Change dev branch used for docs, update static docs

author: Johannes Ranke <jranke@uni-bremen.de> 2022-08-10 15:38:17 +0200
committer: Johannes Ranke <jranke@uni-bremen.de> 2022-08-10 15:38:17 +0200
commit: 6178249bbb5e9de7cb7f34287ee7de28a68fed6c (patch)
tree: 537dcc31245b02adba4a293ce6c90b23b202df25 /docs/dev/articles
parent: 307e77e5bf81c7422055493cee7f073b57069c6c (diff)
18 files changed, 1298 insertions, 957 deletions
diff --git a/docs/dev/articles/FOCUS_L.html b/docs/dev/articles/FOCUS_L.html
index 547ec630..610d1bdd 100644
--- a/docs/dev/articles/FOCUS_L.html
+++ b/docs/dev/articles/FOCUS_L.html
@@ -20,6 +20,8 @@
 <![endif]-->
 </head>
 <body data-spy="scroll" data-target="#toc">
+    
+
     <div class="container template-article">
       <header><div class="navbar navbar-default navbar-fixed-top" role="navigation">
   <div class="container">
@@ -32,7 +34,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">1.0.3.9000</span>
+        <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">1.1.2</span>
       </span>
     </div>
 
@@ -42,7 +44,7 @@
   <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>
@@ -58,6 +60,9 @@
       <a href="../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a>
     </li>
     <li>
+      <a href="../articles/web_only/dimethenamid_2018.html">Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models</a>
+    </li>
+    <li>
       <a href="../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a>
     </li>
     <li>
@@ -80,7 +85,7 @@
       </ul>
 <ul class="nav navbar-nav navbar-right">
 <li>
-  <a href="https://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/" class="external-link">
     <span class="fab fa-github fa-lg"></span>
      
   </a>
@@ -95,693 +100,693 @@
 
       
 
-      </header><script src="FOCUS_L_files/header-attrs-2.6/header-attrs.js"></script><script src="FOCUS_L_files/accessible-code-block-0.0.1/empty-anchor.js"></script><div class="row">
+      </header><script src="FOCUS_L_files/accessible-code-block-0.0.1/empty-anchor.js"></script><div class="row">
   <div class="col-md-9 contents">
     <div class="page-header toc-ignore">
       <h1 data-toc-skip>Example evaluation of FOCUS Laboratory Data L1 to L3</h1>
-                        <h4 class="author">Johannes Ranke</h4>
+                        <h4 data-toc-skip class="author">Johannes Ranke</h4>
             
-            <h4 class="date">Last change 17 November 2016 (rebuilt 2021-02-15)</h4>
+            <h4 data-toc-skip class="date">Last change 18 May 2022 (rebuilt 2022-08-10)</h4>
       
-      <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/master/vignettes/FOCUS_L.rmd"><code>vignettes/FOCUS_L.rmd</code></a></small>
+      <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>
 
     </div>
 
     
     
-<div id="laboratory-data-l1" class="section level1">
-<h1 class="hasAnchor">
-<a href="#laboratory-data-l1" class="anchor"></a>Laboratory Data L1</h1>
+<div class="section level2">
+<h2 id="laboratory-data-l1">Laboratory Data L1<a class="anchor" aria-label="anchor" href="#laboratory-data-l1"></a>
+</h2>
 <p>The following code defines example dataset L1 from the FOCUS kinetics report, p. 284:</p>
 <div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span class="kw"><a href="https://rdrr.io/r/base/library.html">library</a></span><span class="op">(</span><span class="st"><a href="https://pkgdown.jrwb.de/mkin/">"mkin"</a></span>, quietly <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>
-<span class="va">FOCUS_2006_L1</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html">data.frame</a></span><span class="op">(</span>
-  t <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/rep.html">rep</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">1</span>, <span class="fl">2</span>, <span class="fl">3</span>, <span class="fl">5</span>, <span class="fl">7</span>, <span class="fl">14</span>, <span class="fl">21</span>, <span class="fl">30</span><span class="op">)</span>, each <span class="op">=</span> <span class="fl">2</span><span class="op">)</span>,
-  parent <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="fl">88.3</span>, <span class="fl">91.4</span>, <span class="fl">85.6</span>, <span class="fl">84.5</span>, <span class="fl">78.9</span>, <span class="fl">77.6</span>,
-             <span class="fl">72.0</span>, <span class="fl">71.9</span>, <span class="fl">50.3</span>, <span class="fl">59.4</span>, <span class="fl">47.0</span>, <span class="fl">45.1</span>,
-             <span class="fl">27.7</span>, <span class="fl">27.3</span>, <span class="fl">10.0</span>, <span class="fl">10.4</span>, <span class="fl">2.9</span>, <span class="fl">4.0</span><span class="op">)</span><span class="op">)</span>
-<span class="va">FOCUS_2006_L1_mkin</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span><span class="op">(</span><span class="va">FOCUS_2006_L1</span><span class="op">)</span></code></pre></div>
+<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="st"><a href="https://pkgdown.jrwb.de/mkin/">"mkin"</a></span>, quietly <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
+<span><span class="va">FOCUS_2006_L1</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span></span>
+<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">2</span>, <span class="fl">3</span>, <span class="fl">5</span>, <span class="fl">7</span>, <span class="fl">14</span>, <span class="fl">21</span>, <span class="fl">30</span><span class="op">)</span>, each <span class="op">=</span> <span class="fl">2</span><span class="op">)</span>,</span>
+<span>  parent <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">88.3</span>, <span class="fl">91.4</span>, <span class="fl">85.6</span>, <span class="fl">84.5</span>, <span class="fl">78.9</span>, <span class="fl">77.6</span>,</span>
