-#&gt; log_k_m1       -5.24800    0.13320 -5.51800  -4.9770
-#&gt; f_parent_ilr_1  0.04096    0.06312 -0.08746   0.1694
-#&gt; sigma           3.12600    0.35850  2.39600   3.8550
-#&gt; 
-#&gt; Parameter correlation:
-#&gt;                  parent_0 log_k_parent   log_k_m1 f_parent_ilr_1      sigma
-#&gt; parent_0        1.000e+00    5.174e-01 -1.688e-01     -5.471e-01 -3.190e-07
-#&gt; log_k_parent    5.174e-01    1.000e+00 -3.263e-01     -5.426e-01  3.168e-07
-#&gt; log_k_m1       -1.688e-01   -3.263e-01  1.000e+00      7.478e-01 -1.406e-07
-#&gt; f_parent_ilr_1 -5.471e-01   -5.426e-01  7.478e-01      1.000e+00 -1.587e-10
-#&gt; sigma          -3.190e-07    3.168e-07 -1.406e-07     -1.587e-10  1.000e+00
-#&gt; 
-#&gt; Backtransformed parameters:
-#&gt; Confidence intervals for internally transformed parameters are asymmetric.
-#&gt; t-test (unrealistically) based on the assumption of normal distribution
-#&gt; for estimators of untransformed parameters.
-#&gt;                 Estimate t value    Pr(&gt;t)     Lower     Upper
-#&gt; parent_0       99.600000  63.430 2.298e-36 96.400000 1.028e+02
-#&gt; k_parent        0.098700  24.470 4.955e-23  0.090820 1.073e-01
-#&gt; k_m1            0.005261   7.510 6.165e-09  0.004012 6.898e-03
-#&gt; f_parent_to_m1  0.514500  23.070 3.104e-22  0.469100 5.596e-01
-#&gt; sigma           3.126000   8.718 2.235e-10  2.396000 3.855e+00
-#&gt; 
-#&gt; FOCUS Chi2 error levels in percent:
-#&gt;          err.min n.optim df
-#&gt; All data   6.398       4 15
-#&gt; parent     6.459       2  7
-#&gt; m1         4.690       2  8
-#&gt; 
-#&gt; Resulting formation fractions:
-#&gt;                 ff
-#&gt; parent_m1   0.5145
-#&gt; parent_sink 0.4855
-#&gt; 
-#&gt; Estimated disappearance times:
-#&gt;           DT50   DT90
-#&gt; parent   7.023  23.33
-#&gt; m1     131.761 437.70
-#&gt; 
-#&gt; Data:
-#&gt;  time variable observed predicted   residual
-#&gt;     0   parent    99.46  99.59848 -1.385e-01
-#&gt;     0   parent   102.04  99.59848  2.442e+00
-#&gt;     1   parent    93.50  90.23787  3.262e+00
-#&gt;     1   parent    92.50  90.23787  2.262e+00
-#&gt;     3   parent    63.23  74.07319 -1.084e+01
-#&gt;     3   parent    68.99  74.07319 -5.083e+00
-#&gt;     7   parent    52.32  49.91206  2.408e+00
-#&gt;     7   parent    55.13  49.91206  5.218e+00
-#&gt;    14   parent    27.27  25.01257  2.257e+00
-#&gt;    14   parent    26.64  25.01257  1.627e+00
-#&gt;    21   parent    11.50  12.53462 -1.035e+00
-#&gt;    21   parent    11.64  12.53462 -8.946e-01
-#&gt;    35   parent     2.85   3.14787 -2.979e-01
-#&gt;    35   parent     2.91   3.14787 -2.379e-01
-#&gt;    50   parent     0.69   0.71624 -2.624e-02
-#&gt;    50   parent     0.63   0.71624 -8.624e-02
-#&gt;    75   parent     0.05   0.06074 -1.074e-02
-#&gt;    75   parent     0.06   0.06074 -7.381e-04
-#&gt;     1       m1     4.84   4.80296  3.704e-02
-#&gt;     1       m1     5.64   4.80296  8.370e-01
-#&gt;     3       m1    12.91  13.02400 -1.140e-01
-#&gt;     3       m1    12.96  13.02400 -6.400e-02
-#&gt;     7       m1    22.97  25.04476 -2.075e+00
-#&gt;     7       m1    24.47  25.04476 -5.748e-01
-#&gt;    14       m1    41.69  36.69002  5.000e+00
-#&gt;    14       m1    33.21  36.69002 -3.480e+00
-#&gt;    21       m1    44.37  41.65310  2.717e+00
-#&gt;    21       m1    46.44  41.65310  4.787e+00
-#&gt;    35       m1    41.22  43.31312 -2.093e+00
-#&gt;    35       m1    37.95  43.31312 -5.363e+00
-#&gt;    50       m1    41.19  41.21831 -2.831e-02
-#&gt;    50       m1    40.01  41.21831 -1.208e+00
-#&gt;    75       m1    40.09  36.44703  3.643e+00
-#&gt;    75       m1    33.85  36.44703 -2.597e+00
-#&gt;   100       m1    31.04  31.98163 -9.416e-01
-#&gt;   100       m1    33.13  31.98163  1.148e+00
-#&gt;   120       m1    25.15  28.78984 -3.640e+00
-#&gt;   120       m1    33.31  28.78984  4.520e+00</div><div class='input'><span class='no'>f.obs</span> <span class='kw'>&lt;-</span> <span class='fu'>mkinfit</span>(<span class='no'>SFO_SFO.ff</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>error_model</span> <span class='kw'>=</span> <span class='st'>"obs"</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'><span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span>(<span class='no'>f.obs</span>)</div><div class='output co'>#&gt; mkin version used for fitting:    0.9.50.2 
-#&gt; R version used for fitting:       4.0.0 
-#&gt; Date of fit:     Wed May 27 07:03:50 2020 
-#&gt; Date of summary: Wed May 27 07:03:50 2020 
-#&gt; 
-#&gt; Equations:
-#&gt; d_parent/dt = - k_parent * parent
-#&gt; d_m1/dt = + f_parent_to_m1 * k_parent * parent - k_m1 * m1
-#&gt; 
-#&gt; Model predictions using solution type analytical 
-#&gt; 
-#&gt; Fitted using 978 model solutions performed in 0.407 s
-#&gt; 
-#&gt; Error model: Variance unique to each observed variable 
-#&gt; 
-#&gt; Error model algorithm: d_3 
-#&gt; Direct fitting and three-step fitting yield approximately the same likelihood 
-#&gt; 
-#&gt; Starting values for parameters to be optimised:
-#&gt;                   value   type
-#&gt; parent_0       100.7500  state
-#&gt; k_parent         0.1000 deparm
-#&gt; k_m1             0.1001 deparm
-#&gt; f_parent_to_m1   0.5000 deparm
-#&gt; sigma_parent     3.0000  error
-#&gt; sigma_m1         3.0000  error
-#&gt; 
-#&gt; Starting values for the transformed parameters actually optimised:
-#&gt;                     value lower upper
-#&gt; parent_0       100.750000  -Inf   Inf
-#&gt; log_k_parent    -2.302585  -Inf   Inf
-#&gt; log_k_m1        -2.301586  -Inf   Inf
-#&gt; f_parent_ilr_1   0.000000  -Inf   Inf
-#&gt; sigma_parent     3.000000     0   Inf
-#&gt; sigma_m1         3.000000     0   Inf
-#&gt; 
-#&gt; Fixed parameter values:
-#&gt;      value  type
-#&gt; m1_0     0 state
-#&gt; 
-#&gt; Results:
-#&gt; 
-#&gt;        AIC      BIC    logLik
-#&gt;   205.8727 215.6982 -96.93634
-#&gt; 
-#&gt; Optimised, transformed parameters with symmetric confidence intervals:
-#&gt;                Estimate Std. Error    Lower    Upper
-#&gt; parent_0       99.65000    1.70200 96.19000 103.1000
-#&gt; log_k_parent   -2.31300    0.04376 -2.40200  -2.2240
-#&gt; log_k_m1       -5.25000    0.12430 -5.50400  -4.9970
-#&gt; f_parent_ilr_1  0.03861    0.06171 -0.08708   0.1643
-#&gt; sigma_parent    3.40100    0.56820  2.24400   4.5590
-#&gt; sigma_m1        2.85500    0.45240  1.93400   3.7770
-#&gt; 
-#&gt; Parameter correlation:
-#&gt;                parent_0 log_k_parent log_k_m1 f_parent_ilr_1 sigma_parent
-#&gt; parent_0        1.00000      0.51078 -0.19133       -0.59997     0.035670
-#&gt; log_k_parent    0.51078      1.00000 -0.37458       -0.59239     0.069833
-#&gt; log_k_m1       -0.19133     -0.37458  1.00000        0.74398    -0.026158
-#&gt; f_parent_ilr_1 -0.59997     -0.59239  0.74398        1.00000    -0.041369
-#&gt; sigma_parent    0.03567      0.06983 -0.02616       -0.04137     1.000000
-#&gt; sigma_m1       -0.03385     -0.06627  0.02482        0.03926    -0.004628
-#&gt;                 sigma_m1
-#&gt; parent_0       -0.033847
-#&gt; log_k_parent   -0.066265
-#&gt; log_k_m1        0.024823
-#&gt; f_parent_ilr_1  0.039256
-#&gt; sigma_parent   -0.004628
-#&gt; sigma_m1        1.000000
-#&gt; 
-#&gt; Backtransformed parameters:
-#&gt; Confidence intervals for internally transformed parameters are asymmetric.
-#&gt; t-test (unrealistically) based on the assumption of normal distribution
-#&gt; for estimators of untransformed parameters.
-#&gt;                 Estimate t value    Pr(&gt;t)     Lower     Upper
-#&gt; parent_0       99.650000  58.560 2.004e-34 96.190000 1.031e+02
-#&gt; k_parent        0.098970  22.850 1.099e-21  0.090530 1.082e-01
-#&gt; k_m1            0.005245   8.046 1.732e-09  0.004072 6.756e-03
-#&gt; f_parent_to_m1  0.513600  23.560 4.352e-22  0.469300 5.578e-01
-#&gt; sigma_parent    3.401000   5.985 5.662e-07  2.244000 4.559e+00
-#&gt; sigma_m1        2.855000   6.311 2.215e-07  1.934000 3.777e+00
-#&gt; 
-#&gt; FOCUS Chi2 error levels in percent:
-#&gt;          err.min n.optim df
-#&gt; All data   6.398       4 15
-#&gt; parent     6.464       2  7
-#&gt; m1         4.682       2  8
-#&gt; 
-#&gt; Resulting formation fractions:
-#&gt;                 ff
-#&gt; parent_m1   0.5136
-#&gt; parent_sink 0.4864
-#&gt; 
-#&gt; Estimated disappearance times:
-#&gt;           DT50   DT90
-#&gt; parent   7.003  23.26
-#&gt; m1     132.154 439.01
-#&gt; 
-#&gt; Data:
-#&gt;  time variable observed predicted   residual
-#&gt;     0   parent    99.46  99.65417 -1.942e-01
-#&gt;     0   parent   102.04  99.65417  2.386e+00
-#&gt;     1   parent    93.50  90.26332  3.237e+00
-#&gt;     1   parent    92.50  90.26332  2.237e+00
-#&gt;     3   parent    63.23  74.05306 -1.082e+01
-#&gt;     3   parent    68.99  74.05306 -5.063e+00
-#&gt;     7   parent    52.32  49.84325  2.477e+00
-#&gt;     7   parent    55.13  49.84325  5.287e+00
-#&gt;    14   parent    27.27  24.92971  2.340e+00
-#&gt;    14   parent    26.64  24.92971  1.710e+00
-#&gt;    21   parent    11.50  12.46890 -9.689e-01
-#&gt;    21   parent    11.64  12.46890 -8.289e-01
-#&gt;    35   parent     2.85   3.11925 -2.692e-01
-#&gt;    35   parent     2.91   3.11925 -2.092e-01
-#&gt;    50   parent     0.69   0.70679 -1.679e-02
-#&gt;    50   parent     0.63   0.70679 -7.679e-02
-#&gt;    75   parent     0.05   0.05952 -9.523e-03
-#&gt;    75   parent     0.06   0.05952  4.772e-04
-#&gt;     1       m1     4.84   4.81075  2.925e-02
-#&gt;     1       m1     5.64   4.81075  8.292e-01
-#&gt;     3       m1    12.91  13.04196 -1.320e-01
-#&gt;     3       m1    12.96  13.04196 -8.196e-02
-#&gt;     7       m1    22.97  25.06847 -2.098e+00
-#&gt;     7       m1    24.47  25.06847 -5.985e-01
-#&gt;    14       m1    41.69  36.70308  4.987e+00
-#&gt;    14       m1    33.21  36.70308 -3.493e+00
-#&gt;    21       m1    44.37  41.65115  2.719e+00
-#&gt;    21       m1    46.44  41.65115  4.789e+00
-#&gt;    35       m1    41.22  43.29465 -2.075e+00
-#&gt;    35       m1    37.95  43.29465 -5.345e+00
-#&gt;    50       m1    41.19  41.19948 -9.479e-03
-#&gt;    50       m1    40.01  41.19948 -1.189e+00
-#&gt;    75       m1    40.09  36.44035  3.650e+00
-#&gt;    75       m1    33.85  36.44035 -2.590e+00
-#&gt;   100       m1    31.04  31.98773 -9.477e-01
-#&gt;   100       m1    33.13  31.98773  1.142e+00
-#&gt;   120       m1    25.15  28.80429 -3.654e+00
-#&gt;   120       m1    33.31  28.80429  4.506e+00</div><div class='input'><span class='no'>f.tc</span> <span class='kw'>&lt;-</span> <span class='fu'>mkinfit</span>(<span class='no'>SFO_SFO.ff</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>error_model</span> <span class='kw'>=</span> <span class='st'>"tc"</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'><span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span>(<span class='no'>f.tc</span>)</div><div class='output co'>#&gt; mkin version used for fitting:    0.9.50.2 
-#&gt; R version used for fitting:       4.0.0 
-#&gt; Date of fit:     Wed May 27 07:03:51 2020 
-#&gt; Date of summary: Wed May 27 07:03:51 2020 
+<span class='va'>FOMC_SFO</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>
+  parent <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"FOMC"</span>, <span class='st'>"m1"</span><span class='op'>)</span>,
+  m1 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'><span class='va'>fit.FOMC_SFO</span> <span class='op'>&lt;-</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='va'>FOMC_SFO</span>, <span class='va'>FOCUS_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.0499</span></div><div class='input'><span class='co'># Again, we get a warning and try a more sophisticated error model</span>
+<span class='va'>fit.FOMC_SFO.tc</span> <span class='op'>&lt;-</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='va'>FOMC_SFO</span>, <span class='va'>FOCUS_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span><span class='op'>)</span>
+<span class='co'># This model has a higher likelihood, but not significantly so</span>
+<span class='fu'><a href='https://rdrr.io/pkg/lmtest/man/lrtest.html'>lrtest</a></span><span class='op'>(</span><span class='va'>fit.tc</span>, <span class='va'>fit.FOMC_SFO.tc</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; Likelihood ratio test
+#&gt; 
+#&gt; Model 1: FOMC_SFO with error model tc and fixed parameter(s) m1_0
+#&gt; Model 2: SFO_SFO with error model tc and fixed parameter(s) m1_0
+#&gt;   #Df  LogLik Df  Chisq Pr(&gt;Chisq)
+#&gt; 1   7 -64.829                     
+#&gt; 2   6 -64.983 -1 0.3075     0.5792</div><div class='input'><span class='co'># Also, the missing standard error for log_beta and the t-tests for alpha</span>
+<span class='co'># and beta indicate overparameterisation</span>
+<span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span><span class='op'>(</span><span class='va'>fit.FOMC_SFO.tc</span>, data <span class='op'>=</span> <span class='cn'>FALSE</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='warning'>Warning: NaNs produced</span></div><div class='output co'>#&gt; <span class='warning'>Warning: NaNs produced</span></div><div class='output co'>#&gt; <span class='warning'>Warning: diag(.) had 0 or NA entries; non-finite result is doubtful</span></div><div class='output co'>#&gt; mkin version used for fitting:    0.9.50.3 
+#&gt; R version used for fitting:       4.0.3 
+#&gt; Date of fit:     Thu Oct 15 12:40:24 2020 
+#&gt; Date of summary: Thu Oct 15 12:40:24 2020 
 #&gt; 
 #&gt; Equations:
-#&gt; d_parent/dt = - k_parent * parent
-#&gt; d_m1/dt = + f_parent_to_m1 * k_parent * parent - k_m1 * m1
+#&gt; d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
+#&gt; d_m1/dt = + f_parent_to_m1 * (alpha/beta) * 1/((time/beta) + 1) *
+#&gt;            parent - k_m1 * m1
 #&gt; 
-#&gt; Model predictions using solution type analytical 
+#&gt; Model predictions using solution type deSolve 
 #&gt; 
-#&gt; Fitted using 2088 model solutions performed in 0.722 s
+#&gt; Fitted using 3611 model solutions performed in 2.669 s
 #&gt; 
 #&gt; Error model: Two-component variance function 
 #&gt; 
 #&gt; Error model algorithm: d_3 
-#&gt; Direct fitting and three-step fitting yield approximately the same likelihood 
+#&gt; Three-step fitting yielded a higher likelihood than direct fitting 
 #&gt; 
 #&gt; Starting values for parameters to be optimised:
-#&gt;                   value   type
-#&gt; parent_0       100.7500  state
-#&gt; k_parent         0.1000 deparm
-#&gt; k_m1             0.1001 deparm
-#&gt; f_parent_to_m1   0.5000 deparm
-#&gt; sigma_low        0.1000  error
-#&gt; rsd_high         0.1000  error
+#&gt;                 value   type
+#&gt; parent_0       100.75  state
+#&gt; alpha            1.00 deparm
+#&gt; beta            10.00 deparm
+#&gt; k_m1             0.10 deparm
+#&gt; f_parent_to_m1   0.50 deparm
+#&gt; sigma_low        0.10  error
+#&gt; rsd_high         0.10  error
 #&gt; 
 #&gt; Starting values for the transformed parameters actually optimised:
 #&gt;                     value lower upper
 #&gt; parent_0       100.750000  -Inf   Inf
-#&gt; log_k_parent    -2.302585  -Inf   Inf
-#&gt; log_k_m1        -2.301586  -Inf   Inf
+#&gt; log_k_m1        -2.302585  -Inf   Inf
 #&gt; f_parent_ilr_1   0.000000  -Inf   Inf
+#&gt; log_alpha        0.000000  -Inf   Inf
+#&gt; log_beta         2.302585  -Inf   Inf
 #&gt; sigma_low        0.100000     0   Inf
 #&gt; rsd_high         0.100000     0   Inf
 #&gt; 
@@ -930,97 +639,70 @@ Degradation Data. <em>Environments</em> 6(12) 124
 #&gt; 
 #&gt; Results:
 #&gt; 
-#&gt;        AIC      BIC    logLik
-#&gt;   141.9656 151.7911 -64.98278
+#&gt;       AIC      BIC    logLik
+#&gt;   143.658 155.1211 -64.82902
 #&gt; 
 #&gt; Optimised, transformed parameters with symmetric confidence intervals:
-#&gt;                 Estimate Std. Error     Lower     Upper
-#&gt; parent_0       100.70000   2.621000 95.400000 106.10000
-#&gt; log_k_parent    -2.29700   0.008862 -2.315000  -2.27900
-#&gt; log_k_m1        -5.26600   0.091310 -5.452000  -5.08000
-#&gt; f_parent_ilr_1   0.02374   0.055300 -0.088900   0.13640
-#&gt; sigma_low        0.00305   0.004829 -0.006786   0.01289
-#&gt; rsd_high         0.07928   0.009418  0.060100   0.09847
+#&gt;                  Estimate Std. Error     Lower      Upper
+#&gt; parent_0       101.600000  2.6390000 96.240000 107.000000
+#&gt; log_k_m1        -5.284000  0.0928900 -5.473000  -5.095000
+#&gt; f_parent_ilr_1   0.001008  0.0541900 -0.109500   0.111500
+#&gt; log_alpha        5.522000  0.0077300  5.506000   5.538000
+#&gt; log_beta         7.806000        NaN       NaN        NaN
+#&gt; sigma_low        0.002488  0.0002431  0.001992   0.002984
+#&gt; rsd_high         0.079210  0.0093280  0.060180   0.098230
 #&gt; 
 #&gt; Parameter correlation:
-#&gt;                parent_0 log_k_parent log_k_m1 f_parent_ilr_1 sigma_low rsd_high
-#&gt; parent_0        1.00000      0.67644 -0.10215       -0.76822   0.14294 -0.08783
-#&gt; log_k_parent    0.67644      1.00000 -0.15102       -0.59491   0.34611 -0.08125
-#&gt; log_k_m1       -0.10215     -0.15102  1.00000        0.51808  -0.05236  0.01240
-#&gt; f_parent_ilr_1 -0.76822     -0.59491  0.51808        1.00000  -0.13900  0.03248
-#&gt; sigma_low       0.14294      0.34611 -0.05236       -0.13900   1.00000 -0.16546
-#&gt; rsd_high       -0.08783     -0.08125  0.01240        0.03248  -0.16546  1.00000
+#&gt;                 parent_0  log_k_m1 f_parent_ilr_1 log_alpha log_beta sigma_low
+#&gt; parent_0        1.000000 -0.094697       -0.76654   0.70525      NaN  0.016099
+#&gt; log_k_m1       -0.094697  1.000000        0.51404  -0.14347      NaN  0.001576
+#&gt; f_parent_ilr_1 -0.766543  0.514038        1.00000  -0.61368      NaN  0.015465
+#&gt; log_alpha       0.705247 -0.143468       -0.61368   1.00000      NaN  5.871780
+#&gt; log_beta             NaN       NaN            NaN       NaN        1       NaN
+#&gt; sigma_low       0.016099  0.001576        0.01546   5.87178      NaN  1.000000
+#&gt; rsd_high        0.006566 -0.011662       -0.05353   0.04845      NaN -0.652554
+#&gt;                 rsd_high
+#&gt; parent_0        0.006566
+#&gt; log_k_m1       -0.011662
+#&gt; f_parent_ilr_1 -0.053525
+#&gt; log_alpha       0.048451
+#&gt; log_beta             NaN
+#&gt; sigma_low      -0.652554
+#&gt; rsd_high        1.000000
 #&gt; 
 #&gt; Backtransformed parameters:
 #&gt; Confidence intervals for internally transformed parameters are asymmetric.
 #&gt; t-test (unrealistically) based on the assumption of normal distribution
 #&gt; for estimators of untransformed parameters.
-#&gt;                 Estimate  t value    Pr(&gt;t)     Lower     Upper
-#&gt; parent_0       1.007e+02  38.4300 1.180e-28 95.400000 1.061e+02
-#&gt; k_parent       1.006e-01 112.8000 1.718e-43  0.098760 1.024e-01
-#&gt; k_m1           5.167e-03  10.9500 1.171e-12  0.004290 6.223e-03
-#&gt; f_parent_to_m1 5.084e-01  26.0100 2.146e-23  0.468600 5.481e-01
-#&gt; sigma_low      3.050e-03   0.6314 2.661e-01 -0.006786 1.289e-02
-#&gt; rsd_high       7.928e-02   8.4170 6.418e-10  0.060100 9.847e-02
+#&gt;                 Estimate t value    Pr(&gt;t)     Lower     Upper
+#&gt; parent_0       1.016e+02 32.7800 6.312e-26 9.624e+01 1.070e+02
+#&gt; k_m1           5.072e-03 10.1200 1.216e-11 4.197e-03 6.130e-03
+#&gt; f_parent_to_m1 5.004e-01 20.8300 4.318e-20 4.614e-01 5.394e-01
+#&gt; alpha          2.502e+02  0.5624 2.889e-01 2.463e+02 2.542e+02
+#&gt; beta           2.455e+03  0.5549 2.915e-01        NA        NA
+#&gt; sigma_low      2.488e-03  0.4843 3.158e-01 1.992e-03 2.984e-03
+#&gt; rsd_high       7.921e-02  8.4300 8.001e-10 6.018e-02 9.823e-02
 #&gt; 
 #&gt; FOCUS Chi2 error levels in percent:
 #&gt;          err.min n.optim df
-#&gt; All data   6.475       4 15
-#&gt; parent     6.573       2  7
-#&gt; m1         4.671       2  8
+#&gt; All data   6.781       5 14
+#&gt; parent     7.141       3  6
+#&gt; m1         4.640       2  8
 #&gt; 
 #&gt; Resulting formation fractions:
 #&gt;                 ff
-#&gt; parent_m1   0.5084
-#&gt; parent_sink 0.4916
+#&gt; parent_m1   0.5004
+#&gt; parent_sink 0.4996
 #&gt; 
 #&gt; Estimated disappearance times:
-#&gt;           DT50  DT90
-#&gt; parent   6.893  22.9
-#&gt; m1     134.156 445.7
-#&gt; 
-#&gt; Data:
-#&gt;  time variable observed predicted   residual
-#&gt;     0   parent    99.46 100.73434  -1.274340
-#&gt;     0   parent   102.04 100.73434   1.305660
-#&gt;     1   parent    93.50  91.09751   2.402486
-#&gt;     1   parent    92.50  91.09751   1.402486
-#&gt;     3   parent    63.23  74.50141 -11.271410
-#&gt;     3   parent    68.99  74.50141  -5.511410
-#&gt;     7   parent    52.32  49.82880   2.491200
-#&gt;     7   parent    55.13  49.82880   5.301200
-#&gt;    14   parent    27.27  24.64809   2.621908
-#&gt;    14   parent    26.64  24.64809   1.991908
-#&gt;    21   parent    11.50  12.19232  -0.692315
-#&gt;    21   parent    11.64  12.19232  -0.552315
-#&gt;    35   parent     2.85   2.98327  -0.133266
-#&gt;    35   parent     2.91   2.98327  -0.073266
-#&gt;    50   parent     0.69   0.66013   0.029874
-#&gt;    50   parent     0.63   0.66013  -0.030126
-#&gt;    75   parent     0.05   0.05344  -0.003438
-#&gt;    75   parent     0.06   0.05344   0.006562
-#&gt;     1       m1     4.84   4.88645  -0.046451
-#&gt;     1       m1     5.64   4.88645   0.753549
-#&gt;     3       m1    12.91  13.22867  -0.318669
-#&gt;     3       m1    12.96  13.22867  -0.268669
-#&gt;     7       m1    22.97  25.36417  -2.394166
-#&gt;     7       m1    24.47  25.36417  -0.894166
-#&gt;    14       m1    41.69  37.00974   4.680263
-#&gt;    14       m1    33.21  37.00974  -3.799737
-#&gt;    21       m1    44.37  41.90133   2.468669
-#&gt;    21       m1    46.44  41.90133   4.538669
-#&gt;    35       m1    41.22  43.45691  -2.236913
-#&gt;    35       m1    37.95  43.45691  -5.506913
-#&gt;    50       m1    41.19  41.34199  -0.151985
-#&gt;    50       m1    40.01  41.34199  -1.331985
-#&gt;    75       m1    40.09  36.61471   3.475295
-#&gt;    75       m1    33.85  36.61471  -2.764705
-#&gt;   100       m1    31.04  32.20082  -1.160823
-#&gt;   100       m1    33.13  32.20082   0.929177
-#&gt;   120       m1    25.15  29.04130  -3.891304
-#&gt;   120       m1    33.31  29.04130   4.268696</div><div class='input'># }
-
-
+#&gt;           DT50  DT90 DT50back
+#&gt; parent   6.812  22.7    6.834
+#&gt; m1     136.661 454.0       NA</div><div class='input'>
+<span class='co'># We can easily use starting parameters from the parent only fit (only for illustration)</span>
+<span class='va'>fit.FOMC</span> <span class='op'>=</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='st'>"FOMC"</span>, <span class='va'>FOCUS_2006_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span><span class='op'>)</span>
+<span class='va'>fit.FOMC_SFO</span> <span class='op'>&lt;-</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='va'>FOMC_SFO</span>, <span class='va'>FOCUS_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>,
+  parms.ini <span class='op'>=</span> <span class='va'>fit.FOMC</span><span class='op'>$</span><span class='va'>bparms.ode</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span><span class='op'>)</span>
+<span class='co'># }</span>
 </div></pre>
   </div>
   <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
@@ -1037,7 +719,7 @@ Degradation Data. <em>Environments</em> 6(12) 124
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/mkinmod.html b/docs/reference/mkinmod.html
index 40cc2ef4..7d6bc77b 100644
--- a/docs/reference/mkinmod.html
+++ b/docs/reference/mkinmod.html
@@ -40,10 +40,9 @@
 
