Remove outdated comment in FOCUS L vignette, update docs

This also adds the first benchmark results obtained on my laptop system
author: Johannes Ranke <jranke@uni-bremen.de> 2022-05-18 21:26:17 +0200
committer: Johannes Ranke <jranke@uni-bremen.de> 2022-05-18 21:26:17 +0200
commit: 91c5db736a4d3f2290a0cc5698fb4e35ae7bda59 (patch)
tree: 8e9e34d18f055936172329c1248e6e2ff136bff9 /docs/articles
parent: ea57db98cef3fb882f7bd9656b44f270e7bded38 (diff)
26 files changed, 360 insertions, 328 deletions
diff --git a/docs/articles/FOCUS_D.html b/docs/articles/FOCUS_D.html
index 1363ef11..39cf7e1a 100644
--- a/docs/articles/FOCUS_D.html
+++ b/docs/articles/FOCUS_D.html
@@ -105,7 +105,7 @@
       <h1 data-toc-skip>Example evaluation of FOCUS Example Dataset D</h1>
                         <h4 data-toc-skip class="author">Johannes Ranke</h4>
             
-            <h4 data-toc-skip class="date">Last change 31 January 2019 (rebuilt 2022-03-07)</h4>
+            <h4 data-toc-skip class="date">Last change 31 January 2019 (rebuilt 2022-05-18)</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/FOCUS_D.rmd" class="external-link"><code>vignettes/FOCUS_D.rmd</code></a></small>
       <div class="hidden name"><code>FOCUS_D.rmd</code></div>
@@ -191,9 +191,9 @@
 <div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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">fit</span><span class="op">)</span></code></pre></div>
 <pre><code><span class="co">## mkin version used for fitting:    1.1.0 </span>
-<span class="co">## R version used for fitting:       4.1.2 </span>
-<span class="co">## Date of fit:     Mon Mar  7 13:15:58 2022 </span>
-<span class="co">## Date of summary: Mon Mar  7 13:15:59 2022 </span>
+<span class="co">## R version used for fitting:       4.2.0 </span>
+<span class="co">## Date of fit:     Wed May 18 20:42:29 2022 </span>
+<span class="co">## Date of summary: Wed May 18 20:42:30 2022 </span>
 <span class="co">## </span>
 <span class="co">## Equations:</span>
 <span class="co">## d_parent/dt = - k_parent * parent</span>
@@ -201,7 +201,7 @@
 <span class="co">## </span>
 <span class="co">## Model predictions using solution type analytical </span>
 <span class="co">## </span>
-<span class="co">## Fitted using 401 model solutions performed in 0.165 s</span>
+<span class="co">## Fitted using 401 model solutions performed in 0.144 s</span>
 <span class="co">## </span>
 <span class="co">## Error model: Constant variance </span>
 <span class="co">## </span>
@@ -244,11 +244,11 @@
 <span class="co">## </span>
 <span class="co">## Parameter correlation:</span>
 <span class="co">##                   parent_0 log_k_parent   log_k_m1 f_parent_qlogis      sigma</span>
-<span class="co">## parent_0         1.000e+00    5.174e-01 -1.688e-01      -5.471e-01 -1.172e-06</span>
-<span class="co">## log_k_parent     5.174e-01    1.000e+00 -3.263e-01      -5.426e-01 -8.483e-07</span>
-<span class="co">## log_k_m1        -1.688e-01   -3.263e-01  1.000e+00       7.478e-01  8.205e-07</span>
-<span class="co">## f_parent_qlogis -5.471e-01   -5.426e-01  7.478e-01       1.000e+00  1.305e-06</span>
-<span class="co">## sigma           -1.172e-06   -8.483e-07  8.205e-07       1.305e-06  1.000e+00</span>
+<span class="co">## parent_0         1.000e+00    5.174e-01 -1.688e-01      -5.471e-01 -1.174e-06</span>
+<span class="co">## log_k_parent     5.174e-01    1.000e+00 -3.263e-01      -5.426e-01 -8.492e-07</span>
+<span class="co">## log_k_m1        -1.688e-01   -3.263e-01  1.000e+00       7.478e-01  8.220e-07</span>
+<span class="co">## f_parent_qlogis -5.471e-01   -5.426e-01  7.478e-01       1.000e+00  1.307e-06</span>
+<span class="co">## sigma           -1.174e-06   -8.492e-07  8.220e-07       1.307e-06  1.000e+00</span>
 <span class="co">## </span>
 <span class="co">## Backtransformed parameters:</span>
 <span class="co">## Confidence intervals for internally transformed parameters are asymmetric.</span>
@@ -334,7 +334,7 @@
 
 <div class="pkgdown">
   <p></p>
-<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.2.</p>
+<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.3.</p>
 </div>
 