+<span>             <span class="fl">72.0</span>, <span class="fl">71.9</span>, <span class="fl">50.3</span>, <span class="fl">59.4</span>, <span class="fl">47.0</span>, <span class="fl">45.1</span>,</span>
+<span>             <span class="fl">27.7</span>, <span class="fl">27.3</span>, <span class="fl">10.0</span>, <span class="fl">10.4</span>, <span class="fl">2.9</span>, <span class="fl">4.0</span><span class="op">)</span><span class="op">)</span></span>
+<span><span class="va">FOCUS_2006_L1_mkin</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span><span class="op">(</span><span class="va">FOCUS_2006_L1</span><span class="op">)</span></span></code></pre></div>
 <p>Here we use the assumptions of simple first order (SFO), the case of declining rate constant over time (FOMC) and the case of two different phases of the kinetics (DFOP). For a more detailed discussion of the models, please see the FOCUS kinetics report.</p>
 <p>Since mkin version 0.9-32 (July 2014), we can use shorthand notation like <code>"SFO"</code> for parent only degradation models. The following two lines fit the model and produce the summary report of the model fit. This covers the numerical analysis given in the FOCUS report.</p>
 <div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
-<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">summary</a></span><span class="op">(</span><span class="va">m.L1.SFO</span><span class="op">)</span></code></pre></div>
-<pre><code>## mkin version used for fitting:    1.0.3.9000 
-## R version used for fitting:       4.0.3 
-## Date of fit:     Mon Feb 15 17:13:39 2021 
-## Date of summary: Mon Feb 15 17:13:39 2021 
-## 
-## Equations:
-## d_parent/dt = - k_parent * parent
-## 
-## Model predictions using solution type analytical 
-## 
-## Fitted using 133 model solutions performed in 0.032 s
-## 
-## Error model: Constant variance 
-## 
-## Error model algorithm: OLS 
-## 
-## Starting values for parameters to be optimised:
-##          value   type
-## parent_0 89.85  state
-## k_parent  0.10 deparm
-## 
-## Starting values for the transformed parameters actually optimised:
-##                  value lower upper
-## parent_0     89.850000  -Inf   Inf
-## log_k_parent -2.302585  -Inf   Inf
-## 
-## Fixed parameter values:
-## None
-## 
-## Results:
-## 
-##        AIC     BIC    logLik
-##   93.88778 96.5589 -43.94389
-## 
-## Optimised, transformed parameters with symmetric confidence intervals:
-##              Estimate Std. Error  Lower  Upper
-## parent_0       92.470    1.28200 89.740 95.200
-## log_k_parent   -2.347    0.03763 -2.428 -2.267
-## sigma           2.780    0.46330  1.792  3.767
-## 
-## Parameter correlation:
-##                parent_0 log_k_parent      sigma
-## parent_0      1.000e+00    6.186e-01 -1.516e-09
-## log_k_parent  6.186e-01    1.000e+00 -3.124e-09
-## sigma        -1.516e-09   -3.124e-09  1.000e+00
-## 
-## Backtransformed parameters:
-## Confidence intervals for internally transformed parameters are asymmetric.
-## t-test (unrealistically) based on the assumption of normal distribution
-## for estimators of untransformed parameters.
-##          Estimate t value    Pr(&gt;t)    Lower   Upper
-## parent_0 92.47000   72.13 8.824e-21 89.74000 95.2000
-## k_parent  0.09561   26.57 2.487e-14  0.08824  0.1036
-## sigma     2.78000    6.00 1.216e-05  1.79200  3.7670
-## 
-## FOCUS Chi2 error levels in percent:
-##          err.min n.optim df
-## All data   3.424       2  7
-## parent     3.424       2  7
-## 
-## Estimated disappearance times:
-##         DT50  DT90
-## parent 7.249 24.08
-## 
-## Data:
-##  time variable observed predicted residual
-##     0   parent     88.3    92.471  -4.1710
-##     0   parent     91.4    92.471  -1.0710
-##     1   parent     85.6    84.039   1.5610
-##     1   parent     84.5    84.039   0.4610
-##     2   parent     78.9    76.376   2.5241
-##     2   parent     77.6    76.376   1.2241
-##     3   parent     72.0    69.412   2.5884
-##     3   parent     71.9    69.412   2.4884
-##     5   parent     50.3    57.330  -7.0301
-##     5   parent     59.4    57.330   2.0699
-##     7   parent     47.0    47.352  -0.3515
-##     7   parent     45.1    47.352  -2.2515
-##    14   parent     27.7    24.247   3.4528
-##    14   parent     27.3    24.247   3.0528
-##    21   parent     10.0    12.416  -2.4163
-##    21   parent     10.4    12.416  -2.0163
-##    30   parent      2.9     5.251  -2.3513
-##    30   parent      4.0     5.251  -1.2513</code></pre>
+<code class="sourceCode R"><span><span class="va">m.L1.SFO</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="va">FOCUS_2006_L1_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
+<span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.L1.SFO</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## mkin version used for fitting:    1.1.2 </span></span>
+<span><span class="co">## R version used for fitting:       4.2.1 </span></span>
+<span><span class="co">## Date of fit:     Wed Aug 10 15:28:18 2022 </span></span>
+<span><span class="co">## Date of summary: Wed Aug 10 15:28:18 2022 </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Equations:</span></span>
+<span><span class="co">## d_parent/dt = - k_parent * parent</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Model predictions using solution type analytical </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Fitted using 133 model solutions performed in 0.031 s</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Error model: Constant variance </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Error model algorithm: OLS </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Starting values for parameters to be optimised:</span></span>
+<span><span class="co">##          value   type</span></span>