 
 <meta property="og:title" content="Function to set up a kinetic model with one or more state variables — mkinmod" />
-<meta property="og:description" content="The function usually takes several expressions, each assigning a compound
-name to a list, specifying the kinetic model type and reaction or transfer
-to other observed compartments. Instead of specifying several expressions, a
-list of lists can be given in the speclist argument." />
+<meta property="og:description" content="This function is usually called using a call to mkinsub() for each observed
+variable, specifying the corresponding submodel as well as outgoing pathways
+(see examples)." />
 
 
 
@@ -75,7 +74,7 @@ list of lists can be given in the speclist argument." />
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -112,6 +111,9 @@ list of lists can be given in the speclist argument." />
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -120,7 +122,7 @@ list of lists can be given in the speclist argument." />
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -139,43 +141,42 @@ list of lists can be given in the speclist argument." />
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>Function to set up a kinetic model with one or more state variables</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/mkinmod.R'><code>R/mkinmod.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/mkinmod.R'><code>R/mkinmod.R</code></a></small>
     <div class="hidden name"><code>mkinmod.Rd</code></div>
     </div>
 
     <div class="ref-description">
-    <p>The function usually takes several expressions, each assigning a compound
-name to a list, specifying the kinetic model type and reaction or transfer
-to other observed compartments. Instead of specifying several expressions, a
-list of lists can be given in the speclist argument.</p>
+    <p>This function is usually called using a call to <code><a href='mkinsub.html'>mkinsub()</a></code> for each observed
+variable, specifying the corresponding submodel as well as outgoing pathways
+(see examples).</p>
     </div>
 
-    <pre class="usage"><span class='fu'>mkinmod</span>(
-  <span class='no'>...</span>,
-  <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"max"</span>,
-  <span class='kw'>speclist</span> <span class='kw'>=</span> <span class='kw'>NULL</span>,
-  <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>,
-  <span class='kw'>verbose</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>
-)</pre>
+    <pre class="usage"><span class='fu'>mkinmod</span><span class='op'>(</span>
+  <span class='va'>...</span>,
+  use_of_ff <span class='op'>=</span> <span class='st'>"max"</span>,
+  speclist <span class='op'>=</span> <span class='cn'>NULL</span>,
+  quiet <span class='op'>=</span> <span class='cn'>FALSE</span>,
+  verbose <span class='op'>=</span> <span class='cn'>FALSE</span>
+<span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
     <colgroup><col class="name" /><col class="desc" /></colgroup>
     <tr>
       <th>...</th>
-      <td><p>For each observed variable, a list has to be specified as an
-argument, containing at least a component <code>type</code>, specifying the type
-of kinetics to use for the variable. Currently, single first order
-kinetics "SFO", indeterminate order rate equation kinetics "IORE", or
-single first order with reversible binding "SFORB" are implemented for all
-variables, while "FOMC", "DFOP" and "HS" can additionally be chosen for
-the first variable which is assumed to be the source compartment.
-Additionally, each component of the list can include a character vector
-<code>to</code>, specifying names of variables to which a transfer is to be
-assumed in the model.  If the argument <code>use_of_ff</code> is set to "min"
+      <td><p>For each observed variable, a list as obtained by <code><a href='mkinsub.html'>mkinsub()</a></code>
+has to be specified as an argument (see examples).  Currently, single
+first order kinetics "SFO", indeterminate order rate equation kinetics
+"IORE", or single first order with reversible binding "SFORB" are
+implemented for all variables, while "FOMC", "DFOP", "HS" and "logistic"
+can additionally be chosen for the first variable which is assumed to be
+the source compartment.
+Additionally, <code><a href='mkinsub.html'>mkinsub()</a></code> has an argument <code>to</code>, specifying names of
+variables to which a transfer is to be assumed in the model.
+If the argument <code>use_of_ff</code> is set to "min"
 (default) and the model for the compartment is "SFO" or "SFORB", an
-additional component of the list can be "sink=FALSE" effectively fixing
-the flux to sink to zero.</p></td>
+additional <code><a href='mkinsub.html'>mkinsub()</a></code> argument can be <code>sink = FALSE</code>, effectively
+fixing the flux to sink to zero.</p></td>
     </tr>
     <tr>
       <th>use_of_ff</th>
@@ -197,14 +198,14 @@ argument. Default is NULL.</p></td>
     </tr>
     <tr>
       <th>verbose</th>
-      <td><p>If <code>TRUE</code>, passed to <code>cfunction</code> if
+      <td><p>If <code>TRUE</code>, passed to <code><a href='https://rdrr.io/pkg/inline/man/cfunction.html'>inline::cfunction()</a></code> if
 applicable to give detailed information about the C function being built.</p></td>
     </tr>
     </table>
 
     <h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>
 
-    <p>A list of class <code>mkinmod</code> for use with <code><a href='mkinfit.html'>mkinfit</a></code>,
+    <p>A list of class <code>mkinmod</code> for use with <code><a href='mkinfit.html'>mkinfit()</a></code>,
 containing, among others,</p>
 <dt>diffs</dt><dd><p>A vector of string representations of differential equations, one for
 each modelling variable.</p></dd>
@@ -222,11 +223,18 @@ returned by cfunction.</p></dd>
 
     <p>For the definition of model types and their parameters, the equations given
 in the FOCUS and NAFTA guidance documents are used.</p>
+<p>For kinetic models with more than one observed variable, a symbolic solution
+of the system of differential equations is included in the resulting
+mkinmod object in some cases, speeding up the solution.</p>
+<p>If a C compiler is found by <code><a href='https://rdrr.io/pkg/pkgbuild/man/has_compiler.html'>pkgbuild::has_compiler()</a></code> and there
+is more than one observed variable in the specification, C code is generated
+for evaluating the differential equations, compiled using
+<code><a href='https://rdrr.io/pkg/inline/man/cfunction.html'>inline::cfunction()</a></code> and added to the resulting mkinmod object.</p>
     <h2 class="hasAnchor" id="note"><a class="anchor" href="#note"></a>Note</h2>
 
     <p>The IORE submodel is not well tested for metabolites. When using this
-model for metabolites, you may want to read the second note in the help
-page to <code><a href='mkinfit.html'>mkinfit</a></code>.</p>
+model for metabolites, you may want to read the note in the help
+page to <a href='mkinfit.html'>mkinfit</a>.</p>
     <h2 class="hasAnchor" id="references"><a class="anchor" href="#references"></a>References</h2>
 
     <p>FOCUS (2006) &#8220;Guidance Document on Estimating Persistence
@@ -236,27 +244,31 @@ EC Document Reference Sanco/10058/2005 version 2.0, 434 pp,
 <a href='http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics'>http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a></p>
 <p>NAFTA Technical Working Group on Pesticides (not dated) Guidance for
 Evaluating and Calculating Degradation Kinetics in Environmental Media</p>
+    <h2 class="hasAnchor" id="author"><a class="anchor" href="#author"></a>Author</h2>
+
+    <p>Johannes Ranke</p>
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
     <pre class="examples"><div class='input'>
 <span class='co'># Specify the SFO model (this is not needed any more, as we can now mkinfit("SFO", ...)</span>
-<span class='no'>SFO</span> <span class='kw'>&lt;-</span> <span class='fu'>mkinmod</span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>))
+<span class='va'>SFO</span> <span class='op'>&lt;-</span> <span class='fu'>mkinmod</span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span><span class='op'>)</span>
 
 <span class='co'># One parent compound, one metabolite, both single first order</span>
-<span class='no'>SFO_SFO</span> <span class='kw'>&lt;-</span> <span class='fu'>mkinmod</span>(
-  <span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>, <span class='st'>"m1"</span>),
-  <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>))</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>
+<span class='va'>SFO_SFO</span> <span class='op'>&lt;-</span> <span class='fu'>mkinmod</span><span class='op'>(</span>
+  parent <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='st'>"m1"</span><span class='op'>)</span>,
+  m1 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>
 <span class='co'># \dontrun{</span>
 <span class='co'># The above model used to be specified like this, before the advent of mkinsub()</span>
-<span class='no'>SFO_SFO</span> <span class='kw'>&lt;-</span> <span class='fu'>mkinmod</span>(
-  <span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='st'>"m1"</span>),
-  <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>))</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>
+<span class='va'>SFO_SFO</span> <span class='op'>&lt;-</span> <span class='fu'>mkinmod</span><span class='op'>(</span>
+  parent <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>type <span class='op'>=</span> <span class='st'>"SFO"</span>, to <span class='op'>=</span> <span class='st'>"m1"</span><span class='op'>)</span>,
+  m1 <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>type <span class='op'>=</span> <span class='st'>"SFO"</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>
 <span class='co'># Show details of creating the C function</span>
-<span class='no'>SFO_SFO</span> <span class='kw'>&lt;-</span> <span class='fu'>mkinmod</span>(
-  <span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>, <span class='st'>"m1"</span>),
-  <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>), <span class='kw'>verbose</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#&gt; Compilation argument:
-#&gt;  /usr/lib/R/bin/R CMD SHLIB file5d7f45129ff2.c 2&gt; file5d7f45129ff2.c.err.txt 
-#&gt; Program source:
+<span class='va'>SFO_SFO</span> <span class='op'>&lt;-</span> <span class='fu'>mkinmod</span><span class='op'>(</span>
+  parent <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='st'>"m1"</span><span class='op'>)</span>,
+  m1 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span>, verbose <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; Program source:
 #&gt;   1: #include &lt;R.h&gt;
 #&gt;   2: 
 #&gt;   3: 
@@ -276,17 +288,39 @@ Evaluating and Calculating Degradation Kinetics in Environmental Media</p>
 #&gt;  17: f[0] = - k_parent * y[0];
 #&gt;  18: f[1] = + f_parent_to_m1 * k_parent * y[0] - k_m1 * y[1];
 #&gt;  19: }</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>
+<span class='co'># The symbolic solution which is available in this case is not</span>
+<span class='co'># made for human reading but for speed of computation</span>
+<span class='va'>SFO_SFO</span><span class='op'>$</span><span class='va'>deg_func</span>
+</div><div class='output co'>#&gt; function (observed, odeini, odeparms) 
+#&gt; {
+#&gt;     predicted &lt;- numeric(0)
+#&gt;     with(as.list(odeparms), {
+#&gt;         t &lt;- observed[observed$name == "parent", "time"]
+#&gt;         predicted &lt;&lt;- c(predicted, SFO.solution(t, odeini["parent"], 
+#&gt;             k_parent))
+#&gt;         t &lt;- observed[observed$name == "m1", "time"]
+#&gt;         predicted &lt;&lt;- c(predicted, (((k_m1 - k_parent) * odeini["m1"] - 
+#&gt;             f_parent_to_m1 * k_parent * odeini["parent"]) * exp(-k_m1 * 
+#&gt;             t) + f_parent_to_m1 * k_parent * odeini["parent"] * 
+#&gt;             exp(-k_parent * t))/(k_m1 - k_parent))
+#&gt;     })
+#&gt;     return(predicted)
+#&gt; }
+#&gt; &lt;environment: 0x55555b726d88&gt;</div><div class='input'>
 <span class='co'># If we have several parallel metabolites</span>
 <span class='co'># (compare tests/testthat/test_synthetic_data_for_UBA_2014.R)</span>
-<span class='no'>m_synth_DFOP_par</span> <span class='kw'>&lt;-</span> <span class='fu'>mkinmod</span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"DFOP"</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"M1"</span>, <span class='st'>"M2"</span>)),
-                           <span class='kw'>M1</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>),
-                           <span class='kw'>M2</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>),
-                           <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"max"</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-
-<span class='no'>fit_DFOP_par_c</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>m_synth_DFOP_par</span>,
-                          <span class='no'>synthetic_data_for_UBA_2014</span><span class='kw'>[[</span><span class='fl'>12</span>]]$<span class='no'>data</span>,
-                          <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-<span class='co'># }</span></div></pre>
+<span class='va'>m_synth_DFOP_par</span> <span class='op'>&lt;-</span> <span class='fu'>mkinmod</span><span class='op'>(</span>
+ parent <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"DFOP"</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"M1"</span>, <span class='st'>"M2"</span><span class='op'>)</span><span class='op'>)</span>,
+ M1 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span>,
+ M2 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span>,
+ use_of_ff <span class='op'>=</span> <span class='st'>"max"</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+
+<span class='va'>fit_DFOP_par_c</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='va'>m_synth_DFOP_par</span>,
+  <span class='va'>synthetic_data_for_UBA_2014</span><span class='op'>[[</span><span class='fl'>12</span><span class='op'>]</span><span class='op'>]</span><span class='op'>$</span><span class='va'>data</span>,
+  quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.000174</span></div><div class='input'><span class='co'># }</span>
+
+</div></pre>
   </div>
   <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
     <nav id="toc" data-toggle="toc" class="sticky-top">
@@ -302,7 +336,7 @@ Evaluating and Calculating Degradation Kinetics in Environmental Media</p>
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/mkinparplot-1.png b/docs/reference/mkinparplot-1.png
index 31800c09..a78bf313 100644
--- a/docs/reference/mkinparplot-1.png
+++ b/docs/reference/mkinparplot-1.png
diff --git a/docs/reference/mkinparplot.html b/docs/reference/mkinparplot.html
index 4ff4970e..3aa98dbf 100644
--- a/docs/reference/mkinparplot.html
+++ b/docs/reference/mkinparplot.html
@@ -73,7 +73,7 @@ mkinfit." />
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -110,6 +110,9 @@ mkinfit." />
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -118,7 +121,7 @@ mkinfit." />
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -137,7 +140,7 @@ mkinfit." />
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>Function to plot the confidence intervals obtained using mkinfit</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/mkinparplot.R'><code>R/mkinparplot.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/mkinparplot.R'><code>R/mkinparplot.R</code></a></small>
     <div class="hidden name"><code>mkinparplot.Rd</code></div>
     </div>
 
@@ -146,7 +149,7 @@ mkinfit." />
 <code><a href='mkinfit.html'>mkinfit</a></code>.</p>
     </div>
 
-    <pre class="usage"><span class='fu'>mkinparplot</span>(<span class='no'>object</span>)</pre>
+    <pre class="usage"><span class='fu'>mkinparplot</span><span class='op'>(</span><span class='va'>object</span><span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
@@ -161,14 +164,20 @@ mkinfit." />
 
     <p>Nothing is returned by this function, as it is called for its side
 effect, namely to produce a plot.</p>
+    <h2 class="hasAnchor" id="author"><a class="anchor" href="#author"></a>Author</h2>
+
+    <p>Johannes Ranke</p>
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
     <pre class="examples"><div class='input'>
 <span class='co'># \dontrun{</span>
-<span class='no'>model</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(
-  <span class='kw'>T245</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"phenol"</span>), <span class='kw'>sink</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>),
-  <span class='kw'>phenol</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"anisole"</span>)),
-  <span class='kw'>anisole</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>), <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"max"</span>)</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'><span class='no'>fit</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>model</span>, <span class='fu'><a href='https://rdrr.io/r/base/subset.html'>subset</a></span>(<span class='no'>mccall81_245T</span>, <span class='no'>soil</span> <span class='kw'>==</span> <span class='st'>"Commerce"</span>), <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'><span class='fu'>mkinparplot</span>(<span class='no'>fit</span>)</div><div class='img'><img src='mkinparplot-1.png' alt='' width='700' height='433' /></div><div class='input'># }
+<span class='va'>model</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>
+  T245 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, to <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"phenol"</span><span class='op'>)</span>, sink <span class='op'>=</span> <span class='cn'>FALSE</span><span class='op'>)</span>,
+  phenol <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, to <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"anisole"</span><span class='op'>)</span><span class='op'>)</span>,
+  anisole <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span>, use_of_ff <span class='op'>=</span> <span class='st'>"max"</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'><span class='va'>fit</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='va'>model</span>, <span class='fu'><a href='https://rdrr.io/r/base/subset.html'>subset</a></span><span class='op'>(</span><span class='va'>mccall81_245T</span>, <span class='va'>soil</span> <span class='op'>==</span> <span class='st'>"Commerce"</span><span class='op'>)</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'><span class='fu'>mkinparplot</span><span class='op'>(</span><span class='va'>fit</span><span class='op'>)</span>
+</div><div class='img'><img src='mkinparplot-1.png' alt='' width='700' height='433' /></div><div class='input'><span class='co'># }</span>
 </div></pre>
   </div>
   <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
@@ -185,7 +194,7 @@ effect, namely to produce a plot.</p>
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/mkinpredict.html b/docs/reference/mkinpredict.html
index e16de283..17f38938 100644
--- a/docs/reference/mkinpredict.html
+++ b/docs/reference/mkinpredict.html
@@ -74,7 +74,7 @@ kinetic parameters and initial values for the state variables." />
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -111,6 +111,9 @@ kinetic parameters and initial values for the state variables." />
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -119,7 +122,7 @@ kinetic parameters and initial values for the state variables." />
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -138,7 +141,7 @@ kinetic parameters and initial values for the state variables." />
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>Produce predictions from a kinetic model using specific parameters</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/mkinpredict.R'><code>R/mkinpredict.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/mkinpredict.R'><code>R/mkinpredict.R</code></a></small>
     <div class="hidden name"><code>mkinpredict.Rd</code></div>
     </div>
 
@@ -148,49 +151,49 @@ kinetic model as specified by <code><a href='mkinmod.html'>mkinmod</a></code>, u
 kinetic parameters and initial values for the state variables.</p>
     </div>
 
-    <pre class="usage"><span class='fu'>mkinpredict</span>(
-  <span class='no'>x</span>,
-  <span class='no'>odeparms</span>,
-  <span class='no'>odeini</span>,
-  <span class='kw'>outtimes</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/seq.html'>seq</a></span>(<span class='fl'>0</span>, <span class='fl'>120</span>, <span class='kw'>by</span> <span class='kw'>=</span> <span class='fl'>0.1</span>),
-  <span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='st'>"deSolve"</span>,
-  <span class='kw'>use_compiled</span> <span class='kw'>=</span> <span class='st'>"auto"</span>,
-  <span class='kw'>method.ode</span> <span class='kw'>=</span> <span class='st'>"lsoda"</span>,
-  <span class='kw'>atol</span> <span class='kw'>=</span> <span class='fl'>1e-08</span>,
-  <span class='kw'>rtol</span> <span class='kw'>=</span> <span class='fl'>1e-10</span>,
-  <span class='kw'>map_output</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>,
-  <span class='no'>...</span>
-)
+    <pre class="usage"><span class='fu'>mkinpredict</span><span class='op'>(</span>
+  <span class='va'>x</span>,
+  <span class='va'>odeparms</span>,
+  <span class='va'>odeini</span>,
+  outtimes <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/seq.html'>seq</a></span><span class='op'>(</span><span class='fl'>0</span>, <span class='fl'>120</span>, by <span class='op'>=</span> <span class='fl'>0.1</span><span class='op'>)</span>,
+  solution_type <span class='op'>=</span> <span class='st'>"deSolve"</span>,
+  use_compiled <span class='op'>=</span> <span class='st'>"auto"</span>,
+  method.ode <span class='op'>=</span> <span class='st'>"lsoda"</span>,
+  atol <span class='op'>=</span> <span class='fl'>1e-08</span>,
+  rtol <span class='op'>=</span> <span class='fl'>1e-10</span>,
+  map_output <span class='op'>=</span> <span class='cn'>TRUE</span>,
+  <span class='va'>...</span>
+<span class='op'>)</span>
 
 <span class='co'># S3 method for mkinmod</span>
-<span class='fu'>mkinpredict</span>(
-  <span class='no'>x</span>,
-  <span class='kw'>odeparms</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>k_parent_sink</span> <span class='kw'>=</span> <span class='fl'>0.1</span>),
-  <span class='kw'>odeini</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fl'>100</span>),
-  <span class='kw'>outtimes</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/seq.html'>seq</a></span>(<span class='fl'>0</span>, <span class='fl'>120</span>, <span class='kw'>by</span> <span class='kw'>=</span> <span class='fl'>0.1</span>),
-  <span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='st'>"deSolve"</span>,
-  <span class='kw'>use_compiled</span> <span class='kw'>=</span> <span class='st'>"auto"</span>,
-  <span class='kw'>method.ode</span> <span class='kw'>=</span> <span class='st'>"lsoda"</span>,
-  <span class='kw'>atol</span> <span class='kw'>=</span> <span class='fl'>1e-08</span>,
-  <span class='kw'>rtol</span> <span class='kw'>=</span> <span class='fl'>1e-10</span>,
-  <span class='kw'>map_output</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>,
-  <span class='no'>...</span>
-)
+<span class='fu'>mkinpredict</span><span class='op'>(</span>
+  <span class='va'>x</span>,
+  odeparms <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>k_parent_sink <span class='op'>=</span> <span class='fl'>0.1</span><span class='op'>)</span>,
+  odeini <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fl'>100</span><span class='op'>)</span>,
+  outtimes <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/seq.html'>seq</a></span><span class='op'>(</span><span class='fl'>0</span>, <span class='fl'>120</span>, by <span class='op'>=</span> <span class='fl'>0.1</span><span class='op'>)</span>,
+  solution_type <span class='op'>=</span> <span class='st'>"deSolve"</span>,
+  use_compiled <span class='op'>=</span> <span class='st'>"auto"</span>,
+  method.ode <span class='op'>=</span> <span class='st'>"lsoda"</span>,
+  atol <span class='op'>=</span> <span class='fl'>1e-08</span>,
+  rtol <span class='op'>=</span> <span class='fl'>1e-10</span>,
+  map_output <span class='op'>=</span> <span class='cn'>TRUE</span>,
+  <span class='va'>...</span>
+<span class='op'>)</span>
 
 <span class='co'># S3 method for mkinfit</span>
-<span class='fu'>mkinpredict</span>(
-  <span class='no'>x</span>,
-  <span class='kw'>odeparms</span> <span class='kw'>=</span> <span class='no'>x</span>$<span class='no'>bparms.ode</span>,
-  <span class='kw'>odeini</span> <span class='kw'>=</span> <span class='no'>x</span>$<span class='no'>bparms.state</span>,
-  <span class='kw'>outtimes</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/seq.html'>seq</a></span>(<span class='fl'>0</span>, <span class='fl'>120</span>, <span class='kw'>by</span> <span class='kw'>=</span> <span class='fl'>0.1</span>),
-  <span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='st'>"deSolve"</span>,
-  <span class='kw'>use_compiled</span> <span class='kw'>=</span> <span class='st'>"auto"</span>,
-  <span class='kw'>method.ode</span> <span class='kw'>=</span> <span class='st'>"lsoda"</span>,
-  <span class='kw'>atol</span> <span class='kw'>=</span> <span class='fl'>1e-08</span>,
-  <span class='kw'>rtol</span> <span class='kw'>=</span> <span class='fl'>1e-10</span>,
-  <span class='kw'>map_output</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>,
-  <span class='no'>...</span>
-)</pre>
+<span class='fu'>mkinpredict</span><span class='op'>(</span>
+  <span class='va'>x</span>,
+  odeparms <span class='op'>=</span> <span class='va'>x</span><span class='op'>$</span><span class='va'>bparms.ode</span>,
+  odeini <span class='op'>=</span> <span class='va'>x</span><span class='op'>$</span><span class='va'>bparms.state</span>,
+  outtimes <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/seq.html'>seq</a></span><span class='op'>(</span><span class='fl'>0</span>, <span class='fl'>120</span>, by <span class='op'>=</span> <span class='fl'>0.1</span><span class='op'>)</span>,
+  solution_type <span class='op'>=</span> <span class='st'>"deSolve"</span>,
+  use_compiled <span class='op'>=</span> <span class='st'>"auto"</span>,
+  method.ode <span class='op'>=</span> <span class='st'>"lsoda"</span>,
+  atol <span class='op'>=</span> <span class='fl'>1e-08</span>,
+  rtol <span class='op'>=</span> <span class='fl'>1e-10</span>,
+  map_output <span class='op'>=</span> <span class='cn'>TRUE</span>,
+  <span class='va'>...</span>
+<span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
@@ -264,13 +267,17 @@ solver is used.</p></td>
     <h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>
 