       </footer>
diff --git a/docs/articles/FOCUS_L.html b/docs/articles/FOCUS_L.html
index d7412a56..5f41b6a3 100644
--- a/docs/articles/FOCUS_L.html
+++ b/docs/articles/FOCUS_L.html
@@ -105,7 +105,7 @@
       <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 17 November 2016 (rebuilt 2022-03-07)</h4>
+            <h4 data-toc-skip class="date">Last change 17 November 2016 (rebuilt 2022-05-18)</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>
@@ -132,16 +132,16 @@
 <code class="sourceCode R"><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/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></code></pre></div>
 <pre><code><span class="co">## mkin version used for fitting:    1.1.0 </span>
-<span class="co">## R version used for fitting:       4.1.2 </span>
-<span class="co">## Date of fit:     Mon Mar  7 13:16:01 2022 </span>
-<span class="co">## Date of summary: Mon Mar  7 13:16:01 2022 </span>
+<span class="co">## R version used for fitting:       4.2.0 </span>
+<span class="co">## Date of fit:     Wed May 18 20:42:32 2022 </span>
+<span class="co">## Date of summary: Wed May 18 20:42:32 2022 </span>
 <span class="co">## </span>
 <span class="co">## Equations:</span>
 <span class="co">## d_parent/dt = - k_parent * parent</span>
 <span class="co">## </span>
 <span class="co">## Model predictions using solution type analytical </span>
 <span class="co">## </span>
-<span class="co">## Fitted using 133 model solutions performed in 0.032 s</span>
+<span class="co">## Fitted using 133 model solutions performed in 0.031 s</span>
 <span class="co">## </span>
 <span class="co">## Error model: Constant variance </span>
 <span class="co">## </span>
@@ -173,9 +173,9 @@
 <span class="co">## </span>
 <span class="co">## Parameter correlation:</span>
 <span class="co">##                parent_0 log_k_parent      sigma</span>
-<span class="co">## parent_0      1.000e+00    6.186e-01 -1.516e-09</span>
-<span class="co">## log_k_parent  6.186e-01    1.000e+00 -3.124e-09</span>
-<span class="co">## sigma        -1.516e-09   -3.124e-09  1.000e+00</span>
+<span class="co">## parent_0      1.000e+00    6.186e-01 -1.712e-09</span>
+<span class="co">## log_k_parent  6.186e-01    1.000e+00 -3.237e-09</span>
+<span class="co">## sigma        -1.712e-09   -3.237e-09  1.000e+00</span>
 <span class="co">## </span>
 <span class="co">## Backtransformed parameters:</span>
 <span class="co">## Confidence intervals for internally transformed parameters are asymmetric.</span>
@@ -225,29 +225,26 @@
 <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"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><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></code></pre></div>
-<pre><code><span class="co">## Warning in mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet = TRUE): Optimisation did not converge:</span>
-<span class="co">## false convergence (8)</span></code></pre>
-<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html" class="external-link">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></code></pre></div>
+<code class="sourceCode R"><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>
+<span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html" class="external-link">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></code></pre></div>
 <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-6-1.png" width="576"></p>
-<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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></code></pre></div>
 <pre><code><span class="co">## Warning in sqrt(diag(covar)): NaNs produced</span></code></pre>
 <pre><code><span class="co">## Warning in sqrt(1/diag(V)): NaNs produced</span></code></pre>
 <pre><code><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is</span>
 <span class="co">## doubtful</span></code></pre>
 <pre><code><span class="co">## mkin version used for fitting:    1.1.0 </span>
-<span class="co">## R version used for fitting:       4.1.2 </span>
-<span class="co">## Date of fit:     Mon Mar  7 13:16:02 2022 </span>
-<span class="co">## Date of summary: Mon Mar  7 13:16:02 2022 </span>
+<span class="co">## R version used for fitting:       4.2.0 </span>
+<span class="co">## Date of fit:     Wed May 18 20:42:33 2022 </span>
+<span class="co">## Date of summary: Wed May 18 20:42:33 2022 </span>
 <span class="co">## </span>
 <span class="co">## Equations:</span>
 <span class="co">## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent</span>
 <span class="co">## </span>
 <span class="co">## Model predictions using solution type analytical </span>
 <span class="co">## </span>
-<span class="co">## Fitted using 369 model solutions performed in 0.081 s</span>
+<span class="co">## Fitted using 357 model solutions performed in 0.072 s</span>
 <span class="co">## </span>
 <span class="co">## Error model: Constant variance </span>
 <span class="co">## </span>
@@ -268,39 +265,34 @@
 <span class="co">## Fixed parameter values:</span>
 <span class="co">## None</span>
 <span class="co">## </span>
-<span class="co">## </span>
-<span class="co">## Warning(s): </span>
-<span class="co">## Optimisation did not converge:</span>
-<span class="co">## false convergence (8)</span>
-<span class="co">## </span>
 <span class="co">## Results:</span>
 <span class="co">## </span>
-<span class="co">##        AIC      BIC   logLik</span>
-<span class="co">##   95.88781 99.44929 -43.9439</span>
+<span class="co">##        AIC      BIC    logLik</span>
+<span class="co">##   95.88804 99.44953 -43.94402</span>
 <span class="co">## </span>
 <span class="co">## Optimised, transformed parameters with symmetric confidence intervals:</span>
 <span class="co">##           Estimate Std. Error  Lower  Upper</span>
 <span class="co">## parent_0     92.47     1.2820 89.720 95.220</span>
-<span class="co">## log_alpha    13.78        NaN    NaN    NaN</span>
-<span class="co">## log_beta     16.13        NaN    NaN    NaN</span>
-<span class="co">## sigma         2.78     0.4598  1.794  3.766</span>
+<span class="co">## log_alpha    11.37        NaN    NaN    NaN</span>
+<span class="co">## log_beta     13.72        NaN    NaN    NaN</span>
+<span class="co">## sigma         2.78     0.4621  1.789  3.771</span>
 <span class="co">## </span>
 <span class="co">## Parameter correlation:</span>
 <span class="co">##            parent_0 log_alpha log_beta     sigma</span>
-<span class="co">## parent_0  1.0000000       NaN      NaN 0.0001671</span>
+<span class="co">## parent_0  1.0000000       NaN      NaN 0.0005548</span>
 <span class="co">## log_alpha       NaN         1      NaN       NaN</span>
 <span class="co">## log_beta        NaN       NaN        1       NaN</span>
-<span class="co">## sigma     0.0001671       NaN      NaN 1.0000000</span>
+<span class="co">## sigma     0.0005548       NaN      NaN 1.0000000</span>
 <span class="co">## </span>
 <span class="co">## Backtransformed parameters:</span>
 <span class="co">## Confidence intervals for internally transformed parameters are asymmetric.</span>
 <span class="co">## t-test (unrealistically) based on the assumption of normal distribution</span>
 <span class="co">## for estimators of untransformed parameters.</span>
 <span class="co">##           Estimate t value Pr(&gt;t)  Lower  Upper</span>
-<span class="co">## parent_0 9.247e+01      NA     NA 89.720 95.220</span>
-<span class="co">## alpha    9.658e+05      NA     NA     NA     NA</span>
-<span class="co">## beta     1.010e+07      NA     NA     NA     NA</span>
-<span class="co">## sigma    2.780e+00      NA     NA  1.794  3.766</span>
+<span class="co">## parent_0     92.47      NA     NA 89.720 95.220</span>
+<span class="co">## alpha     87110.00      NA     NA     NA     NA</span>
+<span class="co">## beta     911100.00      NA     NA     NA     NA</span>
+<span class="co">## sigma         2.78      NA     NA  1.789  3.771</span>
 <span class="co">## </span>
 <span class="co">## FOCUS Chi2 error levels in percent:</span>
 <span class="co">##          err.min n.optim df</span>
@@ -308,8 +300,8 @@
 <span class="co">## parent     3.619       3  6</span>
 <span class="co">## </span>
 <span class="co">## Estimated disappearance times:</span>
-<span class="co">##        DT50  DT90 DT50back</span>
-<span class="co">## parent 7.25 24.08     7.25</span></code></pre>
+<span class="co">##         DT50  DT90 DT50back</span>
+<span class="co">## parent 7.249 24.08    7.249</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>
@@ -318,7 +310,7 @@
 <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>
-<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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>
   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>,
   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">96.1</span>, <span class="fl">91.8</span>, <span class="fl">41.4</span>, <span class="fl">38.7</span>,
@@ -329,7 +321,7 @@
 <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>
-<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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/pkg/saemix/man/plot-SaemixObject-ANY-method.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>,
      main <span class="op">=</span> <span class="st">"FOCUS L2 - SFO"</span><span class="op">)</span></code></pre></div>
@@ -342,24 +334,24 @@
 <h3 id="fomc-fit-for-l2">FOMC fit for L2<a class="anchor" aria-label="anchor" href="#fomc-fit-for-l2"></a>
 </h3>
 <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"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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/pkg/saemix/man/plot-SaemixObject-ANY-method.html" class="external-link">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></code></pre></div>
 <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">
+<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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></code></pre></div>
 <pre><code><span class="co">## mkin version used for fitting:    1.1.0 </span>
-<span class="co">## R version used for fitting:       4.1.2 </span>
-<span class="co">## Date of fit:     Mon Mar  7 13:16:03 2022 </span>
-<span class="co">## Date of summary: Mon Mar  7 13:16:03 2022 </span>
+<span class="co">## R version used for fitting:       4.2.0 </span>
+<span class="co">## Date of fit:     Wed May 18 20:42:33 2022 </span>
+<span class="co">## Date of summary: Wed May 18 20:42:33 2022 </span>
 <span class="co">## </span>
 <span class="co">## Equations:</span>
 <span class="co">## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent</span>
 <span class="co">## </span>
 <span class="co">## Model predictions using solution type analytical </span>
 <span class="co">## </span>
-<span class="co">## Fitted using 239 model solutions performed in 0.049 s</span>
+<span class="co">## Fitted using 239 model solutions performed in 0.044 s</span>
 <span class="co">## </span>
 <span class="co">## Error model: Constant variance </span>
 <span class="co">## </span>
@@ -394,10 +386,10 @@
 <span class="co">## </span>
 <span class="co">## Parameter correlation:</span>
 <span class="co">##             parent_0  log_alpha   log_beta      sigma</span>
-<span class="co">## parent_0   1.000e+00 -1.151e-01 -2.085e-01 -7.828e-09</span>
-<span class="co">## log_alpha -1.151e-01  1.000e+00  9.741e-01 -1.602e-07</span>
-<span class="co">## log_beta  -2.085e-01  9.741e-01  1.000e+00 -1.372e-07</span>
-<span class="co">## sigma     -7.828e-09 -1.602e-07 -1.372e-07  1.000e+00</span>
+<span class="co">## parent_0   1.000e+00 -1.151e-01 -2.085e-01 -7.637e-09</span>
+<span class="co">## log_alpha -1.151e-01  1.000e+00  9.741e-01 -1.617e-07</span>
+<span class="co">## log_beta  -2.085e-01  9.741e-01  1.000e+00 -1.387e-07</span>
+<span class="co">## sigma     -7.637e-09 -1.617e-07 -1.387e-07  1.000e+00</span>
 <span class="co">## </span>
 <span class="co">## Backtransformed parameters:</span>
 <span class="co">## Confidence intervals for internally transformed parameters are asymmetric.</span>
@@ -423,17 +415,17 @@
 <h3 id="dfop-fit-for-l2">DFOP fit for L2<a class="anchor" aria-label="anchor" href="#dfop-fit-for-l2"></a>
 </h3>
 <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"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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/pkg/saemix/man/plot-SaemixObject-ANY-method.html" class="external-link">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></code></pre></div>
 <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">
+<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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></code></pre></div>
 <pre><code><span class="co">## mkin version used for fitting:    1.1.0 </span>
-<span class="co">## R version used for fitting:       4.1.2 </span>
-<span class="co">## Date of fit:     Mon Mar  7 13:16:03 2022 </span>
-<span class="co">## Date of summary: Mon Mar  7 13:16:03 2022 </span>
+<span class="co">## R version used for fitting:       4.2.0 </span>
+<span class="co">## Date of fit:     Wed May 18 20:42:34 2022 </span>
+<span class="co">## Date of summary: Wed May 18 20:42:34 2022 </span>
 <span class="co">## </span>
 <span class="co">## Equations:</span>
 <span class="co">## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *</span>
@@ -442,7 +434,7 @@
 <span class="co">## </span>
 <span class="co">## Model predictions using solution type analytical </span>
 <span class="co">## </span>
-<span class="co">## Fitted using 581 model solutions performed in 0.132 s</span>
+<span class="co">## Fitted using 581 model solutions performed in 0.121 s</span>
 <span class="co">## </span>
 <span class="co">## Error model: Constant variance </span>
 <span class="co">## </span>
@@ -473,18 +465,18 @@
 <span class="co">## Optimised, transformed parameters with symmetric confidence intervals:</span>
 <span class="co">##          Estimate Std. Error      Lower     Upper</span>
 <span class="co">## parent_0   93.950  9.998e-01    91.5900   96.3100</span>
-<span class="co">## log_k1      3.112  1.842e+03 -4353.0000 4359.0000</span>
+<span class="co">## log_k1      3.113  1.845e+03 -4360.0000 4367.0000</span>
 <span class="co">## log_k2     -1.088  6.285e-02    -1.2370   -0.9394</span>
 <span class="co">## g_qlogis   -0.399  9.946e-02    -0.6342   -0.1638</span>
 <span class="co">## sigma       1.414  2.886e-01     0.7314    2.0960</span>
 <span class="co">## </span>
 <span class="co">## Parameter correlation:</span>
 <span class="co">##            parent_0     log_k1     log_k2   g_qlogis      sigma</span>
-<span class="co">## parent_0  1.000e+00  6.783e-07 -3.390e-10  2.665e-01 -2.967e-10</span>
-<span class="co">## log_k1    6.783e-07  1.000e+00  1.116e-04 -2.196e-04 -1.031e-05</span>
-<span class="co">## log_k2   -3.390e-10  1.116e-04  1.000e+00 -7.903e-01  2.917e-09</span>
-<span class="co">## g_qlogis  2.665e-01 -2.196e-04 -7.903e-01  1.000e+00 -4.408e-09</span>
-<span class="co">## sigma    -2.967e-10 -1.031e-05  2.917e-09 -4.408e-09  1.000e+00</span>
+<span class="co">## parent_0  1.000e+00  6.784e-07 -5.188e-10  2.665e-01 -5.800e-10</span>
+<span class="co">## log_k1    6.784e-07  1.000e+00  1.114e-04 -2.191e-04 -1.029e-05</span>
+<span class="co">## log_k2   -5.188e-10  1.114e-04  1.000e+00 -7.903e-01  5.080e-09</span>
+<span class="co">## g_qlogis  2.665e-01 -2.191e-04 -7.903e-01  1.000e+00 -7.991e-09</span>
+<span class="co">## sigma    -5.800e-10 -1.029e-05  5.080e-09 -7.991e-09  1.000e+00</span>
 <span class="co">## </span>
 <span class="co">## Backtransformed parameters:</span>
 <span class="co">## Confidence intervals for internally transformed parameters are asymmetric.</span>
@@ -492,7 +484,7 @@
 <span class="co">## for estimators of untransformed parameters.</span>
 <span class="co">##          Estimate   t value    Pr(&gt;t)   Lower   Upper</span>
 <span class="co">## parent_0  93.9500 9.397e+01 2.036e-12 91.5900 96.3100</span>
-<span class="co">## k1        22.4800 5.553e-04 4.998e-01  0.0000     Inf</span>
+<span class="co">## k1        22.4800 5.544e-04 4.998e-01  0.0000     Inf</span>
 <span class="co">## k2         0.3369 1.591e+01 4.697e-07  0.2904  0.3909</span>
 <span class="co">## g          0.4016 1.680e+01 3.238e-07  0.3466  0.4591</span>
 <span class="co">## sigma      1.4140 4.899e+00 8.776e-04  0.7314  2.0960</span>
@@ -504,15 +496,15 @@
 <span class="co">## </span>
 <span class="co">## Estimated disappearance times:</span>
 <span class="co">##          DT50  DT90 DT50back DT50_k1 DT50_k2</span>
-<span class="co">## parent 0.5335 5.311    1.599 0.03084   2.058</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. 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>
+<span class="co">## parent 0.5335 5.311    1.599 0.03083   2.058</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>
 </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>
-<div class="sourceCode" id="cb22"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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>
   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>,
   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">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>
@@ -521,7 +513,7 @@
 <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>
-<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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" 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 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>
@@ -534,12 +526,12 @@
 </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>
-<div class="sourceCode" id="cb24"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb22"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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></code></pre></div>
 <pre><code><span class="co">## mkin version used for fitting:    1.1.0 </span>
-<span class="co">## R version used for fitting:       4.1.2 </span>
-<span class="co">## Date of fit:     Mon Mar  7 13:16:04 2022 </span>
-<span class="co">## Date of summary: Mon Mar  7 13:16:04 2022 </span>
+<span class="co">## R version used for fitting:       4.2.0 </span>
+<span class="co">## Date of fit:     Wed May 18 20:42:34 2022 </span>
+<span class="co">## Date of summary: Wed May 18 20:42:35 2022 </span>
 <span class="co">## </span>
 <span class="co">## Equations:</span>
 <span class="co">## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *</span>
@@ -548,7 +540,7 @@
 <span class="co">## </span>
 <span class="co">## Model predictions using solution type analytical </span>
 <span class="co">## </span>
-<span class="co">## Fitted using 376 model solutions performed in 0.08 s</span>
+<span class="co">## Fitted using 376 model solutions performed in 0.073 s</span>
 <span class="co">## </span>
 <span class="co">## Error model: Constant variance </span>
 <span class="co">## </span>
@@ -586,11 +578,11 @@
 <span class="co">## </span>
 <span class="co">## Parameter correlation:</span>
 <span class="co">##            parent_0     log_k1     log_k2   g_qlogis      sigma</span>
-<span class="co">## parent_0  1.000e+00  1.732e-01  2.282e-02  4.009e-01 -9.664e-08</span>
-<span class="co">## log_k1    1.732e-01  1.000e+00  4.945e-01 -5.809e-01  7.147e-07</span>
-<span class="co">## log_k2    2.282e-02  4.945e-01  1.000e+00 -6.812e-01  1.022e-06</span>
-<span class="co">## g_qlogis  4.009e-01 -5.809e-01 -6.812e-01  1.000e+00 -7.926e-07</span>
-<span class="co">## sigma    -9.664e-08  7.147e-07  1.022e-06 -7.926e-07  1.000e+00</span>
+<span class="co">## parent_0  1.000e+00  1.732e-01  2.282e-02  4.009e-01 -9.632e-08</span>
+<span class="co">## log_k1    1.732e-01  1.000e+00  4.945e-01 -5.809e-01  7.145e-07</span>
+<span class="co">## log_k2    2.282e-02  4.945e-01  1.000e+00 -6.812e-01  1.021e-06</span>
+<span class="co">## g_qlogis  4.009e-01 -5.809e-01 -6.812e-01  1.000e+00 -7.925e-07</span>
+<span class="co">## sigma    -9.632e-08  7.145e-07  1.021e-06 -7.925e-07  1.000e+00</span>
 <span class="co">## </span>
 <span class="co">## Backtransformed parameters:</span>
 <span class="co">## Confidence intervals for internally transformed parameters are asymmetric.</span>
@@ -622,7 +614,7 @@
 <span class="co">##    60   parent     22.0     23.26 -1.25919</span>
 <span class="co">##    91   parent     15.0     15.18 -0.18181</span>
 <span class="co">##   120   parent     12.0     10.19  1.81395</span></code></pre>
-<div class="sourceCode" id="cb26"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb24"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.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></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>
@@ -633,13 +625,13 @@
 <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>
-<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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>
   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>,
   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 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></code></pre></div>
 <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">
+<div class="sourceCode" id="cb26"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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" 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 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 L4"</span> <span class="op">=</span> <span class="va">FOCUS_2006_L4_mkin</span><span class="op">)</span>,
@@ -647,19 +639,19 @@
 <span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">mm.L4</span><span class="op">)</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>
-<div class="sourceCode" id="cb29"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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></code></pre></div>
 <pre><code><span class="co">## mkin version used for fitting:    1.1.0 </span>
-<span class="co">## R version used for fitting:       4.1.2 </span>
-<span class="co">## Date of fit:     Mon Mar  7 13:16:04 2022 </span>
-<span class="co">## Date of summary: Mon Mar  7 13:16:05 2022 </span>
+<span class="co">## R version used for fitting:       4.2.0 </span>
+<span class="co">## Date of fit:     Wed May 18 20:42:35 2022 </span>
+<span class="co">## Date of summary: Wed May 18 20:42:35 2022 </span>
 <span class="co">## </span>
 <span class="co">## Equations:</span>
 <span class="co">## d_parent/dt = - k_parent * parent</span>
 <span class="co">## </span>
 <span class="co">## Model predictions using solution type analytical </span>
 <span class="co">## </span>
-<span class="co">## Fitted using 142 model solutions performed in 0.029 s</span>
+<span class="co">## Fitted using 142 model solutions performed in 0.027 s</span>
 <span class="co">## </span>
 <span class="co">## Error model: Constant variance </span>
 <span class="co">## </span>
@@ -691,9 +683,9 @@
 <span class="co">## </span>
 <span class="co">## Parameter correlation:</span>
 <span class="co">##               parent_0 log_k_parent     sigma</span>
-<span class="co">## parent_0     1.000e+00    5.938e-01 3.387e-07</span>
-<span class="co">## log_k_parent 5.938e-01    1.000e+00 5.830e-07</span>
-<span class="co">## sigma        3.387e-07    5.830e-07 1.000e+00</span>
+<span class="co">## parent_0     1.000e+00    5.938e-01 3.440e-07</span>
+<span class="co">## log_k_parent 5.938e-01    1.000e+00 5.885e-07</span>
+<span class="co">## sigma        3.440e-07    5.885e-07 1.000e+00</span>
 <span class="co">## </span>
 <span class="co">## Backtransformed parameters:</span>
 <span class="co">## Confidence intervals for internally transformed parameters are asymmetric.</span>
@@ -712,19 +704,19 @@
 <span class="co">## Estimated disappearance times:</span>
 <span class="co">##        DT50 DT90</span>
 <span class="co">## parent  106  352</span></code></pre>
-<div class="sourceCode" id="cb31"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb29"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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></code></pre></div>
 <pre><code><span class="co">## mkin version used for fitting:    1.1.0 </span>
-<span class="co">## R version used for fitting:       4.1.2 </span>
-<span class="co">## Date of fit:     Mon Mar  7 13:16:04 2022 </span>
-<span class="co">## Date of summary: Mon Mar  7 13:16:05 2022 </span>
+<span class="co">## R version used for fitting:       4.2.0 </span>
+<span class="co">## Date of fit:     Wed May 18 20:42:35 2022 </span>
+<span class="co">## Date of summary: Wed May 18 20:42:35 2022 </span>
 <span class="co">## </span>
 <span class="co">## Equations:</span>
 <span class="co">## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent</span>
 <span class="co">## </span>
 <span class="co">## Model predictions using solution type analytical </span>
 <span class="co">## </span>
-<span class="co">## Fitted using 224 model solutions performed in 0.045 s</span>
+<span class="co">## Fitted using 224 model solutions performed in 0.041 s</span>
 <span class="co">## </span>
 <span class="co">## Error model: Constant variance </span>
 <span class="co">## </span>
@@ -759,10 +751,10 @@
 <span class="co">## </span>
 <span class="co">## Parameter correlation:</span>
 <span class="co">##             parent_0  log_alpha   log_beta      sigma</span>
-<span class="co">## parent_0   1.000e+00 -4.696e-01 -5.543e-01 -2.468e-07</span>
-<span class="co">## log_alpha -4.696e-01  1.000e+00  9.889e-01  2.478e-08</span>
-<span class="co">## log_beta  -5.543e-01  9.889e-01  1.000e+00  5.211e-08</span>
-<span class="co">## sigma     -2.468e-07  2.478e-08  5.211e-08  1.000e+00</span>
+<span class="co">## parent_0   1.000e+00 -4.696e-01 -5.543e-01 -2.563e-07</span>
+<span class="co">## log_alpha -4.696e-01  1.000e+00  9.889e-01  4.066e-08</span>
+<span class="co">## log_beta  -5.543e-01  9.889e-01  1.000e+00  6.818e-08</span>
+<span class="co">## sigma     -2.563e-07  4.066e-08  6.818e-08  1.000e+00</span>
 <span class="co">## </span>
 <span class="co">## Backtransformed parameters:</span>
 <span class="co">## Confidence intervals for internally transformed parameters are asymmetric.</span>
@@ -811,7 +803,7 @@
 
