Fix and rebuild documentation, see NEWS

I had to fix the two pathway vignettes, as they did not work with
the released version any more. So they and the multistart vignette
which got some small fixes as well were rebuilt.

Complete rebuild of the online docs with the released version. The
documentation of the 'hierarchial_kinetics' format had to be fixed
as well.

1 files changed, 179 insertions, 77 deletions

diff --git a/docs/articles/FOCUS_L.html b/docs/articles/FOCUS_L.html
index f02febc4..e47ed9d7 100644
--- a/docs/articles/FOCUS_L.html
+++ b/docs/articles/FOCUS_L.html
@@ -33,14 +33,14 @@
       </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">1.2.0</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">1.2.3</span>
       </span>
     </div>
 
     <div id="navbar" class="navbar-collapse collapse">
       <ul class="nav navbar-nav">
 <li>
-  <a href="../reference/index.html">Functions and data</a>
+  <a href="../reference/index.html">Reference</a>
 </li>
 <li class="dropdown">
   <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false">
@@ -52,6 +52,9 @@
 <li>
       <a href="../articles/mkin.html">Introduction to mkin</a>
     </li>
+    <li class="divider">
+    </li>
+<li class="dropdown-header">Example evaluations with (generalised) nonlinear least squares</li>
     <li>
       <a href="../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a>
     </li>
@@ -59,22 +62,31 @@
       <a href="../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a>
     </li>
     <li>
-      <a href="../articles/web_only/dimethenamid_2018.html">Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models</a>
+      <a href="../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a>
+    </li>
+    <li class="divider">
     </li>
+<li class="dropdown-header">Example evaluations with hierarchical models (nonlinear mixed-effects models)</li>
     <li>
-      <a href="../articles/web_only/multistart.html">Short demo of the multistart method</a>
+      <a href="../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a>
     </li>
     <li>
-      <a href="../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a>
+      <a href="../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a>
     </li>
     <li>
-      <a href="../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a>
+      <a href="../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a>
     </li>
     <li>
-      <a href="../articles/twa.html">Calculation of time weighted average concentrations with mkin</a>
+      <a href="../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a>
     </li>
     <li>
-      <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
+      <a href="../articles/web_only/multistart.html">Short demo of the multistart method</a>
+    </li>
+    <li class="divider">
+    </li>
+<li class="dropdown-header">Performance</li>
+    <li>
+      <a href="../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a>
     </li>
     <li>
       <a href="../articles/web_only/benchmarks.html">Benchmark timings for mkin</a>
@@ -82,6 +94,15 @@
     <li>
       <a href="../articles/web_only/saem_benchmarks.html">Benchmark timings for saem.mmkin</a>
     </li>
+    <li class="divider">
+    </li>
+<li class="dropdown-header">Miscellaneous</li>
+    <li>
+      <a href="../articles/twa.html">Calculation of time weighted average concentrations with mkin</a>
+    </li>
+    <li>
+      <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -105,13 +126,16 @@
 
       
 
-      </header><script src="FOCUS_L_files/accessible-code-block-0.0.1/empty-anchor.js"></script><div class="row">
+      </header><div class="row">
   <div class="col-md-9 contents">
     <div class="page-header toc-ignore">
-      <h1 data-toc-skip>Example evaluation of FOCUS Laboratory Data L1 to L3</h1>
-                        <h4 data-toc-skip class="author">Johannes Ranke</h4>
+      <h1 data-toc-skip>Example evaluation of FOCUS Laboratory Data L1
+to L3</h1>
+                        <h4 data-toc-skip class="author">Johannes
+Ranke</h4>
             