+<span><span class="co">## parent_0 89.85  state</span></span>
+<span><span class="co">## k_parent  0.10 deparm</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Starting values for the transformed parameters actually optimised:</span></span>
+<span><span class="co">##                  value lower upper</span></span>
+<span><span class="co">## parent_0     89.850000  -Inf   Inf</span></span>
+<span><span class="co">## log_k_parent -2.302585  -Inf   Inf</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Fixed parameter values:</span></span>
+<span><span class="co">## None</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Results:</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">##        AIC     BIC    logLik</span></span>
+<span><span class="co">##   93.88778 96.5589 -43.94389</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Optimised, transformed parameters with symmetric confidence intervals:</span></span>
+<span><span class="co">##              Estimate Std. Error  Lower  Upper</span></span>
+<span><span class="co">## parent_0       92.470    1.28200 89.740 95.200</span></span>
+<span><span class="co">## log_k_parent   -2.347    0.03763 -2.428 -2.267</span></span>
+<span><span class="co">## sigma           2.780    0.46330  1.792  3.767</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Parameter correlation:</span></span>
+<span><span class="co">##                parent_0 log_k_parent      sigma</span></span>
+<span><span class="co">## parent_0      1.000e+00    6.186e-01 -1.516e-09</span></span>
+<span><span class="co">## log_k_parent  6.186e-01    1.000e+00 -3.124e-09</span></span>
+<span><span class="co">## sigma        -1.516e-09   -3.124e-09  1.000e+00</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Backtransformed parameters:</span></span>
+<span><span class="co">## Confidence intervals for internally transformed parameters are asymmetric.</span></span>
+<span><span class="co">## t-test (unrealistically) based on the assumption of normal distribution</span></span>
+<span><span class="co">## for estimators of untransformed parameters.</span></span>
+<span><span class="co">##          Estimate t value    Pr(&gt;t)    Lower   Upper</span></span>
+<span><span class="co">## parent_0 92.47000   72.13 8.824e-21 89.74000 95.2000</span></span>
+<span><span class="co">## k_parent  0.09561   26.57 2.487e-14  0.08824  0.1036</span></span>
+<span><span class="co">## sigma     2.78000    6.00 1.216e-05  1.79200  3.7670</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## FOCUS Chi2 error levels in percent:</span></span>
+<span><span class="co">##          err.min n.optim df</span></span>
+<span><span class="co">## All data   3.424       2  7</span></span>
+<span><span class="co">## parent     3.424       2  7</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Estimated disappearance times:</span></span>
+<span><span class="co">##         DT50  DT90</span></span>
+<span><span class="co">## parent 7.249 24.08</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Data:</span></span>
+<span><span class="co">##  time variable observed predicted residual</span></span>
+<span><span class="co">##     0   parent     88.3    92.471  -4.1710</span></span>
+<span><span class="co">##     0   parent     91.4    92.471  -1.0710</span></span>
+<span><span class="co">##     1   parent     85.6    84.039   1.5610</span></span>
+<span><span class="co">##     1   parent     84.5    84.039   0.4610</span></span>
+<span><span class="co">##     2   parent     78.9    76.376   2.5241</span></span>
+<span><span class="co">##     2   parent     77.6    76.376   1.2241</span></span>
+<span><span class="co">##     3   parent     72.0    69.412   2.5884</span></span>
+<span><span class="co">##     3   parent     71.9    69.412   2.4884</span></span>
+<span><span class="co">##     5   parent     50.3    57.330  -7.0301</span></span>
+<span><span class="co">##     5   parent     59.4    57.330   2.0699</span></span>
+<span><span class="co">##     7   parent     47.0    47.352  -0.3515</span></span>
+<span><span class="co">##     7   parent     45.1    47.352  -2.2515</span></span>
+<span><span class="co">##    14   parent     27.7    24.247   3.4528</span></span>
+<span><span class="co">##    14   parent     27.3    24.247   3.0528</span></span>
+<span><span class="co">##    21   parent     10.0    12.416  -2.4163</span></span>
+<span><span class="co">##    21   parent     10.4    12.416  -2.0163</span></span>
+<span><span class="co">##    30   parent      2.9     5.251  -2.3513</span></span>
+<span><span class="co">##    30   parent      4.0     5.251  -1.2513</span></span></code></pre>
 <p>A plot of the fit is obtained with the plot function for mkinfit objects.</p>
 <div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-method.html">plot</a></span><span class="op">(</span><span class="va">m.L1.SFO</span>, show_errmin <span class="op">=</span> <span class="cn">TRUE</span>, main <span class="op">=</span> <span class="st">"FOCUS L1 - SFO"</span><span class="op">)</span></code></pre></div>
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">m.L1.SFO</span>, show_errmin <span class="op">=</span> <span class="cn">TRUE</span>, main <span class="op">=</span> <span class="st">"FOCUS L1 - SFO"</span><span class="op">)</span></span></code></pre></div>
 <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-4-1.png" width="576"></p>
 <p>The residual plot can be easily obtained by</p>
 <div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span class="fu"><a href="../reference/mkinresplot.html">mkinresplot</a></span><span class="op">(</span><span class="va">m.L1.SFO</span>, ylab <span class="op">=</span> <span class="st">"Observed"</span>, xlab <span class="op">=</span> <span class="st">"Time"</span><span class="op">)</span></code></pre></div>