     <p>A matrix with the numeric solution in wide format</p>
+    <h2 class="hasAnchor" id="author"><a class="anchor" href="#author"></a>Author</h2>
+
+    <p>Johannes Ranke</p>
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
     <pre class="examples"><div class='input'>
-<span class='no'>SFO</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>degradinol</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>))
+<span class='va'>SFO</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>degradinol <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span><span class='op'>)</span>
 <span class='co'># Compare solution types</span>
-<span class='fu'>mkinpredict</span>(<span class='no'>SFO</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>k_degradinol</span> <span class='kw'>=</span> <span class='fl'>0.3</span>), <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>degradinol</span> <span class='kw'>=</span> <span class='fl'>100</span>), <span class='fl'>0</span>:<span class='fl'>20</span>,
-      <span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='st'>"analytical"</span>)</div><div class='output co'>#&gt;    time  degradinol
+<span class='fu'>mkinpredict</span><span class='op'>(</span><span class='va'>SFO</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>k_degradinol <span class='op'>=</span> <span class='fl'>0.3</span><span class='op'>)</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>degradinol <span class='op'>=</span> <span class='fl'>100</span><span class='op'>)</span>, <span class='fl'>0</span><span class='op'>:</span><span class='fl'>20</span>,
+      solution_type <span class='op'>=</span> <span class='st'>"analytical"</span><span class='op'>)</span>
+</div><div class='output co'>#&gt;    time  degradinol
 #&gt; 0     0 100.0000000
 #&gt; 1     1  74.0818221
 #&gt; 2     2  54.8811636
@@ -291,8 +298,9 @@ solver is used.</p></td>
 #&gt; 17   17   0.6096747
 #&gt; 18   18   0.4516581
 #&gt; 19   19   0.3345965
-#&gt; 20   20   0.2478752</div><div class='input'><span class='fu'>mkinpredict</span>(<span class='no'>SFO</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>k_degradinol</span> <span class='kw'>=</span> <span class='fl'>0.3</span>), <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>degradinol</span> <span class='kw'>=</span> <span class='fl'>100</span>), <span class='fl'>0</span>:<span class='fl'>20</span>,
-      <span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='st'>"deSolve"</span>)</div><div class='output co'>#&gt;    time  degradinol
+#&gt; 20   20   0.2478752</div><div class='input'><span class='fu'>mkinpredict</span><span class='op'>(</span><span class='va'>SFO</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>k_degradinol <span class='op'>=</span> <span class='fl'>0.3</span><span class='op'>)</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>degradinol <span class='op'>=</span> <span class='fl'>100</span><span class='op'>)</span>, <span class='fl'>0</span><span class='op'>:</span><span class='fl'>20</span>,
+      solution_type <span class='op'>=</span> <span class='st'>"deSolve"</span><span class='op'>)</span>
+</div><div class='output co'>#&gt;    time  degradinol
 #&gt; 0     0 100.0000000
 #&gt; 1     1  74.0818221
 #&gt; 2     2  54.8811636
@@ -313,8 +321,9 @@ solver is used.</p></td>
 #&gt; 17   17   0.6096747
 #&gt; 18   18   0.4516581
 #&gt; 19   19   0.3345965
-#&gt; 20   20   0.2478752</div><div class='input'><span class='fu'>mkinpredict</span>(<span class='no'>SFO</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>k_degradinol</span> <span class='kw'>=</span> <span class='fl'>0.3</span>), <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>degradinol</span> <span class='kw'>=</span> <span class='fl'>100</span>), <span class='fl'>0</span>:<span class='fl'>20</span>,
-      <span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='st'>"deSolve"</span>, <span class='kw'>use_compiled</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>)</div><div class='output co'>#&gt;    time  degradinol
+#&gt; 20   20   0.2478752</div><div class='input'><span class='fu'>mkinpredict</span><span class='op'>(</span><span class='va'>SFO</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>k_degradinol <span class='op'>=</span> <span class='fl'>0.3</span><span class='op'>)</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>degradinol <span class='op'>=</span> <span class='fl'>100</span><span class='op'>)</span>, <span class='fl'>0</span><span class='op'>:</span><span class='fl'>20</span>,
+      solution_type <span class='op'>=</span> <span class='st'>"deSolve"</span>, use_compiled <span class='op'>=</span> <span class='cn'>FALSE</span><span class='op'>)</span>
+</div><div class='output co'>#&gt;    time  degradinol
 #&gt; 0     0 100.0000000
 #&gt; 1     1  74.0818221
 #&gt; 2     2  54.8811636
@@ -335,8 +344,9 @@ solver is used.</p></td>
 #&gt; 17   17   0.6096747
 #&gt; 18   18   0.4516581
 #&gt; 19   19   0.3345965
-#&gt; 20   20   0.2478752</div><div class='input'><span class='fu'>mkinpredict</span>(<span class='no'>SFO</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>k_degradinol</span> <span class='kw'>=</span> <span class='fl'>0.3</span>), <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>degradinol</span> <span class='kw'>=</span> <span class='fl'>100</span>), <span class='fl'>0</span>:<span class='fl'>20</span>,
-      <span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='st'>"eigen"</span>)</div><div class='output co'>#&gt;    time  degradinol
+#&gt; 20   20   0.2478752</div><div class='input'><span class='fu'>mkinpredict</span><span class='op'>(</span><span class='va'>SFO</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>k_degradinol <span class='op'>=</span> <span class='fl'>0.3</span><span class='op'>)</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>degradinol <span class='op'>=</span> <span class='fl'>100</span><span class='op'>)</span>, <span class='fl'>0</span><span class='op'>:</span><span class='fl'>20</span>,
+      solution_type <span class='op'>=</span> <span class='st'>"eigen"</span><span class='op'>)</span>
+</div><div class='output co'>#&gt;    time  degradinol
 #&gt; 0     0 100.0000000
 #&gt; 1     1  74.0818221
 #&gt; 2     2  54.8811636
@@ -359,59 +369,68 @@ solver is used.</p></td>
 #&gt; 19   19   0.3345965
 #&gt; 20   20   0.2478752</div><div class='input'>
 <span class='co'># Compare integration methods to analytical solution</span>
-<span class='fu'>mkinpredict</span>(<span class='no'>SFO</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>k_degradinol</span> <span class='kw'>=</span> <span class='fl'>0.3</span>), <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>degradinol</span> <span class='kw'>=</span> <span class='fl'>100</span>), <span class='fl'>0</span>:<span class='fl'>20</span>,
-      <span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='st'>"analytical"</span>)[<span class='fl'>21</span>,]</div><div class='output co'>#&gt;       time degradinol 
-#&gt; 20.0000000  0.2478752 </div><div class='input'><span class='fu'>mkinpredict</span>(<span class='no'>SFO</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>k_degradinol</span> <span class='kw'>=</span> <span class='fl'>0.3</span>), <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>degradinol</span> <span class='kw'>=</span> <span class='fl'>100</span>), <span class='fl'>0</span>:<span class='fl'>20</span>,
-      <span class='kw'>method</span> <span class='kw'>=</span> <span class='st'>"lsoda"</span>)[<span class='fl'>21</span>,]</div><div class='output co'>#&gt;       time degradinol 
-#&gt; 20.0000000  0.2478752 </div><div class='input'><span class='fu'>mkinpredict</span>(<span class='no'>SFO</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>k_degradinol</span> <span class='kw'>=</span> <span class='fl'>0.3</span>), <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>degradinol</span> <span class='kw'>=</span> <span class='fl'>100</span>), <span class='fl'>0</span>:<span class='fl'>20</span>,
-      <span class='kw'>method</span> <span class='kw'>=</span> <span class='st'>"ode45"</span>)[<span class='fl'>21</span>,]</div><div class='output co'>#&gt;       time degradinol 
-#&gt; 20.0000000  0.2478752 </div><div class='input'><span class='fu'>mkinpredict</span>(<span class='no'>SFO</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>k_degradinol</span> <span class='kw'>=</span> <span class='fl'>0.3</span>), <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>degradinol</span> <span class='kw'>=</span> <span class='fl'>100</span>), <span class='fl'>0</span>:<span class='fl'>20</span>,
-      <span class='kw'>method</span> <span class='kw'>=</span> <span class='st'>"rk4"</span>)[<span class='fl'>21</span>,]</div><div class='output co'>#&gt;       time degradinol 
+<span class='fu'>mkinpredict</span><span class='op'>(</span><span class='va'>SFO</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>k_degradinol <span class='op'>=</span> <span class='fl'>0.3</span><span class='op'>)</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>degradinol <span class='op'>=</span> <span class='fl'>100</span><span class='op'>)</span>, <span class='fl'>0</span><span class='op'>:</span><span class='fl'>20</span>,
+      solution_type <span class='op'>=</span> <span class='st'>"analytical"</span><span class='op'>)</span><span class='op'>[</span><span class='fl'>21</span>,<span class='op'>]</span>
+</div><div class='output co'>#&gt;       time degradinol 
+#&gt; 20.0000000  0.2478752 </div><div class='input'><span class='fu'>mkinpredict</span><span class='op'>(</span><span class='va'>SFO</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>k_degradinol <span class='op'>=</span> <span class='fl'>0.3</span><span class='op'>)</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>degradinol <span class='op'>=</span> <span class='fl'>100</span><span class='op'>)</span>, <span class='fl'>0</span><span class='op'>:</span><span class='fl'>20</span>,
+      method <span class='op'>=</span> <span class='st'>"lsoda"</span><span class='op'>)</span><span class='op'>[</span><span class='fl'>21</span>,<span class='op'>]</span>
+</div><div class='output co'>#&gt;       time degradinol 
+#&gt; 20.0000000  0.2478752 </div><div class='input'><span class='fu'>mkinpredict</span><span class='op'>(</span><span class='va'>SFO</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>k_degradinol <span class='op'>=</span> <span class='fl'>0.3</span><span class='op'>)</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>degradinol <span class='op'>=</span> <span class='fl'>100</span><span class='op'>)</span>, <span class='fl'>0</span><span class='op'>:</span><span class='fl'>20</span>,
+      method <span class='op'>=</span> <span class='st'>"ode45"</span><span class='op'>)</span><span class='op'>[</span><span class='fl'>21</span>,<span class='op'>]</span>
+</div><div class='output co'>#&gt;       time degradinol 
+#&gt; 20.0000000  0.2478752 </div><div class='input'><span class='fu'>mkinpredict</span><span class='op'>(</span><span class='va'>SFO</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>k_degradinol <span class='op'>=</span> <span class='fl'>0.3</span><span class='op'>)</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>degradinol <span class='op'>=</span> <span class='fl'>100</span><span class='op'>)</span>, <span class='fl'>0</span><span class='op'>:</span><span class='fl'>20</span>,
+      method <span class='op'>=</span> <span class='st'>"rk4"</span><span class='op'>)</span><span class='op'>[</span><span class='fl'>21</span>,<span class='op'>]</span>
+</div><div class='output co'>#&gt;       time degradinol 
 #&gt; 20.0000000  0.2480043 </div><div class='input'><span class='co'># rk4 is not as precise here</span>
 
 <span class='co'># The number of output times used to make a lot of difference until the</span>
 <span class='co'># default for atol was adjusted</span>
-<span class='fu'>mkinpredict</span>(<span class='no'>SFO</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>k_degradinol</span> <span class='kw'>=</span> <span class='fl'>0.3</span>), <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>degradinol</span> <span class='kw'>=</span> <span class='fl'>100</span>),
-      <span class='fu'><a href='https://rdrr.io/r/base/seq.html'>seq</a></span>(<span class='fl'>0</span>, <span class='fl'>20</span>, <span class='kw'>by</span> <span class='kw'>=</span> <span class='fl'>0.1</span>))[<span class='fl'>201</span>,]</div><div class='output co'>#&gt;       time degradinol 
-#&gt; 20.0000000  0.2478752 </div><div class='input'><span class='fu'>mkinpredict</span>(<span class='no'>SFO</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>k_degradinol</span> <span class='kw'>=</span> <span class='fl'>0.3</span>), <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>degradinol</span> <span class='kw'>=</span> <span class='fl'>100</span>),
-      <span class='fu'><a href='https://rdrr.io/r/base/seq.html'>seq</a></span>(<span class='fl'>0</span>, <span class='fl'>20</span>, <span class='kw'>by</span> <span class='kw'>=</span> <span class='fl'>0.01</span>))[<span class='fl'>2001</span>,]</div><div class='output co'>#&gt;       time degradinol 
+<span class='fu'>mkinpredict</span><span class='op'>(</span><span class='va'>SFO</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>k_degradinol <span class='op'>=</span> <span class='fl'>0.3</span><span class='op'>)</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>degradinol <span class='op'>=</span> <span class='fl'>100</span><span class='op'>)</span>,
+      <span class='fu'><a href='https://rdrr.io/r/base/seq.html'>seq</a></span><span class='op'>(</span><span class='fl'>0</span>, <span class='fl'>20</span>, by <span class='op'>=</span> <span class='fl'>0.1</span><span class='op'>)</span><span class='op'>)</span><span class='op'>[</span><span class='fl'>201</span>,<span class='op'>]</span>
+</div><div class='output co'>#&gt;       time degradinol 
+#&gt; 20.0000000  0.2478752 </div><div class='input'><span class='fu'>mkinpredict</span><span class='op'>(</span><span class='va'>SFO</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>k_degradinol <span class='op'>=</span> <span class='fl'>0.3</span><span class='op'>)</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>degradinol <span class='op'>=</span> <span class='fl'>100</span><span class='op'>)</span>,
+      <span class='fu'><a href='https://rdrr.io/r/base/seq.html'>seq</a></span><span class='op'>(</span><span class='fl'>0</span>, <span class='fl'>20</span>, by <span class='op'>=</span> <span class='fl'>0.01</span><span class='op'>)</span><span class='op'>)</span><span class='op'>[</span><span class='fl'>2001</span>,<span class='op'>]</span>
+</div><div class='output co'>#&gt;       time degradinol 
 #&gt; 20.0000000  0.2478752 </div><div class='input'>
 <span class='co'># Comparison of the performance of solution types</span>
-<span class='no'>SFO_SFO</span> <span class='kw'>=</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='st'>"m1"</span>),
-                  <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>), <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"max"</span>)</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'><span class='kw'>if</span>(<span class='fu'><a href='https://rdrr.io/r/base/library.html'>require</a></span>(<span class='no'>rbenchmark</span>)) {
-  <span class='fu'><a href='https://rdrr.io/pkg/rbenchmark/man/benchmark.html'>benchmark</a></span>(<span class='kw'>replications</span> <span class='kw'>=</span> <span class='fl'>10</span>, <span class='kw'>order</span> <span class='kw'>=</span> <span class='st'>"relative"</span>, <span class='kw'>columns</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"test"</span>, <span class='st'>"relative"</span>, <span class='st'>"elapsed"</span>),
-    <span class='kw'>eigen</span> <span class='kw'>=</span> <span class='fu'>mkinpredict</span>(<span class='no'>SFO_SFO</span>,
-      <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>k_parent</span> <span class='kw'>=</span> <span class='fl'>0.15</span>, <span class='kw'>f_parent_to_m1</span> <span class='kw'>=</span> <span class='fl'>0.5</span>, <span class='kw'>k_m1</span> <span class='kw'>=</span> <span class='fl'>0.01</span>),
-      <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fl'>100</span>, <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fl'>0</span>), <span class='fu'><a href='https://rdrr.io/r/base/seq.html'>seq</a></span>(<span class='fl'>0</span>, <span class='fl'>20</span>, <span class='kw'>by</span> <span class='kw'>=</span> <span class='fl'>0.1</span>),
-      <span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='st'>"eigen"</span>)[<span class='fl'>201</span>,],
-    <span class='kw'>deSolve_compiled</span> <span class='kw'>=</span> <span class='fu'>mkinpredict</span>(<span class='no'>SFO_SFO</span>,
-      <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>k_parent</span> <span class='kw'>=</span> <span class='fl'>0.15</span>, <span class='kw'>f_parent_to_m1</span> <span class='kw'>=</span> <span class='fl'>0.5</span>, <span class='kw'>k_m1</span> <span class='kw'>=</span> <span class='fl'>0.01</span>),
-      <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fl'>100</span>, <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fl'>0</span>), <span class='fu'><a href='https://rdrr.io/r/base/seq.html'>seq</a></span>(<span class='fl'>0</span>, <span class='fl'>20</span>, <span class='kw'>by</span> <span class='kw'>=</span> <span class='fl'>0.1</span>),
-      <span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='st'>"deSolve"</span>)[<span class='fl'>201</span>,],
-    <span class='kw'>deSolve</span> <span class='kw'>=</span> <span class='fu'>mkinpredict</span>(<span class='no'>SFO_SFO</span>,
-      <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>k_parent</span> <span class='kw'>=</span> <span class='fl'>0.15</span>, <span class='kw'>f_parent_to_m1</span> <span class='kw'>=</span> <span class='fl'>0.5</span>, <span class='kw'>k_m1</span> <span class='kw'>=</span> <span class='fl'>0.01</span>),
-      <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fl'>100</span>, <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fl'>0</span>), <span class='fu'><a href='https://rdrr.io/r/base/seq.html'>seq</a></span>(<span class='fl'>0</span>, <span class='fl'>20</span>, <span class='kw'>by</span> <span class='kw'>=</span> <span class='fl'>0.1</span>),
-      <span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='st'>"deSolve"</span>, <span class='kw'>use_compiled</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>)[<span class='fl'>201</span>,],
-    <span class='kw'>analytical</span> <span class='kw'>=</span> <span class='fu'>mkinpredict</span>(<span class='no'>SFO_SFO</span>,
-      <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>k_parent</span> <span class='kw'>=</span> <span class='fl'>0.15</span>, <span class='kw'>f_parent_to_m1</span> <span class='kw'>=</span> <span class='fl'>0.5</span>, <span class='kw'>k_m1</span> <span class='kw'>=</span> <span class='fl'>0.01</span>),
-      <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fl'>100</span>, <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fl'>0</span>), <span class='fu'><a href='https://rdrr.io/r/base/seq.html'>seq</a></span>(<span class='fl'>0</span>, <span class='fl'>20</span>, <span class='kw'>by</span> <span class='kw'>=</span> <span class='fl'>0.1</span>),
-      <span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='st'>"analytical"</span>, <span class='kw'>use_compiled</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>)[<span class='fl'>201</span>,])
-}</div><div class='output co'>#&gt;               test relative elapsed
-#&gt; 2 deSolve_compiled     1.00   0.004
-#&gt; 4       analytical     1.00   0.004
-#&gt; 1            eigen     4.75   0.019
-#&gt; 3          deSolve    54.75   0.219</div><div class='input'>
+<span class='va'>SFO_SFO</span> <span class='op'>=</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>type <span class='op'>=</span> <span class='st'>"SFO"</span>, to <span class='op'>=</span> <span class='st'>"m1"</span><span class='op'>)</span>,
+                  m1 <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>type <span class='op'>=</span> <span class='st'>"SFO"</span><span class='op'>)</span>, use_of_ff <span class='op'>=</span> <span class='st'>"max"</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'><span class='kw'>if</span><span class='op'>(</span><span class='kw'><a href='https://rdrr.io/r/base/library.html'>require</a></span><span class='op'>(</span><span class='va'><a href='http://rbenchmark.googlecode.com'>rbenchmark</a></span><span class='op'>)</span><span class='op'>)</span> <span class='op'>{</span>
+  <span class='fu'><a href='https://rdrr.io/pkg/rbenchmark/man/benchmark.html'>benchmark</a></span><span class='op'>(</span>replications <span class='op'>=</span> <span class='fl'>10</span>, order <span class='op'>=</span> <span class='st'>"relative"</span>, columns <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"test"</span>, <span class='st'>"relative"</span>, <span class='st'>"elapsed"</span><span class='op'>)</span>,
+    eigen <span class='op'>=</span> <span class='fu'>mkinpredict</span><span class='op'>(</span><span class='va'>SFO_SFO</span>,
+      <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>k_parent <span class='op'>=</span> <span class='fl'>0.15</span>, f_parent_to_m1 <span class='op'>=</span> <span class='fl'>0.5</span>, k_m1 <span class='op'>=</span> <span class='fl'>0.01</span><span class='op'>)</span>,
+      <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fl'>100</span>, m1 <span class='op'>=</span> <span class='fl'>0</span><span class='op'>)</span>, <span class='fu'><a href='https://rdrr.io/r/base/seq.html'>seq</a></span><span class='op'>(</span><span class='fl'>0</span>, <span class='fl'>20</span>, by <span class='op'>=</span> <span class='fl'>0.1</span><span class='op'>)</span>,
+      solution_type <span class='op'>=</span> <span class='st'>"eigen"</span><span class='op'>)</span><span class='op'>[</span><span class='fl'>201</span>,<span class='op'>]</span>,
+    deSolve_compiled <span class='op'>=</span> <span class='fu'>mkinpredict</span><span class='op'>(</span><span class='va'>SFO_SFO</span>,
+      <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>k_parent <span class='op'>=</span> <span class='fl'>0.15</span>, f_parent_to_m1 <span class='op'>=</span> <span class='fl'>0.5</span>, k_m1 <span class='op'>=</span> <span class='fl'>0.01</span><span class='op'>)</span>,
+      <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fl'>100</span>, m1 <span class='op'>=</span> <span class='fl'>0</span><span class='op'>)</span>, <span class='fu'><a href='https://rdrr.io/r/base/seq.html'>seq</a></span><span class='op'>(</span><span class='fl'>0</span>, <span class='fl'>20</span>, by <span class='op'>=</span> <span class='fl'>0.1</span><span class='op'>)</span>,
+      solution_type <span class='op'>=</span> <span class='st'>"deSolve"</span><span class='op'>)</span><span class='op'>[</span><span class='fl'>201</span>,<span class='op'>]</span>,
+    deSolve <span class='op'>=</span> <span class='fu'>mkinpredict</span><span class='op'>(</span><span class='va'>SFO_SFO</span>,
+      <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>k_parent <span class='op'>=</span> <span class='fl'>0.15</span>, f_parent_to_m1 <span class='op'>=</span> <span class='fl'>0.5</span>, k_m1 <span class='op'>=</span> <span class='fl'>0.01</span><span class='op'>)</span>,
+      <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fl'>100</span>, m1 <span class='op'>=</span> <span class='fl'>0</span><span class='op'>)</span>, <span class='fu'><a href='https://rdrr.io/r/base/seq.html'>seq</a></span><span class='op'>(</span><span class='fl'>0</span>, <span class='fl'>20</span>, by <span class='op'>=</span> <span class='fl'>0.1</span><span class='op'>)</span>,
+      solution_type <span class='op'>=</span> <span class='st'>"deSolve"</span>, use_compiled <span class='op'>=</span> <span class='cn'>FALSE</span><span class='op'>)</span><span class='op'>[</span><span class='fl'>201</span>,<span class='op'>]</span>,
+    analytical <span class='op'>=</span> <span class='fu'>mkinpredict</span><span class='op'>(</span><span class='va'>SFO_SFO</span>,
+      <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>k_parent <span class='op'>=</span> <span class='fl'>0.15</span>, f_parent_to_m1 <span class='op'>=</span> <span class='fl'>0.5</span>, k_m1 <span class='op'>=</span> <span class='fl'>0.01</span><span class='op'>)</span>,
+      <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fl'>100</span>, m1 <span class='op'>=</span> <span class='fl'>0</span><span class='op'>)</span>, <span class='fu'><a href='https://rdrr.io/r/base/seq.html'>seq</a></span><span class='op'>(</span><span class='fl'>0</span>, <span class='fl'>20</span>, by <span class='op'>=</span> <span class='fl'>0.1</span><span class='op'>)</span>,
+      solution_type <span class='op'>=</span> <span class='st'>"analytical"</span>, use_compiled <span class='op'>=</span> <span class='cn'>FALSE</span><span class='op'>)</span><span class='op'>[</span><span class='fl'>201</span>,<span class='op'>]</span><span class='op'>)</span>
+<span class='op'>}</span>
+</div><div class='output co'>#&gt;               test relative elapsed
+#&gt; 4       analytical      1.0   0.005
+#&gt; 2 deSolve_compiled      1.2   0.006
+#&gt; 1            eigen      4.0   0.020
+#&gt; 3          deSolve     45.6   0.228</div><div class='input'>
 <span class='co'># \dontrun{</span>
   <span class='co'># Predict from a fitted model</span>
-  <span class='no'>f</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>SFO_SFO</span>, <span class='no'>FOCUS_2006_C</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-  <span class='no'>f</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>SFO_SFO</span>, <span class='no'>FOCUS_2006_C</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='st'>"deSolve"</span>)
-  <span class='fu'><a href='https://rdrr.io/r/utils/head.html'>head</a></span>(<span class='fu'>mkinpredict</span>(<span class='no'>f</span>))</div><div class='output co'>#&gt;     time   parent       m1
+  <span class='va'>f</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='va'>SFO_SFO</span>, <span class='va'>FOCUS_2006_C</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+  <span class='va'>f</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='va'>SFO_SFO</span>, <span class='va'>FOCUS_2006_C</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, solution_type <span class='op'>=</span> <span class='st'>"deSolve"</span><span class='op'>)</span>
+  <span class='fu'><a href='https://rdrr.io/r/utils/head.html'>head</a></span><span class='op'>(</span><span class='fu'>mkinpredict</span><span class='op'>(</span><span class='va'>f</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='output co'>#&gt;     time   parent       m1
 #&gt; 0    0.0 82.49216 0.000000
 #&gt; 0.1  0.1 80.00562 1.236198
 #&gt; 0.2  0.2 77.59404 2.422818
 #&gt; 0.3  0.3 75.25514 3.561476
 #&gt; 0.4  0.4 72.98675 4.653740
-#&gt; 0.5  0.5 70.78673 5.701130</div><div class='input'># }
+#&gt; 0.5  0.5 70.78673 5.701130</div><div class='input'><span class='co'># }</span>
 
 </div></pre>
   </div>
@@ -429,7 +448,7 @@ solver is used.</p></td>
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/mkinresplot-1.png b/docs/reference/mkinresplot-1.png
index bb9657b4..8114b6cd 100644
--- a/docs/reference/mkinresplot-1.png
+++ b/docs/reference/mkinresplot-1.png
diff --git a/docs/reference/mkinresplot.html b/docs/reference/mkinresplot.html
index 82afe2e2..d917860a 100644
--- a/docs/reference/mkinresplot.html
+++ b/docs/reference/mkinresplot.html
@@ -75,7 +75,7 @@ argument show_residuals = TRUE." />
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -112,6 +112,9 @@ argument show_residuals = TRUE." />
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -120,7 +123,7 @@ argument show_residuals = TRUE." />
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -139,7 +142,7 @@ argument show_residuals = TRUE." />
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>Function to plot residuals stored in an mkin object</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/mkinresplot.R'><code>R/mkinresplot.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/mkinresplot.R'><code>R/mkinresplot.R</code></a></small>
     <div class="hidden name"><code>mkinresplot.Rd</code></div>
     </div>
 
@@ -150,21 +153,21 @@ the residuals can be obtained using <code><a href='plot.mkinfit.html'>plot.mkinf
 argument <code>show_residuals = TRUE</code>.</p>
     </div>
 
-    <pre class="usage"><span class='fu'>mkinresplot</span>(
-  <span class='no'>object</span>,
-  <span class='kw'>obs_vars</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/names.html'>names</a></span>(<span class='no'>object</span>$<span class='no'>mkinmod</span>$<span class='no'>map</span>),
-  <span class='kw'>xlim</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='fl'>0</span>, <span class='fl'>1.1</span> * <span class='fu'><a href='https://rdrr.io/r/base/Extremes.html'>max</a></span>(<span class='no'>object</span>$<span class='no'>data</span>$<span class='no'>time</span>)),
-  <span class='kw'>standardized</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>,
-  <span class='kw'>xlab</span> <span class='kw'>=</span> <span class='st'>"Time"</span>,
-  <span class='kw'>ylab</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/ifelse.html'>ifelse</a></span>(<span class='no'>standardized</span>, <span class='st'>"Standardized residual"</span>, <span class='st'>"Residual"</span>),
-  <span class='kw'>maxabs</span> <span class='kw'>=</span> <span class='st'>"auto"</span>,
-  <span class='kw'>legend</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>,
-  <span class='kw'>lpos</span> <span class='kw'>=</span> <span class='st'>"topright"</span>,
-  <span class='kw'>col_obs</span> <span class='kw'>=</span> <span class='st'>"auto"</span>,
-  <span class='kw'>pch_obs</span> <span class='kw'>=</span> <span class='st'>"auto"</span>,
-  <span class='kw'>frame</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>,
-  <span class='no'>...</span>
-)</pre>
+    <pre class="usage"><span class='fu'>mkinresplot</span><span class='op'>(</span>
+  <span class='va'>object</span>,
+  obs_vars <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/names.html'>names</a></span><span class='op'>(</span><span class='va'>object</span><span class='op'>$</span><span class='va'>mkinmod</span><span class='op'>$</span><span class='va'>map</span><span class='op'>)</span>,
+  xlim <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>0</span>, <span class='fl'>1.1</span> <span class='op'>*</span> <span class='fu'><a href='https://rdrr.io/r/base/Extremes.html'>max</a></span><span class='op'>(</span><span class='va'>object</span><span class='op'>$</span><span class='va'>data</span><span class='op'>$</span><span class='va'>time</span><span class='op'>)</span><span class='op'>)</span>,
+  standardized <span class='op'>=</span> <span class='cn'>FALSE</span>,
+  xlab <span class='op'>=</span> <span class='st'>"Time"</span>,
+  ylab <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/ifelse.html'>ifelse</a></span><span class='op'>(</span><span class='va'>standardized</span>, <span class='st'>"Standardized residual"</span>, <span class='st'>"Residual"</span><span class='op'>)</span>,
+  maxabs <span class='op'>=</span> <span class='st'>"auto"</span>,
+  legend <span class='op'>=</span> <span class='cn'>TRUE</span>,
+  lpos <span class='op'>=</span> <span class='st'>"topright"</span>,
+  col_obs <span class='op'>=</span> <span class='st'>"auto"</span>,
+  pch_obs <span class='op'>=</span> <span class='st'>"auto"</span>,
+  frame <span class='op'>=</span> <span class='cn'>TRUE</span>,
+  <span class='va'>...</span>
+<span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
@@ -224,7 +227,7 @@ be passed on to <code><a href='https://rdrr.io/r/graphics/legend.html'>legend</a
     </tr>
     <tr>
       <th>...</th>
-      <td><p>further arguments passed to <code><a href='https://rdrr.io/r/base/plot.html'>plot</a></code>.</p></td>
+      <td><p>further arguments passed to <code><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></code>.</p></td>
     </tr>
     </table>
 