-            <h4 data-toc-skip class="date">Last change 18 May 2022 (rebuilt 2022-11-17)</h4>
+            <h4 data-toc-skip class="date">Last change 18 May 2022
+(rebuilt 2023-04-20)</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/FOCUS_L.rmd" class="external-link"><code>vignettes/FOCUS_L.rmd</code></a></small>
       <div class="hidden name"><code>FOCUS_L.rmd</code></div>
@@ -123,7 +147,8 @@
 <div class="section level2">
 <h2 id="laboratory-data-l1">Laboratory Data L1<a class="anchor" aria-label="anchor" href="#laboratory-data-l1"></a>
 </h2>
-<p>The following code defines example dataset L1 from the FOCUS kinetics report, p. 284:</p>
+<p>The following code defines example dataset L1 from the FOCUS kinetics
+report, p. 284:</p>
 <div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">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>
 <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" class="external-link">data.frame</a></span><span class="op">(</span></span>
@@ -132,22 +157,29 @@
 <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>
 <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="op">)</span><span class="op">)</span></span>
 <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></span></code></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>
+<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"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><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>
 <span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.L1.SFO</span><span class="op">)</span></span></code></pre></div>
-<pre><code><span><span class="co">## mkin version used for fitting:    1.2.0 </span></span>
-<span><span class="co">## R version used for fitting:       4.2.2 </span></span>
-<span><span class="co">## Date of fit:     Thu Nov 17 14:04:25 2022 </span></span>
-<span><span class="co">## Date of summary: Thu Nov 17 14:04:25 2022 </span></span>
+<pre><code><span><span class="co">## mkin version used for fitting:    1.2.3 </span></span>
+<span><span class="co">## R version used for fitting:       4.2.3 </span></span>
+<span><span class="co">## Date of fit:     Thu Apr 20 07:37:15 2023 </span></span>
+<span><span class="co">## Date of summary: Thu Apr 20 07:37:15 2023 </span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## Equations:</span></span>
 <span><span class="co">## d_parent/dt = - k_parent * parent</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## Model predictions using solution type analytical </span></span>
 <span><span class="co">## </span></span>
-<span><span class="co">## Fitted using 133 model solutions performed in 0.033 s</span></span>
+<span><span class="co">## Fitted using 133 model solutions performed in 0.011 s</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## Error model: Constant variance </span></span>
 <span><span class="co">## </span></span>
@@ -221,7 +253,8 @@
 <span><span class="co">##    21   parent     10.4    12.416  -2.0163</span></span>
 <span><span class="co">##    30   parent      2.9     5.251  -2.3513</span></span>
 <span><span class="co">##    30   parent      4.0     5.251  -1.2513</span></span></code></pre>
-<p>A plot of the fit is obtained with the plot function for mkinfit objects.</p>
+<p>A plot of the fit is obtained with the plot function for mkinfit
+objects.</p>
 <div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">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></span></code></pre></div>
 <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-4-1.png" width="576"></p>
@@ -241,19 +274,19 @@
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">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></span></code></pre></div>
 <pre><code><span><span class="co">## Warning in sqrt(diag(covar)): NaNs produced</span></span></code></pre>
 <pre><code><span><span class="co">## Warning in sqrt(1/diag(V)): NaNs produced</span></span></code></pre>
-<pre><code><span><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is</span></span>
-<span><span class="co">## doubtful</span></span></code></pre>
-<pre><code><span><span class="co">## mkin version used for fitting:    1.2.0 </span></span>
-<span><span class="co">## R version used for fitting:       4.2.2 </span></span>
-<span><span class="co">## Date of fit:     Thu Nov 17 14:04:25 2022 </span></span>
-<span><span class="co">## Date of summary: Thu Nov 17 14:04:25 2022 </span></span>
+<pre><code><span><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result</span></span>
+<span><span class="co">## is doubtful</span></span></code></pre>
+<pre><code><span><span class="co">## mkin version used for fitting:    1.2.3 </span></span>
+<span><span class="co">## R version used for fitting:       4.2.3 </span></span>
+<span><span class="co">## Date of fit:     Thu Apr 20 07:37:16 2023 </span></span>
+<span><span class="co">## Date of summary: Thu Apr 20 07:37:16 2023 </span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## Equations:</span></span>
 <span><span class="co">## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## Model predictions using solution type analytical </span></span>
 <span><span class="co">## </span></span>
-<span><span class="co">## Fitted using 369 model solutions performed in 0.08 s</span></span>
+<span><span class="co">## Fitted using 369 model solutions performed in 0.025 s</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## Error model: Constant variance </span></span>
 <span><span class="co">## </span></span>