+<code class="sourceCode R"><span><span class="fu"><a href="../reference/mkinresplot.html">mkinresplot</a></span><span class="op">(</span><span class="va">m.L1.SFO</span>, ylab <span class="op">=</span> <span class="st">"Observed"</span>, xlab <span class="op">=</span> <span class="st">"Time"</span><span class="op">)</span></span></code></pre></div>
 <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-5-1.png" width="576"></p>
 <p>For comparison, the FOMC model is fitted as well, and the <span class="math inline">\(\chi^2\)</span> error level is checked.</p>
 <div class="sourceCode" id="cb6"><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>## Warning in mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet = TRUE): Optimisation did not converge:
-## false convergence (8)</code></pre>
+<code class="sourceCode R"><span><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></code></pre></div>
+<pre><code><span><span class="co">## Warning in mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet = TRUE): Optimisation did not converge:</span></span>
+<span><span class="co">## false convergence (8)</span></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-method.html">plot</a></span><span class="op">(</span><span class="va">m.L1.FOMC</span>, show_errmin <span class="op">=</span> <span class="cn">TRUE</span>, main <span class="op">=</span> <span class="st">"FOCUS L1 - FOMC"</span><span class="op">)</span></code></pre></div>
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">m.L1.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></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">
-<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html">summary</a></span><span class="op">(</span><span class="va">m.L1.FOMC</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></code></pre></div>
-<pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
-<pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
-<pre><code>## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
-## doubtful</code></pre>
-<pre><code>## mkin version used for fitting:    1.0.3.9000 
-## R version used for fitting:       4.0.3 
-## Date of fit:     Mon Feb 15 17:13:40 2021 
-## Date of summary: Mon Feb 15 17:13:40 2021 
-## 
-## Equations:
-## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
-## 
-## Model predictions using solution type analytical 
-## 
-## Fitted using 369 model solutions performed in 0.084 s
-## 
-## Error model: Constant variance 
-## 
-## Error model algorithm: OLS 
-## 
-## Starting values for parameters to be optimised:
-##          value   type
-## parent_0 89.85  state
-## alpha     1.00 deparm
-## beta     10.00 deparm
-## 
-## Starting values for the transformed parameters actually optimised:
-##               value lower upper
-## parent_0  89.850000  -Inf   Inf
-## log_alpha  0.000000  -Inf   Inf
-## log_beta   2.302585  -Inf   Inf
-## 
-## Fixed parameter values:
-## None
-## 
-## 
-## Warning(s): 
-## Optimisation did not converge:
-## false convergence (8)
-## 
-## Results:
-## 
-##        AIC      BIC   logLik
-##   95.88781 99.44929 -43.9439
-## 
-## Optimised, transformed parameters with symmetric confidence intervals:
-##           Estimate Std. Error  Lower  Upper
-## parent_0     92.47     1.2820 89.720 95.220
-## log_alpha    13.78        NaN    NaN    NaN
-## log_beta     16.13        NaN    NaN    NaN
-## sigma         2.78     0.4598  1.794  3.766
-## 
-## Parameter correlation:
-##            parent_0 log_alpha log_beta     sigma
-## parent_0  1.0000000       NaN      NaN 0.0001671
-## log_alpha       NaN         1      NaN       NaN
-## log_beta        NaN       NaN        1       NaN
-## sigma     0.0001671       NaN      NaN 1.0000000
-## 
-## Backtransformed parameters:
-## Confidence intervals for internally transformed parameters are asymmetric.
-## t-test (unrealistically) based on the assumption of normal distribution
-## for estimators of untransformed parameters.
-##           Estimate t value Pr(&gt;t)  Lower  Upper
-## parent_0 9.247e+01      NA     NA 89.720 95.220
-## alpha    9.658e+05      NA     NA     NA     NA
-## beta     1.010e+07      NA     NA     NA     NA
-## sigma    2.780e+00      NA     NA  1.794  3.766
-## 
-## FOCUS Chi2 error levels in percent:
-##          err.min n.optim df
-## All data   3.619       3  6
-## parent     3.619       3  6
-## 
-## Estimated disappearance times:
-##        DT50  DT90 DT50back
-## parent 7.25 24.08     7.25</code></pre>
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.L1.FOMC</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Warning in sqrt(diag(covar)): NaNs produced</span></span></code></pre>
+<pre><code><span><span class="co">## Warning in sqrt(1/diag(V)): NaNs produced</span></span></code></pre>
+<pre><code><span><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is</span></span>
+<span><span class="co">## doubtful</span></span></code></pre>
+<pre><code><span><span class="co">## mkin version used for fitting:    1.1.2 </span></span>
+<span><span class="co">## R version used for fitting:       4.2.1 </span></span>
+<span><span class="co">## Date of fit:     Wed Aug 10 15:28:18 2022 </span></span>
+<span><span class="co">## Date of summary: Wed Aug 10 15:28:18 2022 </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Equations:</span></span>
+<span><span class="co">## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Model predictions using solution type analytical </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Fitted using 369 model solutions performed in 0.082 s</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Error model: Constant variance </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Error model algorithm: OLS </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Starting values for parameters to be optimised:</span></span>