@@ -237,10 +240,16 @@ effect, namely to produce a plot.</p>
     <div class='dont-index'><p><code><a href='mkinplot.html'>mkinplot</a></code>, for a way to plot the data and the fitted
 lines of the mkinfit object, and <code><a href='plot.mkinfit.html'>plot_res</a></code> for a function
 combining the plot of the fit and the residual plot.</p></div>
+    <h2 class="hasAnchor" id="author"><a class="anchor" href="#author"></a>Author</h2>
+
+    <p>Johannes Ranke</p>
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
     <pre class="examples"><div class='input'>
-<span class='no'>model</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>, <span class='st'>"m1"</span>), <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>))</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'><span class='no'>fit</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>model</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'><span class='fu'>mkinresplot</span>(<span class='no'>fit</span>, <span class='st'>"m1"</span>)</div><div class='img'><img src='mkinresplot-1.png' alt='' width='700' height='433' /></div><div class='input'>
+<span class='va'>model</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='st'>"m1"</span><span class='op'>)</span>, m1 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'><span class='va'>fit</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='va'>model</span>, <span class='va'>FOCUS_2006_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.0165</span></div><div class='input'><span class='fu'>mkinresplot</span><span class='op'>(</span><span class='va'>fit</span>, <span class='st'>"m1"</span><span class='op'>)</span>
+</div><div class='img'><img src='mkinresplot-1.png' alt='' width='700' height='433' /></div><div class='input'>
 </div></pre>
   </div>
   <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
@@ -257,7 +266,7 @@ combining the plot of the fit and the residual plot.</p></div>
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/mkinsub.html b/docs/reference/mkinsub.html
index ac1220e0..77ee41f8 100644
--- a/docs/reference/mkinsub.html
+++ b/docs/reference/mkinsub.html
@@ -73,7 +73,7 @@ mkinmod." />
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -110,6 +110,9 @@ mkinmod." />
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -118,7 +121,7 @@ mkinmod." />
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -137,7 +140,7 @@ mkinmod." />
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>Function to set up a kinetic submodel for one state variable</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/mkinsub.R'><code>R/mkinsub.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/mkinsub.R'><code>R/mkinsub.R</code></a></small>
     <div class="hidden name"><code>mkinsub.Rd</code></div>
     </div>
 
@@ -146,7 +149,7 @@ mkinmod." />
 <code><a href='mkinmod.html'>mkinmod</a></code>.</p>
     </div>
 
-    <pre class="usage"><span class='fu'>mkinsub</span>(<span class='no'>submodel</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='kw'>NULL</span>, <span class='kw'>sink</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>full_name</span> <span class='kw'>=</span> <span class='fl'>NA</span>)</pre>
+    <pre class="usage"><span class='fu'>mkinsub</span><span class='op'>(</span><span class='va'>submodel</span>, to <span class='op'>=</span> <span class='cn'>NULL</span>, sink <span class='op'>=</span> <span class='cn'>TRUE</span>, full_name <span class='op'>=</span> <span class='cn'>NA</span><span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
@@ -178,22 +181,28 @@ results on other operating systems or system configurations.</p></td>
     <h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>
 
     <p>A list for use with <code><a href='mkinmod.html'>mkinmod</a></code>.</p>
+    <h2 class="hasAnchor" id="author"><a class="anchor" href="#author"></a>Author</h2>
+
+    <p>Johannes Ranke</p>
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
     <pre class="examples"><div class='input'>
 <span class='co'># One parent compound, one metabolite, both single first order.</span>
-<span class='no'>SFO_SFO</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(
-  <span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='st'>"m1"</span>),
-  <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>))</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>
+<span class='va'>SFO_SFO</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>
+  parent <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>type <span class='op'>=</span> <span class='st'>"SFO"</span>, to <span class='op'>=</span> <span class='st'>"m1"</span><span class='op'>)</span>,
+  m1 <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>type <span class='op'>=</span> <span class='st'>"SFO"</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>
 <span class='co'># The same model using mkinsub</span>
-<span class='no'>SFO_SFO.2</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(
-  <span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'>mkinsub</span>(<span class='st'>"SFO"</span>, <span class='st'>"m1"</span>),
-  <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'>mkinsub</span>(<span class='st'>"SFO"</span>))</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>
+<span class='va'>SFO_SFO.2</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>
+  parent <span class='op'>=</span> <span class='fu'>mkinsub</span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='st'>"m1"</span><span class='op'>)</span>,
+  m1 <span class='op'>=</span> <span class='fu'>mkinsub</span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>
 <span class='co'># \dontrun{</span>
   <span class='co'># Now supplying full names</span>
-  <span class='no'>SFO_SFO.2</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(
-    <span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'>mkinsub</span>(<span class='st'>"SFO"</span>, <span class='st'>"m1"</span>, <span class='kw'>full_name</span> <span class='kw'>=</span> <span class='st'>"Test compound"</span>),
-    <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'>mkinsub</span>(<span class='st'>"SFO"</span>, <span class='kw'>full_name</span> <span class='kw'>=</span> <span class='st'>"Metabolite M1"</span>))</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'> # }
+  <span class='va'>SFO_SFO.2</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>
+    parent <span class='op'>=</span> <span class='fu'>mkinsub</span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='st'>"m1"</span>, full_name <span class='op'>=</span> <span class='st'>"Test compound"</span><span class='op'>)</span>,
+    m1 <span class='op'>=</span> <span class='fu'>mkinsub</span><span class='op'>(</span><span class='st'>"SFO"</span>, full_name <span class='op'>=</span> <span class='st'>"Metabolite M1"</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'> <span class='co'># }</span>
 </div></pre>
   </div>
   <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
@@ -210,7 +219,7 @@ results on other operating systems or system configurations.</p></td>
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/mmkin-1.png b/docs/reference/mmkin-1.png
index 135d5446..c8f79dcb 100644
--- a/docs/reference/mmkin-1.png
+++ b/docs/reference/mmkin-1.png
diff --git a/docs/reference/mmkin-2.png b/docs/reference/mmkin-2.png
index 40109afc..5dd60e1c 100644
--- a/docs/reference/mmkin-2.png
+++ b/docs/reference/mmkin-2.png
diff --git a/docs/reference/mmkin-3.png b/docs/reference/mmkin-3.png
index e80448ab..9351ca24 100644
--- a/docs/reference/mmkin-3.png
+++ b/docs/reference/mmkin-3.png
diff --git a/docs/reference/mmkin-4.png b/docs/reference/mmkin-4.png
index 02976ced..69bd6e50 100644
--- a/docs/reference/mmkin-4.png
+++ b/docs/reference/mmkin-4.png
diff --git a/docs/reference/mmkin-5.png b/docs/reference/mmkin-5.png
index 4c771bc9..c1c05eea 100644
--- a/docs/reference/mmkin-5.png
+++ b/docs/reference/mmkin-5.png
diff --git a/docs/reference/mmkin.html b/docs/reference/mmkin.html
index 67837ea3..7a01313f 100644
--- a/docs/reference/mmkin.html
+++ b/docs/reference/mmkin.html
@@ -75,7 +75,7 @@ datasets specified in its first two arguments." />
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -112,6 +112,9 @@ datasets specified in its first two arguments." />
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -120,7 +123,7 @@ datasets specified in its first two arguments." />
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -140,7 +143,7 @@ datasets specified in its first two arguments." />
     <div class="page-header">
     <h1>Fit one or more kinetic models with one or more state variables to one or
 more datasets</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/mmkin.R'><code>R/mmkin.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/mmkin.R'><code>R/mmkin.R</code></a></small>
     <div class="hidden name"><code>mmkin.Rd</code></div>
     </div>
 
@@ -149,13 +152,13 @@ more datasets</h1>
 datasets specified in its first two arguments.</p>
     </div>
 
-    <pre class="usage"><span class='fu'>mmkin</span>(
-  <span class='kw'>models</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"SFO"</span>, <span class='st'>"FOMC"</span>, <span class='st'>"DFOP"</span>),
-  <span class='no'>datasets</span>,
-  <span class='kw'>cores</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/Round.html'>round</a></span>(<span class='fu'>detectCores</span>()/<span class='fl'>2</span>),
-  <span class='kw'>cluster</span> <span class='kw'>=</span> <span class='kw'>NULL</span>,
-  <span class='no'>...</span>
-)</pre>
+    <pre class="usage"><span class='fu'>mmkin</span><span class='op'>(</span>
+  models <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='st'>"FOMC"</span>, <span class='st'>"DFOP"</span><span class='op'>)</span>,
+  <span class='va'>datasets</span>,
+  cores <span class='op'>=</span> <span class='fu'>detectCores</span><span class='op'>(</span><span class='op'>)</span>,
+  cluster <span class='op'>=</span> <span class='cn'>NULL</span>,
+  <span class='va'>...</span>
+<span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
@@ -176,7 +179,8 @@ data for <code><a href='mkinfit.html'>mkinfit</a></code>.</p></td>
       <td><p>The number of cores to be used for multicore processing. This
 is only used when the <code>cluster</code> argument is <code>NULL</code>. On Windows
 machines, cores &gt; 1 is not supported, you need to use the <code>cluster</code>
-argument to use multiple logical processors.</p></td>
+argument to use multiple logical processors. Per default, all cores
+detected by <code><a href='https://rdrr.io/r/parallel/detectCores.html'>parallel::detectCores()</a></code> are used.</p></td>
     </tr>
     <tr>
       <th>cluster</th>
@@ -192,49 +196,64 @@ for parallel execution.</p></td>
     <h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>
 
     <p>A two-dimensional <code><a href='https://rdrr.io/r/base/array.html'>array</a></code> of <code><a href='mkinfit.html'>mkinfit</a></code>
-objects that can be indexed using the model names for the first index (row index)
-and the dataset names for the second index (column index).</p>
+objects and/or try-errors that can be indexed using the model names for the
+first index (row index) and the dataset names for the second index (column
+index).</p>
     <h2 class="hasAnchor" id="see-also"><a class="anchor" href="#see-also"></a>See also</h2>
 
-    <div class='dont-index'><p><code><a href='Extract.mmkin.html'>[.mmkin</a></code> for subsetting, <code><a href='plot.mmkin.html'>plot.mmkin</a></code> for
+    <div class='dont-index'><p><code><a href='[.mmkin.html'>[.mmkin</a></code> for subsetting, <code><a href='plot.mmkin.html'>plot.mmkin</a></code> for
 plotting.</p></div>
+    <h2 class="hasAnchor" id="author"><a class="anchor" href="#author"></a>Author</h2>
+
+    <p>Johannes Ranke</p>
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
     <pre class="examples"><div class='input'>
 <span class='co'># \dontrun{</span>
-<span class='no'>m_synth_SFO_lin</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>, <span class='st'>"M1"</span>),
-                           <span class='kw'>M1</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>, <span class='st'>"M2"</span>),
-                           <span class='kw'>M2</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>), <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"max"</span>)</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>
-<span class='no'>m_synth_FOMC_lin</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"FOMC"</span>, <span class='st'>"M1"</span>),
-                            <span class='kw'>M1</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>, <span class='st'>"M2"</span>),
-                            <span class='kw'>M2</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>), <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"max"</span>)</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>
-<span class='no'>models</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>SFO_lin</span> <span class='kw'>=</span> <span class='no'>m_synth_SFO_lin</span>, <span class='kw'>FOMC_lin</span> <span class='kw'>=</span> <span class='no'>m_synth_FOMC_lin</span>)
-<span class='no'>datasets</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/lapply.html'>lapply</a></span>(<span class='no'>synthetic_data_for_UBA_2014</span>[<span class='fl'>1</span>:<span class='fl'>3</span>], <span class='kw'>function</span>(<span class='no'>x</span>) <span class='no'>x</span>$<span class='no'>data</span>)
-<span class='fu'><a href='https://rdrr.io/r/base/names.html'>names</a></span>(<span class='no'>datasets</span>) <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/paste.html'>paste</a></span>(<span class='st'>"Dataset"</span>, <span class='fl'>1</span>:<span class='fl'>3</span>)
-
-<span class='no'>time_default</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/system.time.html'>system.time</a></span>(<span class='no'>fits.0</span> <span class='kw'>&lt;-</span> <span class='fu'>mmkin</span>(<span class='no'>models</span>, <span class='no'>datasets</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>))
-<span class='no'>time_1</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/system.time.html'>system.time</a></span>(<span class='no'>fits.4</span> <span class='kw'>&lt;-</span> <span class='fu'>mmkin</span>(<span class='no'>models</span>, <span class='no'>datasets</span>, <span class='kw'>cores</span> <span class='kw'>=</span> <span class='fl'>1</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>))</div><div class='output co'>#&gt; <span class='warning'>Warning: Optimisation did not converge:</span>
-#&gt; <span class='warning'>false convergence (8)</span></div><div class='input'>
-<span class='no'>time_default</span></div><div class='output co'>#&gt;    user  system elapsed 
-#&gt;   4.471   0.405   1.961 </div><div class='input'><span class='no'>time_1</span></div><div class='output co'>#&gt;    user  system elapsed 
-#&gt;   5.883   0.000   5.887 </div><div class='input'>
-<span class='fu'><a href='endpoints.html'>endpoints</a></span>(<span class='no'>fits.0</span><span class='kw'>[[</span><span class='st'>"SFO_lin"</span>, <span class='fl'>2</span>]])</div><div class='output co'>#&gt; $ff
+<span class='va'>m_synth_SFO_lin</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='st'>"M1"</span><span class='op'>)</span>,
+                           M1 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='st'>"M2"</span><span class='op'>)</span>,
+                           M2 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span>, use_of_ff <span class='op'>=</span> <span class='st'>"max"</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>
+<span class='va'>m_synth_FOMC_lin</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"FOMC"</span>, <span class='st'>"M1"</span><span class='op'>)</span>,
+                            M1 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='st'>"M2"</span><span class='op'>)</span>,
+                            M2 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span>, use_of_ff <span class='op'>=</span> <span class='st'>"max"</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>
+<span class='va'>models</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>SFO_lin <span class='op'>=</span> <span class='va'>m_synth_SFO_lin</span>, FOMC_lin <span class='op'>=</span> <span class='va'>m_synth_FOMC_lin</span><span class='op'>)</span>
+<span class='va'>datasets</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/lapply.html'>lapply</a></span><span class='op'>(</span><span class='va'>synthetic_data_for_UBA_2014</span><span class='op'>[</span><span class='fl'>1</span><span class='op'>:</span><span class='fl'>3</span><span class='op'>]</span>, <span class='kw'>function</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span> <span class='va'>x</span><span class='op'>$</span><span class='va'>data</span><span class='op'>)</span>
+<span class='fu'><a href='https://rdrr.io/r/base/names.html'>names</a></span><span class='op'>(</span><span class='va'>datasets</span><span class='op'>)</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/paste.html'>paste</a></span><span class='op'>(</span><span class='st'>"Dataset"</span>, <span class='fl'>1</span><span class='op'>:</span><span class='fl'>3</span><span class='op'>)</span>
+
+<span class='va'>time_default</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/system.time.html'>system.time</a></span><span class='op'>(</span><span class='va'>fits.0</span> <span class='op'>&lt;-</span> <span class='fu'>mmkin</span><span class='op'>(</span><span class='va'>models</span>, <span class='va'>datasets</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span><span class='op'>)</span>
+<span class='va'>time_1</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/system.time.html'>system.time</a></span><span class='op'>(</span><span class='va'>fits.4</span> <span class='op'>&lt;-</span> <span class='fu'>mmkin</span><span class='op'>(</span><span class='va'>models</span>, <span class='va'>datasets</span>, cores <span class='op'>=</span> <span class='fl'>1</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='warning'>Warning: Optimisation did not converge:</span>
+#&gt; <span class='warning'>false convergence (8)</span></div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.0117</span></div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.0174</span></div><div class='input'>
+<span class='va'>time_default</span>
+</div><div class='output co'>#&gt;    user  system elapsed 
+#&gt;   4.828   0.413   1.467 </div><div class='input'><span class='va'>time_1</span>
+</div><div class='output co'>#&gt;    user  system elapsed 
+#&gt;   5.228   0.000   5.231 </div><div class='input'>
+<span class='fu'><a href='endpoints.html'>endpoints</a></span><span class='op'>(</span><span class='va'>fits.0</span><span class='op'>[[</span><span class='st'>"SFO_lin"</span>, <span class='fl'>2</span><span class='op'>]</span><span class='op'>]</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; $ff
 #&gt;   parent_M1 parent_sink       M1_M2     M1_sink 
-#&gt;   0.7340479   0.2659521   0.7505687   0.2494313 
+#&gt;   0.7340478   0.2659522   0.7505691   0.2494309 
 #&gt; 
 #&gt; $distimes
 #&gt;              DT50       DT90
 #&gt; parent  0.8777688   2.915885
-#&gt; M1      2.3257457   7.725960
-#&gt; M2     33.7200848 112.015697
+#&gt; M1      2.3257466   7.725963
+#&gt; M2     33.7200800 112.015681
 #&gt; </div><div class='input'>
 <span class='co'># plot.mkinfit handles rows or columns of mmkin result objects</span>
-<span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='no'>fits.0</span>[<span class='fl'>1</span>, ])</div><div class='img'><img src='mmkin-1.png' alt='' width='700' height='433' /></div><div class='input'><span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='no'>fits.0</span>[<span class='fl'>1</span>, ], <span class='kw'>obs_var</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"M1"</span>, <span class='st'>"M2"</span>))</div><div class='img'><img src='mmkin-2.png' alt='' width='700' height='433' /></div><div class='input'><span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='no'>fits.0</span>[, <span class='fl'>1</span>])</div><div class='img'><img src='mmkin-3.png' alt='' width='700' height='433' /></div><div class='input'><span class='co'># Use double brackets to extract a single mkinfit object, which will be plotted</span>
+<span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>fits.0</span><span class='op'>[</span><span class='fl'>1</span>, <span class='op'>]</span><span class='op'>)</span>
+</div><div class='img'><img src='mmkin-1.png' alt='' width='700' height='433' /></div><div class='input'><span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>fits.0</span><span class='op'>[</span><span class='fl'>1</span>, <span class='op'>]</span>, obs_var <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"M1"</span>, <span class='st'>"M2"</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='img'><img src='mmkin-2.png' alt='' width='700' height='433' /></div><div class='input'><span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>fits.0</span><span class='op'>[</span>, <span class='fl'>1</span><span class='op'>]</span><span class='op'>)</span>
+</div><div class='img'><img src='mmkin-3.png' alt='' width='700' height='433' /></div><div class='input'><span class='co'># Use double brackets to extract a single mkinfit object, which will be plotted</span>
 <span class='co'># by plot.mkinfit and can be plotted using plot_sep</span>
-<span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='no'>fits.0</span><span class='kw'>[[</span><span class='fl'>1</span>, <span class='fl'>1</span>]], <span class='kw'>sep_obs</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>show_residuals</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>show_errmin</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='img'><img src='mmkin-4.png' alt='' width='700' height='433' /></div><div class='input'><span class='fu'><a href='plot.mkinfit.html'>plot_sep</a></span>(<span class='no'>fits.0</span><span class='kw'>[[</span><span class='fl'>1</span>, <span class='fl'>1</span>]])
+<span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>fits.0</span><span class='op'>[[</span><span class='fl'>1</span>, <span class='fl'>1</span><span class='op'>]</span><span class='op'>]</span>, sep_obs <span class='op'>=</span> <span class='cn'>TRUE</span>, show_residuals <span class='op'>=</span> <span class='cn'>TRUE</span>, show_errmin <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+</div><div class='img'><img src='mmkin-4.png' alt='' width='700' height='433' /></div><div class='input'><span class='fu'><a href='plot.mkinfit.html'>plot_sep</a></span><span class='op'>(</span><span class='va'>fits.0</span><span class='op'>[[</span><span class='fl'>1</span>, <span class='fl'>1</span><span class='op'>]</span><span class='op'>]</span><span class='op'>)</span>
 <span class='co'># Plotting with mmkin (single brackets, extracting an mmkin object) does not</span>
 <span class='co'># allow to plot the observed variables separately</span>
-<span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='no'>fits.0</span>[<span class='fl'>1</span>, <span class='fl'>1</span>])</div><div class='img'><img src='mmkin-5.png' alt='' width='700' height='433' /></div><div class='input'># }
+<span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>fits.0</span><span class='op'>[</span><span class='fl'>1</span>, <span class='fl'>1</span><span class='op'>]</span><span class='op'>)</span>
+</div><div class='img'><img src='mmkin-5.png' alt='' width='700' height='433' /></div><div class='input'><span class='co'># }</span>
 
 </div></pre>
   </div>
@@ -252,7 +271,7 @@ plotting.</p></div>
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/nafta-1.png b/docs/reference/nafta-1.png
index 9025f2bb..4593158c 100644
--- a/docs/reference/nafta-1.png
+++ b/docs/reference/nafta-1.png
diff --git a/docs/reference/nafta.html b/docs/reference/nafta.html
index 34cce546..9630e230 100644
--- a/docs/reference/nafta.html
+++ b/docs/reference/nafta.html
@@ -76,7 +76,7 @@ order of increasing model complexity, i.e. SFO, then IORE, and finally DFOP." />
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -113,6 +113,9 @@ order of increasing model complexity, i.e. SFO, then IORE, and finally DFOP." />
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -121,7 +124,7 @@ order of increasing model complexity, i.e. SFO, then IORE, and finally DFOP." />
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -140,7 +143,7 @@ order of increasing model complexity, i.e. SFO, then IORE, and finally DFOP." />
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>Evaluate parent kinetics using the NAFTA guidance</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/nafta.R'><code>R/nafta.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/nafta.R'><code>R/nafta.R</code></a></small>
     <div class="hidden name"><code>nafta.Rd</code></div>
     </div>
 
@@ -152,10 +155,10 @@ and plotting.</p>
 order of increasing model complexity, i.e. SFO, then IORE, and finally DFOP.</p>
     </div>
 
-    <pre class="usage"><span class='fu'>nafta</span>(<span class='no'>ds</span>, <span class='kw'>title</span> <span class='kw'>=</span> <span class='fl'>NA</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>, <span class='no'>...</span>)
+    <pre class="usage"><span class='fu'>nafta</span><span class='op'>(</span><span class='va'>ds</span>, title <span class='op'>=</span> <span class='cn'>NA</span>, quiet <span class='op'>=</span> <span class='cn'>FALSE</span>, <span class='va'>...</span><span class='op'>)</span>
 
 <span class='co'># S3 method for nafta</span>
-<span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span>(<span class='no'>x</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>digits</span> <span class='kw'>=</span> <span class='fl'>3</span>, <span class='no'>...</span>)</pre>
+<span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span><span class='op'>(</span><span class='va'>x</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, digits <span class='op'>=</span> <span class='fl'>3</span>, <span class='va'>...</span><span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
@@ -208,10 +211,15 @@ Degradation
 <code><a href='mmkin.html'>mmkin</a></code> object containing the fits of the three models. The
 list element named "title" contains the title of the dataset used. The
 list element "data" contains the dataset used in the fits.</p>
+    <h2 class="hasAnchor" id="author"><a class="anchor" href="#author"></a>Author</h2>
+
+    <p>Johannes Ranke</p>
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
     <pre class="examples"><div class='input'>
-  <span class='no'>nafta_evaluation</span> <span class='kw'>&lt;-</span> <span class='fu'>nafta</span>(<span class='no'>NAFTA_SOP_Appendix_D</span>, <span class='kw'>cores</span> <span class='kw'>=</span> <span class='fl'>1</span>)</div><div class='output co'>#&gt; <span class='message'>The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></div><div class='output co'>#&gt; <span class='message'>The representative half-life of the IORE model is longer than the one corresponding</span></div><div class='output co'>#&gt; <span class='message'>to the terminal degradation rate found with the DFOP model.</span></div><div class='output co'>#&gt; <span class='message'>The representative half-life obtained from the DFOP model may be used</span></div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span>(<span class='no'>nafta_evaluation</span>)</div><div class='output co'>#&gt; Sums of squares:
+  <span class='va'>nafta_evaluation</span> <span class='op'>&lt;-</span> <span class='fu'>nafta</span><span class='op'>(</span><span class='va'>NAFTA_SOP_Appendix_D</span>, cores <span class='op'>=</span> <span class='fl'>1</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.00192</span></div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.00258</span></div><div class='output co'>#&gt; <span class='message'>The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></div><div class='output co'>#&gt; <span class='message'>The representative half-life of the IORE model is longer than the one corresponding</span></div><div class='output co'>#&gt; <span class='message'>to the terminal degradation rate found with the DFOP model.</span></div><div class='output co'>#&gt; <span class='message'>The representative half-life obtained from the DFOP model may be used</span></div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span><span class='op'>(</span><span class='va'>nafta_evaluation</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; Sums of squares:
 #&gt;       SFO      IORE      DFOP 
 #&gt; 1378.6832  615.7730  517.8836 
 #&gt; 
@@ -220,17 +228,17 @@ list element "data" contains the dataset used in the fits.</p>
 #&gt; 
 #&gt; Parameters:
 #&gt; $SFO
-#&gt;               Estimate   Pr(&gt;t)    Lower   Upper
-#&gt; parent_0       83.7558 1.80e-14 77.18268 90.3288
-#&gt; k_parent_sink   0.0017 7.43e-05  0.00112  0.0026
-#&gt; sigma           8.7518 1.22e-05  5.64278 11.8608
+#&gt;          Estimate   Pr(&gt;t)    Lower   Upper
+#&gt; parent_0  83.7558 1.80e-14 77.18268 90.3288
+#&gt; k_parent   0.0017 7.43e-05  0.00112  0.0026
+#&gt; sigma      8.7518 1.22e-05  5.64278 11.8608
 #&gt; 
 #&gt; $IORE
-#&gt;                     Estimate Pr(&gt;t)    Lower    Upper
-#&gt; parent_0            9.69e+01     NA 8.88e+01 1.05e+02
-#&gt; k__iore_parent_sink 8.40e-14     NA 1.79e-18 3.94e-09
-#&gt; N_parent            6.68e+00     NA 4.19e+00 9.17e+00
-#&gt; sigma               5.85e+00     NA 3.76e+00 7.94e+00
+#&gt;                Estimate Pr(&gt;t)    Lower    Upper
+#&gt; parent_0       9.69e+01     NA 8.88e+01 1.05e+02
+#&gt; k__iore_parent 8.40e-14     NA 1.79e-18 3.94e-09
+#&gt; N_parent       6.68e+00     NA 4.19e+00 9.17e+00
+#&gt; sigma          5.85e+00     NA 3.76e+00 7.94e+00
 #&gt; 
 #&gt; $DFOP
 #&gt;          Estimate   Pr(&gt;t)    Lower    Upper
@@ -248,7 +256,8 @@ list element "data" contains the dataset used in the fits.</p>
 #&gt; DFOP  429    2380      841
 #&gt; 
 #&gt; Representative half-life:
-#&gt; [1] 841.41</div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='no'>nafta_evaluation</span>)</div><div class='img'><img src='nafta-1.png' alt='' width='700' height='433' /></div><div class='input'>
+#&gt; [1] 841.41</div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>nafta_evaluation</span><span class='op'>)</span>
+</div><div class='img'><img src='nafta-1.png' alt='' width='700' height='433' /></div><div class='input'>
 </div></pre>
   </div>
   <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
@@ -265,7 +274,7 @@ list element "data" contains the dataset used in the fits.</p>
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/nlme-1.png b/docs/reference/nlme-1.png
index bc04dea8..193722c7 100644
--- a/docs/reference/nlme-1.png
+++ b/docs/reference/nlme-1.png
diff --git a/docs/reference/nlme.html b/docs/reference/nlme.html
index 85929929..4e61a08b 100644
--- a/docs/reference/nlme.html
+++ b/docs/reference/nlme.html
@@ -43,7 +43,7 @@
 <meta property="og:description" content="These functions facilitate setting up a nonlinear mixed effects model for
 an mmkin row object. An mmkin row object is essentially a list of mkinfit
 objects that have been obtained by fitting the same model to a list of
-datasets." />
+datasets. They are used internally by the nlme.mmkin() method." />
 