@@ -316,14 +349,40 @@
 <span><span class="co">## Estimated disappearance times:</span></span>
 <span><span class="co">##        DT50  DT90 DT50back</span></span>
 <span><span class="co">## parent 7.25 24.08     7.25</span></span></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>
+<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>
 </div>
 <div class="section level2">
 <h2 id="laboratory-data-l2">Laboratory Data L2<a class="anchor" aria-label="anchor" href="#laboratory-data-l2"></a>
 </h2>
-<p>The following code defines example dataset L2 from the FOCUS kinetics report, p. 287:</p>
+<p>The following code defines example dataset L2 from the FOCUS kinetics
+report, p. 287:</p>
 <div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">FOCUS_2006_L2</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span></span>
 <span>  t <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/rep.html" class="external-link">rep</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">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>,</span>
@@ -334,15 +393,28 @@
 <div class="section level3">
 <h3 id="sfo-fit-for-l2">SFO fit for L2<a class="anchor" aria-label="anchor" href="#sfo-fit-for-l2"></a>
 </h3>
-<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>
+<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"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><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>
 <span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">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>,</span>
 <span>     main <span class="op">=</span> <span class="st">"FOCUS L2 - SFO"</span><span class="op">)</span></span></code></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>
-<p>We may add that it is difficult to judge the random nature of the residuals just from the three samplings at days 0, 1 and 3. Also, it is not clear <em>a priori</em> why a consistent underestimation after the approximate DT90 should be irrelevant. However, this can be rationalised by the fact that the FOCUS fate models generally only implement SFO kinetics.</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>
+<p>We may add that it is difficult to judge the random nature of the
+residuals just from the three samplings at days 0, 1 and 3. Also, it is
+not clear <em>a priori</em> why a consistent underestimation after the
+approximate DT90 should be irrelevant. However, this can be rationalised
+by the fact that the FOCUS fate models generally only implement SFO
+kinetics.</p>
 </div>
 <div class="section level3">
 <h3 id="fomc-fit-for-l2">FOMC fit for L2<a class="anchor" aria-label="anchor" href="#fomc-fit-for-l2"></a>
@@ -355,17 +427,17 @@
 <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-9-1.png" width="672"></p>
 <div class="sourceCode" id="cb17"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">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></span></code></pre></div>
-<pre><code><span><span class="co">## mkin version used for fitting:    1.2.0 </span></span>
-<span><span class="co">## R version used for fitting:       4.2.2 </span></span>
-<span><span class="co">## Date of fit:     Thu Nov 17 14:04:26 2022 </span></span>
-<span><span class="co">## Date of summary: Thu Nov 17 14:04:26 2022 </span></span>
+<pre><code><span><span class="co">## mkin version used for fitting:    1.2.3 </span></span>
+<span><span class="co">## R version used for fitting:       4.2.3 </span></span>
+<span><span class="co">## Date of fit:     Thu Apr 20 07:37:16 2023 </span></span>
+<span><span class="co">## Date of summary: Thu Apr 20 07:37:16 2023 </span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## Equations:</span></span>
 <span><span class="co">## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## Model predictions using solution type analytical </span></span>
 <span><span class="co">## </span></span>
-<span><span class="co">## Fitted using 239 model solutions performed in 0.048 s</span></span>
+<span><span class="co">## Fitted using 239 model solutions performed in 0.015 s</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## Error model: Constant variance </span></span>
 <span><span class="co">## </span></span>
@@ -423,7 +495,10 @@
 <span><span class="co">## Estimated disappearance times:</span></span>
 <span><span class="co">##          DT50  DT90 DT50back</span></span>
 <span><span class="co">## parent 0.8092 5.356    1.612</span></span></code></pre>
-<p>The error level at which the <span class="math inline">\(\chi^2\)</span> test passes is much lower in this case. Therefore, the FOMC model provides a better description of the data, as less experimental error has to be assumed in order to explain the data.</p>
+<p>The error level at which the <span class="math inline">\(\chi^2\)</span> test passes is much lower in this
+case. Therefore, the FOMC model provides a better description of the
+data, as less experimental error has to be assumed in order to explain
+the data.</p>
 </div>
 <div class="section level3">
 <h3 id="dfop-fit-for-l2">DFOP fit for L2<a class="anchor" aria-label="anchor" href="#dfop-fit-for-l2"></a>
@@ -436,10 +511,10 @@
 <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-10-1.png" width="672"></p>
 <div class="sourceCode" id="cb20"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">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></span></code></pre></div>
-<pre><code><span><span class="co">## mkin version used for fitting:    1.2.0 </span></span>