 <div class="pkgdown">
   <p></p>
-<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.2.</p>
+<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.3.</p>
 </div>
 
       </footer>
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 b6130527..b56e91e1 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/index.html b/docs/articles/index.html
index f340896b..89eb092b 100644
--- a/docs/articles/index.html
+++ b/docs/articles/index.html
@@ -112,7 +112,7 @@
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.2.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.3.</p>
 </div>
 
       </footer></div>
diff --git a/docs/articles/mkin.html b/docs/articles/mkin.html
index 60d2ef1c..a32f4b41 100644
--- a/docs/articles/mkin.html
+++ b/docs/articles/mkin.html
@@ -105,7 +105,7 @@
       <h1 data-toc-skip>Introduction to mkin</h1>
                         <h4 data-toc-skip class="author">Johannes Ranke</h4>
             
-            <h4 data-toc-skip class="date">Last change 15 February 2021 (rebuilt 2022-03-07)</h4>
+            <h4 data-toc-skip class="date">Last change 15 February 2021 (rebuilt 2022-05-18)</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/mkin.rmd" class="external-link"><code>vignettes/mkin.rmd</code></a></small>
       <div class="hidden name"><code>mkin.rmd</code></div>
@@ -264,7 +264,7 @@
 
 <div class="pkgdown">
   <p></p>
-<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.2.</p>
+<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.3.</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
index 63246387..d1e7048d 100644
--- a/docs/articles/mkin_files/figure-html/unnamed-chunk-2-1.png
+++ 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 d45b0ff4..dad8ee44 100644
--- a/docs/articles/twa.html
+++ b/docs/articles/twa.html
@@ -105,7 +105,7 @@
       <h1 data-toc-skip>Calculation of time weighted average concentrations with mkin</h1>
                         <h4 data-toc-skip class="author">Johannes Ranke</h4>
             
-            <h4 data-toc-skip class="date">Last change 18 September 2019 (rebuilt 2022-03-07)</h4>
+            <h4 data-toc-skip class="date">Last change 18 September 2019 (rebuilt 2022-05-18)</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/twa.rmd" class="external-link"><code>vignettes/twa.rmd</code></a></small>
       <div class="hidden name"><code>twa.rmd</code></div>
@@ -168,7 +168,7 @@
 
 <div class="pkgdown">
   <p></p>
-<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.2.</p>
+<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.3.</p>
 </div>
 
       </footer>
diff --git a/docs/articles/web_only/FOCUS_Z.html b/docs/articles/web_only/FOCUS_Z.html
index 43508280..0dafb98a 100644
--- a/docs/articles/web_only/FOCUS_Z.html
+++ b/docs/articles/web_only/FOCUS_Z.html
@@ -105,7 +105,7 @@
       <h1 data-toc-skip>Example evaluation of FOCUS dataset Z</h1>
                         <h4 data-toc-skip class="author">Johannes Ranke</h4>
             
-            <h4 data-toc-skip class="date">Last change 16 January 2018 (rebuilt 2022-03-07)</h4>
+            <h4 data-toc-skip class="date">Last change 16 January 2018 (rebuilt 2022-05-18)</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/FOCUS_Z.rmd" class="external-link"><code>vignettes/web_only/FOCUS_Z.rmd</code></a></small>
       <div class="hidden name"><code>FOCUS_Z.rmd</code></div>
@@ -234,33 +234,31 @@
                      quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></code></pre></div>
 <pre><code><span class="co">## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.5$bparms.ode, :</span>
 <span class="co">## Observations with value of zero were removed from the data</span></code></pre>
-<pre><code><span class="co">## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.5$bparms.ode, : Optimisation did not converge:</span>
-<span class="co">## false convergence (8)</span></code></pre>
-<div class="sourceCode" id="cb33"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb32"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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></code></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"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb33"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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.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></code></pre></div>
 <pre><code><span class="co">##             Estimate se_notrans t value     Pr(&gt;t)     Lower      Upper</span>
-<span class="co">## Z0_0       96.838822   1.994274 48.5584 4.0280e-42 92.826981 100.850664</span>
-<span class="co">## k_Z0        2.215393   0.118458 18.7019 1.0413e-23  1.989456   2.466989</span>
-<span class="co">## k_Z1        0.478305   0.028258 16.9266 6.2418e-22  0.424708   0.538666</span>
-<span class="co">## k_Z2        0.451627   0.042139 10.7176 1.6314e-14  0.374339   0.544872</span>
-<span class="co">## k_Z3        0.058692   0.015245  3.8499 1.7803e-04  0.034808   0.098965</span>
-<span class="co">## f_Z2_to_Z3  0.471502   0.058351  8.0805 9.6608e-11  0.357769   0.588274</span>
+<span class="co">## Z0_0       96.838397   1.994270 48.5583 4.0284e-42 92.826435 100.850359</span>
+<span class="co">## k_Z0        2.215406   0.118459 18.7018 1.0416e-23  1.989466   2.467005</span>
+<span class="co">## k_Z1        0.478300   0.028257 16.9267 6.2409e-22  0.424702   0.538662</span>
+<span class="co">## k_Z2        0.451616   0.042137 10.7178 1.6305e-14  0.374328   0.544863</span>
+<span class="co">## k_Z3        0.058693   0.015245  3.8499 1.7803e-04  0.034805   0.098976</span>
+<span class="co">## f_Z2_to_Z3  0.471509   0.058352  8.0804 9.6622e-11  0.357739   0.588317</span>
 <span class="co">## sigma       3.984431   0.383402 10.3923 4.5575e-14  3.213126   4.755736</span></code></pre>
-<div class="sourceCode" id="cb36"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb35"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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></code></pre></div>
 <pre><code><span class="co">## $ff</span>
 <span class="co">##   Z2_Z3 Z2_sink </span>
-<span class="co">##  0.4715  0.5285 </span>
+<span class="co">## 0.47151 0.52849 </span>
 <span class="co">## </span>
 <span class="co">## $distimes</span>
 <span class="co">##        DT50    DT90</span>
 <span class="co">## Z0  0.31288  1.0394</span>
-<span class="co">## Z1  1.44917  4.8141</span>
-<span class="co">## Z2  1.53478  5.0984</span>
-<span class="co">## Z3 11.80986 39.2315</span></code></pre>
+<span class="co">## Z1  1.44919  4.8141</span>
+<span class="co">## Z2  1.53481  5.0985</span>
+<span class="co">## Z3 11.80971 39.2310</span></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 class="section level2">
@@ -268,32 +266,34 @@
 </h2>
 <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"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb37"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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/mkinmod.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/mkinmod.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/mkinmod.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/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span><span class="op">)</span><span class="op">)</span></code></pre></div>
 <pre><code><span class="co">## Temporary DLL for differentials generated and loaded</span></code></pre>
-<div class="sourceCode" id="cb40"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb39"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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></code></pre></div>
 <pre><code><span class="co">## Warning in mkinfit(Z.mkin.1, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with</span>
 <span class="co">## value of zero were removed from the data</span></code></pre>
-<div class="sourceCode" id="cb42"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb41"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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></code></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"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb42"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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.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></code></pre></div>
 <pre><code><span class="co">## NULL</span></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"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb44"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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/mkinmod.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/mkinmod.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/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span><span class="op">)</span></code></pre></div>
 <pre><code><span class="co">## Temporary DLL for differentials generated and loaded</span></code></pre>
-<div class="sourceCode" id="cb47"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb46"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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></code></pre></div>
 <pre><code><span class="co">## Warning in mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with</span>
 <span class="co">## value of zero were removed from the data</span></code></pre>
+<pre><code><span class="co">## Warning in mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE): Optimisation did not converge:</span>
+<span class="co">## false convergence (8)</span></code></pre>
 <div class="sourceCode" id="cb49"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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></code></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png" width="700"></p>
@@ -359,11 +359,11 @@
 <span class="co">## </span>
 <span class="co">## $SFORB</span>
 <span class="co">##     Z0_b1     Z0_b2     Z3_b1     Z3_b2 </span>
-<span class="co">## 2.4471322 0.0075125 0.0800069 0.0000000 </span>
+<span class="co">## 2.4471376 0.0075126 0.0800073 0.0000000 </span>
 <span class="co">## </span>
 <span class="co">## $distimes</span>
 <span class="co">##      DT50   DT90 DT50back DT50_Z0_b1 DT50_Z0_b2 DT50_Z3_b1 DT50_Z3_b2</span>
-<span class="co">## Z0 0.3043 1.1848  0.35666    0.28325     92.266         NA         NA</span>
+<span class="co">## Z0 0.3043 1.1848  0.35666    0.28325     92.264         NA         NA</span>
 <span class="co">## Z1 1.5148 5.0320       NA         NA         NA         NA         NA</span>
 <span class="co">## Z2 1.6414 5.4526       NA         NA         NA         NA         NA</span>
 <span class="co">## Z3     NA     NA       NA         NA         NA     8.6636        Inf</span></code></pre>
@@ -398,7 +398,7 @@
 