 
 
@@ -75,7 +75,7 @@ datasets." />
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -112,6 +112,9 @@ datasets." />
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -120,7 +123,7 @@ datasets." />
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -139,7 +142,7 @@ datasets." />
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>Helper functions to create nlme models from mmkin row objects</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/nlme.R'><code>R/nlme.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/nlme.R'><code>R/nlme.R</code></a></small>
     <div class="hidden name"><code>nlme.Rd</code></div>
     </div>
 
@@ -147,14 +150,14 @@ datasets." />
     <p>These functions facilitate setting up a nonlinear mixed effects model for
 an mmkin row object. An mmkin row object is essentially a list of mkinfit
 objects that have been obtained by fitting the same model to a list of
-datasets.</p>
+datasets. They are used internally by the <code><a href='nlme.mmkin.html'>nlme.mmkin()</a></code> method.</p>
     </div>
 
-    <pre class="usage"><span class='fu'>nlme_function</span>(<span class='no'>object</span>)
+    <pre class="usage"><span class='fu'>nlme_function</span><span class='op'>(</span><span class='va'>object</span><span class='op'>)</span>
 
-<span class='fu'>mean_degparms</span>(<span class='no'>object</span>, <span class='kw'>random</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>)
+<span class='fu'>mean_degparms</span><span class='op'>(</span><span class='va'>object</span>, random <span class='op'>=</span> <span class='cn'>FALSE</span><span class='op'>)</span>
 
-<span class='fu'>nlme_data</span>(<span class='no'>object</span>)</pre>
+<span class='fu'>nlme_data</span><span class='op'>(</span><span class='va'>object</span><span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
@@ -175,50 +178,51 @@ datasets.</p>
 <p>If random is FALSE (default), a named vector containing mean values
 of the fitted degradation model parameters. If random is TRUE, a list with
 fixed and random effects, in the format required by the start argument of
-nlme for the case of a single grouping variable ds?</p>
+nlme for the case of a single grouping variable ds.</p>
 <p>A <code><a href='https://rdrr.io/pkg/nlme/man/groupedData.html'>groupedData</a></code> object</p>
     <h2 class="hasAnchor" id="see-also"><a class="anchor" href="#see-also"></a>See also</h2>
 
     <div class='dont-index'><p><code><a href='nlme.mmkin.html'>nlme.mmkin</a></code></p></div>
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
-    <pre class="examples"><div class='input'><span class='no'>sampling_times</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='fl'>0</span>, <span class='fl'>1</span>, <span class='fl'>3</span>, <span class='fl'>7</span>, <span class='fl'>14</span>, <span class='fl'>28</span>, <span class='fl'>60</span>, <span class='fl'>90</span>, <span class='fl'>120</span>)
-<span class='no'>m_SFO</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>))
-<span class='no'>d_SFO_1</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinpredict.html'>mkinpredict</a></span>(<span class='no'>m_SFO</span>,
-  <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>k_parent</span> <span class='kw'>=</span> <span class='fl'>0.1</span>),
-  <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fl'>98</span>), <span class='no'>sampling_times</span>)
-<span class='no'>d_SFO_1_long</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkin_wide_to_long.html'>mkin_wide_to_long</a></span>(<span class='no'>d_SFO_1</span>, <span class='kw'>time</span> <span class='kw'>=</span> <span class='st'>"time"</span>)
-<span class='no'>d_SFO_2</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinpredict.html'>mkinpredict</a></span>(<span class='no'>m_SFO</span>,
-  <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>k_parent</span> <span class='kw'>=</span> <span class='fl'>0.05</span>),
-  <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fl'>102</span>), <span class='no'>sampling_times</span>)
-<span class='no'>d_SFO_2_long</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkin_wide_to_long.html'>mkin_wide_to_long</a></span>(<span class='no'>d_SFO_2</span>, <span class='kw'>time</span> <span class='kw'>=</span> <span class='st'>"time"</span>)
-<span class='no'>d_SFO_3</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinpredict.html'>mkinpredict</a></span>(<span class='no'>m_SFO</span>,
-  <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>k_parent</span> <span class='kw'>=</span> <span class='fl'>0.02</span>),
-  <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fl'>103</span>), <span class='no'>sampling_times</span>)
-<span class='no'>d_SFO_3_long</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkin_wide_to_long.html'>mkin_wide_to_long</a></span>(<span class='no'>d_SFO_3</span>, <span class='kw'>time</span> <span class='kw'>=</span> <span class='st'>"time"</span>)
-
-<span class='no'>d1</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='add_err.html'>add_err</a></span>(<span class='no'>d_SFO_1</span>, <span class='kw'>function</span>(<span class='no'>value</span>) <span class='fl'>3</span>, <span class='kw'>n</span> <span class='kw'>=</span> <span class='fl'>1</span>)
-<span class='no'>d2</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='add_err.html'>add_err</a></span>(<span class='no'>d_SFO_2</span>, <span class='kw'>function</span>(<span class='no'>value</span>) <span class='fl'>2</span>, <span class='kw'>n</span> <span class='kw'>=</span> <span class='fl'>1</span>)
-<span class='no'>d3</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='add_err.html'>add_err</a></span>(<span class='no'>d_SFO_3</span>, <span class='kw'>function</span>(<span class='no'>value</span>) <span class='fl'>4</span>, <span class='kw'>n</span> <span class='kw'>=</span> <span class='fl'>1</span>)
-<span class='no'>ds</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>d1</span> <span class='kw'>=</span> <span class='no'>d1</span>, <span class='kw'>d2</span> <span class='kw'>=</span> <span class='no'>d2</span>, <span class='kw'>d3</span> <span class='kw'>=</span> <span class='no'>d3</span>)
-
-<span class='no'>f</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mmkin.html'>mmkin</a></span>(<span class='st'>"SFO"</span>, <span class='no'>ds</span>, <span class='kw'>cores</span> <span class='kw'>=</span> <span class='fl'>1</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-<span class='no'>mean_dp</span> <span class='kw'>&lt;-</span> <span class='fu'>mean_degparms</span>(<span class='no'>f</span>)
-<span class='no'>grouped_data</span> <span class='kw'>&lt;-</span> <span class='fu'>nlme_data</span>(<span class='no'>f</span>)
-<span class='no'>nlme_f</span> <span class='kw'>&lt;-</span> <span class='fu'>nlme_function</span>(<span class='no'>f</span>)
+    <pre class="examples"><div class='input'><span class='va'>sampling_times</span> <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>0</span>, <span class='fl'>1</span>, <span class='fl'>3</span>, <span class='fl'>7</span>, <span class='fl'>14</span>, <span class='fl'>28</span>, <span class='fl'>60</span>, <span class='fl'>90</span>, <span class='fl'>120</span><span class='op'>)</span>
+<span class='va'>m_SFO</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span><span class='op'>)</span>
+<span class='va'>d_SFO_1</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinpredict.html'>mkinpredict</a></span><span class='op'>(</span><span class='va'>m_SFO</span>,
+  <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>k_parent <span class='op'>=</span> <span class='fl'>0.1</span><span class='op'>)</span>,
+  <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fl'>98</span><span class='op'>)</span>, <span class='va'>sampling_times</span><span class='op'>)</span>
+<span class='va'>d_SFO_1_long</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkin_wide_to_long.html'>mkin_wide_to_long</a></span><span class='op'>(</span><span class='va'>d_SFO_1</span>, time <span class='op'>=</span> <span class='st'>"time"</span><span class='op'>)</span>
+<span class='va'>d_SFO_2</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinpredict.html'>mkinpredict</a></span><span class='op'>(</span><span class='va'>m_SFO</span>,
+  <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>k_parent <span class='op'>=</span> <span class='fl'>0.05</span><span class='op'>)</span>,
+  <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fl'>102</span><span class='op'>)</span>, <span class='va'>sampling_times</span><span class='op'>)</span>
+<span class='va'>d_SFO_2_long</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkin_wide_to_long.html'>mkin_wide_to_long</a></span><span class='op'>(</span><span class='va'>d_SFO_2</span>, time <span class='op'>=</span> <span class='st'>"time"</span><span class='op'>)</span>
+<span class='va'>d_SFO_3</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinpredict.html'>mkinpredict</a></span><span class='op'>(</span><span class='va'>m_SFO</span>,
+  <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>k_parent <span class='op'>=</span> <span class='fl'>0.02</span><span class='op'>)</span>,
+  <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fl'>103</span><span class='op'>)</span>, <span class='va'>sampling_times</span><span class='op'>)</span>
+<span class='va'>d_SFO_3_long</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkin_wide_to_long.html'>mkin_wide_to_long</a></span><span class='op'>(</span><span class='va'>d_SFO_3</span>, time <span class='op'>=</span> <span class='st'>"time"</span><span class='op'>)</span>
+
+<span class='va'>d1</span> <span class='op'>&lt;-</span> <span class='fu'><a href='add_err.html'>add_err</a></span><span class='op'>(</span><span class='va'>d_SFO_1</span>, <span class='kw'>function</span><span class='op'>(</span><span class='va'>value</span><span class='op'>)</span> <span class='fl'>3</span>, n <span class='op'>=</span> <span class='fl'>1</span><span class='op'>)</span>
+<span class='va'>d2</span> <span class='op'>&lt;-</span> <span class='fu'><a href='add_err.html'>add_err</a></span><span class='op'>(</span><span class='va'>d_SFO_2</span>, <span class='kw'>function</span><span class='op'>(</span><span class='va'>value</span><span class='op'>)</span> <span class='fl'>2</span>, n <span class='op'>=</span> <span class='fl'>1</span><span class='op'>)</span>
+<span class='va'>d3</span> <span class='op'>&lt;-</span> <span class='fu'><a href='add_err.html'>add_err</a></span><span class='op'>(</span><span class='va'>d_SFO_3</span>, <span class='kw'>function</span><span class='op'>(</span><span class='va'>value</span><span class='op'>)</span> <span class='fl'>4</span>, n <span class='op'>=</span> <span class='fl'>1</span><span class='op'>)</span>
+<span class='va'>ds</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>d1 <span class='op'>=</span> <span class='va'>d1</span>, d2 <span class='op'>=</span> <span class='va'>d2</span>, d3 <span class='op'>=</span> <span class='va'>d3</span><span class='op'>)</span>
+
+<span class='va'>f</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mmkin.html'>mmkin</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='va'>ds</span>, cores <span class='op'>=</span> <span class='fl'>1</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+<span class='va'>mean_dp</span> <span class='op'>&lt;-</span> <span class='fu'>mean_degparms</span><span class='op'>(</span><span class='va'>f</span><span class='op'>)</span>
+<span class='va'>grouped_data</span> <span class='op'>&lt;-</span> <span class='fu'>nlme_data</span><span class='op'>(</span><span class='va'>f</span><span class='op'>)</span>
+<span class='va'>nlme_f</span> <span class='op'>&lt;-</span> <span class='fu'>nlme_function</span><span class='op'>(</span><span class='va'>f</span><span class='op'>)</span>
 <span class='co'># These assignments are necessary for these objects to be</span>
 <span class='co'># visible to nlme and augPred when evaluation is done by</span>
 <span class='co'># pkgdown to generated the html docs.</span>
-<span class='fu'><a href='https://rdrr.io/r/base/assign.html'>assign</a></span>(<span class='st'>"nlme_f"</span>, <span class='no'>nlme_f</span>, <span class='fu'><a href='https://rdrr.io/r/base/environment.html'>globalenv</a></span>())
-<span class='fu'><a href='https://rdrr.io/r/base/assign.html'>assign</a></span>(<span class='st'>"grouped_data"</span>, <span class='no'>grouped_data</span>, <span class='fu'><a href='https://rdrr.io/r/base/environment.html'>globalenv</a></span>())
-
-<span class='fu'><a href='https://rdrr.io/r/base/library.html'>library</a></span>(<span class='no'>nlme</span>)
-<span class='no'>m_nlme</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/pkg/nlme/man/nlme.html'>nlme</a></span>(<span class='no'>value</span> ~ <span class='fu'>nlme_f</span>(<span class='no'>name</span>, <span class='no'>time</span>, <span class='no'>parent_0</span>, <span class='no'>log_k_parent_sink</span>),
-  <span class='kw'>data</span> <span class='kw'>=</span> <span class='no'>grouped_data</span>,
-  <span class='kw'>fixed</span> <span class='kw'>=</span> <span class='no'>parent_0</span> + <span class='no'>log_k_parent_sink</span> ~ <span class='fl'>1</span>,
-  <span class='kw'>random</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/pkg/nlme/man/pdDiag.html'>pdDiag</a></span>(<span class='no'>parent_0</span> + <span class='no'>log_k_parent_sink</span> ~ <span class='fl'>1</span>),
-  <span class='kw'>start</span> <span class='kw'>=</span> <span class='no'>mean_dp</span>)
-<span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span>(<span class='no'>m_nlme</span>)</div><div class='output co'>#&gt; Nonlinear mixed-effects model fit by maximum likelihood
+<span class='fu'><a href='https://rdrr.io/r/base/assign.html'>assign</a></span><span class='op'>(</span><span class='st'>"nlme_f"</span>, <span class='va'>nlme_f</span>, <span class='fu'><a href='https://rdrr.io/r/base/environment.html'>globalenv</a></span><span class='op'>(</span><span class='op'>)</span><span class='op'>)</span>
+<span class='fu'><a href='https://rdrr.io/r/base/assign.html'>assign</a></span><span class='op'>(</span><span class='st'>"grouped_data"</span>, <span class='va'>grouped_data</span>, <span class='fu'><a href='https://rdrr.io/r/base/environment.html'>globalenv</a></span><span class='op'>(</span><span class='op'>)</span><span class='op'>)</span>
+
+<span class='kw'><a href='https://rdrr.io/r/base/library.html'>library</a></span><span class='op'>(</span><span class='va'><a href='https://svn.r-project.org/R-packages/trunk/nlme'>nlme</a></span><span class='op'>)</span>
+<span class='va'>m_nlme</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/pkg/nlme/man/nlme.html'>nlme</a></span><span class='op'>(</span><span class='va'>value</span> <span class='op'>~</span> <span class='fu'>nlme_f</span><span class='op'>(</span><span class='va'>name</span>, <span class='va'>time</span>, <span class='va'>parent_0</span>, <span class='va'>log_k_parent_sink</span><span class='op'>)</span>,
+  data <span class='op'>=</span> <span class='va'>grouped_data</span>,
+  fixed <span class='op'>=</span> <span class='va'>parent_0</span> <span class='op'>+</span> <span class='va'>log_k_parent_sink</span> <span class='op'>~</span> <span class='fl'>1</span>,
+  random <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/pkg/nlme/man/pdDiag.html'>pdDiag</a></span><span class='op'>(</span><span class='va'>parent_0</span> <span class='op'>+</span> <span class='va'>log_k_parent_sink</span> <span class='op'>~</span> <span class='fl'>1</span><span class='op'>)</span>,
+  start <span class='op'>=</span> <span class='va'>mean_dp</span><span class='op'>)</span>
+<span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span><span class='op'>(</span><span class='va'>m_nlme</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; Nonlinear mixed-effects model fit by maximum likelihood
 #&gt;   Model: value ~ nlme_f(name, time, parent_0, log_k_parent_sink) 
 #&gt;  Data: grouped_data 
 #&gt;        AIC      BIC    logLik
@@ -228,24 +232,25 @@ nlme for the case of a single grouping variable ds?</p>
 #&gt;  Formula: list(parent_0 ~ 1, log_k_parent_sink ~ 1)
 #&gt;  Level: ds
 #&gt;  Structure: Diagonal
-#&gt;            parent_0 log_k_parent_sink Residual
-#&gt; StdDev: 0.004139378         0.6800778 2.489396
+#&gt;             parent_0 log_k_parent_sink Residual
+#&gt; StdDev: 0.0006768135         0.6800777 2.489397
 #&gt; 
 #&gt; Fixed effects: parent_0 + log_k_parent_sink ~ 1 
 #&gt;                       Value Std.Error DF   t-value p-value
-#&gt; parent_0          101.74884 0.6456057 44 157.60213       0
-#&gt; log_k_parent_sink  -3.05575 0.4015812 44  -7.60929       0
+#&gt; parent_0          101.74884 0.6456014 44 157.60321       0
+#&gt; log_k_parent_sink  -3.05575 0.4015811 44  -7.60929       0
 #&gt;  Correlation: 
 #&gt;                   prnt_0
 #&gt; log_k_parent_sink 0.026 
 #&gt; 
 #&gt; Standardized Within-Group Residuals:
-#&gt;         Min          Q1         Med          Q3         Max 
-#&gt; -2.13168782 -0.68780415  0.08282907  0.85913228  2.95298904 
+#&gt;        Min         Q1        Med         Q3        Max 
+#&gt; -2.1317488 -0.6878121  0.0828385  0.8592270  2.9529864 
 #&gt; 
 #&gt; Number of Observations: 48
-#&gt; Number of Groups: 3 </div><div class='input'><span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='fu'><a href='https://rdrr.io/pkg/nlme/man/augPred.html'>augPred</a></span>(<span class='no'>m_nlme</span>, <span class='kw'>level</span> <span class='kw'>=</span> <span class='fl'>0</span>:<span class='fl'>1</span>), <span class='kw'>layout</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='fl'>3</span>, <span class='fl'>1</span>))</div><div class='img'><img src='nlme-1.png' alt='' width='700' height='433' /></div><div class='input'># augPred does not seem to work on fits with more than one state
-# variable
+#&gt; Number of Groups: 3 </div><div class='input'><span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/pkg/nlme/man/augPred.html'>augPred</a></span><span class='op'>(</span><span class='va'>m_nlme</span>, level <span class='op'>=</span> <span class='fl'>0</span><span class='op'>:</span><span class='fl'>1</span><span class='op'>)</span>, layout <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>3</span>, <span class='fl'>1</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='img'><img src='nlme-1.png' alt='' width='700' height='433' /></div><div class='input'><span class='co'># augPred does not seem to work on fits with more than one state</span>
+<span class='co'># variable</span>
 
 </div></pre>
   </div>
@@ -263,7 +268,7 @@ nlme for the case of a single grouping variable ds?</p>
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/nlme.mmkin-1.png b/docs/reference/nlme.mmkin-1.png
index 67f279da..564f7e2b 100644
--- a/docs/reference/nlme.mmkin-1.png
+++ b/docs/reference/nlme.mmkin-1.png
diff --git a/docs/reference/nlme.mmkin-2.png b/docs/reference/nlme.mmkin-2.png
index 16a5d7bd..a9ce4636 100644
--- a/docs/reference/nlme.mmkin-2.png
+++ b/docs/reference/nlme.mmkin-2.png
diff --git a/docs/reference/nlme.mmkin-3.png b/docs/reference/nlme.mmkin-3.png
index 73426834..0b7ce0f6 100644
--- a/docs/reference/nlme.mmkin-3.png
+++ b/docs/reference/nlme.mmkin-3.png
diff --git a/docs/reference/nlme.mmkin-4.png b/docs/reference/nlme.mmkin-4.png
index 9b46b425..d7c68dd5 100644
--- a/docs/reference/nlme.mmkin-4.png
+++ b/docs/reference/nlme.mmkin-4.png
diff --git a/docs/reference/nlme.mmkin-5.png b/docs/reference/nlme.mmkin-5.png
index 3398dd4a..2c299b08 100644
--- a/docs/reference/nlme.mmkin-5.png
+++ b/docs/reference/nlme.mmkin-5.png
diff --git a/docs/reference/nlme.mmkin-6.png b/docs/reference/nlme.mmkin-6.png
index 7b663991..2bcb9cec 100644
--- a/docs/reference/nlme.mmkin-6.png
+++ b/docs/reference/nlme.mmkin-6.png
diff --git a/docs/reference/nlme.mmkin-7.png b/docs/reference/nlme.mmkin-7.png
index d2c38a63..30e2d351 100644
--- a/docs/reference/nlme.mmkin-7.png
+++ b/docs/reference/nlme.mmkin-7.png
diff --git a/docs/reference/nlme.mmkin.html b/docs/reference/nlme.mmkin.html
index c0fb499d..af3b712c 100644
--- a/docs/reference/nlme.mmkin.html
+++ b/docs/reference/nlme.mmkin.html
@@ -74,7 +74,7 @@ have been obtained by fitting the same model to a list of datasets." />
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -111,6 +111,9 @@ have been obtained by fitting the same model to a list of datasets." />
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -119,7 +122,7 @@ have been obtained by fitting the same model to a list of datasets." />
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -138,7 +141,7 @@ have been obtained by fitting the same model to a list of datasets." />
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>Create an nlme model for an mmkin row object</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/nlme.mmkin.R'><code>R/nlme.mmkin.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/nlme.mmkin.R'><code>R/nlme.mmkin.R</code></a></small>
     <div class="hidden name"><code>nlme.mmkin.Rd</code></div>
     </div>
 
@@ -149,28 +152,28 @@ have been obtained by fitting the same model to a list of datasets.</p>
     </div>
 
     <pre class="usage"><span class='co'># S3 method for mmkin</span>
-<span class='fu'>nlme</span>(
-  <span class='no'>model</span>,
-  <span class='kw'>data</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/sys.parent.html'>sys.frame</a></span>(<span class='fu'><a href='https://rdrr.io/r/base/sys.parent.html'>sys.parent</a></span>()),
-  <span class='no'>fixed</span>,
-  <span class='kw'>random</span> <span class='kw'>=</span> <span class='no'>fixed</span>,
-  <span class='no'>groups</span>,
-  <span class='no'>start</span>,
-  <span class='kw'>correlation</span> <span class='kw'>=</span> <span class='kw'>NULL</span>,
-  <span class='kw'>weights</span> <span class='kw'>=</span> <span class='kw'>NULL</span>,
-  <span class='no'>subset</span>,
-  <span class='kw'>method</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"ML"</span>, <span class='st'>"REML"</span>),
-  <span class='kw'>na.action</span> <span class='kw'>=</span> <span class='no'>na.fail</span>,
-  <span class='no'>naPattern</span>,
-  <span class='kw'>control</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(),
-  <span class='kw'>verbose</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>
-)
+<span class='fu'><a href='https://rdrr.io/pkg/nlme/man/nlme.html'>nlme</a></span><span class='op'>(</span>
+  <span class='va'>model</span>,
+  data <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/sys.parent.html'>sys.frame</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/sys.parent.html'>sys.parent</a></span><span class='op'>(</span><span class='op'>)</span><span class='op'>)</span>,
+  <span class='va'>fixed</span>,
+  random <span class='op'>=</span> <span class='va'>fixed</span>,
+  <span class='va'>groups</span>,
+  <span class='va'>start</span>,
+  correlation <span class='op'>=</span> <span class='cn'>NULL</span>,
+  weights <span class='op'>=</span> <span class='cn'>NULL</span>,
+  <span class='va'>subset</span>,
+  method <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"ML"</span>, <span class='st'>"REML"</span><span class='op'>)</span>,
+  na.action <span class='op'>=</span> <span class='va'>na.fail</span>,
+  <span class='va'>naPattern</span>,
+  control <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span><span class='op'>)</span>,
+  verbose <span class='op'>=</span> <span class='cn'>FALSE</span>
+<span class='op'>)</span>
 
 <span class='co'># S3 method for nlme.mmkin</span>
-<span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span>(<span class='no'>x</span>, <span class='no'>...</span>)
+<span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span><span class='op'>(</span><span class='va'>x</span>, <span class='va'>...</span><span class='op'>)</span>
 
 <span class='co'># S3 method for nlme.mmkin</span>
-<span class='fu'><a href='https://rdrr.io/r/stats/update.html'>update</a></span>(<span class='no'>object</span>, <span class='no'>...</span>)</pre>
+<span class='fu'><a href='https://rdrr.io/r/stats/update.html'>update</a></span><span class='op'>(</span><span class='va'>object</span>, <span class='va'>...</span><span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
@@ -181,7 +184,7 @@ have been obtained by fitting the same model to a list of datasets.</p>
     </tr>
     <tr>
       <th>data</th>
-      <td><p>Should the data be printed?</p></td>
+      <td><p>Ignored, data are taken from the mmkin model</p></td>
     </tr>
     <tr>
       <th>fixed</th>
@@ -254,165 +257,181 @@ parameters taken from the mmkin object are used</p></td>
 with additional elements</p>
     <h2 class="hasAnchor" id="see-also"><a class="anchor" href="#see-also"></a>See also</h2>
 