-<span><span class="co">## R version used for fitting:       4.2.2 </span></span>
-<span><span class="co">## Date of fit:     Thu Nov 17 14:04:27 2022 </span></span>
-<span><span class="co">## Date of summary: Thu Nov 17 14:04:27 2022 </span></span>
+<pre><code><span><span class="co">## mkin version used for fitting:    1.2.3 </span></span>
+<span><span class="co">## R version used for fitting:       4.2.3 </span></span>
+<span><span class="co">## Date of fit:     Thu Apr 20 07:37:16 2023 </span></span>
+<span><span class="co">## Date of summary: Thu Apr 20 07:37:16 2023 </span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## Equations:</span></span>
 <span><span class="co">## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *</span></span>
@@ -448,7 +523,7 @@
 <span><span class="co">## </span></span>
 <span><span class="co">## Model predictions using solution type analytical </span></span>
 <span><span class="co">## </span></span>
-<span><span class="co">## Fitted using 581 model solutions performed in 0.128 s</span></span>
+<span><span class="co">## Fitted using 581 model solutions performed in 0.04 s</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## Error model: Constant variance </span></span>
 <span><span class="co">## </span></span>
@@ -511,13 +586,15 @@
 <span><span class="co">## Estimated disappearance times:</span></span>
 <span><span class="co">##          DT50  DT90 DT50back DT50_k1 DT50_k2</span></span>
 <span><span class="co">## parent 0.5335 5.311    1.599 0.03084   2.058</span></span></code></pre>
-<p>Here, the DFOP model is clearly the best-fit model for dataset L2 based on the chi^2 error level criterion.</p>
+<p>Here, the DFOP model is clearly the best-fit model for dataset L2
+based on the chi^2 error level criterion.</p>
 </div>
 </div>
 <div class="section level2">
 <h2 id="laboratory-data-l3">Laboratory Data L3<a class="anchor" aria-label="anchor" href="#laboratory-data-l3"></a>
 </h2>
-<p>The following code defines example dataset L3 from the FOCUS kinetics report, p. 290.</p>
+<p>The following code defines example dataset L3 from the FOCUS kinetics
+report, p. 290.</p>
 <div class="sourceCode" id="cb22"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">FOCUS_2006_L3</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span></span>
 <span>  t <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">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>,</span>
@@ -526,26 +603,35 @@
 <div class="section level3">
 <h3 id="fit-multiple-models">Fit multiple models<a class="anchor" aria-label="anchor" href="#fit-multiple-models"></a>
 </h3>
-<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>
+<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"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="co"># Only use one core here, not to offend the CRAN checks</span></span>
 <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" class="external-link">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>
 <span>               <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">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>
 <span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">mm.L3</span><span class="op">)</span></span></code></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>
+<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>
 <div class="section level3">
 <h3 id="accessing-mmkin-objects">Accessing mmkin objects<a class="anchor" aria-label="anchor" href="#accessing-mmkin-objects"></a>
 </h3>
-<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>
+<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"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">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></span></code></pre></div>
-<pre><code><span><span class="co">## mkin version used for fitting:    1.2.0 </span></span>
-<span><span class="co">## R version used for fitting:       4.2.2 </span></span>
-<span><span class="co">## Date of fit:     Thu Nov 17 14:04:27 2022 </span></span>
-<span><span class="co">## Date of summary: Thu Nov 17 14:04:28 2022 </span></span>
+<pre><code><span><span class="co">## mkin version used for fitting:    1.2.3 </span></span>
+<span><span class="co">## R version used for fitting:       4.2.3 </span></span>
+<span><span class="co">## Date of fit:     Thu Apr 20 07:37:17 2023 </span></span>
+<span><span class="co">## Date of summary: Thu Apr 20 07:37:17 2023 </span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## Equations:</span></span>
 <span><span class="co">## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *</span></span>
@@ -554,7 +640,7 @@
 <span><span class="co">## </span></span>
 <span><span class="co">## Model predictions using solution type analytical </span></span>
 <span><span class="co">## </span></span>
-<span><span class="co">## Fitted using 376 model solutions performed in 0.078 s</span></span>
+<span><span class="co">## Fitted using 376 model solutions performed in 0.024 s</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## Error model: Constant variance </span></span>
 <span><span class="co">## </span></span>
@@ -631,20 +717,30 @@
 <div class="sourceCode" id="cb26"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">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></span></code></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>
+<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>
 </div>
 </div>