 <div class="pkgdown">
   <p></p>
-<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.2.</p>
+<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.3.</p>
 </div>
 
       </footer>
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 bc6efaf7..229bae82 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 55c1b645..e13ad9aa 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 8e63cd04..ae160414 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 3902e059..23e270d1 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_5-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png
index d95cac25..77965455 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 cb333a1c..250d0df5 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_9-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png
index db807f14..5a01c03e 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 996e5d49..df1e06db 100644
--- a/docs/articles/web_only/NAFTA_examples.html
+++ b/docs/articles/web_only/NAFTA_examples.html
@@ -43,7 +43,7 @@
   <a href="../../reference/index.html">Functions and data</a>
 </li>
 <li class="dropdown">
-  <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" aria-expanded="false">
+  <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false">
     Articles
      
     <span class="caret"></span>
@@ -105,7 +105,7 @@
       <h1 data-toc-skip>Evaluation of example datasets from Attachment 1 to the US EPA SOP for the NAFTA guidance</h1>
                         <h4 data-toc-skip class="author">Johannes Ranke</h4>
             
-            <h4 data-toc-skip class="date">26 February 2019 (rebuilt 2022-03-02)</h4>
+            <h4 data-toc-skip class="date">26 February 2019 (rebuilt 2022-05-18)</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/NAFTA_examples.rmd" class="external-link"><code>vignettes/web_only/NAFTA_examples.rmd</code></a></small>
       <div class="hidden name"><code>NAFTA_examples.rmd</code></div>
@@ -161,7 +161,7 @@
 <span class="co">##          Estimate   Pr(&gt;t)   Lower    Upper</span>
 <span class="co">## parent_0 9.99e+01 1.41e-26 98.8116 101.0810</span>
 <span class="co">## k1       2.67e-02 5.05e-06  0.0243   0.0295</span>
-<span class="co">## k2       2.26e-12 5.00e-01  0.0000      Inf</span>
+<span class="co">## k2       2.95e-12 5.00e-01  0.0000      Inf</span>
 <span class="co">## g        6.47e-01 3.67e-06  0.6248   0.6677</span>
 <span class="co">## sigma    1.27e+00 8.91e-06  0.8395   1.6929</span>
 <span class="co">## </span>
@@ -170,7 +170,7 @@
 <span class="co">##      DT50     DT90 DT50_rep</span>
 <span class="co">## SFO  67.7 2.25e+02 6.77e+01</span>
 <span class="co">## IORE 58.2 1.07e+03 3.22e+02</span>
-<span class="co">## DFOP 55.5 5.59e+11 3.07e+11</span>
+<span class="co">## DFOP 55.5 4.28e+11 2.35e+11</span>
 <span class="co">## </span>
 <span class="co">## Representative half-life:</span>
 <span class="co">## [1] 321.51</span></code></pre>
@@ -212,7 +212,7 @@
 <span class="co">##          Estimate   Pr(&gt;t)   Lower   Upper</span>
 <span class="co">## parent_0 9.84e+01 1.24e-27 97.8078 98.9187</span>
 <span class="co">## k1       1.55e-02 4.10e-04  0.0143  0.0167</span>
-<span class="co">## k2       8.63e-12 5.00e-01  0.0000     Inf</span>
+<span class="co">## k2       9.41e-12 5.00e-01  0.0000     Inf</span>
 <span class="co">## g        6.89e-01 2.92e-03  0.6626  0.7142</span>
 <span class="co">## sigma    6.48e-01 2.38e-05  0.4147  0.8813</span>
 <span class="co">## </span>
@@ -221,7 +221,7 @@
 <span class="co">##      DT50     DT90 DT50_rep</span>
 <span class="co">## SFO  86.6 2.88e+02 8.66e+01</span>
 <span class="co">## IORE 85.5 7.17e+02 2.16e+02</span>
-<span class="co">## DFOP 83.6 1.32e+11 8.04e+10</span>
+<span class="co">## DFOP 83.6 1.21e+11 7.36e+10</span>
 <span class="co">## </span>
 <span class="co">## Representative half-life:</span>
 <span class="co">## [1] 215.87</span></code></pre>
@@ -263,7 +263,7 @@
 <span class="co">##          Estimate   Pr(&gt;t)   Lower   Upper</span>
 <span class="co">## parent_0 9.66e+01 1.57e-25 95.3476 97.8979</span>
 <span class="co">## k1       2.55e-02 7.33e-06  0.0233  0.0278</span>
-<span class="co">## k2       3.22e-11 5.00e-01  0.0000     Inf</span>
+<span class="co">## k2       4.40e-11 5.00e-01  0.0000     Inf</span>
 <span class="co">## g        8.61e-01 7.55e-06  0.8314  0.8867</span>
 <span class="co">## sigma    1.46e+00 6.93e-06  0.9661  1.9483</span>
 <span class="co">## </span>
@@ -272,7 +272,7 @@
 <span class="co">##      DT50     DT90 DT50_rep</span>
 <span class="co">## SFO  38.6 1.28e+02 3.86e+01</span>
 <span class="co">## IORE 34.0 1.77e+02 5.32e+01</span>
-<span class="co">## DFOP 34.1 1.01e+10 2.15e+10</span>
+<span class="co">## DFOP 34.1 7.43e+09 1.58e+10</span>
 <span class="co">## </span>
 <span class="co">## Representative half-life:</span>
 <span class="co">## [1] 53.17</span></code></pre>
@@ -314,7 +314,7 @@
 <span class="co">##          Estimate   Pr(&gt;t)   Lower    Upper</span>
 <span class="co">## parent_0 9.89e+01 9.44e-49 95.4640 102.2573</span>
 <span class="co">## k1       1.81e-02 1.75e-01  0.0116   0.0281</span>
-<span class="co">## k2       3.63e-10 5.00e-01  0.0000      Inf</span>
+<span class="co">## k2       2.81e-10 5.00e-01  0.0000      Inf</span>
 <span class="co">## g        6.06e-01 2.19e-01  0.4826   0.7178</span>
 <span class="co">## sigma    7.40e+00 2.97e-15  6.0201   8.7754</span>
 <span class="co">## </span>
@@ -323,7 +323,7 @@
 <span class="co">##      DT50     DT90 DT50_rep</span>
 <span class="co">## SFO  94.3 3.13e+02 9.43e+01</span>
 <span class="co">## IORE 96.7 1.51e+03 4.55e+02</span>
-<span class="co">## DFOP 96.4 3.77e+09 1.91e+09</span>
+<span class="co">## DFOP 96.4 4.87e+09 2.46e+09</span>
 <span class="co">## </span>
 <span class="co">## Representative half-life:</span>
 <span class="co">## [1] 454.55</span></code></pre>
@@ -434,7 +434,7 @@
 <span class="co">##      DT50     DT90 DT50_rep</span>
 <span class="co">## SFO  16.9 5.63e+01 1.69e+01</span>
 <span class="co">## IORE 11.6 3.37e+02 1.01e+02</span>
-<span class="co">## DFOP 10.5 1.38e+12 7.69e+11</span>
+<span class="co">## DFOP 10.5 1.38e+12 7.68e+11</span>
 <span class="co">## </span>
 <span class="co">## Representative half-life:</span>
 <span class="co">## [1] 101.43</span></code></pre>
@@ -445,17 +445,12 @@
 </h3>
 <div class="sourceCode" id="cb37"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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></code></pre></div>
-<pre><code><span class="co">## Warning in sqrt(diag(covar)): NaNs produced</span></code></pre>
-<pre><code><span class="co">## Warning in sqrt(diag(covar_notrans)): NaNs produced</span></code></pre>
-<pre><code><span class="co">## Warning in sqrt(1/diag(V)): NaNs produced</span></code></pre>
-<pre><code><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is</span>
-<span class="co">## doubtful</span></code></pre>
 <pre><code><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></code></pre>
 <pre><code><span class="co">## The half-life obtained from the IORE model may be used</span></code></pre>
-<div class="sourceCode" id="cb44"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb40"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p9b</span><span class="op">)</span></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p9b-1.png" width="700"></p>
-<div class="sourceCode" id="cb45"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb41"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p9b</span><span class="op">)</span></code></pre></div>
 <pre><code><span class="co">## Sums of squares:</span>
 <span class="co">##      SFO     IORE     DFOP </span>
@@ -482,8 +477,8 @@
 <span class="co">##          Estimate   Pr(&gt;t)   Lower   Upper</span>
 <span class="co">## parent_0  94.7123 1.61e-16 93.1355 96.2891</span>
 <span class="co">## k1         0.0389 1.08e-04  0.0266  0.0569</span>
-<span class="co">## k2         0.0389 2.23e-04  0.0255  0.0592</span>
-<span class="co">## g          0.5256      NaN      NA      NA</span>
+<span class="co">## k2         0.0389 2.24e-04  0.0255  0.0592</span>
+<span class="co">## g          0.5256 5.00e-01  0.0000  1.0000</span>
 <span class="co">## sigma      1.5957 2.50e-04  0.9135  2.2779</span>
 <span class="co">## </span>
 <span class="co">## </span>
@@ -500,7 +495,7 @@
 <div class="section level3">
 <h3 id="example-on-page-10">Example on page 10<a class="anchor" aria-label="anchor" href="#example-on-page-10"></a>
 </h3>
-<div class="sourceCode" id="cb47"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb43"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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></code></pre></div>
 <pre><code><span class="co">## Warning in sqrt(diag(covar)): NaNs produced</span></code></pre>
 <pre><code><span class="co">## Warning in sqrt(1/diag(V)): NaNs produced</span></code></pre>
@@ -508,10 +503,10 @@
 <span class="co">## doubtful</span></code></pre>
 <pre><code><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></code></pre>
 <pre><code><span class="co">## The half-life obtained from the IORE model may be used</span></code></pre>
-<div class="sourceCode" id="cb53"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb49"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p10</span><span class="op">)</span></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p10-1.png" width="700"></p>
-<div class="sourceCode" id="cb54"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb50"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p10</span><span class="op">)</span></code></pre></div>
 <pre><code><span class="co">## Sums of squares:</span>
 <span class="co">##      SFO     IORE     DFOP </span>
@@ -537,8 +532,8 @@
 <span class="co">## $DFOP</span>
 <span class="co">##          Estimate   Pr(&gt;t)   Lower    Upper</span>
 <span class="co">## parent_0 101.7315 1.41e-09 91.6534 111.8097</span>
-<span class="co">## k1         0.0495 6.58e-03  0.0303   0.0809</span>
-<span class="co">## k2         0.0495 2.60e-03  0.0410   0.0598</span>
+<span class="co">## k1         0.0495 6.32e-03  0.0241   0.1018</span>
+<span class="co">## k2         0.0495 2.41e-03  0.0272   0.0901</span>
 <span class="co">## g          0.4487 5.00e-01      NA       NA</span>
 <span class="co">## sigma      8.0152 2.50e-04  4.5886  11.4418</span>
 <span class="co">## </span>
@@ -560,14 +555,14 @@
 <div class="section level3">
 <h3 id="example-on-page-11">Example on page 11<a class="anchor" aria-label="anchor" href="#example-on-page-11"></a>
 </h3>
-<div class="sourceCode" id="cb56"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb52"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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></code></pre></div>
 <pre><code><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></code></pre>
 <pre><code><span class="co">## The half-life obtained from the IORE model may be used</span></code></pre>
-<div class="sourceCode" id="cb59"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb55"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p11</span><span class="op">)</span></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p11-1.png" width="700"></p>
-<div class="sourceCode" id="cb60"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb56"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p11</span><span class="op">)</span></code></pre></div>
 <pre><code><span class="co">## Sums of squares:</span>
 <span class="co">##      SFO     IORE     DFOP </span>
@@ -594,7 +589,7 @@
 <span class="co">##          Estimate   Pr(&gt;t)    Lower    Upper</span>
 <span class="co">## parent_0 1.05e+02 9.47e-13  99.9990 109.1224</span>
 <span class="co">## k1       4.41e-02 5.95e-03   0.0296   0.0658</span>
-<span class="co">## k2       9.94e-13 5.00e-01   0.0000      Inf</span>
+<span class="co">## k2       9.93e-13 5.00e-01   0.0000      Inf</span>
 <span class="co">## g        3.22e-01 1.45e-03   0.2814   0.3650</span>
 <span class="co">## sigma    3.22e+00 3.52e-04   1.8410   4.5906</span>
 <span class="co">## </span>
@@ -606,7 +601,7 @@
 <span class="co">## DFOP 3.07e+11 1.93e+12 6.98e+11</span>
 <span class="co">## </span>
 <span class="co">## Representative half-life:</span>
-<span class="co">## [1] 41148170</span></code></pre>
+<span class="co">## [1] 41148171</span></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>
@@ -617,21 +612,19 @@
 <div class="section level3">
 <h3 id="example-on-page-12-upper-panel">Example on page 12, upper panel<a class="anchor" aria-label="anchor" href="#example-on-page-12-upper-panel"></a>
 </h3>
-<div class="sourceCode" id="cb62"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb58"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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></code></pre></div>
 <pre><code><span class="co">## Warning in summary.mkinfit(x): Could not calculate correlation; no covariance</span>
+<span class="co">## matrix</span>
+
+<span class="co">## Warning in summary.mkinfit(x): Could not calculate correlation; no covariance</span>
 <span class="co">## matrix</span></code></pre>
-<pre><code><span class="co">## Warning in sqrt(diag(covar)): NaNs produced</span></code></pre>
-<pre><code><span class="co">## Warning in sqrt(diag(covar_notrans)): NaNs produced</span></code></pre>
-<pre><code><span class="co">## Warning in sqrt(1/diag(V)): NaNs produced</span></code></pre>
-<pre><code><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is</span>
-<span class="co">## doubtful</span></code></pre>
 <pre><code><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></code></pre>
 <pre><code><span class="co">## The half-life obtained from the IORE model may be used</span></code></pre>
-<div class="sourceCode" id="cb70"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb62"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p12a</span><span class="op">)</span></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p12a-1.png" width="700"></p>
-<div class="sourceCode" id="cb71"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb63"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p12a</span><span class="op">)</span></code></pre></div>