-    <div class='dont-index'><p><code><a href='nlme.html'>nlme_function</a></code></p></div>
+    <div class='dont-index'><p><code><a href='nlme_function.html'>nlme_function</a></code></p></div>
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
-    <pre class="examples"><div class='input'><span class='no'>ds</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/lapply.html'>lapply</a></span>(<span class='no'>experimental_data_for_UBA_2019</span>[<span class='fl'>6</span>:<span class='fl'>10</span>],
- <span class='kw'>function</span>(<span class='no'>x</span>) <span class='fu'><a href='https://rdrr.io/r/base/subset.html'>subset</a></span>(<span class='no'>x</span>$<span class='no'>data</span>[<span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"name"</span>, <span class='st'>"time"</span>, <span class='st'>"value"</span>)], <span class='no'>name</span> <span class='kw'>==</span> <span class='st'>"parent"</span>))
-<span class='no'>f</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mmkin.html'>mmkin</a></span>(<span class='st'>"SFO"</span>, <span class='no'>ds</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>cores</span> <span class='kw'>=</span> <span class='fl'>1</span>)
-<span class='fu'><a href='https://rdrr.io/r/base/library.html'>library</a></span>(<span class='no'>nlme</span>)
-<span class='fu'><a href='endpoints.html'>endpoints</a></span>(<span class='no'>f</span><span class='kw'>[[</span><span class='fl'>1</span>]])</div><div class='output co'>#&gt; $distimes
+    <pre class="examples"><div class='input'><span class='va'>ds</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/lapply.html'>lapply</a></span><span class='op'>(</span><span class='va'>experimental_data_for_UBA_2019</span><span class='op'>[</span><span class='fl'>6</span><span class='op'>:</span><span class='fl'>10</span><span class='op'>]</span>,
+ <span class='kw'>function</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span> <span class='fu'><a href='https://rdrr.io/r/base/subset.html'>subset</a></span><span class='op'>(</span><span class='va'>x</span><span class='op'>$</span><span class='va'>data</span><span class='op'>[</span><span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"name"</span>, <span class='st'>"time"</span>, <span class='st'>"value"</span><span class='op'>)</span><span class='op'>]</span>, <span class='va'>name</span> <span class='op'>==</span> <span class='st'>"parent"</span><span class='op'>)</span><span class='op'>)</span>
+<span class='va'>f</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mmkin.html'>mmkin</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='va'>ds</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, cores <span class='op'>=</span> <span class='fl'>1</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.0195</span></div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.011</span></div><div class='input'><span class='kw'><a href='https://rdrr.io/r/base/library.html'>library</a></span><span class='op'>(</span><span class='va'><a href='https://svn.r-project.org/R-packages/trunk/nlme'>nlme</a></span><span class='op'>)</span>
+<span class='fu'><a href='endpoints.html'>endpoints</a></span><span class='op'>(</span><span class='va'>f</span><span class='op'>[[</span><span class='fl'>1</span><span class='op'>]</span><span class='op'>]</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; $distimes
 #&gt;            DT50     DT90
 #&gt; parent 11.96183 39.73634
-#&gt; </div><div class='input'><span class='no'>f_nlme</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/pkg/nlme/man/nlme.html'>nlme</a></span>(<span class='no'>f</span>)
-<span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span>(<span class='no'>f_nlme</span>)</div><div class='output co'>#&gt; Nonlinear mixed-effects model fit by maximum likelihood
-#&gt;   Model: value ~ (mkin::get_deg_func())(name, time, parent_0, log_k_parent_sink) 
+#&gt; </div><div class='input'><span class='va'>f_nlme</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/pkg/nlme/man/nlme.html'>nlme</a></span><span class='op'>(</span><span class='va'>f</span><span class='op'>)</span>
+<span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span><span class='op'>(</span><span class='va'>f_nlme</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; Nonlinear mixed-effects model fit by maximum likelihood
+#&gt;   Model: value ~ (mkin::get_deg_func())(name, time, parent_0, log_k_parent) 
 #&gt;   Data: "Not shown" 
 #&gt;   Log-likelihood: -307.5269
-#&gt;   Fixed: list(parent_0 ~ 1, log_k_parent_sink ~ 1) 
-#&gt;          parent_0 log_k_parent_sink 
-#&gt;         85.540979         -3.229602 
+#&gt;   Fixed: list(parent_0 ~ 1, log_k_parent ~ 1) 
+#&gt;     parent_0 log_k_parent 
+#&gt;    85.541149    -3.229596 
 #&gt; 
 #&gt; Random effects:
-#&gt;  Formula: list(parent_0 ~ 1, log_k_parent_sink ~ 1)
+#&gt;  Formula: list(parent_0 ~ 1, log_k_parent ~ 1)
 #&gt;  Level: ds
 #&gt;  Structure: Diagonal
-#&gt;         parent_0 log_k_parent_sink Residual
-#&gt; StdDev: 1.308245          1.288586 6.304923
+#&gt;         parent_0 log_k_parent Residual
+#&gt; StdDev:  1.30857     1.288591 6.304906
 #&gt; 
 #&gt; Number of Observations: 90
-#&gt; Number of Groups: 5 </div><div class='input'><span class='fu'><a href='endpoints.html'>endpoints</a></span>(<span class='no'>f_nlme</span>)</div><div class='output co'>#&gt; $distimes
+#&gt; Number of Groups: 5 </div><div class='input'><span class='fu'><a href='endpoints.html'>endpoints</a></span><span class='op'>(</span><span class='va'>f_nlme</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; $distimes
 #&gt;            DT50     DT90
-#&gt; parent 17.51556 58.18543
+#&gt; parent 17.51545 58.18505
 #&gt; </div><div class='input'><span class='co'># \dontrun{</span>
-  <span class='no'>f_nlme_2</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/pkg/nlme/man/nlme.html'>nlme</a></span>(<span class='no'>f</span>, <span class='kw'>start</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>parent_0</span> <span class='kw'>=</span> <span class='fl'>100</span>, <span class='kw'>log_k_parent_sink</span> <span class='kw'>=</span> <span class='fl'>0.1</span>))
-  <span class='fu'><a href='https://rdrr.io/r/stats/update.html'>update</a></span>(<span class='no'>f_nlme_2</span>, <span class='kw'>random</span> <span class='kw'>=</span> <span class='no'>parent_0</span> ~ <span class='fl'>1</span>)</div><div class='output co'>#&gt; Nonlinear mixed-effects model fit by maximum likelihood
-#&gt;   Model: value ~ (mkin::get_deg_func())(name, time, parent_0, log_k_parent_sink) 
+  <span class='va'>f_nlme_2</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/pkg/nlme/man/nlme.html'>nlme</a></span><span class='op'>(</span><span class='va'>f</span>, start <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>parent_0 <span class='op'>=</span> <span class='fl'>100</span>, log_k_parent_sink <span class='op'>=</span> <span class='fl'>0.1</span><span class='op'>)</span><span class='op'>)</span>
+  <span class='fu'><a href='https://rdrr.io/r/stats/update.html'>update</a></span><span class='op'>(</span><span class='va'>f_nlme_2</span>, random <span class='op'>=</span> <span class='va'>parent_0</span> <span class='op'>~</span> <span class='fl'>1</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; Nonlinear mixed-effects model fit by maximum likelihood
+#&gt;   Model: value ~ (mkin::get_deg_func())(name, time, parent_0, log_k_parent) 
 #&gt;   Data: "Not shown" 
 #&gt;   Log-likelihood: -404.3729
-#&gt;   Fixed: list(parent_0 ~ 1, log_k_parent_sink ~ 1) 
-#&gt;          parent_0 log_k_parent_sink 
-#&gt;         75.933480         -3.555983 
+#&gt;   Fixed: list(parent_0 ~ 1, log_k_parent ~ 1) 
+#&gt;     parent_0 log_k_parent 
+#&gt;    75.933480    -3.555983 
 #&gt; 
 #&gt; Random effects:
 #&gt;  Formula: parent_0 ~ 1 | ds
 #&gt;            parent_0 Residual
-#&gt; StdDev: 0.002416802 21.63027
+#&gt; StdDev: 0.002416792 21.63027
 #&gt; 
 #&gt; Number of Observations: 90
 #&gt; Number of Groups: 5 </div><div class='input'>  <span class='co'># Test on some real data</span>
-  <span class='no'>ds_2</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/lapply.html'>lapply</a></span>(<span class='no'>experimental_data_for_UBA_2019</span>[<span class='fl'>6</span>:<span class='fl'>10</span>],
-   <span class='kw'>function</span>(<span class='no'>x</span>) <span class='no'>x</span>$<span class='no'>data</span>[<span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"name"</span>, <span class='st'>"time"</span>, <span class='st'>"value"</span>)])
-  <span class='no'>m_sfo_sfo</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>, <span class='st'>"A1"</span>),
-    <span class='kw'>A1</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>), <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"min"</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-  <span class='no'>m_sfo_sfo_ff</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>, <span class='st'>"A1"</span>),
-    <span class='kw'>A1</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>), <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"max"</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-  <span class='no'>m_fomc_sfo</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"FOMC"</span>, <span class='st'>"A1"</span>),
-    <span class='kw'>A1</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>), <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-  <span class='no'>m_dfop_sfo</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"DFOP"</span>, <span class='st'>"A1"</span>),
-    <span class='kw'>A1</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>), <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-
-  <span class='no'>f_2</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mmkin.html'>mmkin</a></span>(<span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='st'>"SFO-SFO"</span> <span class='kw'>=</span> <span class='no'>m_sfo_sfo</span>,
-   <span class='st'>"SFO-SFO-ff"</span> <span class='kw'>=</span> <span class='no'>m_sfo_sfo_ff</span>,
-   <span class='st'>"FOMC-SFO"</span> <span class='kw'>=</span> <span class='no'>m_fomc_sfo</span>,
-   <span class='st'>"DFOP-SFO"</span> <span class='kw'>=</span> <span class='no'>m_dfop_sfo</span>),
-    <span class='no'>ds_2</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-  <span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='no'>f_2</span>[<span class='st'>"SFO-SFO"</span>, <span class='fl'>3</span>:<span class='fl'>4</span>]) <span class='co'># Separate fits for datasets 3 and 4</span></div><div class='img'><img src='nlme.mmkin-1.png' alt='' width='700' height='433' /></div><div class='input'>
-  <span class='no'>f_nlme_sfo_sfo</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/pkg/nlme/man/nlme.html'>nlme</a></span>(<span class='no'>f_2</span>[<span class='st'>"SFO-SFO"</span>, ])
+  <span class='va'>ds_2</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/lapply.html'>lapply</a></span><span class='op'>(</span><span class='va'>experimental_data_for_UBA_2019</span><span class='op'>[</span><span class='fl'>6</span><span class='op'>:</span><span class='fl'>10</span><span class='op'>]</span>,
+   <span class='kw'>function</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span> <span class='va'>x</span><span class='op'>$</span><span class='va'>data</span><span class='op'>[</span><span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"name"</span>, <span class='st'>"time"</span>, <span class='st'>"value"</span><span class='op'>)</span><span class='op'>]</span><span class='op'>)</span>
+  <span class='va'>m_sfo_sfo</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='st'>"A1"</span><span class='op'>)</span>,
+    A1 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span>, use_of_ff <span class='op'>=</span> <span class='st'>"min"</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+  <span class='va'>m_sfo_sfo_ff</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='st'>"A1"</span><span class='op'>)</span>,
+    A1 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span>, use_of_ff <span class='op'>=</span> <span class='st'>"max"</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+  <span class='va'>m_fomc_sfo</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"FOMC"</span>, <span class='st'>"A1"</span><span class='op'>)</span>,
+    A1 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+  <span class='va'>m_dfop_sfo</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"DFOP"</span>, <span class='st'>"A1"</span><span class='op'>)</span>,
+    A1 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+
+  <span class='va'>f_2</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mmkin.html'>mmkin</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span><span class='st'>"SFO-SFO"</span> <span class='op'>=</span> <span class='va'>m_sfo_sfo</span>,
+   <span class='st'>"SFO-SFO-ff"</span> <span class='op'>=</span> <span class='va'>m_sfo_sfo_ff</span>,
+   <span class='st'>"FOMC-SFO"</span> <span class='op'>=</span> <span class='va'>m_fomc_sfo</span>,
+   <span class='st'>"DFOP-SFO"</span> <span class='op'>=</span> <span class='va'>m_dfop_sfo</span><span class='op'>)</span>,
+    <span class='va'>ds_2</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+  <span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>f_2</span><span class='op'>[</span><span class='st'>"SFO-SFO"</span>, <span class='fl'>3</span><span class='op'>:</span><span class='fl'>4</span><span class='op'>]</span><span class='op'>)</span> <span class='co'># Separate fits for datasets 3 and 4</span>
+</div><div class='img'><img src='nlme.mmkin-1.png' alt='' width='700' height='433' /></div><div class='input'>
+  <span class='va'>f_nlme_sfo_sfo</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/pkg/nlme/man/nlme.html'>nlme</a></span><span class='op'>(</span><span class='va'>f_2</span><span class='op'>[</span><span class='st'>"SFO-SFO"</span>, <span class='op'>]</span><span class='op'>)</span>
   <span class='co'># plot(f_nlme_sfo_sfo) # not feasible with pkgdown figures</span>
-  <span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='no'>f_nlme_sfo_sfo</span>, <span class='fl'>3</span>:<span class='fl'>4</span>) <span class='co'># Global mixed model: Fits for datasets 3 and 4</span></div><div class='img'><img src='nlme.mmkin-2.png' alt='' width='700' height='433' /></div><div class='input'>
+  <span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>f_nlme_sfo_sfo</span>, <span class='fl'>3</span><span class='op'>:</span><span class='fl'>4</span><span class='op'>)</span> <span class='co'># Global mixed model: Fits for datasets 3 and 4</span>
+</div><div class='img'><img src='nlme.mmkin-2.png' alt='' width='700' height='433' /></div><div class='input'>
   <span class='co'># With formation fractions</span>
-  <span class='no'>f_nlme_sfo_sfo_ff</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/pkg/nlme/man/nlme.html'>nlme</a></span>(<span class='no'>f_2</span>[<span class='st'>"SFO-SFO-ff"</span>, ])
-  <span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='no'>f_nlme_sfo_sfo_ff</span>, <span class='fl'>3</span>:<span class='fl'>4</span>) <span class='co'># chi2 different due to different df attribution</span></div><div class='img'><img src='nlme.mmkin-3.png' alt='' width='700' height='433' /></div><div class='input'>
+  <span class='va'>f_nlme_sfo_sfo_ff</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/pkg/nlme/man/nlme.html'>nlme</a></span><span class='op'>(</span><span class='va'>f_2</span><span class='op'>[</span><span class='st'>"SFO-SFO-ff"</span>, <span class='op'>]</span><span class='op'>)</span>
+  <span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>f_nlme_sfo_sfo_ff</span>, <span class='fl'>3</span><span class='op'>:</span><span class='fl'>4</span><span class='op'>)</span> <span class='co'># chi2 different due to different df attribution</span>
+</div><div class='img'><img src='nlme.mmkin-3.png' alt='' width='700' height='433' /></div><div class='input'>
   <span class='co'># For more parameters, we need to increase pnlsMaxIter and the tolerance</span>
   <span class='co'># to get convergence</span>
-  <span class='no'>f_nlme_fomc_sfo</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/pkg/nlme/man/nlme.html'>nlme</a></span>(<span class='no'>f_2</span>[<span class='st'>"FOMC-SFO"</span>, ],
-    <span class='kw'>control</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>pnlsMaxIter</span> <span class='kw'>=</span> <span class='fl'>100</span>, <span class='kw'>tolerance</span> <span class='kw'>=</span> <span class='fl'>1e-4</span>), <span class='kw'>verbose</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#&gt; 
+  <span class='va'>f_nlme_fomc_sfo</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/pkg/nlme/man/nlme.html'>nlme</a></span><span class='op'>(</span><span class='va'>f_2</span><span class='op'>[</span><span class='st'>"FOMC-SFO"</span>, <span class='op'>]</span>,
+    control <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>pnlsMaxIter <span class='op'>=</span> <span class='fl'>100</span>, tolerance <span class='op'>=</span> <span class='fl'>1e-4</span><span class='op'>)</span>, verbose <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; 
 #&gt; **Iteration 1
-#&gt; LME step: Loglik: -394.1603, nlminb iterations: 2
+#&gt; LME step: Loglik: -394.1603, nlminb iterations: 3
 #&gt; reStruct  parameters:
 #&gt;        ds1        ds2        ds3        ds4        ds5 
-#&gt; -0.2079863  0.8563823  1.7454253  1.0917707  1.2756955 
+#&gt; -0.2079793  0.8563830  1.7454105  1.0917354  1.2756825 
 #&gt;  Beginning PNLS step: ..  completed fit_nlme() step.
-#&gt; PNLS step: RSS =  643.8814 
-#&gt;  fixed effects: 94.17379  -5.473189  -0.6970234  -0.202509  2.103883  
+#&gt; PNLS step: RSS =  643.8803 
+#&gt;  fixed effects: 94.17379  -5.473193  -0.6970236  -0.2025091  2.103883  
 #&gt;  iterations: 100 
 #&gt; Convergence crit. (must all become &lt;= tolerance = 0.0001):
 #&gt;     fixed  reStruct 
-#&gt; 0.7959873 0.1447512 
+#&gt; 0.7960134 0.1447728 
 #&gt; 
 #&gt; **Iteration 2
 #&gt; LME step: Loglik: -396.3824, nlminb iterations: 7
 #&gt; reStruct  parameters:
 #&gt;           ds1           ds2           ds3           ds4           ds5 
-#&gt; -1.712406e-01 -2.278541e-05  1.842120e+00  1.073975e+00  1.322924e+00 
+#&gt; -1.712404e-01 -2.432655e-05  1.842120e+00  1.073975e+00  1.322925e+00 
 #&gt;  Beginning PNLS step: ..  completed fit_nlme() step.
-#&gt; PNLS step: RSS =  643.8025 
-#&gt;  fixed effects: 94.17385  -5.473491  -0.6970406  -0.2025139  2.103871  
+#&gt; PNLS step: RSS =  643.8035 
+#&gt;  fixed effects: 94.17385  -5.473487  -0.6970404  -0.2025137  2.103871  
 #&gt;  iterations: 100 
 #&gt; Convergence crit. (must all become &lt;= tolerance = 0.0001):
-#&gt;       fixed    reStruct 
-#&gt; 5.51758e-05 1.26861e-03 
+#&gt;        fixed     reStruct 
+#&gt; 5.382757e-05 1.236667e-03 
 #&gt; 
 #&gt; **Iteration 3
 #&gt; LME step: Loglik: -396.3825, nlminb iterations: 7
 #&gt; reStruct  parameters:
 #&gt;           ds1           ds2           ds3           ds4           ds5 
-#&gt; -0.1712500923 -0.0001515734  1.8420972550  1.0739796967  1.3229177241 
+#&gt; -0.1712499044 -0.0001499831  1.8420971364  1.0739799123  1.3229167796 
 #&gt;  Beginning PNLS step: ..  completed fit_nlme() step.
-#&gt; PNLS step: RSS =  643.7941 
-#&gt;  fixed effects: 94.17386  -5.473523  -0.6970424  -0.2025146  2.103869  
+#&gt; PNLS step: RSS =  643.7948 
+#&gt;  fixed effects: 94.17386  -5.473521  -0.6970422  -0.2025144  2.10387  
 #&gt;  iterations: 100 
 #&gt; Convergence crit. (must all become &lt;= tolerance = 0.0001):
 #&gt;        fixed     reStruct 
-#&gt; 5.792621e-06 1.335434e-04 
+#&gt; 6.072817e-06 1.400857e-04 
 #&gt; 
 #&gt; **Iteration 4
 #&gt; LME step: Loglik: -396.3825, nlminb iterations: 7
 #&gt; reStruct  parameters:
 #&gt;           ds1           ds2           ds3           ds4           ds5 
-#&gt; -0.1712517206 -0.0001651603  1.8420950864  1.0739800294  1.3229173529 
+#&gt; -0.1712529502 -0.0001641277  1.8420957542  1.0739797181  1.3229173076 
 #&gt;  Beginning PNLS step: ..  completed fit_nlme() step.
-#&gt; PNLS step: RSS =  643.7949 
-#&gt;  fixed effects: 94.17386  -5.473521  -0.6970423  -0.2025145  2.10387  
+#&gt; PNLS step: RSS =  643.7936 
+#&gt;  fixed effects: 94.17386  -5.473526  -0.6970426  -0.2025146  2.103869  
 #&gt;  iterations: 100 
 #&gt; Convergence crit. (must all become &lt;= tolerance = 0.0001):
 #&gt;        fixed     reStruct 
-#&gt; 4.025781e-07 9.628656e-06 </div><div class='input'>  <span class='no'>f_nlme_dfop_sfo</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/pkg/nlme/man/nlme.html'>nlme</a></span>(<span class='no'>f_2</span>[<span class='st'>"DFOP-SFO"</span>, ],
-    <span class='kw'>control</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>pnlsMaxIter</span> <span class='kw'>=</span> <span class='fl'>120</span>, <span class='kw'>tolerance</span> <span class='kw'>=</span> <span class='fl'>5e-4</span>), <span class='kw'>verbose</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#&gt; 
+#&gt; 1.027451e-06 2.275704e-05 </div><div class='input'>  <span class='va'>f_nlme_dfop_sfo</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/pkg/nlme/man/nlme.html'>nlme</a></span><span class='op'>(</span><span class='va'>f_2</span><span class='op'>[</span><span class='st'>"DFOP-SFO"</span>, <span class='op'>]</span>,
+    control <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>pnlsMaxIter <span class='op'>=</span> <span class='fl'>120</span>, tolerance <span class='op'>=</span> <span class='fl'>5e-4</span><span class='op'>)</span>, verbose <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; 
 #&gt; **Iteration 1
-#&gt; LME step: Loglik: -404.9583, nlminb iterations: 1
+#&gt; LME step: Loglik: -404.9582, nlminb iterations: 1
 #&gt; reStruct  parameters:
 #&gt;        ds1        ds2        ds3        ds4        ds5        ds6 
-#&gt; -0.4114357  0.9798641  1.6990035  0.7293314  0.3354323  1.7113047 
+#&gt; -0.4114355  0.9798697  1.6990037  0.7293315  0.3354323  1.7113046 
 #&gt;  Beginning PNLS step: ..  completed fit_nlme() step.
-#&gt; PNLS step: RSS =  630.3642 
-#&gt;  fixed effects: 93.82269  -5.455991  -0.6788957  -1.862196  -4.199671  0.0553284  
+#&gt; PNLS step: RSS =  630.3644 
+#&gt;  fixed effects: 93.82269  -5.455991  -0.6788957  -1.862196  -4.199671  0.05532828  
 #&gt;  iterations: 120 
 #&gt; Convergence crit. (must all become &lt;= tolerance = 0.0005):
 #&gt;     fixed  reStruct 
-#&gt; 0.7879730 0.5822574 
+#&gt; 0.7885368 0.5822683 
 #&gt; 
 #&gt; **Iteration 2
 #&gt; LME step: Loglik: -407.7755, nlminb iterations: 11
 #&gt; reStruct  parameters:
 #&gt;          ds1          ds2          ds3          ds4          ds5          ds6 
-#&gt; -0.371224105  0.003056163  1.789939431  0.724671132  0.301602942  1.754200482 
+#&gt; -0.371224133  0.003056179  1.789939402  0.724671158  0.301602977  1.754200729 
 #&gt;  Beginning PNLS step: ..  completed fit_nlme() step.
-#&gt; PNLS step: RSS =  630.364 
-#&gt;  fixed effects: 93.82269  -5.455991  -0.6788958  -1.862196  -4.199671  0.05532834  
+#&gt; PNLS step: RSS =  630.3633 
+#&gt;  fixed effects: 93.82269  -5.455992  -0.6788958  -1.862196  -4.199671  0.05532831  
 #&gt;  iterations: 120 
 #&gt; Convergence crit. (must all become &lt;= tolerance = 0.0005):
 #&gt;        fixed     reStruct 
-#&gt; 9.814652e-07 1.059239e-05 </div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='no'>f_2</span>[<span class='st'>"FOMC-SFO"</span>, <span class='fl'>3</span>:<span class='fl'>4</span>])</div><div class='img'><img src='nlme.mmkin-4.png' alt='' width='700' height='433' /></div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='no'>f_nlme_fomc_sfo</span>, <span class='fl'>3</span>:<span class='fl'>4</span>)</div><div class='img'><img src='nlme.mmkin-5.png' alt='' width='700' height='433' /></div><div class='input'>
-  <span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='no'>f_2</span>[<span class='st'>"DFOP-SFO"</span>, <span class='fl'>3</span>:<span class='fl'>4</span>])</div><div class='img'><img src='nlme.mmkin-6.png' alt='' width='700' height='433' /></div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='no'>f_nlme_dfop_sfo</span>, <span class='fl'>3</span>:<span class='fl'>4</span>)</div><div class='img'><img src='nlme.mmkin-7.png' alt='' width='700' height='433' /></div><div class='input'>
-  <span class='fu'><a href='https://rdrr.io/r/stats/anova.html'>anova</a></span>(<span class='no'>f_nlme_dfop_sfo</span>, <span class='no'>f_nlme_fomc_sfo</span>, <span class='no'>f_nlme_sfo_sfo</span>)</div><div class='output co'>#&gt;                 Model df       AIC       BIC    logLik   Test   L.Ratio p-value
-#&gt; f_nlme_dfop_sfo     1 13  843.8547  884.6201 -408.9274                         
-#&gt; f_nlme_fomc_sfo     2 11  818.5151  853.0089 -398.2576 1 vs 2  21.33957  &lt;.0001
-#&gt; f_nlme_sfo_sfo      3  9 1085.1821 1113.4043 -533.5910 2 vs 3 270.66697  &lt;.0001</div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/stats/anova.html'>anova</a></span>(<span class='no'>f_nlme_dfop_sfo</span>, <span class='no'>f_nlme_sfo_sfo</span>) <span class='co'># if we ignore FOMC</span></div><div class='output co'>#&gt;                 Model df       AIC       BIC    logLik   Test  L.Ratio p-value
-#&gt; f_nlme_dfop_sfo     1 13  843.8547  884.6201 -408.9274                        
+#&gt; 4.789774e-07 2.200661e-05 </div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>f_2</span><span class='op'>[</span><span class='st'>"FOMC-SFO"</span>, <span class='fl'>3</span><span class='op'>:</span><span class='fl'>4</span><span class='op'>]</span><span class='op'>)</span>
+</div><div class='img'><img src='nlme.mmkin-4.png' alt='' width='700' height='433' /></div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>f_nlme_fomc_sfo</span>, <span class='fl'>3</span><span class='op'>:</span><span class='fl'>4</span><span class='op'>)</span>
+</div><div class='img'><img src='nlme.mmkin-5.png' alt='' width='700' height='433' /></div><div class='input'>
+  <span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>f_2</span><span class='op'>[</span><span class='st'>"DFOP-SFO"</span>, <span class='fl'>3</span><span class='op'>:</span><span class='fl'>4</span><span class='op'>]</span><span class='op'>)</span>
+</div><div class='img'><img src='nlme.mmkin-6.png' alt='' width='700' height='433' /></div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>f_nlme_dfop_sfo</span>, <span class='fl'>3</span><span class='op'>:</span><span class='fl'>4</span><span class='op'>)</span>
+</div><div class='img'><img src='nlme.mmkin-7.png' alt='' width='700' height='433' /></div><div class='input'>
+  <span class='fu'><a href='https://rdrr.io/r/stats/anova.html'>anova</a></span><span class='op'>(</span><span class='va'>f_nlme_dfop_sfo</span>, <span class='va'>f_nlme_fomc_sfo</span>, <span class='va'>f_nlme_sfo_sfo</span><span class='op'>)</span>
+</div><div class='output co'>#&gt;                 Model df       AIC       BIC    logLik   Test   L.Ratio p-value
+#&gt; f_nlme_dfop_sfo     1 13  843.8547  884.6201 -408.9273                         
+#&gt; f_nlme_fomc_sfo     2 11  818.5149  853.0087 -398.2575 1 vs 2  21.33975  &lt;.0001
+#&gt; f_nlme_sfo_sfo      3  9 1085.1821 1113.4043 -533.5910 2 vs 3 270.66716  &lt;.0001</div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/stats/anova.html'>anova</a></span><span class='op'>(</span><span class='va'>f_nlme_dfop_sfo</span>, <span class='va'>f_nlme_sfo_sfo</span><span class='op'>)</span> <span class='co'># if we ignore FOMC</span>
+</div><div class='output co'>#&gt;                 Model df       AIC       BIC    logLik   Test  L.Ratio p-value
+#&gt; f_nlme_dfop_sfo     1 13  843.8547  884.6201 -408.9273                        
 #&gt; f_nlme_sfo_sfo      2  9 1085.1821 1113.4043 -533.5910 1 vs 2 249.3274  &lt;.0001</div><div class='input'>
-  <span class='fu'><a href='endpoints.html'>endpoints</a></span>(<span class='no'>f_nlme_sfo_sfo</span>)</div><div class='output co'>#&gt; $ff
+  <span class='fu'><a href='endpoints.html'>endpoints</a></span><span class='op'>(</span><span class='va'>f_nlme_sfo_sfo</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; $ff
 #&gt; parent_sink   parent_A1     A1_sink 
 #&gt;   0.5912432   0.4087568   1.0000000 
 #&gt; 
@@ -420,15 +439,16 @@ with additional elements</p>
 #&gt;            DT50     DT90
 #&gt; parent 19.13518  63.5657
 #&gt; A1     66.02155 219.3189
-#&gt; </div><div class='input'>  <span class='fu'><a href='endpoints.html'>endpoints</a></span>(<span class='no'>f_nlme_dfop_sfo</span>)</div><div class='output co'>#&gt; $ff
+#&gt; </div><div class='input'>  <span class='fu'><a href='endpoints.html'>endpoints</a></span><span class='op'>(</span><span class='va'>f_nlme_dfop_sfo</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; $ff
 #&gt;   parent_A1 parent_sink 
 #&gt;   0.2768574   0.7231426 
 #&gt; 
 #&gt; $distimes
-#&gt;             DT50     DT90  DT50_k1  DT50_k2
-#&gt; parent  11.07091 104.6320 4.462384 46.20825
-#&gt; A1     162.30518 539.1661       NA       NA
-#&gt; </div><div class='input'># }
+#&gt;             DT50     DT90 DT50back  DT50_k1  DT50_k2
+#&gt; parent  11.07091 104.6320 31.49738 4.462384 46.20825
+#&gt; A1     162.30536 539.1667       NA       NA       NA
+#&gt; </div><div class='input'><span class='co'># }</span>
 </div></pre>
   </div>
   <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
@@ -445,7 +465,7 @@ with additional elements</p>
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/parms.html b/docs/reference/parms.html
index f62b3898..30dc7770 100644
--- a/docs/reference/parms.html
+++ b/docs/reference/parms.html
@@ -74,7 +74,7 @@ considering the error structure that was assumed for the fit." />
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -111,6 +111,9 @@ considering the error structure that was assumed for the fit." />
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -119,7 +122,7 @@ considering the error structure that was assumed for the fit." />
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -138,7 +141,7 @@ considering the error structure that was assumed for the fit." />
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>Extract model parameters from mkinfit models</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/parms.mkinfit.R'><code>R/parms.mkinfit.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/parms.mkinfit.R'><code>R/parms.mkinfit.R</code></a></small>
     <div class="hidden name"><code>parms.Rd</code></div>
     </div>
 