+<span><span class="co">##          value   type</span></span>
+<span><span class="co">## parent_0 89.85  state</span></span>
+<span><span class="co">## alpha     1.00 deparm</span></span>
+<span><span class="co">## beta     10.00 deparm</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Starting values for the transformed parameters actually optimised:</span></span>
+<span><span class="co">##               value lower upper</span></span>
+<span><span class="co">## parent_0  89.850000  -Inf   Inf</span></span>
+<span><span class="co">## log_alpha  0.000000  -Inf   Inf</span></span>
+<span><span class="co">## log_beta   2.302585  -Inf   Inf</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Fixed parameter values:</span></span>
+<span><span class="co">## None</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Warning(s): </span></span>
+<span><span class="co">## Optimisation did not converge:</span></span>
+<span><span class="co">## false convergence (8)</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Results:</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">##        AIC      BIC   logLik</span></span>
+<span><span class="co">##   95.88781 99.44929 -43.9439</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Optimised, transformed parameters with symmetric confidence intervals:</span></span>
+<span><span class="co">##           Estimate Std. Error  Lower  Upper</span></span>
+<span><span class="co">## parent_0     92.47     1.2820 89.720 95.220</span></span>
+<span><span class="co">## log_alpha    13.78        NaN    NaN    NaN</span></span>
+<span><span class="co">## log_beta     16.13        NaN    NaN    NaN</span></span>
+<span><span class="co">## sigma         2.78     0.4598  1.794  3.766</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Parameter correlation:</span></span>
+<span><span class="co">##            parent_0 log_alpha log_beta     sigma</span></span>
+<span><span class="co">## parent_0  1.0000000       NaN      NaN 0.0001671</span></span>
+<span><span class="co">## log_alpha       NaN         1      NaN       NaN</span></span>
+<span><span class="co">## log_beta        NaN       NaN        1       NaN</span></span>
+<span><span class="co">## sigma     0.0001671       NaN      NaN 1.0000000</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Backtransformed parameters:</span></span>
+<span><span class="co">## Confidence intervals for internally transformed parameters are asymmetric.</span></span>
+<span><span class="co">## t-test (unrealistically) based on the assumption of normal distribution</span></span>
+<span><span class="co">## for estimators of untransformed parameters.</span></span>
+<span><span class="co">##           Estimate t value Pr(&gt;t)  Lower  Upper</span></span>
+<span><span class="co">## parent_0 9.247e+01      NA     NA 89.720 95.220</span></span>
+<span><span class="co">## alpha    9.658e+05      NA     NA     NA     NA</span></span>
+<span><span class="co">## beta     1.010e+07      NA     NA     NA     NA</span></span>
+<span><span class="co">## sigma    2.780e+00      NA     NA  1.794  3.766</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## FOCUS Chi2 error levels in percent:</span></span>
+<span><span class="co">##          err.min n.optim df</span></span>
+<span><span class="co">## All data   3.619       3  6</span></span>
+<span><span class="co">## parent     3.619       3  6</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Estimated disappearance times:</span></span>
+<span><span class="co">##        DT50  DT90 DT50back</span></span>
+<span><span class="co">## parent 7.25 24.08     7.25</span></span></code></pre>
 <p>We get a warning that the default optimisation algorithm <code>Port</code> did not converge, which is an indication that the model is overparameterised, <em>i.e.</em> contains too many parameters that are ill-defined as a consequence.</p>
 <p>And in fact, due to the higher number of parameters, and the lower number of degrees of freedom of the fit, the <span class="math inline">\(\chi^2\)</span> error level is actually higher for the FOMC model (3.6%) than for the SFO model (3.4%). Additionally, the parameters <code>log_alpha</code> and <code>log_beta</code> internally fitted in the model have excessive confidence intervals, that span more than 25 orders of magnitude (!) when backtransformed to the scale of <code>alpha</code> and <code>beta</code>. Also, the t-test for significant difference from zero does not indicate such a significant difference, with p-values greater than 0.1, and finally, the parameter correlation of <code>log_alpha</code> and <code>log_beta</code> is 1.000, clearly indicating that the model is overparameterised.</p>
 <p>The <span class="math inline">\(\chi^2\)</span> error levels reported in Appendix 3 and Appendix 7 to the FOCUS kinetics report are rounded to integer percentages and partly deviate by one percentage point from the results calculated by mkin. The reason for this is not known. However, mkin gives the same <span class="math inline">\(\chi^2\)</span> error levels as the kinfit package and the calculation routines of the kinfit package have been extensively compared to the results obtained by the KinGUI software, as documented in the kinfit package vignette. KinGUI was the first widely used standard package in this field. Also, the calculation of <span class="math inline">\(\chi^2\)</span> error levels was compared with KinGUII, CAKE and DegKin manager in a project sponsored by the German Umweltbundesamt <span class="citation">(Ranke 2014)</span>.</p>
 </div>
-<div id="laboratory-data-l2" class="section level1">
-<h1 class="hasAnchor">
-<a href="#laboratory-data-l2" class="anchor"></a>Laboratory Data L2</h1>