 <pre><code><span class="co">## Sums of squares:</span>
 <span class="co">##      SFO     IORE     DFOP </span>
@@ -655,12 +648,12 @@
 <span class="co">## sigma             3.965     NA    NA    NA</span>
 <span class="co">## </span>
 <span class="co">## $DFOP</span>
-<span class="co">##          Estimate   Pr(&gt;t)   Lower   Upper</span>
-<span class="co">## parent_0  100.521 2.74e-10 92.2366 108.805</span>
-<span class="co">## k1          0.124 2.53e-05  0.0908   0.170</span>
-<span class="co">## k2          0.124 2.52e-02  0.0456   0.339</span>
-<span class="co">## g           0.793      NaN      NA      NA</span>
-<span class="co">## sigma       7.048 2.50e-04  4.0349  10.061</span>
+<span class="co">##          Estimate Pr(&gt;t) Lower Upper</span>
+<span class="co">## parent_0  100.521     NA    NA    NA</span>
+<span class="co">## k1          0.124     NA    NA    NA</span>
+<span class="co">## k2          0.124     NA    NA    NA</span>
+<span class="co">## g           0.793     NA    NA    NA</span>
+<span class="co">## sigma       7.048     NA    NA    NA</span>
 <span class="co">## </span>
 <span class="co">## </span>
 <span class="co">## DTx values:</span>
@@ -675,18 +668,17 @@
 <div class="section level3">
 <h3 id="example-on-page-12-lower-panel">Example on page 12, lower panel<a class="anchor" aria-label="anchor" href="#example-on-page-12-lower-panel"></a>
 </h3>
-<div class="sourceCode" id="cb73"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb65"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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></code></pre></div>
 <pre><code><span class="co">## Warning in qt(alpha/2, rdf): NaNs produced</span></code></pre>
 <pre><code><span class="co">## Warning in qt(1 - alpha/2, rdf): NaNs produced</span></code></pre>
-<pre><code><span class="co">## Warning in sqrt(diag(covar_notrans)): NaNs produced</span></code></pre>
 <pre><code><span class="co">## Warning in pt(abs(tval), rdf, lower.tail = FALSE): NaNs produced</span></code></pre>
 <pre><code><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></code></pre>
 <pre><code><span class="co">## The half-life obtained from the IORE model may be used</span></code></pre>
-<div class="sourceCode" id="cb80"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb71"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p12b</span><span class="op">)</span></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p12b-1.png" width="700"></p>
-<div class="sourceCode" id="cb81"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb72"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p12b</span><span class="op">)</span></code></pre></div>
 <pre><code><span class="co">## Sums of squares:</span>
 <span class="co">##      SFO     IORE     DFOP </span>
@@ -730,14 +722,18 @@
 <div class="section level3">
 <h3 id="example-on-page-13">Example on page 13<a class="anchor" aria-label="anchor" href="#example-on-page-13"></a>
 </h3>
-<div class="sourceCode" id="cb83"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb74"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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></code></pre></div>
+<pre><code><span class="co">## Warning in sqrt(diag(covar)): NaNs produced</span></code></pre>
+<pre><code><span class="co">## Warning in sqrt(1/diag(V)): NaNs produced</span></code></pre>
+<pre><code><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is</span>
+<span class="co">## doubtful</span></code></pre>
 <pre><code><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></code></pre>
 <pre><code><span class="co">## The half-life obtained from the IORE model may be used</span></code></pre>
-<div class="sourceCode" id="cb86"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb80"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p13</span><span class="op">)</span></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p13-1.png" width="700"></p>
-<div class="sourceCode" id="cb87"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb81"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p13</span><span class="op">)</span></code></pre></div>
 <pre><code><span class="co">## Sums of squares:</span>
 <span class="co">##      SFO     IORE     DFOP </span>
@@ -763,9 +759,9 @@
 <span class="co">## $DFOP</span>
 <span class="co">##          Estimate Pr(&gt;t)    Lower    Upper</span>
 <span class="co">## parent_0 92.73500     NA 8.95e+01 95.92118</span>
-<span class="co">## k1        0.00258     NA 4.14e-04  0.01611</span>
-<span class="co">## k2        0.00258     NA 1.74e-03  0.00383</span>
-<span class="co">## g         0.16452     NA 0.00e+00  1.00000</span>
+<span class="co">## k1        0.00258     NA 4.24e-04  0.01573</span>
+<span class="co">## k2        0.00258     NA 1.76e-03  0.00379</span>
+<span class="co">## g         0.16452     NA       NA       NA</span>
 <span class="co">## sigma     3.41172     NA 2.02e+00  4.79960</span>
 <span class="co">## </span>
 <span class="co">## </span>
@@ -782,7 +778,7 @@
 <div class="section level2">
 <h2 id="dt50-not-observed-in-the-study-and-dfop-problems-in-pestdf">DT50 not observed in the study and DFOP problems in PestDF<a class="anchor" aria-label="anchor" href="#dt50-not-observed-in-the-study-and-dfop-problems-in-pestdf"></a>
 </h2>
-<div class="sourceCode" id="cb89"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb83"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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></code></pre></div>
 <pre><code><span class="co">## Warning in sqrt(diag(covar)): NaNs produced</span></code></pre>
 <pre><code><span class="co">## Warning in sqrt(1/diag(V)): NaNs produced</span></code></pre>
@@ -790,10 +786,10 @@
 <span class="co">## doubtful</span></code></pre>
 <pre><code><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></code></pre>
 <pre><code><span class="co">## The half-life obtained from the IORE model may be used</span></code></pre>
-<div class="sourceCode" id="cb95"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb89"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p14</span><span class="op">)</span></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p14-1.png" width="700"></p>
-<div class="sourceCode" id="cb96"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb90"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p14</span><span class="op">)</span></code></pre></div>
 <pre><code><span class="co">## Sums of squares:</span>
 <span class="co">##      SFO     IORE     DFOP </span>
@@ -820,7 +816,7 @@
 <span class="co">##          Estimate   Pr(&gt;t)    Lower    Upper</span>
 <span class="co">## parent_0 1.00e+02 2.96e-28 99.40280 101.2768</span>
 <span class="co">## k1       9.53e-03 1.20e-01  0.00638   0.0143</span>
-<span class="co">## k2       6.08e-12 5.00e-01  0.00000      Inf</span>
+<span class="co">## k2       5.03e-12 5.00e-01  0.00000      Inf</span>
 <span class="co">## g        3.98e-01 2.19e-01  0.30481   0.4998</span>
 <span class="co">## sigma    1.17e+00 7.68e-06  0.77406   1.5610</span>
 <span class="co">## </span>
@@ -829,7 +825,7 @@
 <span class="co">##          DT50     DT90 DT50_rep</span>
 <span class="co">## SFO  2.48e+02 8.25e+02 2.48e+02</span>
 <span class="co">## IORE 4.34e+02 2.22e+04 6.70e+03</span>
-<span class="co">## DFOP 3.05e+10 2.95e+11 1.14e+11</span>
+<span class="co">## DFOP 3.69e+10 3.57e+11 1.38e+11</span>
 <span class="co">## </span>
 <span class="co">## Representative half-life:</span>
 <span class="co">## [1] 6697.44</span></code></pre>
@@ -838,14 +834,18 @@
 <div class="section level2">
 <h2 id="n-is-less-than-1-and-dfop-fraction-parameter-is-below-zero">N is less than 1 and DFOP fraction parameter is below zero<a class="anchor" aria-label="anchor" href="#n-is-less-than-1-and-dfop-fraction-parameter-is-below-zero"></a>
 </h2>
-<div class="sourceCode" id="cb98"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb92"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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></code></pre></div>
+<pre><code><span class="co">## Warning in sqrt(diag(covar)): NaNs produced</span></code></pre>
+<pre><code><span class="co">## Warning in sqrt(1/diag(V)): NaNs produced</span></code></pre>
+<pre><code><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is</span>
+<span class="co">## doubtful</span></code></pre>
 <pre><code><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></code></pre>
 <pre><code><span class="co">## The half-life obtained from the IORE model may be used</span></code></pre>
-<div class="sourceCode" id="cb101"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb98"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p15a</span><span class="op">)</span></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p15a-1.png" width="700"></p>
-<div class="sourceCode" id="cb102"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb99"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p15a</span><span class="op">)</span></code></pre></div>
 <pre><code><span class="co">## Sums of squares:</span>
 <span class="co">##      SFO     IORE     DFOP </span>
@@ -871,9 +871,9 @@
 <span class="co">## $DFOP</span>
 <span class="co">##          Estimate   Pr(&gt;t)    Lower    Upper</span>
 <span class="co">## parent_0 97.96751 2.85e-13 94.21913 101.7159</span>
-<span class="co">## k1        0.00952 6.28e-02  0.00250   0.0363</span>
-<span class="co">## k2        0.00952 1.27e-04  0.00646   0.0140</span>
-<span class="co">## g         0.21241 5.00e-01  0.00000   1.0000</span>
+<span class="co">## k1        0.00952 6.28e-02  0.00260   0.0349</span>
+<span class="co">## k2        0.00952 1.27e-04  0.00652   0.0139</span>
+<span class="co">## g         0.21241 5.00e-01       NA       NA</span>
 <span class="co">## sigma     4.18778 2.50e-04  2.39747   5.9781</span>
 <span class="co">## </span>
 <span class="co">## </span>
@@ -885,18 +885,14 @@
 <span class="co">## </span>
 <span class="co">## Representative half-life:</span>
 <span class="co">## [1] 41.33</span></code></pre>
-<div class="sourceCode" id="cb104"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb101"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="va">p15b</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p15b"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></code></pre></div>
-<pre><code><span class="co">## Warning in sqrt(diag(covar)): NaNs produced</span></code></pre>
-<pre><code><span class="co">## Warning in sqrt(1/diag(V)): NaNs produced</span></code></pre>
-<pre><code><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is</span>
-<span class="co">## doubtful</span></code></pre>
 <pre><code><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></code></pre>
 <pre><code><span class="co">## The half-life obtained from the IORE model may be used</span></code></pre>
-<div class="sourceCode" id="cb110"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb104"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p15b</span><span class="op">)</span></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p15b-1.png" width="700"></p>
-<div class="sourceCode" id="cb111"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb105"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p15b</span><span class="op">)</span></code></pre></div>
 <pre><code><span class="co">## Sums of squares:</span>
 <span class="co">##       SFO      IORE      DFOP </span>
@@ -916,15 +912,15 @@
 <span class="co">##                Estimate   Pr(&gt;t)    Lower  Upper</span>
 <span class="co">## parent_0          99.83 1.81e-16 97.51349 102.14</span>
 <span class="co">## k__iore_parent     0.38 3.22e-01  0.00352  41.05</span>
-<span class="co">## N_parent           0.00 5.00e-01 -1.07696   1.08</span>
+<span class="co">## N_parent           0.00 5.00e-01 -1.07695   1.08</span>
 <span class="co">## sigma              2.21 2.57e-04  1.23245   3.19</span>
 <span class="co">## </span>
 <span class="co">## $DFOP</span>
 <span class="co">##          Estimate Pr(&gt;t)    Lower    Upper</span>
 <span class="co">## parent_0 1.01e+02     NA 9.82e+01 1.04e+02</span>
-<span class="co">## k1       4.86e-03     NA 8.63e-04 2.73e-02</span>
+<span class="co">## k1       4.86e-03     NA 8.62e-04 2.74e-02</span>
 <span class="co">## k2       4.86e-03     NA 3.21e-03 7.35e-03</span>
-<span class="co">## g        1.88e-01     NA       NA       NA</span>
+<span class="co">## g        1.88e-01     NA 0.00e+00 1.00e+00</span>
 <span class="co">## sigma    2.76e+00     NA 1.58e+00 3.94e+00</span>
 <span class="co">## </span>
 <span class="co">## </span>
@@ -941,16 +937,16 @@
 <div class="section level2">
 <h2 id="the-dfop-fraction-parameter-is-greater-than-1">The DFOP fraction parameter is greater than 1<a class="anchor" aria-label="anchor" href="#the-dfop-fraction-parameter-is-greater-than-1"></a>
 </h2>
-<div class="sourceCode" id="cb113"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb107"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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></code></pre></div>
 <pre><code><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></code></pre>
 <pre><code><span class="co">## The representative half-life of the IORE model is longer than the one corresponding</span></code></pre>
 <pre><code><span class="co">## to the terminal degradation rate found with the DFOP model.</span></code></pre>
 <pre><code><span class="co">## The representative half-life obtained from the DFOP model may be used</span></code></pre>
-<div class="sourceCode" id="cb118"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb112"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p16</span><span class="op">)</span></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p16-1.png" width="700"></p>
-<div class="sourceCode" id="cb119"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb113"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p16</span><span class="op">)</span></code></pre></div>
 <pre><code><span class="co">## Sums of squares:</span>
 <span class="co">##      SFO     IORE     DFOP </span>
@@ -1026,7 +1022,7 @@
 