@@ -148,17 +151,21 @@ model parameters, in order to avoid working with a fitted model without
 considering the error structure that was assumed for the fit.</p>
     </div>
 
-    <pre class="usage"><span class='fu'>parms</span>(<span class='no'>object</span>, <span class='no'>...</span>)
+    <pre class="usage"><span class='fu'>parms</span><span class='op'>(</span><span class='va'>object</span>, <span class='va'>...</span><span class='op'>)</span>
 
 <span class='co'># S3 method for mkinfit</span>
-<span class='fu'>parms</span>(<span class='no'>object</span>, <span class='kw'>transformed</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>, <span class='no'>...</span>)</pre>
+<span class='fu'>parms</span><span class='op'>(</span><span class='va'>object</span>, transformed <span class='op'>=</span> <span class='cn'>FALSE</span>, <span class='va'>...</span><span class='op'>)</span>
+
+<span class='co'># S3 method for mmkin</span>
+<span class='fu'>parms</span><span class='op'>(</span><span class='va'>object</span>, transformed <span class='op'>=</span> <span class='cn'>FALSE</span>, <span class='va'>...</span><span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
     <colgroup><col class="name" /><col class="desc" /></colgroup>
     <tr>
       <th>object</th>
-      <td><p>A fitted model object</p></td>
+      <td><p>A fitted model object. Methods are implemented for
+<code><a href='mkinfit.html'>mkinfit()</a></code> objects and for <code><a href='mmkin.html'>mmkin()</a></code> objects.</p></td>
     </tr>
     <tr>
       <th>...</th>
@@ -173,24 +180,94 @@ as used internally during the optimisation?</p></td>
 
     <h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>
 
-    <p>A numeric vector of fitted model parameters</p>
+    <p>For mkinfit objects, a numeric vector of fitted model parameters.
+For mmkin row objects, a matrix with the parameters with a
+row for each dataset. If the mmkin object has more than one row, a list of
+such matrices is returned.</p>
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
-    <pre class="examples"><div class='input'><span class='no'>fit</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='st'>"SFO"</span>, <span class='no'>FOCUS_2006_C</span>)</div><div class='output co'>#&gt; <span class='message'>Ordinary least squares optimisation</span></div><div class='output co'>#&gt; Sum of squared residuals at call 1: 2388.077
-#&gt; Sum of squared residuals at call 3: 2388.077
-#&gt; Sum of squared residuals at call 4: 247.1962
-#&gt; Sum of squared residuals at call 7: 200.6791
-#&gt; Sum of squared residuals at call 10: 197.7231
-#&gt; Sum of squared residuals at call 11: 197.0872
-#&gt; Sum of squared residuals at call 14: 196.535
-#&gt; Sum of squared residuals at call 15: 196.535
-#&gt; Sum of squared residuals at call 16: 196.535
-#&gt; Sum of squared residuals at call 17: 196.5334
-#&gt; Sum of squared residuals at call 20: 196.5334
-#&gt; Sum of squared residuals at call 25: 196.5334
-#&gt; Negative log-likelihood at call 31: 26.64668</div><div class='output co'>#&gt; <span class='message'>Optimisation successfully terminated.</span></div><div class='input'><span class='fu'>parms</span>(<span class='no'>fit</span>)</div><div class='output co'>#&gt;      parent_0 k_parent_sink         sigma 
-#&gt;    82.4921598     0.3060633     4.6730124 </div><div class='input'><span class='fu'>parms</span>(<span class='no'>fit</span>, <span class='kw'>transformed</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#&gt;          parent_0 log_k_parent_sink             sigma 
-#&gt;         82.492160         -1.183963          4.673012 </div></pre>
+    <pre class="examples"><div class='input'><span class='co'># mkinfit objects</span>
+<span class='va'>fit</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='va'>FOCUS_2006_C</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+<span class='fu'>parms</span><span class='op'>(</span><span class='va'>fit</span><span class='op'>)</span>
+</div><div class='output co'>#&gt;   parent_0   k_parent      sigma 
+#&gt; 82.4921598  0.3060633  4.6730124 </div><div class='input'><span class='fu'>parms</span><span class='op'>(</span><span class='va'>fit</span>, transformed <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+</div><div class='output co'>#&gt;     parent_0 log_k_parent        sigma 
+#&gt;    82.492160    -1.183963     4.673012 </div><div class='input'>
+<span class='co'># mmkin objects</span>
+<span class='va'>ds</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/lapply.html'>lapply</a></span><span class='op'>(</span><span class='va'>experimental_data_for_UBA_2019</span><span class='op'>[</span><span class='fl'>6</span><span class='op'>:</span><span class='fl'>10</span><span class='op'>]</span>,
+ <span class='kw'>function</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span> <span class='fu'><a href='https://rdrr.io/r/base/subset.html'>subset</a></span><span class='op'>(</span><span class='va'>x</span><span class='op'>$</span><span class='va'>data</span><span class='op'>[</span><span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"name"</span>, <span class='st'>"time"</span>, <span class='st'>"value"</span><span class='op'>)</span><span class='op'>]</span><span class='op'>)</span><span class='op'>)</span>
+<span class='fu'><a href='https://rdrr.io/r/base/names.html'>names</a></span><span class='op'>(</span><span class='va'>ds</span><span class='op'>)</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/paste.html'>paste</a></span><span class='op'>(</span><span class='st'>"Dataset"</span>, <span class='fl'>6</span><span class='op'>:</span><span class='fl'>10</span><span class='op'>)</span>
+<span class='co'># \dontrun{</span>
+<span class='va'>fits</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mmkin.html'>mmkin</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='st'>"FOMC"</span>, <span class='st'>"DFOP"</span><span class='op'>)</span>, <span class='va'>ds</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, cores <span class='op'>=</span> <span class='fl'>1</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.0195</span></div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.00408</span></div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.0492</span></div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.00985</span></div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.00815</span></div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.011</span></div><div class='input'><span class='fu'>parms</span><span class='op'>(</span><span class='va'>fits</span><span class='op'>[</span><span class='st'>"SFO"</span>, <span class='op'>]</span><span class='op'>)</span>
+</div><div class='output co'>#&gt;            Dataset 6    Dataset 7  Dataset 8  Dataset 9  Dataset 10
+#&gt; parent_0 88.52275400 82.666781678 86.8547308 91.7779306 82.14809450
+#&gt; k_parent  0.05794659  0.009647805  0.2102974  0.1232258  0.00720421
+#&gt; sigma     5.15274487  7.040168584  3.6769645  6.4669234  6.50457673</div><div class='input'><span class='fu'>parms</span><span class='op'>(</span><span class='va'>fits</span><span class='op'>[</span>, <span class='fl'>2</span><span class='op'>]</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; $SFO
+#&gt;             Dataset 7
+#&gt; parent_0 82.666781678
+#&gt; k_parent  0.009647805
+#&gt; sigma     7.040168584
+#&gt; 
+#&gt; $FOMC
+#&gt;           Dataset 7
+#&gt; parent_0 92.6837649
+#&gt; alpha     0.4967832
+#&gt; beta     14.1451255
+#&gt; sigma     1.9167519
+#&gt; 
+#&gt; $DFOP
+#&gt;             Dataset 7
+#&gt; parent_0 91.058971503
+#&gt; k1        0.044946770
+#&gt; k2        0.002868336
+#&gt; g         0.526942415
+#&gt; sigma     2.221302196
+#&gt; </div><div class='input'><span class='fu'>parms</span><span class='op'>(</span><span class='va'>fits</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; $SFO
+#&gt;            Dataset 6    Dataset 7  Dataset 8  Dataset 9  Dataset 10
+#&gt; parent_0 88.52275400 82.666781678 86.8547308 91.7779306 82.14809450
+#&gt; k_parent  0.05794659  0.009647805  0.2102974  0.1232258  0.00720421
+#&gt; sigma     5.15274487  7.040168584  3.6769645  6.4669234  6.50457673
+#&gt; 
+#&gt; $FOMC
+#&gt;          Dataset 6  Dataset 7 Dataset 8 Dataset 9 Dataset 10
+#&gt; parent_0 95.558575 92.6837649 90.719787 98.383939 94.8481458
+#&gt; alpha     1.338667  0.4967832  1.639099  1.074460  0.2805272
+#&gt; beta     13.033315 14.1451255  5.007077  4.397126  6.9052224
+#&gt; sigma     1.847671  1.9167519  1.066063  3.146056  1.6222778
+#&gt; 
+#&gt; $DFOP
+#&gt;            Dataset 6    Dataset 7   Dataset 8   Dataset 9   Dataset 10
+#&gt; parent_0 96.55213663 91.058971503 90.34509469 98.14858850 94.311323409
+#&gt; k1        0.21954589  0.044946770  0.41232289  0.31697588  0.080663853
+#&gt; k2        0.02957934  0.002868336  0.07581767  0.03260384  0.003425417
+#&gt; g         0.44845068  0.526942415  0.66091965  0.65322767  0.342652880
+#&gt; sigma     1.35690468  2.221302196  1.34169076  2.87159846  1.942067831
+#&gt; </div><div class='input'><span class='fu'>parms</span><span class='op'>(</span><span class='va'>fits</span>, transformed <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; $SFO
+#&gt;              Dataset 6 Dataset 7 Dataset 8 Dataset 9 Dataset 10
+#&gt; parent_0     88.522754 82.666782 86.854731 91.777931  82.148094
+#&gt; log_k_parent -2.848234 -4.641025 -1.559232 -2.093737  -4.933090
+#&gt; sigma         5.152745  7.040169  3.676964  6.466923   6.504577
+#&gt; 
+#&gt; $FOMC
+#&gt;            Dataset 6  Dataset 7  Dataset 8   Dataset 9 Dataset 10
+#&gt; parent_0  95.5585751 92.6837649 90.7197870 98.38393897  94.848146
+#&gt; log_alpha  0.2916741 -0.6996015  0.4941466  0.07181816  -1.271085
+#&gt; log_beta   2.5675088  2.6493701  1.6108523  1.48095106   1.932278
+#&gt; sigma      1.8476712  1.9167519  1.0660627  3.14605557   1.622278
+#&gt; 
+#&gt; $DFOP
+#&gt;           Dataset 6   Dataset 7  Dataset 8  Dataset 9 Dataset 10
+#&gt; parent_0 96.5521366 91.05897150 90.3450947 98.1485885  94.311323
+#&gt; log_k1   -1.5161940 -3.10227638 -0.8859485 -1.1489296  -2.517465
+#&gt; log_k2   -3.5206791 -5.85402317 -2.5794240 -3.4233253  -5.676532
+#&gt; g_ilr    -0.1463234  0.07627854  0.4719196  0.4477805  -0.460676
+#&gt; sigma     1.3569047  2.22130220  1.3416908  2.8715985   1.942068
+#&gt; </div><div class='input'><span class='co'># }</span>
+</div></pre>
   </div>
   <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
     <nav id="toc" data-toggle="toc" class="sticky-top">
@@ -206,7 +283,7 @@ as used internally during the optimisation?</p></td>
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/plot.mkinfit-1.png b/docs/reference/plot.mkinfit-1.png
index c6a415d7..fc195031 100644
--- a/docs/reference/plot.mkinfit-1.png
+++ b/docs/reference/plot.mkinfit-1.png
diff --git a/docs/reference/plot.mkinfit-2.png b/docs/reference/plot.mkinfit-2.png
index 5dd3731e..994b516e 100644
--- a/docs/reference/plot.mkinfit-2.png
+++ b/docs/reference/plot.mkinfit-2.png
diff --git a/docs/reference/plot.mkinfit-3.png b/docs/reference/plot.mkinfit-3.png
index 59cf8f8d..28789544 100644
--- a/docs/reference/plot.mkinfit-3.png
+++ b/docs/reference/plot.mkinfit-3.png
diff --git a/docs/reference/plot.mkinfit-4.png b/docs/reference/plot.mkinfit-4.png
index d9867952..edea6fce 100644
--- a/docs/reference/plot.mkinfit-4.png
+++ b/docs/reference/plot.mkinfit-4.png
diff --git a/docs/reference/plot.mkinfit-5.png b/docs/reference/plot.mkinfit-5.png
index 1109c8df..b4b6528b 100644
--- a/docs/reference/plot.mkinfit-5.png
+++ b/docs/reference/plot.mkinfit-5.png
diff --git a/docs/reference/plot.mkinfit-6.png b/docs/reference/plot.mkinfit-6.png
index 230c90e9..a939f8e9 100644
--- a/docs/reference/plot.mkinfit-6.png
+++ b/docs/reference/plot.mkinfit-6.png
diff --git a/docs/reference/plot.mkinfit-7.png b/docs/reference/plot.mkinfit-7.png
index b23427b5..ae7807a8 100644
--- a/docs/reference/plot.mkinfit-7.png
+++ b/docs/reference/plot.mkinfit-7.png
diff --git a/docs/reference/plot.mkinfit.html b/docs/reference/plot.mkinfit.html
index f78ccf73..b82a8170 100644
--- a/docs/reference/plot.mkinfit.html
+++ b/docs/reference/plot.mkinfit.html
@@ -74,7 +74,7 @@ observed data together with the solution of the fitted model." />
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -111,6 +111,9 @@ observed data together with the solution of the fitted model." />
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -119,7 +122,7 @@ observed data together with the solution of the fitted model." />
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -138,7 +141,7 @@ observed data together with the solution of the fitted model." />
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>Plot the observed data and the fitted model of an mkinfit object</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/plot.mkinfit.R'><code>R/plot.mkinfit.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/plot.mkinfit.R'><code>R/plot.mkinfit.R</code></a></small>
     <div class="hidden name"><code>plot.mkinfit.Rd</code></div>
     </div>
 
@@ -149,49 +152,49 @@ observed data together with the solution of the fitted model.</p>
     </div>
 
     <pre class="usage"><span class='co'># S3 method for mkinfit</span>
-<span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(
-  <span class='no'>x</span>,
-  <span class='kw'>fit</span> <span class='kw'>=</span> <span class='no'>x</span>,
-  <span class='kw'>obs_vars</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/names.html'>names</a></span>(<span class='no'>fit</span>$<span class='no'>mkinmod</span>$<span class='no'>map</span>),
-  <span class='kw'>xlab</span> <span class='kw'>=</span> <span class='st'>"Time"</span>,
-  <span class='kw'>ylab</span> <span class='kw'>=</span> <span class='st'>"Observed"</span>,
-  <span class='kw'>xlim</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/range.html'>range</a></span>(<span class='no'>fit</span>$<span class='no'>data</span>$<span class='no'>time</span>),
-  <span class='kw'>ylim</span> <span class='kw'>=</span> <span class='st'>"default"</span>,
-  <span class='kw'>col_obs</span> <span class='kw'>=</span> <span class='fl'>1</span>:<span class='fu'><a href='https://rdrr.io/r/base/length.html'>length</a></span>(<span class='no'>obs_vars</span>),
-  <span class='kw'>pch_obs</span> <span class='kw'>=</span> <span class='no'>col_obs</span>,
-  <span class='kw'>lty_obs</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/rep.html'>rep</a></span>(<span class='fl'>1</span>, <span class='fu'><a href='https://rdrr.io/r/base/length.html'>length</a></span>(<span class='no'>obs_vars</span>)),
-  <span class='kw'>add</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>,
-  <span class='kw'>legend</span> <span class='kw'>=</span> !<span class='no'>add</span>,
-  <span class='kw'>show_residuals</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>,
-  <span class='kw'>show_errplot</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>,
-  <span class='kw'>maxabs</span> <span class='kw'>=</span> <span class='st'>"auto"</span>,
-  <span class='kw'>sep_obs</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>,
-  <span class='kw'>rel.height.middle</span> <span class='kw'>=</span> <span class='fl'>0.9</span>,
-  <span class='kw'>row_layout</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>,
-  <span class='kw'>lpos</span> <span class='kw'>=</span> <span class='st'>"topright"</span>,
-  <span class='kw'>inset</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='fl'>0.05</span>, <span class='fl'>0.05</span>),
-  <span class='kw'>show_errmin</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>,
-  <span class='kw'>errmin_digits</span> <span class='kw'>=</span> <span class='fl'>3</span>,
-  <span class='kw'>frame</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>,
-  <span class='no'>...</span>
-)
-
-<span class='fu'>plot_sep</span>(
-  <span class='no'>fit</span>,
-  <span class='kw'>show_errmin</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>,
-  <span class='kw'>show_residuals</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/ifelse.html'>ifelse</a></span>(<span class='fu'><a href='https://rdrr.io/r/base/identical.html'>identical</a></span>(<span class='no'>fit</span>$<span class='no'>err_mod</span>, <span class='st'>"const"</span>), <span class='fl'>TRUE</span>, <span class='st'>"standardized"</span>),
-  <span class='no'>...</span>
-)
-
-<span class='fu'>plot_res</span>(
-  <span class='no'>fit</span>,
-  <span class='kw'>sep_obs</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>,
-  <span class='kw'>show_errmin</span> <span class='kw'>=</span> <span class='no'>sep_obs</span>,
-  <span class='kw'>standardized</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/ifelse.html'>ifelse</a></span>(<span class='fu'><a href='https://rdrr.io/r/base/identical.html'>identical</a></span>(<span class='no'>fit</span>$<span class='no'>err_mod</span>, <span class='st'>"const"</span>), <span class='fl'>FALSE</span>, <span class='fl'>TRUE</span>),
-  <span class='no'>...</span>
-)
-
-<span class='fu'>plot_err</span>(<span class='no'>fit</span>, <span class='kw'>sep_obs</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>, <span class='kw'>show_errmin</span> <span class='kw'>=</span> <span class='no'>sep_obs</span>, <span class='no'>...</span>)</pre>
+<span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span>
+  <span class='va'>x</span>,
+  fit <span class='op'>=</span> <span class='va'>x</span>,
+  obs_vars <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/names.html'>names</a></span><span class='op'>(</span><span class='va'>fit</span><span class='op'>$</span><span class='va'>mkinmod</span><span class='op'>$</span><span class='va'>map</span><span class='op'>)</span>,
+  xlab <span class='op'>=</span> <span class='st'>"Time"</span>,
+  ylab <span class='op'>=</span> <span class='st'>"Observed"</span>,
+  xlim <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/range.html'>range</a></span><span class='op'>(</span><span class='va'>fit</span><span class='op'>$</span><span class='va'>data</span><span class='op'>$</span><span class='va'>time</span><span class='op'>)</span>,
+  ylim <span class='op'>=</span> <span class='st'>"default"</span>,
+  col_obs <span class='op'>=</span> <span class='fl'>1</span><span class='op'>:</span><span class='fu'><a href='https://rdrr.io/r/base/length.html'>length</a></span><span class='op'>(</span><span class='va'>obs_vars</span><span class='op'>)</span>,
+  pch_obs <span class='op'>=</span> <span class='va'>col_obs</span>,
+  lty_obs <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/rep.html'>rep</a></span><span class='op'>(</span><span class='fl'>1</span>, <span class='fu'><a href='https://rdrr.io/r/base/length.html'>length</a></span><span class='op'>(</span><span class='va'>obs_vars</span><span class='op'>)</span><span class='op'>)</span>,
+  add <span class='op'>=</span> <span class='cn'>FALSE</span>,
+  legend <span class='op'>=</span> <span class='op'>!</span><span class='va'>add</span>,
+  show_residuals <span class='op'>=</span> <span class='cn'>FALSE</span>,
+  show_errplot <span class='op'>=</span> <span class='cn'>FALSE</span>,
+  maxabs <span class='op'>=</span> <span class='st'>"auto"</span>,
+  sep_obs <span class='op'>=</span> <span class='cn'>FALSE</span>,
+  rel.height.middle <span class='op'>=</span> <span class='fl'>0.9</span>,
+  row_layout <span class='op'>=</span> <span class='cn'>FALSE</span>,
+  lpos <span class='op'>=</span> <span class='st'>"topright"</span>,
+  inset <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>0.05</span>, <span class='fl'>0.05</span><span class='op'>)</span>,
+  show_errmin <span class='op'>=</span> <span class='cn'>FALSE</span>,
+  errmin_digits <span class='op'>=</span> <span class='fl'>3</span>,
+  frame <span class='op'>=</span> <span class='cn'>TRUE</span>,
+  <span class='va'>...</span>
+<span class='op'>)</span>
+
+<span class='fu'>plot_sep</span><span class='op'>(</span>
+  <span class='va'>fit</span>,
+  show_errmin <span class='op'>=</span> <span class='cn'>TRUE</span>,
+  show_residuals <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/ifelse.html'>ifelse</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/identical.html'>identical</a></span><span class='op'>(</span><span class='va'>fit</span><span class='op'>$</span><span class='va'>err_mod</span>, <span class='st'>"const"</span><span class='op'>)</span>, <span class='cn'>TRUE</span>, <span class='st'>"standardized"</span><span class='op'>)</span>,
+  <span class='va'>...</span>
+<span class='op'>)</span>
+
+<span class='fu'>plot_res</span><span class='op'>(</span>
+  <span class='va'>fit</span>,
+  sep_obs <span class='op'>=</span> <span class='cn'>FALSE</span>,
+  show_errmin <span class='op'>=</span> <span class='va'>sep_obs</span>,
+  standardized <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/ifelse.html'>ifelse</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/identical.html'>identical</a></span><span class='op'>(</span><span class='va'>fit</span><span class='op'>$</span><span class='va'>err_mod</span>, <span class='st'>"const"</span><span class='op'>)</span>, <span class='cn'>FALSE</span>, <span class='cn'>TRUE</span><span class='op'>)</span>,
+  <span class='va'>...</span>
+<span class='op'>)</span>
+
+<span class='fu'>plot_err</span><span class='op'>(</span><span class='va'>fit</span>, sep_obs <span class='op'>=</span> <span class='cn'>FALSE</span>, show_errmin <span class='op'>=</span> <span class='va'>sep_obs</span>, <span class='va'>...</span><span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
@@ -311,7 +314,7 @@ chi2 error percentage.</p></td>
     </tr>
     <tr>
       <th>...</th>
-      <td><p>Further arguments passed to <code><a href='https://rdrr.io/r/base/plot.html'>plot</a></code>.</p></td>
+      <td><p>Further arguments passed to <code><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></code>.</p></td>
     </tr>
     <tr>
       <th>standardized</th>
@@ -328,22 +331,35 @@ standardized in the residual plot?</p></td>
     <p>If the current plot device is a <code><a href='https://rdrr.io/pkg/tikzDevice/man/tikz.html'>tikz</a></code> device, then
 latex is being used for the formatting of the chi2 error level, if
 <code>show_errmin = TRUE</code>.</p>
+    <h2 class="hasAnchor" id="author"><a class="anchor" href="#author"></a>Author</h2>
+
+    <p>Johannes Ranke</p>
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
     <pre class="examples"><div class='input'>
 <span class='co'># One parent compound, one metabolite, both single first order, path from</span>
 <span class='co'># parent to sink included</span>
 <span class='co'># \dontrun{</span>
-<span class='no'>SFO_SFO</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>, <span class='st'>"m1"</span>, <span class='kw'>full</span> <span class='kw'>=</span> <span class='st'>"Parent"</span>),
-                   <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>, <span class='kw'>full</span> <span class='kw'>=</span> <span class='st'>"Metabolite M1"</span> ))</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'><span class='no'>fit</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>SFO_SFO</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'><span class='no'>fit</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>SFO_SFO</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>error_model</span> <span class='kw'>=</span> <span class='st'>"tc"</span>)</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'><span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='no'>fit</span>)</div><div class='img'><img src='plot.mkinfit-1.png' alt='' width='700' height='433' /></div><div class='input'><span class='fu'>plot_res</span>(<span class='no'>fit</span>)</div><div class='img'><img src='plot.mkinfit-2.png' alt='' width='700' height='433' /></div><div class='input'><span class='fu'>plot_res</span>(<span class='no'>fit</span>, <span class='kw'>standardized</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>)</div><div class='img'><img src='plot.mkinfit-3.png' alt='' width='700' height='433' /></div><div class='input'><span class='fu'>plot_err</span>(<span class='no'>fit</span>)</div><div class='img'><img src='plot.mkinfit-4.png' alt='' width='700' height='433' /></div><div class='input'>
+<span class='va'>SFO_SFO</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='st'>"m1"</span>, full <span class='op'>=</span> <span class='st'>"Parent"</span><span class='op'>)</span>,
+                   m1 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, full <span class='op'>=</span> <span class='st'>"Metabolite M1"</span> <span class='op'>)</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'><span class='va'>fit</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='va'>SFO_SFO</span>, <span class='va'>FOCUS_2006_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.0165</span></div><div class='input'><span class='va'>fit</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='va'>SFO_SFO</span>, <span class='va'>FOCUS_2006_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'><span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>fit</span><span class='op'>)</span>
+</div><div class='img'><img src='plot.mkinfit-1.png' alt='' width='700' height='433' /></div><div class='input'><span class='fu'>plot_res</span><span class='op'>(</span><span class='va'>fit</span><span class='op'>)</span>
+</div><div class='img'><img src='plot.mkinfit-2.png' alt='' width='700' height='433' /></div><div class='input'><span class='fu'>plot_res</span><span class='op'>(</span><span class='va'>fit</span>, standardized <span class='op'>=</span> <span class='cn'>FALSE</span><span class='op'>)</span>
+</div><div class='img'><img src='plot.mkinfit-3.png' alt='' width='700' height='433' /></div><div class='input'><span class='fu'>plot_err</span><span class='op'>(</span><span class='va'>fit</span><span class='op'>)</span>
+</div><div class='img'><img src='plot.mkinfit-4.png' alt='' width='700' height='433' /></div><div class='input'>
 <span class='co'># Show the observed variables separately, with residuals</span>
-<span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='no'>fit</span>, <span class='kw'>sep_obs</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>show_residuals</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>lpos</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"topright"</span>, <span class='st'>"bottomright"</span>),
-     <span class='kw'>show_errmin</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='img'><img src='plot.mkinfit-5.png' alt='' width='700' height='433' /></div><div class='input'>
+<span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>fit</span>, sep_obs <span class='op'>=</span> <span class='cn'>TRUE</span>, show_residuals <span class='op'>=</span> <span class='cn'>TRUE</span>, lpos <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"topright"</span>, <span class='st'>"bottomright"</span><span class='op'>)</span>,
+     show_errmin <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+</div><div class='img'><img src='plot.mkinfit-5.png' alt='' width='700' height='433' /></div><div class='input'>
 <span class='co'># The same can be obtained with less typing, using the convenience function plot_sep</span>
-<span class='fu'>plot_sep</span>(<span class='no'>fit</span>, <span class='kw'>lpos</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"topright"</span>, <span class='st'>"bottomright"</span>))</div><div class='img'><img src='plot.mkinfit-6.png' alt='' width='700' height='433' /></div><div class='input'>
+<span class='fu'>plot_sep</span><span class='op'>(</span><span class='va'>fit</span>, lpos <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"topright"</span>, <span class='st'>"bottomright"</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='img'><img src='plot.mkinfit-6.png' alt='' width='700' height='433' /></div><div class='input'>
 <span class='co'># Show the observed variables separately, with the error model</span>
-<span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='no'>fit</span>, <span class='kw'>sep_obs</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>show_errplot</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>lpos</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"topright"</span>, <span class='st'>"bottomright"</span>),
-     <span class='kw'>show_errmin</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='img'><img src='plot.mkinfit-7.png' alt='' width='700' height='433' /></div><div class='input'># }
+<span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>fit</span>, sep_obs <span class='op'>=</span> <span class='cn'>TRUE</span>, show_errplot <span class='op'>=</span> <span class='cn'>TRUE</span>, lpos <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"topright"</span>, <span class='st'>"bottomright"</span><span class='op'>)</span>,
+     show_errmin <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+</div><div class='img'><img src='plot.mkinfit-7.png' alt='' width='700' height='433' /></div><div class='input'><span class='co'># }</span>
 