 <div class="section level2">
 <h2 id="laboratory-data-l4">Laboratory Data L4<a class="anchor" aria-label="anchor" href="#laboratory-data-l4"></a>
 </h2>
-<p>The following code defines example dataset L4 from the FOCUS kinetics report, p. 293:</p>
+<p>The following code defines example dataset L4 from the FOCUS kinetics
+report, p. 293:</p>
 <div class="sourceCode" id="cb27"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">FOCUS_2006_L4</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span></span>
 <span>  t <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">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>,</span>
 <span>  parent <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">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>
 <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></span></code></pre></div>
-<p>Fits of the SFO and FOMC models, plots and summaries are produced below:</p>
+<p>Fits of the SFO and FOMC models, plots and summaries are produced
+below:</p>
 <div class="sourceCode" id="cb28"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="co"># Only use one core here, not to offend the CRAN checks</span></span>
 <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" class="external-link">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>
@@ -652,20 +748,24 @@
 <span>               quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">mm.L4</span><span class="op">)</span></span></code></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>
+<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"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">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></span></code></pre></div>
-<pre><code><span><span class="co">## mkin version used for fitting:    1.2.0 </span></span>
-<span><span class="co">## R version used for fitting:       4.2.2 </span></span>
-<span><span class="co">## Date of fit:     Thu Nov 17 14:04:28 2022 </span></span>
-<span><span class="co">## Date of summary: Thu Nov 17 14:04:29 2022 </span></span>
+<pre><code><span><span class="co">## mkin version used for fitting:    1.2.3 </span></span>
+<span><span class="co">## R version used for fitting:       4.2.3 </span></span>
+<span><span class="co">## Date of fit:     Thu Apr 20 07:37:17 2023 </span></span>
+<span><span class="co">## Date of summary: Thu Apr 20 07:37:17 2023 </span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## Equations:</span></span>
 <span><span class="co">## d_parent/dt = - k_parent * parent</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## Model predictions using solution type analytical </span></span>
 <span><span class="co">## </span></span>
-<span><span class="co">## Fitted using 142 model solutions performed in 0.029 s</span></span>
+<span><span class="co">## Fitted using 142 model solutions performed in 0.009 s</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## Error model: Constant variance </span></span>
 <span><span class="co">## </span></span>
@@ -720,17 +820,17 @@
 <span><span class="co">## parent  106  352</span></span></code></pre>
 <div class="sourceCode" id="cb31"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">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></span></code></pre></div>
-<pre><code><span><span class="co">## mkin version used for fitting:    1.2.0 </span></span>
-<span><span class="co">## R version used for fitting:       4.2.2 </span></span>
-<span><span class="co">## Date of fit:     Thu Nov 17 14:04:28 2022 </span></span>
-<span><span class="co">## Date of summary: Thu Nov 17 14:04:29 2022 </span></span>
+<pre><code><span><span class="co">## mkin version used for fitting:    1.2.3 </span></span>
+<span><span class="co">## R version used for fitting:       4.2.3 </span></span>
+<span><span class="co">## Date of fit:     Thu Apr 20 07:37:17 2023 </span></span>
+<span><span class="co">## Date of summary: Thu Apr 20 07:37:17 2023 </span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## Equations:</span></span>
 <span><span class="co">## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## Model predictions using solution type analytical </span></span>
 <span><span class="co">## </span></span>
-<span><span class="co">## Fitted using 224 model solutions performed in 0.046 s</span></span>
+<span><span class="co">## Fitted using 224 model solutions performed in 0.014 s</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## Error model: Constant variance </span></span>
 <span><span class="co">## </span></span>
@@ -792,9 +892,11 @@
 <div class="section level2">
 <h2 class="unnumbered" id="references">References<a class="anchor" aria-label="anchor" href="#references"></a>
 </h2>
-<div id="refs" class="references hanging-indent">
-<div id="ref-ranke2014">
-<p>Ranke, Johannes. 2014. “Prüfung und Validierung von Modellierungssoftware als Alternative zu ModelMaker 4.0.” Umweltbundesamt Projektnummer 27452.</p>
+<div id="refs" class="references csl-bib-body hanging-indent">
+<div id="ref-ranke2014" class="csl-entry">
+Ranke, Johannes. 2014. <span>“<span class="nocase">Prüfung und
+Validierung von Modellierungssoftware als Alternative zu ModelMaker
+4.0</span>.”</span> Umweltbundesamt Projektnummer 27452.
 </div>
 </div>
 </div>
@@ -817,7 +919,7 @@
 
 <div class="pkgdown">
   <p></p>
-<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
+<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p>
 </div>
 
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