 <div class="pkgdown">
   <p></p>
-<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.2.</p>
+<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.3.</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 75611a70..a53c48b2 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/p15a-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p15a-1.png
index b6faeff9..fb211a8e 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 6b9ba98c..9aedbf16 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/p5b-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p5b-1.png
index db90244b..034eed46 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 a33372e8..86cd9755 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 d64ea98d..10225504 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/benchmarks.html b/docs/articles/web_only/benchmarks.html
index 2eea3cb2..058d43fa 100644
--- a/docs/articles/web_only/benchmarks.html
+++ b/docs/articles/web_only/benchmarks.html
@@ -43,7 +43,7 @@
   <a href="../../reference/index.html">Functions and data</a>
 </li>
 <li class="dropdown">
-  <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" aria-expanded="false">
+  <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false">
     Articles
      
     <span class="caret"></span>
@@ -105,7 +105,7 @@
       <h1 data-toc-skip>Benchmark timings for mkin</h1>
                         <h4 data-toc-skip class="author">Johannes Ranke</h4>
             
-            <h4 data-toc-skip class="date">Last change 13 May 2020 (rebuilt 2022-03-02)</h4>
+            <h4 data-toc-skip class="date">Last change 13 May 2020 (rebuilt 2022-05-18)</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/benchmarks.rmd" class="external-link"><code>vignettes/web_only/benchmarks.rmd</code></a></small>
       <div class="hidden name"><code>benchmarks.rmd</code></div>
@@ -121,7 +121,7 @@
 <p>Parent only:</p>
 <div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><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/pkg/saemix/man/subset.html" class="external-link">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">FOCUS_D</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/subset.html" class="external-link">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" class="external-link">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="va">t1</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">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" 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="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>
@@ -179,74 +179,83 @@
 <div class="section level2">
 <h2 id="results">Results<a class="anchor" aria-label="anchor" href="#results"></a>
 </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 class="section level3">
 <h3 id="parent-only">Parent only<a class="anchor" aria-label="anchor" href="#parent-only"></a>
 </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">
+<table style="width:100%;" class="table">
+<colgroup>
+<col width="84%">
+<col width="7%">
+<col width="8%">
+</colgroup>
 <thead><tr class="header">
-<th align="left">mkin version</th>
-<th align="right">t1 [s]</th>
-<th align="right">t2 [s]</th>
+<th align="left"></th>
+<th align="right">t1</th>
+<th align="right">t2</th>
 </tr></thead>
 <tbody>
 <tr class="odd">
-<td align="left">0.9.48.1</td>
+<td align="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 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="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 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="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 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="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 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="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 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="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 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="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.50.3</td>
 <td align="right">1.752</td>
 <td align="right">4.156</td>
 </tr>
 <tr class="even">
-<td align="left">0.9.50.4</td>
+<td align="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.50.4</td>
 <td align="right">1.786</td>
 <td align="right">3.729</td>
 </tr>
 <tr class="odd">
-<td align="left">1.0.3</td>
+<td align="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 1.0.3</td>
 <td align="right">1.881</td>
 <td align="right">3.504</td>
 </tr>
 <tr class="even">
-<td align="left">1.0.4</td>
+<td align="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 1.0.4</td>
 <td align="right">1.867</td>
 <td align="right">3.450</td>
 </tr>
 <tr class="odd">
-<td align="left">1.1.0</td>
+<td align="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 1.1.0</td>
 <td align="right">1.938</td>
 <td align="right">3.517</td>
 </tr>
+<tr class="even">
+<td align="left">Linux, Intel(R) Core(TM) i7-4710MQ CPU @ 2.50GHz, mkin version 1.1.0</td>
+<td align="right">1.621</td>
+<td align="right">3.123</td>
+</tr>
 </tbody>
 </table>
 </div>
@@ -255,79 +264,91 @@
 </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">
+<colgroup>
+<col width="78%">
+<col width="6%">
+<col width="7%">
+<col width="6%">
+</colgroup>
 <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>
+<th align="left"></th>
+<th align="right">t3</th>
+<th align="right">t4</th>
+<th align="right">t5</th>
 </tr></thead>
 <tbody>
 <tr class="odd">
-<td align="left">0.9.48.1</td>
+<td align="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 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="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 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="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 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="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 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="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 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="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 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="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.50.3</td>
 <td align="right">1.430</td>
 <td align="right">6.615</td>
 <td align="right">2.878</td>
 </tr>
 <tr class="even">
-<td align="left">0.9.50.4</td>
+<td align="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.50.4</td>
 <td align="right">1.397</td>
 <td align="right">7.251</td>
 <td align="right">2.810</td>
 </tr>
 <tr class="odd">
-<td align="left">1.0.3</td>
+<td align="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 1.0.3</td>
 <td align="right">1.430</td>
 <td align="right">6.344</td>
 <td align="right">2.798</td>
 </tr>
 <tr class="even">
-<td align="left">1.0.4</td>
+<td align="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 1.0.4</td>
 <td align="right">1.415</td>
 <td align="right">6.364</td>
 <td align="right">2.820</td>
 </tr>
 <tr class="odd">
-<td align="left">1.1.0</td>
+<td align="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 1.1.0</td>
 <td align="right">1.470</td>
 <td align="right">6.508</td>
 <td align="right">2.894</td>
 </tr>
+<tr class="even">
+<td align="left">Linux, Intel(R) Core(TM) i7-4710MQ CPU @ 2.50GHz, mkin version 1.1.0</td>
+<td align="right">3.319</td>
+<td align="right">18.209</td>
+<td align="right">7.773</td>
+</tr>
 </tbody>
 </table>
 </div>
@@ -336,18 +357,27 @@
 </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">
+<colgroup>
+<col width="64%">
+<col width="5%">
+<col width="5%">
+<col width="5%">
+<col width="6%">
+<col width="5%">
+<col width="6%">
+</colgroup>
 <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>
+<th align="left"></th>
+<th align="right">t6</th>
+<th align="right">t7</th>
+<th align="right">t8</th>
+<th align="right">t9</th>
+<th align="right">t10</th>
+<th align="right">t11</th>
 </tr></thead>
 <tbody>
 <tr class="odd">
-<td align="left">0.9.48.1</td>
+<td align="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1</td>
 <td align="right">2.623</td>
 <td align="right">4.587</td>
 <td align="right">7.525</td>
@@ -356,7 +386,7 @@
 <td align="right">31.267</td>
 </tr>
 <tr class="even">
-<td align="left">0.9.49.1</td>
+<td align="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1</td>
 <td align="right">2.542</td>
 <td align="right">4.128</td>
 <td align="right">4.632</td>
@@ -365,7 +395,7 @@
 <td align="right">5.636</td>
 </tr>
 <tr class="odd">
-<td align="left">0.9.49.2</td>
+<td align="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2</td>
 <td align="right">2.723</td>
 <td align="right">4.478</td>
 <td align="right">4.862</td>
@@ -374,7 +404,7 @@
 <td align="right">5.574</td>
 </tr>
 <tr class="even">
-<td align="left">0.9.49.3</td>
+<td align="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3</td>
 <td align="right">2.643</td>
 <td align="right">4.374</td>
 <td align="right">7.020</td>
@@ -383,7 +413,7 @@
 <td align="right">7.365</td>
 </tr>
 <tr class="odd">
-<td align="left">0.9.49.4</td>
+<td align="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4</td>
 <td align="right">2.635</td>
 <td align="right">4.259</td>
 <td align="right">4.737</td>
@@ -392,7 +422,7 @@
 <td align="right">5.626</td>
 </tr>
 <tr class="even">
-<td align="left">0.9.50.2</td>
+<td align="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.50.2</td>
 <td align="right">0.777</td>
 <td align="right">1.236</td>
 <td align="right">1.332</td>
@@ -401,7 +431,7 @@
 <td align="right">2.987</td>
 </tr>
 <tr class="odd">
-<td align="left">0.9.50.3</td>
+<td align="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.50.3</td>
 <td align="right">0.858</td>
 <td align="right">1.264</td>
 <td align="right">1.333</td>
@@ -410,7 +440,7 @@
 <td align="right">3.073</td>
 </tr>
 <tr class="even">
-<td align="left">0.9.50.4</td>
+<td align="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.50.4</td>
 <td align="right">0.783</td>
 <td align="right">1.282</td>
 <td align="right">1.486</td>
@@ -419,7 +449,7 @@
 <td align="right">3.105</td>
 </tr>
 <tr class="odd">
-<td align="left">1.0.3</td>
+<td align="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 1.0.3</td>
 <td align="right">0.763</td>
 <td align="right">1.244</td>
 <td align="right">1.457</td>
@@ -428,7 +458,7 @@
 <td align="right">2.839</td>
 </tr>
 <tr class="even">
-<td align="left">1.0.4</td>
+<td align="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 1.0.4</td>
 <td align="right">0.785</td>
 <td align="right">1.252</td>
 <td align="right">1.466</td>
@@ -437,7 +467,7 @@
 <td align="right">2.826</td>
 </tr>
 <tr class="odd">
-<td align="left">1.1.0</td>
+<td align="left">Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 1.1.0</td>
 <td align="right">0.810</td>
 <td align="right">1.264</td>
 <td align="right">1.503</td>
@@ -445,6 +475,15 @@
 <td align="right">1.984</td>
 <td align="right">2.847</td>
 </tr>
+<tr class="even">
+<td align="left">Linux, Intel(R) Core(TM) i7-4710MQ CPU @ 2.50GHz, mkin version 1.1.0</td>
+<td align="right">2.348</td>
+<td align="right">3.579</td>
+<td align="right">4.254</td>
+<td align="right">11.315</td>
+<td align="right">5.981</td>
+<td align="right">8.368</td>
+</tr>
 </tbody>
 </table>
 </div>
@@ -468,7 +507,7 @@
 