 </div></pre>
   </div>
@@ -361,7 +377,7 @@ latex is being used for the formatting of the chi2 error level, if
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/plot.mmkin-1.png b/docs/reference/plot.mmkin-1.png
index 8cf969c9..438d5a53 100644
--- a/docs/reference/plot.mmkin-1.png
+++ b/docs/reference/plot.mmkin-1.png
diff --git a/docs/reference/plot.mmkin-2.png b/docs/reference/plot.mmkin-2.png
index 45d67b55..ee04b3c4 100644
--- a/docs/reference/plot.mmkin-2.png
+++ b/docs/reference/plot.mmkin-2.png
diff --git a/docs/reference/plot.mmkin-3.png b/docs/reference/plot.mmkin-3.png
index c58b371a..e06ed002 100644
--- a/docs/reference/plot.mmkin-3.png
+++ b/docs/reference/plot.mmkin-3.png
diff --git a/docs/reference/plot.mmkin-4.png b/docs/reference/plot.mmkin-4.png
index 47cd7eec..5869df55 100644
--- a/docs/reference/plot.mmkin-4.png
+++ b/docs/reference/plot.mmkin-4.png
diff --git a/docs/reference/plot.mmkin-5.png b/docs/reference/plot.mmkin-5.png
index 44037bb4..927c573b 100644
--- a/docs/reference/plot.mmkin-5.png
+++ b/docs/reference/plot.mmkin-5.png
diff --git a/docs/reference/plot.mmkin.html b/docs/reference/plot.mmkin.html
index 6c9f2449..2003b210 100644
--- a/docs/reference/plot.mmkin.html
+++ b/docs/reference/plot.mmkin.html
@@ -76,7 +76,7 @@ the fit of at least one model to the same dataset is shown." />
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -113,6 +113,9 @@ the fit of at least one model to the same dataset is shown." />
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -121,7 +124,7 @@ the fit of at least one model to the same dataset is shown." />
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -141,31 +144,31 @@ the fit of at least one model to the same dataset is shown." />
     <div class="page-header">
     <h1>Plot model fits (observed and fitted) and the residuals for a row or column
 of an mmkin object</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/plot.mmkin.R'><code>R/plot.mmkin.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/plot.mmkin.R'><code>R/plot.mmkin.R</code></a></small>
     <div class="hidden name"><code>plot.mmkin.Rd</code></div>
     </div>
 
     <div class="ref-description">
-    <p>When x is a row selected from an mmkin object (<code><a href='Extract.mmkin.html'>[.mmkin</a></code>), the
+    <p>When x is a row selected from an mmkin object (<code><a href='[.mmkin.html'>[.mmkin</a></code>), the
 same model fitted for at least one dataset is shown. When it is a column,
 the fit of at least one model to the same dataset is shown.</p>
     </div>
 
     <pre class="usage"><span class='co'># S3 method for mmkin</span>
-<span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(
-  <span class='no'>x</span>,
-  <span class='kw'>main</span> <span class='kw'>=</span> <span class='st'>"auto"</span>,
-  <span class='kw'>legends</span> <span class='kw'>=</span> <span class='fl'>1</span>,
-  <span class='kw'>resplot</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"time"</span>, <span class='st'>"errmod"</span>),
-  <span class='kw'>standardized</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>,
-  <span class='kw'>show_errmin</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>,
-  <span class='kw'>errmin_var</span> <span class='kw'>=</span> <span class='st'>"All data"</span>,
-  <span class='kw'>errmin_digits</span> <span class='kw'>=</span> <span class='fl'>3</span>,
-  <span class='kw'>cex</span> <span class='kw'>=</span> <span class='fl'>0.7</span>,
-  <span class='kw'>rel.height.middle</span> <span class='kw'>=</span> <span class='fl'>0.9</span>,
-  <span class='kw'>ymax</span> <span class='kw'>=</span> <span class='st'>"auto"</span>,
-  <span class='no'>...</span>
-)</pre>
+<span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span>
+  <span class='va'>x</span>,
+  main <span class='op'>=</span> <span class='st'>"auto"</span>,
+  legends <span class='op'>=</span> <span class='fl'>1</span>,
+  resplot <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"time"</span>, <span class='st'>"errmod"</span><span class='op'>)</span>,
+  standardized <span class='op'>=</span> <span class='cn'>FALSE</span>,
+  show_errmin <span class='op'>=</span> <span class='cn'>TRUE</span>,
+  errmin_var <span class='op'>=</span> <span class='st'>"All data"</span>,
+  errmin_digits <span class='op'>=</span> <span class='fl'>3</span>,
+  cex <span class='op'>=</span> <span class='fl'>0.7</span>,
+  rel.height.middle <span class='op'>=</span> <span class='fl'>0.9</span>,
+  ymax <span class='op'>=</span> <span class='st'>"auto"</span>,
+  <span class='va'>...</span>
+<span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
@@ -237,21 +240,30 @@ than two rows of plots are shown.</p></td>
 
     <p>If the current plot device is a <code><a href='https://rdrr.io/pkg/tikzDevice/man/tikz.html'>tikz</a></code> device, then
 latex is being used for the formatting of the chi2 error level.</p>
+    <h2 class="hasAnchor" id="author"><a class="anchor" href="#author"></a>Author</h2>
+
+    <p>Johannes Ranke</p>
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
     <pre class="examples"><div class='input'>
   <span class='co'># \dontrun{</span>
   <span class='co'># Only use one core not to offend CRAN checks</span>
-  <span class='no'>fits</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mmkin.html'>mmkin</a></span>(<span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"FOMC"</span>, <span class='st'>"HS"</span>),
-                <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='st'>"FOCUS B"</span> <span class='kw'>=</span> <span class='no'>FOCUS_2006_B</span>, <span class='st'>"FOCUS C"</span> <span class='kw'>=</span> <span class='no'>FOCUS_2006_C</span>), <span class='co'># named list for titles</span>
-                <span class='kw'>cores</span> <span class='kw'>=</span> <span class='fl'>1</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>error_model</span> <span class='kw'>=</span> <span class='st'>"tc"</span>)</div><div class='output co'>#&gt; <span class='warning'>Warning: Optimisation did not converge:</span>
-#&gt; <span class='warning'>iteration limit reached without convergence (10)</span></div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='no'>fits</span>[, <span class='st'>"FOCUS C"</span>])</div><div class='img'><img src='plot.mmkin-1.png' alt='' width='700' height='433' /></div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='no'>fits</span>[<span class='st'>"FOMC"</span>, ])</div><div class='img'><img src='plot.mmkin-2.png' alt='' width='700' height='433' /></div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='no'>fits</span>[<span class='st'>"FOMC"</span>, ], <span class='kw'>show_errmin</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>)</div><div class='img'><img src='plot.mmkin-3.png' alt='' width='700' height='433' /></div><div class='input'>
+  <span class='va'>fits</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mmkin.html'>mmkin</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"FOMC"</span>, <span class='st'>"HS"</span><span class='op'>)</span>,
+                <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span><span class='st'>"FOCUS B"</span> <span class='op'>=</span> <span class='va'>FOCUS_2006_B</span>, <span class='st'>"FOCUS C"</span> <span class='op'>=</span> <span class='va'>FOCUS_2006_C</span><span class='op'>)</span>, <span class='co'># named list for titles</span>
+                cores <span class='op'>=</span> <span class='fl'>1</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='warning'>Warning: Optimisation did not converge:</span>
+#&gt; <span class='warning'>iteration limit reached without convergence (10)</span></div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>fits</span><span class='op'>[</span>, <span class='st'>"FOCUS C"</span><span class='op'>]</span><span class='op'>)</span>
+</div><div class='img'><img src='plot.mmkin-1.png' alt='' width='700' height='433' /></div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>fits</span><span class='op'>[</span><span class='st'>"FOMC"</span>, <span class='op'>]</span><span class='op'>)</span>
+</div><div class='img'><img src='plot.mmkin-2.png' alt='' width='700' height='433' /></div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>fits</span><span class='op'>[</span><span class='st'>"FOMC"</span>, <span class='op'>]</span>, show_errmin <span class='op'>=</span> <span class='cn'>FALSE</span><span class='op'>)</span>
+</div><div class='img'><img src='plot.mmkin-3.png' alt='' width='700' height='433' /></div><div class='input'>
   <span class='co'># We can also plot a single fit, if we like the way plot.mmkin works, but then the plot</span>
   <span class='co'># height should be smaller than the plot width (this is not possible for the html pages</span>
   <span class='co'># generated by pkgdown, as far as I know).</span>
-  <span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='no'>fits</span>[<span class='st'>"FOMC"</span>, <span class='st'>"FOCUS C"</span>]) <span class='co'># same as plot(fits[1, 2])</span></div><div class='img'><img src='plot.mmkin-4.png' alt='' width='700' height='433' /></div><div class='input'>
+  <span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>fits</span><span class='op'>[</span><span class='st'>"FOMC"</span>, <span class='st'>"FOCUS C"</span><span class='op'>]</span><span class='op'>)</span> <span class='co'># same as plot(fits[1, 2])</span>
+</div><div class='img'><img src='plot.mmkin-4.png' alt='' width='700' height='433' /></div><div class='input'>
   <span class='co'># Show the error models</span>
-  <span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='no'>fits</span>[<span class='st'>"FOMC"</span>, ], <span class='kw'>resplot</span> <span class='kw'>=</span> <span class='st'>"errmod"</span>)</div><div class='img'><img src='plot.mmkin-5.png' alt='' width='700' height='433' /></div><div class='input'>  # }
+  <span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>fits</span><span class='op'>[</span><span class='st'>"FOMC"</span>, <span class='op'>]</span>, resplot <span class='op'>=</span> <span class='st'>"errmod"</span><span class='op'>)</span>
+</div><div class='img'><img src='plot.mmkin-5.png' alt='' width='700' height='433' /></div><div class='input'>  <span class='co'># }</span>
 
 </div></pre>
   </div>
@@ -269,7 +281,7 @@ latex is being used for the formatting of the chi2 error level.</p>
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/plot.nlme.mmkin-1.png b/docs/reference/plot.nlme.mmkin-1.png
index fe2ef7d3..63ea381c 100644
--- a/docs/reference/plot.nlme.mmkin-1.png
+++ b/docs/reference/plot.nlme.mmkin-1.png
diff --git a/docs/reference/plot.nlme.mmkin-2.png b/docs/reference/plot.nlme.mmkin-2.png
index c82d0271..df4c955e 100644
--- a/docs/reference/plot.nlme.mmkin-2.png
+++ b/docs/reference/plot.nlme.mmkin-2.png
diff --git a/docs/reference/plot.nlme.mmkin.html b/docs/reference/plot.nlme.mmkin.html
index 17ec06cf..82d73dfb 100644
--- a/docs/reference/plot.nlme.mmkin.html
+++ b/docs/reference/plot.nlme.mmkin.html
@@ -72,7 +72,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -109,6 +109,9 @@
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -117,7 +120,7 @@
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -136,7 +139,7 @@
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>Plot a fitted nonlinear mixed model obtained via an mmkin row object</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/plot.nlme.mmkin.R'><code>R/plot.nlme.mmkin.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/plot.nlme.mmkin.R'><code>R/plot.nlme.mmkin.R</code></a></small>
     <div class="hidden name"><code>plot.nlme.mmkin.Rd</code></div>
     </div>
 
@@ -145,21 +148,21 @@
     </div>
 
     <pre class="usage"><span class='co'># S3 method for nlme.mmkin</span>
-<span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(
-  <span class='no'>x</span>,
-  <span class='kw'>i</span> <span class='kw'>=</span> <span class='fl'>1</span>:<span class='fu'><a href='https://rdrr.io/r/base/nrow.html'>ncol</a></span>(<span class='no'>x</span>$<span class='no'>mmkin_orig</span>),
-  <span class='kw'>main</span> <span class='kw'>=</span> <span class='st'>"auto"</span>,
-  <span class='kw'>legends</span> <span class='kw'>=</span> <span class='fl'>1</span>,
-  <span class='kw'>resplot</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"time"</span>, <span class='st'>"errmod"</span>),
-  <span class='kw'>standardized</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>,
-  <span class='kw'>show_errmin</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>,
-  <span class='kw'>errmin_var</span> <span class='kw'>=</span> <span class='st'>"All data"</span>,
-  <span class='kw'>errmin_digits</span> <span class='kw'>=</span> <span class='fl'>3</span>,
-  <span class='kw'>cex</span> <span class='kw'>=</span> <span class='fl'>0.7</span>,
-  <span class='kw'>rel.height.middle</span> <span class='kw'>=</span> <span class='fl'>0.9</span>,
-  <span class='kw'>ymax</span> <span class='kw'>=</span> <span class='st'>"auto"</span>,
-  <span class='no'>...</span>
-)</pre>
+<span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span>
+  <span class='va'>x</span>,
+  i <span class='op'>=</span> <span class='fl'>1</span><span class='op'>:</span><span class='fu'><a href='https://rdrr.io/r/base/nrow.html'>ncol</a></span><span class='op'>(</span><span class='va'>x</span><span class='op'>$</span><span class='va'>mmkin_orig</span><span class='op'>)</span>,
+  main <span class='op'>=</span> <span class='st'>"auto"</span>,
+  legends <span class='op'>=</span> <span class='fl'>1</span>,
+  resplot <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"time"</span>, <span class='st'>"errmod"</span><span class='op'>)</span>,
+  standardized <span class='op'>=</span> <span class='cn'>FALSE</span>,
+  show_errmin <span class='op'>=</span> <span class='cn'>TRUE</span>,
+  errmin_var <span class='op'>=</span> <span class='st'>"All data"</span>,
+  errmin_digits <span class='op'>=</span> <span class='fl'>3</span>,
+  cex <span class='op'>=</span> <span class='fl'>0.7</span>,
+  rel.height.middle <span class='op'>=</span> <span class='fl'>0.9</span>,
+  ymax <span class='op'>=</span> <span class='st'>"auto"</span>,
+  <span class='va'>...</span>
+<span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
@@ -231,17 +234,22 @@ than two rows of plots are shown.</p></td>
     <h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>
 
     <p>The function is called for its side effect.</p>
+    <h2 class="hasAnchor" id="author"><a class="anchor" href="#author"></a>Author</h2>
+
+    <p>Johannes Ranke</p>
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
-    <pre class="examples"><div class='input'><span class='no'>ds</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/lapply.html'>lapply</a></span>(<span class='no'>experimental_data_for_UBA_2019</span>[<span class='fl'>6</span>:<span class='fl'>10</span>],
- <span class='kw'>function</span>(<span class='no'>x</span>) <span class='fu'><a href='https://rdrr.io/r/base/subset.html'>subset</a></span>(<span class='no'>x</span>$<span class='no'>data</span>[<span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"name"</span>, <span class='st'>"time"</span>, <span class='st'>"value"</span>)], <span class='no'>name</span> <span class='kw'>==</span> <span class='st'>"parent"</span>))
-<span class='no'>f</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mmkin.html'>mmkin</a></span>(<span class='st'>"SFO"</span>, <span class='no'>ds</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>cores</span> <span class='kw'>=</span> <span class='fl'>1</span>)
-<span class='co'>#plot(f) # too many panels for pkgdown</span>
-<span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='no'>f</span>[, <span class='fl'>3</span>:<span class='fl'>4</span>])</div><div class='img'><img src='plot.nlme.mmkin-1.png' alt='' width='700' height='433' /></div><div class='input'><span class='fu'><a href='https://rdrr.io/r/base/library.html'>library</a></span>(<span class='no'>nlme</span>)
-<span class='no'>f_nlme</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/pkg/nlme/man/nlme.html'>nlme</a></span>(<span class='no'>f</span>)
+    <pre class="examples"><div class='input'><span class='va'>ds</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/lapply.html'>lapply</a></span><span class='op'>(</span><span class='va'>experimental_data_for_UBA_2019</span><span class='op'>[</span><span class='fl'>6</span><span class='op'>:</span><span class='fl'>10</span><span class='op'>]</span>,
+ <span class='kw'>function</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span> <span class='fu'><a href='https://rdrr.io/r/base/subset.html'>subset</a></span><span class='op'>(</span><span class='va'>x</span><span class='op'>$</span><span class='va'>data</span><span class='op'>[</span><span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"name"</span>, <span class='st'>"time"</span>, <span class='st'>"value"</span><span class='op'>)</span><span class='op'>]</span>, <span class='va'>name</span> <span class='op'>==</span> <span class='st'>"parent"</span><span class='op'>)</span><span class='op'>)</span>
+<span class='va'>f</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mmkin.html'>mmkin</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='va'>ds</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, cores <span class='op'>=</span> <span class='fl'>1</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.0195</span></div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.011</span></div><div class='input'><span class='co'>#plot(f) # too many panels for pkgdown</span>
+<span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>f</span><span class='op'>[</span>, <span class='fl'>3</span><span class='op'>:</span><span class='fl'>4</span><span class='op'>]</span><span class='op'>)</span>
+</div><div class='img'><img src='plot.nlme.mmkin-1.png' alt='' width='700' height='433' /></div><div class='input'><span class='kw'><a href='https://rdrr.io/r/base/library.html'>library</a></span><span class='op'>(</span><span class='va'><a href='https://svn.r-project.org/R-packages/trunk/nlme'>nlme</a></span><span class='op'>)</span>
+<span class='va'>f_nlme</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/pkg/nlme/man/nlme.html'>nlme</a></span><span class='op'>(</span><span class='va'>f</span><span class='op'>)</span>
 
 <span class='co'>#plot(f_nlme) # too many panels for pkgdown</span>
-<span class='fu'><a href='https://rdrr.io/r/base/plot.html'>plot</a></span>(<span class='no'>f_nlme</span>, <span class='fl'>3</span>:<span class='fl'>4</span>)</div><div class='img'><img src='plot.nlme.mmkin-2.png' alt='' width='700' height='433' /></div></pre>
+<span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>f_nlme</span>, <span class='fl'>3</span><span class='op'>:</span><span class='fl'>4</span><span class='op'>)</span>
+</div><div class='img'><img src='plot.nlme.mmkin-2.png' alt='' width='700' height='433' /></div></pre>
   </div>
   <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
     <nav id="toc" data-toggle="toc" class="sticky-top">
@@ -257,7 +265,7 @@ than two rows of plots are shown.</p></td>
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/print.mkinds.html b/docs/reference/print.mkinds.html
index af85c78f..7c7f6647 100644
--- a/docs/reference/print.mkinds.html
+++ b/docs/reference/print.mkinds.html
@@ -72,7 +72,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -109,6 +109,9 @@
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -117,7 +120,7 @@
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -136,7 +139,7 @@
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>Print mkinds objects</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/mkinds.R'><code>R/mkinds.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/mkinds.R'><code>R/mkinds.R</code></a></small>
     <div class="hidden name"><code>print.mkinds.Rd</code></div>
     </div>
 
@@ -145,7 +148,7 @@
     </div>
 
     <pre class="usage"><span class='co'># S3 method for mkinds</span>
-<span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span>(<span class='no'>x</span>, <span class='no'>...</span>)</pre>
+<span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span><span class='op'>(</span><span class='va'>x</span>, <span class='va'>...</span><span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
@@ -176,7 +179,7 @@
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/sigma_twocomp.html b/docs/reference/sigma_twocomp.html
index 1e1f5798..26b08765 100644
--- a/docs/reference/sigma_twocomp.html
+++ b/docs/reference/sigma_twocomp.html
@@ -73,7 +73,7 @@ dependence of the measured value \(y\):" />
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -110,6 +110,9 @@ dependence of the measured value \(y\):" />
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -118,7 +121,7 @@ dependence of the measured value \(y\):" />
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -137,7 +140,7 @@ dependence of the measured value \(y\):" />
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>Two-component error model</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/sigma_twocomp.R'><code>R/sigma_twocomp.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/sigma_twocomp.R'><code>R/sigma_twocomp.R</code></a></small>
     <div class="hidden name"><code>sigma_twocomp.Rd</code></div>
     </div>
 
@@ -146,7 +149,7 @@ dependence of the measured value \(y\):" />
 dependence of the measured value \(y\):</p>
     </div>
 
-    <pre class="usage"><span class='fu'>sigma_twocomp</span>(<span class='no'>y</span>, <span class='no'>sigma_low</span>, <span class='no'>rsd_high</span>)</pre>
+    <pre class="usage"><span class='fu'>sigma_twocomp</span><span class='op'>(</span><span class='va'>y</span>, <span class='va'>sigma_low</span>, <span class='va'>rsd_high</span><span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
@@ -201,7 +204,7 @@ measurement error in analytical chemistry. Technometrics 37(2), 176-184.</p>
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
diff --git a/docs/reference/summary.mkinfit.html b/docs/reference/summary.mkinfit.html
index ad6217e6..a2ef3b75 100644
--- a/docs/reference/summary.mkinfit.html
+++ b/docs/reference/summary.mkinfit.html
@@ -76,7 +76,7 @@ values." />
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -113,6 +113,9 @@ values." />
     <li>
       <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
     </li>
+    <li>
+      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -121,7 +124,7 @@ values." />
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -140,7 +143,7 @@ values." />
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>Summary method for class "mkinfit"</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/summary.mkinfit.R'><code>R/summary.mkinfit.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/summary.mkinfit.R'><code>R/summary.mkinfit.R</code></a></small>
     <div class="hidden name"><code>summary.mkinfit.Rd</code></div>
     </div>
 
@@ -153,10 +156,10 @@ values.</p>
     </div>
 
     <pre class="usage"><span class='co'># S3 method for mkinfit</span>
-<span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span>(<span class='no'>object</span>, <span class='kw'>data</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>distimes</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>alpha</span> <span class='kw'>=</span> <span class='fl'>0.05</span>, <span class='no'>...</span>)
+<span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span><span class='op'>(</span><span class='va'>object</span>, data <span class='op'>=</span> <span class='cn'>TRUE</span>, distimes <span class='op'>=</span> <span class='cn'>TRUE</span>, alpha <span class='op'>=</span> <span class='fl'>0.05</span>, <span class='va'>...</span><span class='op'>)</span>
 
 <span class='co'># S3 method for summary.mkinfit</span>
-<span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span>(<span class='no'>x</span>, <span class='kw'>digits</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/Extremes.html'>max</a></span>(<span class='fl'>3</span>, <span class='fu'><a href='https://rdrr.io/r/base/options.html'>getOption</a></span>(<span class='st'>"digits"</span>) - <span class='fl'>3</span>), <span class='no'>...</span>)</pre>
+<span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span><span class='op'>(</span><span class='va'>x</span>, digits <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/Extremes.html'>max</a></span><span class='op'>(</span><span class='fl'>3</span>, <span class='fu'><a href='https://rdrr.io/r/base/options.html'>getOption</a></span><span class='op'>(</span><span class='st'>"digits"</span><span class='op'>)</span> <span class='op'>-</span> <span class='fl'>3</span><span class='op'>)</span>, <span class='va'>...</span><span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
@@ -226,20 +229,24 @@ and Degradation Kinetics from Environmental Fate Studies on Pesticides in
 EU Registration&#8221; Report of the FOCUS Work Group on Degradation Kinetics,
 EC Document Reference Sanco/10058/2005 version 2.0, 434 pp,
 <a href='http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics'>http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a></p>
+    <h2 class="hasAnchor" id="author"><a class="anchor" href="#author"></a>Author</h2>
+
+    <p>Johannes Ranke</p>
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
     <pre class="examples"><div class='input'>
-  <span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span>(<span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>)), <span class='no'>FOCUS_2006_A</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>))</div><div class='output co'>#&gt; mkin version used for fitting:    0.9.50.2 
-#&gt; R version used for fitting:       4.0.0 
-#&gt; Date of fit:     Wed May 27 07:05:18 2020 
-#&gt; Date of summary: Wed May 27 07:05:18 2020 
+  <span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span><span class='op'>(</span><span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span><span class='op'>)</span>, <span class='va'>FOCUS_2006_A</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; mkin version used for fitting:    0.9.50.3 
+#&gt; R version used for fitting:       4.0.3 
+#&gt; Date of fit:     Thu Oct 15 12:41:58 2020 
+#&gt; Date of summary: Thu Oct 15 12:41:58 2020 
 #&gt; 
 #&gt; Equations:
 #&gt; d_parent/dt = - k_parent * parent
 #&gt; 
 #&gt; Model predictions using solution type analytical 
 #&gt; 
-#&gt; Fitted using 131 model solutions performed in 0.026 s
+#&gt; Fitted using 131 model solutions performed in 0.029 s
 #&gt; 
 #&gt; Error model: Constant variance 
 #&gt; 
@@ -271,9 +278,9 @@ EC Document Reference Sanco/10058/2005 version 2.0, 434 pp,
 #&gt; 
 #&gt; Parameter correlation:
 #&gt;               parent_0 log_k_parent     sigma
-#&gt; parent_0     1.000e+00    5.428e-01 1.648e-07
-#&gt; log_k_parent 5.428e-01    1.000e+00 2.513e-07
-#&gt; sigma        1.648e-07    2.513e-07 1.000e+00
+#&gt; parent_0     1.000e+00    5.428e-01 1.642e-07
+#&gt; log_k_parent 5.428e-01    1.000e+00 2.507e-07
+#&gt; sigma        1.642e-07    2.507e-07 1.000e+00
 #&gt; 
 #&gt; Backtransformed parameters:
 #&gt; Confidence intervals for internally transformed parameters are asymmetric.
@@ -319,7 +326,7 @@ EC Document Reference Sanco/10058/2005 version 2.0, 434 pp,
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
author	Johannes Ranke <jranke@uni-bremen.de>	2020-10-15 12:53:23 +0200
committer	Johannes Ranke <jranke@uni-bremen.de>	2020-10-15 12:53:23 +0200
commit	5b1179f0daff9077e1370065f9b9f03a2d0e0450 (patch)
tree	01f30f5763c279b942458843939d4f02be6ca455 /docs
parent	272aba066f0d7502e319b7e7f14009318cd44348 (diff)