+<div class="section level2">
+<h2 id="laboratory-data-l2">Laboratory Data L2<a class="anchor" aria-label="anchor" href="#laboratory-data-l2"></a>
+</h2>
 <p>The following code defines example dataset L2 from the FOCUS kinetics report, p. 287:</p>
 <div class="sourceCode" id="cb14"><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">data.frame</a></span><span class="op">(</span>
-  t <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/rep.html">rep</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">1</span>, <span class="fl">3</span>, <span class="fl">7</span>, <span class="fl">14</span>, <span class="fl">28</span><span class="op">)</span>, each <span class="op">=</span> <span class="fl">2</span><span class="op">)</span>,
-  parent <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="fl">96.1</span>, <span class="fl">91.8</span>, <span class="fl">41.4</span>, <span class="fl">38.7</span>,
-             <span class="fl">19.3</span>, <span class="fl">22.3</span>, <span class="fl">4.6</span>, <span class="fl">4.6</span>,
-             <span class="fl">2.6</span>, <span class="fl">1.2</span>, <span class="fl">0.3</span>, <span class="fl">0.6</span><span class="op">)</span><span class="op">)</span>
-<span class="va">FOCUS_2006_L2_mkin</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span><span class="op">(</span><span class="va">FOCUS_2006_L2</span><span class="op">)</span></code></pre></div>
-<div id="sfo-fit-for-l2" class="section level2">
-<h2 class="hasAnchor">
-<a href="#sfo-fit-for-l2" class="anchor"></a>SFO fit for L2</h2>
+<code class="sourceCode R"><span><span class="va">FOCUS_2006_L2</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span></span>
+<span>  t <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/rep.html" class="external-link">rep</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">1</span>, <span class="fl">3</span>, <span class="fl">7</span>, <span class="fl">14</span>, <span class="fl">28</span><span class="op">)</span>, each <span class="op">=</span> <span class="fl">2</span><span class="op">)</span>,</span>
+<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>,</span>
+<span>             <span class="fl">19.3</span>, <span class="fl">22.3</span>, <span class="fl">4.6</span>, <span class="fl">4.6</span>,</span>
+<span>             <span class="fl">2.6</span>, <span class="fl">1.2</span>, <span class="fl">0.3</span>, <span class="fl">0.6</span><span class="op">)</span><span class="op">)</span></span>
+<span><span class="va">FOCUS_2006_L2_mkin</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span><span class="op">(</span><span class="va">FOCUS_2006_L2</span><span class="op">)</span></span></code></pre></div>
+<div class="section level3">
+<h3 id="sfo-fit-for-l2">SFO fit for L2<a class="anchor" aria-label="anchor" href="#sfo-fit-for-l2"></a>
+</h3>
 <p>Again, the SFO model is fitted and the result is plotted. The residual plot can be obtained simply by adding the argument <code>show_residuals</code> to the plot command.</p>
 <div class="sourceCode" id="cb15"><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-method.html">plot</a></span><span class="op">(</span><span class="va">m.L2.SFO</span>, show_residuals <span class="op">=</span> <span class="cn">TRUE</span>, show_errmin <span class="op">=</span> <span class="cn">TRUE</span>,
-     main <span class="op">=</span> <span class="st">"FOCUS L2 - SFO"</span><span class="op">)</span></code></pre></div>
+<code class="sourceCode R"><span><span class="va">m.L2.SFO</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="va">FOCUS_2006_L2_mkin</span>, quiet<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span></span>
+<span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">m.L2.SFO</span>, show_residuals <span class="op">=</span> <span class="cn">TRUE</span>, show_errmin <span class="op">=</span> <span class="cn">TRUE</span>,</span>
+<span>     main <span class="op">=</span> <span class="st">"FOCUS L2 - SFO"</span><span class="op">)</span></span></code></pre></div>
 <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-8-1.png" width="672"></p>
 <p>The <span class="math inline">\(\chi^2\)</span> error level of 14% suggests that the model does not fit very well. This is also obvious from the plots of the fit, in which we have included the residual plot.</p>
 <p>In the FOCUS kinetics report, it is stated that there is no apparent systematic error observed from the residual plot up to the measured DT90 (approximately at day 5), and there is an underestimation beyond that point.</p>
 <p>We may add that it is difficult to judge the random nature of the residuals just from the three samplings at days 0, 1 and 3. Also, it is not clear <em>a priori</em> why a consistent underestimation after the approximate DT90 should be irrelevant. However, this can be rationalised by the fact that the FOCUS fate models generally only implement SFO kinetics.</p>
 </div>
-<div id="fomc-fit-for-l2" class="section level2">
-<h2 class="hasAnchor">
-<a href="#fomc-fit-for-l2" class="anchor"></a>FOMC fit for L2</h2>
+<div class="section level3">
+<h3 id="fomc-fit-for-l2">FOMC fit for L2<a class="anchor" aria-label="anchor" href="#fomc-fit-for-l2"></a>
+</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">
-<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-method.html">plot</a></span><span class="op">(</span><span class="va">m.L2.FOMC</span>, show_residuals <span class="op">=</span> <span class="cn">TRUE</span>,
-     main <span class="op">=</span> <span class="st">"FOCUS L2 - FOMC"</span><span class="op">)</span></code></pre></div>
+<code class="sourceCode R"><span><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>