 <div class="pkgdown">
   <p></p>
-<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.2.</p>
+<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.3.</p>
 </div>
 
       </footer>
diff --git a/docs/articles/web_only/compiled_models.html b/docs/articles/web_only/compiled_models.html
index 35ea6f27..330c25c6 100644
--- a/docs/articles/web_only/compiled_models.html
+++ b/docs/articles/web_only/compiled_models.html
@@ -43,7 +43,7 @@
   <a href="../../reference/index.html">Functions and data</a>
 </li>
 <li class="dropdown">
-  <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" aria-expanded="false">
+  <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false">
     Articles
      
     <span class="caret"></span>
@@ -105,7 +105,7 @@
       <h1 data-toc-skip>Performance benefit by using compiled model definitions in mkin</h1>
                         <h4 data-toc-skip class="author">Johannes Ranke</h4>
             
-            <h4 data-toc-skip class="date">2022-03-02</h4>
+            <h4 data-toc-skip class="date">2022-05-18</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/compiled_models.rmd" class="external-link"><code>vignettes/web_only/compiled_models.rmd</code></a></small>
       <div class="hidden name"><code>compiled_models.rmd</code></div>
@@ -141,11 +141,11 @@
   m1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span><span class="op">)</span></code></pre></div>
 <pre><code><span class="co">## Temporary DLL for differentials generated and loaded</span></code></pre>
 <div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span class="va">FOCUS_D</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/saemix/man/subset.html" class="external-link">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></code></pre></div>
+<code class="sourceCode R"><span class="va">FOCUS_D</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/subset.html" class="external-link">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></code></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 sourceCode r">
 <code class="sourceCode R"><span class="kw">if</span> <span class="op">(</span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">require</a></span><span class="op">(</span><span class="va"><a href="http://rbenchmark.googlecode.com" class="external-link">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" class="external-link">benchmark</a></span><span class="op">(</span>
+  <span class="va">b.1</span> <span class="op">&lt;-</span> <span class="fu">benchmark</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>,
@@ -162,11 +162,7 @@
 <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" class="external-link">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></code></pre></div>
-<pre><code><span class="co">##                    test replications relative elapsed</span>
-<span class="co">## 4            analytical            1    1.000   0.216</span>
-<span class="co">## 3     deSolve, compiled            1    1.708   0.369</span>
-<span class="co">## 2      Eigenvalue based            1    1.866   0.403</span>
-<span class="co">## 1 deSolve, not compiled            1   34.009   7.346</span></code></pre>
+<pre><code><span class="co">## [1] "R package rbenchmark is not available"</span></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 class="section level2">
@@ -179,7 +175,7 @@
     parent <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.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/mkinmod.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" class="external-link">benchmark</a></span><span class="op">(</span>
+  <span class="va">b.2</span> <span class="op">&lt;-</span> <span class="fu">benchmark</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>,
@@ -191,16 +187,14 @@
   <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" class="external-link">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></code></pre></div>
-<pre><code><span class="co">## Temporary DLL for differentials generated and loaded</span></code></pre>
-<pre><code><span class="co">##                    test replications relative elapsed</span>
-<span class="co">## 2     deSolve, compiled            1    1.000   0.533</span>
-<span class="co">## 1 deSolve, not compiled            1   25.146  13.403</span></code></pre>
-<p>Here we get a performance benefit of a factor of 25 using the version of the differential equation model compiled from C code!</p>
+<pre><code><span class="co">## Loading required package: rbenchmark</span></code></pre>
+<pre><code><span class="co">## [1] "R package benchmark is not available"</span></code></pre>
+<p>Here we get a performance benefit of a factor of NA using the version of the differential equation model compiled from C code!</p>
 <p>This vignette was built with mkin 1.1.0 on</p>
-<pre><code><span class="co">## R version 4.1.2 (2021-11-01)</span>
+<pre><code><span class="co">## R version 4.2.0 (2022-04-22)</span>
 <span class="co">## Platform: x86_64-pc-linux-gnu (64-bit)</span>
 <span class="co">## Running under: Debian GNU/Linux 11 (bullseye)</span></code></pre>
-<pre><code><span class="co">## CPU model: AMD Ryzen 7 1700 Eight-Core Processor</span></code></pre>
+<pre><code><span class="co">## CPU model: Intel(R) Core(TM) i7-4710MQ CPU @ 2.50GHz</span></code></pre>
 </div>
   </div>
 
@@ -221,7 +215,7 @@
 
 <div class="pkgdown">
   <p></p>
-<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.2.</p>
+<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.3.</p>
 </div>
 
       </footer>
diff --git a/docs/articles/web_only/dimethenamid_2018.html b/docs/articles/web_only/dimethenamid_2018.html
index 09aa5150..7650f06f 100644
--- a/docs/articles/web_only/dimethenamid_2018.html
+++ b/docs/articles/web_only/dimethenamid_2018.html
@@ -105,7 +105,7 @@
       <h1 data-toc-skip>Example evaluations of the dimethenamid data from 2018</h1>
                         <h4 data-toc-skip class="author">Johannes Ranke</h4>
             
-            <h4 data-toc-skip class="date">Last change 7 March 2022, built on 16 Mar 2022</h4>
+            <h4 data-toc-skip class="date">Last change 7 March 2022, built on 18 May 2022</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/dimethenamid_2018.rmd" class="external-link"><code>vignettes/web_only/dimethenamid_2018.rmd</code></a></small>
       <div class="hidden name"><code>dimethenamid_2018.rmd</code></div>
@@ -178,7 +178,7 @@ Status of individual fits:
 
       dataset
 model  Calke Borstel Flaach BBA 2.2 BBA 2.3 Elliot
-  DFOP OK    OK      C      OK      C       OK    
+  DFOP OK    OK      OK     OK      C       OK    
 