+<span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">m.L2.FOMC</span>, show_residuals <span class="op">=</span> <span class="cn">TRUE</span>,</span>
+<span>     main <span class="op">=</span> <span class="st">"FOCUS L2 - FOMC"</span><span class="op">)</span></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">
-<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html">summary</a></span><span class="op">(</span><span class="va">m.L2.FOMC</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></code></pre></div>
-<pre><code>## mkin version used for fitting:    1.0.3.9000 
-## R version used for fitting:       4.0.3 
-## Date of fit:     Mon Feb 15 17:13:40 2021 
-## Date of summary: Mon Feb 15 17:13:40 2021 
-## 
-## Equations:
-## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
-## 
-## Model predictions using solution type analytical 
-## 
-## Fitted using 239 model solutions performed in 0.05 s
-## 
-## Error model: Constant variance 
-## 
-## Error model algorithm: OLS 
-## 
-## Starting values for parameters to be optimised:
-##          value   type
-## parent_0 93.95  state
-## alpha     1.00 deparm
-## beta     10.00 deparm
-## 
-## Starting values for the transformed parameters actually optimised:
-##               value lower upper
-## parent_0  93.950000  -Inf   Inf
-## log_alpha  0.000000  -Inf   Inf
-## log_beta   2.302585  -Inf   Inf
-## 
-## Fixed parameter values:
-## None
-## 
-## Results:
-## 
-##        AIC      BIC    logLik
-##   61.78966 63.72928 -26.89483
-## 
-## Optimised, transformed parameters with symmetric confidence intervals:
-##           Estimate Std. Error    Lower   Upper
-## parent_0   93.7700     1.6130 90.05000 97.4900
-## log_alpha   0.3180     0.1559 -0.04149  0.6776
-## log_beta    0.2102     0.2493 -0.36460  0.7850
-## sigma       2.2760     0.4645  1.20500  3.3470
-## 
-## Parameter correlation:
-##             parent_0  log_alpha   log_beta      sigma
-## parent_0   1.000e+00 -1.151e-01 -2.085e-01 -7.828e-09
-## log_alpha -1.151e-01  1.000e+00  9.741e-01 -1.602e-07
-## log_beta  -2.085e-01  9.741e-01  1.000e+00 -1.372e-07
-## sigma     -7.828e-09 -1.602e-07 -1.372e-07  1.000e+00
-## 
-## Backtransformed parameters:
-## Confidence intervals for internally transformed parameters are asymmetric.
-## t-test (unrealistically) based on the assumption of normal distribution
-## for estimators of untransformed parameters.
-##          Estimate t value    Pr(&gt;t)   Lower  Upper
-## parent_0   93.770  58.120 4.267e-12 90.0500 97.490
-## alpha       1.374   6.414 1.030e-04  0.9594  1.969
-## beta        1.234   4.012 1.942e-03  0.6945  2.192
-## sigma       2.276   4.899 5.977e-04  1.2050  3.347
-## 
-## FOCUS Chi2 error levels in percent:
-##          err.min n.optim df
-## All data   6.205       3  3
-## parent     6.205       3  3
-## 
-## Estimated disappearance times:
-##          DT50  DT90 DT50back
-## parent 0.8092 5.356    1.612</code></pre>
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.L2.FOMC</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## mkin version used for fitting:    1.1.2 </span></span>
+<span><span class="co">## R version used for fitting:       4.2.1 </span></span>
+<span><span class="co">## Date of fit:     Wed Aug 10 15:28:19 2022 </span></span>
+<span><span class="co">## Date of summary: Wed Aug 10 15:28:19 2022 </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Equations:</span></span>
+<span><span class="co">## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Model predictions using solution type analytical </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Fitted using 239 model solutions performed in 0.048 s</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Error model: Constant variance </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Error model algorithm: OLS </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Starting values for parameters to be optimised:</span></span>
+<span><span class="co">##          value   type</span></span>
+<span><span class="co">## parent_0 93.95  state</span></span>
+<span><span class="co">## alpha     1.00 deparm</span></span>
+<span><span class="co">## beta     10.00 deparm</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Starting values for the transformed parameters actually optimised:</span></span>
+<span><span class="co">##               value lower upper</span></span>
+<span><span class="co">## parent_0  93.950000  -Inf   Inf</span></span>
+<span><span class="co">## log_alpha  0.000000  -Inf   Inf</span></span>
+<span><span class="co">## log_beta   2.302585  -Inf   Inf</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Fixed parameter values:</span></span>
+<span><span class="co">## None</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Results:</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">##        AIC      BIC    logLik</span></span>
+<span><span class="co">##   61.78966 63.72928 -26.89483</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Optimised, transformed parameters with symmetric confidence intervals:</span></span>
+<span><span class="co">##           Estimate Std. Error    Lower   Upper</span></span>
+<span><span class="co">## parent_0   93.7700     1.6130 90.05000 97.4900</span></span>
+<span><span class="co">## log_alpha   0.3180     0.1559 -0.04149  0.6776</span></span>
+<span><span class="co">## log_beta    0.2102     0.2493 -0.36460  0.7850</span></span>
+<span><span class="co">## sigma       2.2760     0.4645  1.20500  3.3470</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Parameter correlation:</span></span>
+<span><span class="co">##             parent_0  log_alpha   log_beta      sigma</span></span>
+<span><span class="co">## parent_0   1.000e+00 -1.151e-01 -2.085e-01 -7.828e-09</span></span>
+<span><span class="co">## log_alpha -1.151e-01  1.000e+00  9.741e-01 -1.602e-07</span></span>