 OK: No warnings
 C: Optimisation did not converge:
@@ -231,32 +231,41 @@ f_parent_nlme_dfop_tc       3 10 671.91 702.34 -325.96 2 vs 3  134.69  &lt;.0001
 <p>The saemix package provided the first Open Source implementation of the Stochastic Approximation to the Expectation Maximisation (SAEM) algorithm. SAEM fits of degradation models can be conveniently performed using an interface to the saemix package available in current development versions of the mkin package.</p>
 <p>The corresponding SAEM fits of the four combinations of degradation and error models are fitted below. As there is no convergence criterion implemented in the saemix package, the convergence plots need to be manually checked for every fit. We define control settings that work well for all the parent data fits shown in this vignette.</p>
 <div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">saemix</span><span class="op">)</span>
-<span class="va">saemix_control</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/saemix/man/saemixControl.html" class="external-link">saemixControl</a></span><span class="op">(</span>nbiter.saemix <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">800</span>, <span class="fl">300</span><span class="op">)</span>, nb.chains <span class="op">=</span> <span class="fl">15</span>,
+<code class="sourceCode R"><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">saemix</span><span class="op">)</span></code></pre></div>
+<pre><code>Loading required package: npde</code></pre>
+<pre><code>Package saemix, version 3.0
+  please direct bugs, questions and feedback to emmanuelle.comets@inserm.fr</code></pre>
+<pre><code>
+Attaching package: 'saemix'</code></pre>
+<pre><code>The following objects are masked from 'package:npde':
+
+    kurtosis, skewness</code></pre>
+<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="va">saemix_control</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/saemix/man/saemixControl.html" class="external-link">saemixControl</a></span><span class="op">(</span>nbiter.saemix <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">800</span>, <span class="fl">300</span><span class="op">)</span>, nb.chains <span class="op">=</span> <span class="fl">15</span>,
     print <span class="op">=</span> <span class="cn">FALSE</span>, save <span class="op">=</span> <span class="cn">FALSE</span>, save.graphs <span class="op">=</span> <span class="cn">FALSE</span>, displayProgress <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>
 <span class="va">saemix_control_moreiter</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/saemix/man/saemixControl.html" class="external-link">saemixControl</a></span><span class="op">(</span>nbiter.saemix <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">1600</span>, <span class="fl">300</span><span class="op">)</span>, nb.chains <span class="op">=</span> <span class="fl">15</span>,
     print <span class="op">=</span> <span class="cn">FALSE</span>, save <span class="op">=</span> <span class="cn">FALSE</span>, save.graphs <span class="op">=</span> <span class="cn">FALSE</span>, displayProgress <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>
 <span class="va">saemix_control_10k</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/saemix/man/saemixControl.html" class="external-link">saemixControl</a></span><span class="op">(</span>nbiter.saemix <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">10000</span>, <span class="fl">300</span><span class="op">)</span>, nb.chains <span class="op">=</span> <span class="fl">15</span>,
     print <span class="op">=</span> <span class="cn">FALSE</span>, save <span class="op">=</span> <span class="cn">FALSE</span>, save.graphs <span class="op">=</span> <span class="cn">FALSE</span>, displayProgress <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></code></pre></div>
 <p>The convergence plot for the SFO model using constant variance is shown below.</p>
-<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="va">f_parent_saemix_sfo_const</span> <span class="op">&lt;-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,
   control <span class="op">=</span> <span class="va">saemix_control</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span>
 <span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_parent_saemix_sfo_const</span><span class="op">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></code></pre></div>
 <p><img src="dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_const-1.png" width="700"></p>
 <p>Obviously the selected number of iterations is sufficient to reach convergence. This can also be said for the SFO fit using the two-component error model.</p>
-<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="va">f_parent_saemix_sfo_tc</span> <span class="op">&lt;-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,
   control <span class="op">=</span> <span class="va">saemix_control</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span>
 <span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_parent_saemix_sfo_tc</span><span class="op">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></code></pre></div>
 <p><img src="dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_tc-1.png" width="700"></p>
 <p>When fitting the DFOP model with constant variance (see below), parameter convergence is not as unambiguous.</p>
-<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb22"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="va">f_parent_saemix_dfop_const</span> <span class="op">&lt;-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,
   control <span class="op">=</span> <span class="va">saemix_control</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span>
 <span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_const</span><span class="op">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></code></pre></div>
 <p><img src="dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_const-1.png" width="700"></p>
-<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_const</span><span class="op">)</span></code></pre></div>
 <pre><code>Kinetic nonlinear mixed-effects model fit by SAEM
 Structural model:
@@ -277,21 +286,23 @@ DMTA_0    97.99583 96.50079 99.4909
 k1         0.06377  0.03432  0.0932
 k2         0.00848  0.00444  0.0125
 g          0.95701  0.91313  1.0009
-a.1        1.82141  1.65974  1.9831
-SD.DMTA_0  1.64787  0.45779  2.8379
+a.1        1.82141  1.60516  2.0377
+SD.DMTA_0  1.64787  0.45729  2.8384
 SD.k1      0.57439  0.24731  0.9015
-SD.k2      0.03296 -2.50143  2.5673
-SD.g       1.10266  0.32371  1.8816</code></pre>
+SD.k2      0.03296 -2.50524  2.5712
+SD.g       1.10266  0.32354  1.8818</code></pre>
 <p>While the other parameters converge to credible values, the variance of k2 (<code>omega2.k2</code>) converges to a very small value. The printout of the <code>saem.mmkin</code> model shows that the estimated standard deviation of k2 across the population of soils (<code>SD.k2</code>) is ill-defined, indicating overparameterisation of this model.</p>
 <p>When the DFOP model is fitted with the two-component error model, we also observe that the estimated variance of k2 becomes very small, while being ill-defined, as illustrated by the excessive confidence interval of <code>SD.k2</code>.</p>
-<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="va">f_parent_saemix_dfop_tc</span> <span class="op">&lt;-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,
   control <span class="op">=</span> <span class="va">saemix_control</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span>
 <span class="va">f_parent_saemix_dfop_tc_moreiter</span> <span class="op">&lt;-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,
-  control <span class="op">=</span> <span class="va">saemix_control_moreiter</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span>
-<span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></code></pre></div>
+  control <span class="op">=</span> <span class="va">saemix_control_moreiter</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span></code></pre></div>
+<pre><code>Likelihood cannot be computed by Importance Sampling.</code></pre>
+<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></code></pre></div>
 <p><img src="dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc-1.png" width="700"></p>
-<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb28"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc</span><span class="op">)</span></code></pre></div>
 <pre><code>Kinetic nonlinear mixed-effects model fit by SAEM
 Structural model:
@@ -307,21 +318,21 @@ Likelihood computed by importance sampling
   666 664   -323
 
 Fitted parameters:
-          estimate    lower    upper
-DMTA_0    98.27617  96.3088 100.2436
-k1         0.06437   0.0337   0.0950
-k2         0.00880   0.0063   0.0113
-g          0.95249   0.9100   0.9949
-a.1        1.06161   0.8625   1.2607
-b.1        0.02967   0.0226   0.0367
-SD.DMTA_0  2.06075   0.4187   3.7028
-SD.k1      0.59357   0.2561   0.9310
-SD.k2      0.00292 -10.2960  10.3019
-SD.g       1.05725   0.3808   1.7337</code></pre>
+          estimate     lower    upper
+DMTA_0    9.82e+01  96.27937 100.1783
+k1        6.41e-02   0.03333   0.0948
+k2        8.56e-03   0.00608   0.0110
+g         9.55e-01   0.91440   0.9947
+a.1       1.07e+00   0.86542   1.2647
+b.1       2.96e-02   0.02258   0.0367
+SD.DMTA_0 2.04e+00   0.40629   3.6678
+SD.k1     5.98e-01   0.25796   0.9373
+SD.k2     5.28e-04 -58.93251  58.9336
+SD.g      1.04e+00   0.36509   1.7083</code></pre>
 <p>Doubling the number of iterations in the first phase of the algorithm leads to a slightly lower likelihood, and therefore to slightly higher AIC and BIC values. With even more iterations, the algorithm stops with an error message. This is related to the variance of k2 approximating zero and has been submitted as a <a href="https://github.com/saemixdevelopment/saemixextension/issues/29" class="external-link">bug to the saemix package</a>, as the algorithm does not converge in this case.</p>
 <p>An alternative way to fit DFOP in combination with the two-component error model is to use the model formulation with transformed parameters as used per default in mkin. When using this option, convergence is slower, but eventually the algorithm stops as well with the same error message.</p>
 <p>The four combinations (SFO/const, SFO/tc, DFOP/const and DFOP/tc) and the version with increased iterations can be compared using the model comparison function of the saemix package:</p>
-<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb30"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="va">AIC_parent_saemix</span> <span class="op">&lt;-</span> <span class="fu">saemix</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/compare.saemix.html" class="external-link">compare.saemix</a></span><span class="op">(</span>
   <span class="va">f_parent_saemix_sfo_const</span><span class="op">$</span><span class="va">so</span>,
   <span class="va">f_parent_saemix_sfo_tc</span><span class="op">$</span><span class="va">so</span>,
@@ -329,7 +340,7 @@ SD.g       1.05725   0.3808   1.7337</code></pre>
   <span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span>,
   <span class="va">f_parent_saemix_dfop_tc_moreiter</span><span class="op">$</span><span class="va">so</span><span class="op">)</span></code></pre></div>
 <pre><code>Likelihoods calculated by importance sampling</code></pre>
-<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb32"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/colnames.html" class="external-link">rownames</a></span><span class="op">(</span><span class="va">AIC_parent_saemix</span><span class="op">)</span> <span class="op">&lt;-</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 const"</span>, <span class="st">"SFO tc"</span>, <span class="st">"DFOP const"</span>, <span class="st">"DFOP tc"</span>, <span class="st">"DFOP tc more iterations"</span><span class="op">)</span>
 <span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">AIC_parent_saemix</span><span class="op">)</span></code></pre></div>
@@ -337,10 +348,10 @@ SD.g       1.05725   0.3808   1.7337</code></pre>
 SFO const               796.38 795.34
 SFO tc                  798.38 797.13
 DFOP const              705.75 703.88
-DFOP tc                 665.65 663.57
-DFOP tc more iterations 665.88 663.80</code></pre>
+DFOP tc                 665.72 663.63
+DFOP tc more iterations    NaN    NaN</code></pre>
 <p>In order to check the influence of the likelihood calculation algorithms implemented in saemix, the likelihood from Gaussian quadrature is added to the best fit, and the AIC values obtained from the three methods are compared.</p>
-<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb34"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span> <span class="op">&lt;-</span>
   <span class="fu">saemix</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/llgq.saemix.html" class="external-link">llgq.saemix</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span><span class="op">)</span>
 <span class="va">AIC_parent_saemix_methods</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>
@@ -350,9 +361,9 @@ DFOP tc more iterations 665.88 663.80</code></pre>
 <span class="op">)</span>
 <span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">AIC_parent_saemix_methods</span><span class="op">)</span></code></pre></div>
 <pre><code>    is     gq    lin 
-665.65 665.68 665.11 </code></pre>
+665.72 665.88 665.15 </code></pre>
 <p>The AIC values based on importance sampling and Gaussian quadrature are very similar. Using linearisation is known to be less accurate, but still gives a similar value. In order to illustrate that the comparison of the three method depends on the degree of convergence obtained in the fit, the same comparison is shown below for the fit using the defaults for the number of iterations and the number of MCMC chains.</p>
-<div class="sourceCode" id="cb29"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb36"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="va">f_parent_saemix_dfop_tc_defaults</span> <span class="op">&lt;-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span><span class="op">)</span>
 <span class="va">f_parent_saemix_dfop_tc_defaults</span><span class="op">$</span><span class="va">so</span> <span class="op">&lt;-</span>
   <span class="fu">saemix</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/llgq.saemix.html" class="external-link">llgq.saemix</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc_defaults</span><span class="op">$</span><span class="va">so</span><span class="op">)</span>
@@ -363,14 +374,14 @@ DFOP tc more iterations 665.88 663.80</code></pre>
 <span class="op">)</span>
 <span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">AIC_parent_saemix_methods_defaults</span><span class="op">)</span></code></pre></div>
 <pre><code>    is     gq    lin 
-668.27 718.36 666.49 </code></pre>
+668.91 663.61 667.40 </code></pre>
 </div>
 </div>
 <div class="section level3">
 <h3 id="comparison">Comparison<a class="anchor" aria-label="anchor" href="#comparison"></a>
 </h3>
 <p>The following table gives the AIC values obtained with both backend packages using the same control parameters (800 iterations burn-in, 300 iterations second phase, 15 chains). Note that</p>
-<div class="sourceCode" id="cb31"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb38"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="va">AIC_all</span> <span class="op">&lt;-</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>
   check.names <span class="op">=</span> <span class="cn">FALSE</span>,
   <span class="st">"Degradation model"</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">"SFO"</span>, <span class="st">"DFOP"</span>, <span class="st">"DFOP"</span><span class="op">)</span>,
@@ -395,7 +406,7 @@ DFOP tc more iterations 665.88 663.80</code></pre>
 <td align="left">SFO</td>
 <td align="left">const</td>
 <td align="right">796.60</td>
-<td align="right">796.60</td>
+<td align="right">794.17</td>
 <td align="right">796.38</td>
 </tr>
 <tr class="even">
@@ -409,15 +420,15 @@ DFOP tc more iterations 665.88 663.80</code></pre>
 <td align="left">DFOP</td>
 <td align="left">const</td>
 <td align="right">NA</td>
-<td align="right">671.98</td>
+<td align="right">704.95</td>
 <td align="right">705.75</td>
 </tr>
 <tr class="even">
 <td align="left">DFOP</td>
 <td align="left">tc</td>
 <td align="right">671.91</td>
-<td align="right">665.11</td>
-<td align="right">665.65</td>
+<td align="right">665.15</td>
+<td align="right">665.72</td>
 </tr>
 </tbody>
 </table>
@@ -464,7 +475,7 @@ DFOP tc more iterations 665.88 663.80</code></pre>
 
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-<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.2.</p>
+<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.3.</p>
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diff --git a/docs/articles/web_only/mkin_benchmarks.rda b/docs/articles/web_only/mkin_benchmarks.rda
new file mode 100644
index 00000000..e26caf64
--- /dev/null
+++ b/docs/articles/web_only/mkin_benchmarks.rda
author	Johannes Ranke <jranke@uni-bremen.de>	2022-05-18 21:26:17 +0200
committer	Johannes Ranke <jranke@uni-bremen.de>	2022-05-18 21:26:17 +0200
commit	91c5db736a4d3f2290a0cc5698fb4e35ae7bda59 (patch)
tree	8e9e34d18f055936172329c1248e6e2ff136bff9 /docs/articles
parent	ea57db98cef3fb882f7bd9656b44f270e7bded38 (diff)