+<span><span class="co">## log_beta  -2.085e-01  9.741e-01  1.000e+00 -1.372e-07</span></span>
+<span><span class="co">## sigma     -7.828e-09 -1.602e-07 -1.372e-07  1.000e+00</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Backtransformed parameters:</span></span>
+<span><span class="co">## Confidence intervals for internally transformed parameters are asymmetric.</span></span>
+<span><span class="co">## t-test (unrealistically) based on the assumption of normal distribution</span></span>
+<span><span class="co">## for estimators of untransformed parameters.</span></span>
+<span><span class="co">##          Estimate t value    Pr(&gt;t)   Lower  Upper</span></span>
+<span><span class="co">## parent_0   93.770  58.120 4.267e-12 90.0500 97.490</span></span>
+<span><span class="co">## alpha       1.374   6.414 1.030e-04  0.9594  1.969</span></span>
+<span><span class="co">## beta        1.234   4.012 1.942e-03  0.6945  2.192</span></span>
+<span><span class="co">## sigma       2.276   4.899 5.977e-04  1.2050  3.347</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## FOCUS Chi2 error levels in percent:</span></span>
+<span><span class="co">##          err.min n.optim df</span></span>
+<span><span class="co">## All data   6.205       3  3</span></span>
+<span><span class="co">## parent     6.205       3  3</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Estimated disappearance times:</span></span>
+<span><span class="co">##          DT50  DT90 DT50back</span></span>
+<span><span class="co">## parent 0.8092 5.356    1.612</span></span></code></pre>
 <p>The error level at which the <span class="math inline">\(\chi^2\)</span> test passes is much lower in this case. Therefore, the FOMC model provides a better description of the data, as less experimental error has to be assumed in order to explain the data.</p>
 </div>
-<div id="dfop-fit-for-l2" class="section level2">
-<h2 class="hasAnchor">
-<a href="#dfop-fit-for-l2" class="anchor"></a>DFOP fit for L2</h2>
+<div class="section level3">
+<h3 id="dfop-fit-for-l2">DFOP fit for L2<a class="anchor" aria-label="anchor" href="#dfop-fit-for-l2"></a>
+</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">
-<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-method.html">plot</a></span><span class="op">(</span><span class="va">m.L2.DFOP</span>, show_residuals <span class="op">=</span> <span class="cn">TRUE</span>, show_errmin <span class="op">=</span> <span class="cn">TRUE</span>,
-     main <span class="op">=</span> <span class="st">"FOCUS L2 - DFOP"</span><span class="op">)</span></code></pre></div>
+<code class="sourceCode R"><span><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>
+<span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">m.L2.DFOP</span>, show_residuals <span class="op">=</span> <span class="cn">TRUE</span>, show_errmin <span class="op">=</span> <span class="cn">TRUE</span>,</span>
+<span>     main <span class="op">=</span> <span class="st">"FOCUS L2 - DFOP"</span><span class="op">)</span></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">
-<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html">summary</a></span><span class="op">(</span><span class="va">m.L2.DFOP</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></code></pre></div>
-<pre><code>## mkin version used for fitting:    1.0.3.9000 
-## R version used for fitting:       4.0.3 
-## Date of fit:     Mon Feb 15 17:13:41 2021 
-## Date of summary: Mon Feb 15 17:13:41 2021 
-## 
-## Equations:
-## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
-##            time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
-##            * parent
-## 
-## Model predictions using solution type analytical 
-## 
-## Fitted using 581 model solutions performed in 0.134 s
-## 
-## Error model: Constant variance 
-## 
-## Error model algorithm: OLS 
-## 
-## Starting values for parameters to be optimised:
-##          value   type
-## parent_0 93.95  state
-## k1        0.10 deparm
-## k2        0.01 deparm
-## g         0.50 deparm
-## 
-## Starting values for the transformed parameters actually optimised:
-##              value lower upper
-## parent_0 93.950000  -Inf   Inf
-## log_k1   -2.302585  -Inf   Inf
-## log_k2   -4.605170  -Inf   Inf
-## g_qlogis  0.000000  -Inf   Inf
-## 
-## Fixed parameter values:
-## None
-## 
-## Results:
-## 
-##        AIC      BIC    logLik
-##   52.36695 54.79148 -21.18347
-## 
-## Optimised, transformed parameters with symmetric confidence intervals:
-##          Estimate Std. Error      Lower     Upper
-## parent_0   93.950  9.998e-01    91.5900   96.3100
-## log_k1      3.112  1.842e+03 -4353.0000 4359.0000
-## log_k2     -1.088  6.285e-02    -1.2370   -0.9394
-## g_qlogis   -0.399  9.946e-02    -0.6342   -0.1638
-## sigma       1.414  2.886e-01     0.7314    2.0960
-## 
-## Parameter correlation:
-##            parent_0     log_k1     log_k2   g_qlogis      sigma
-## parent_0  1.000e+00  6.783e-07 -3.390e-10  2.665e-01 -2.967e-10
-## log_k1    6.783e-07  1.000e+00  1.116e-04 -2.196e-04 -1.031e-05
-## log_k2   -3.390e-10  1.116e-04  1.000e+00 -7.903e-01  2.917e-09
-## g_qlogis  2.665e-01 -2.196e-04 -7.903e-01  1.000e+00 -4.408e-09
-## sigma    -2.967e-10 -1.031e-05  2.917e-09 -4.408e-09  1.000e+00
-## 
-## Backtransformed parameters:
-## Confidence intervals for internally transformed parameters are asymmetric.
-## t-test (unrealistically) based on the assumption of normal distribution
-## for estimators of untransformed parameters.
-##          Estimate   t value    Pr(&gt;t)   Lower   Upper
-## parent_0  93.9500 9.397e+01 2.036e-12 91.5900 96.3100
-## k1        22.4800 5.553e-04 4.998e-01  0.0000     Inf
-## k2         0.3369 1.591e+01 4.697e-07  0.2904  0.3909
-## g          0.4016 1.680e+01 3.238e-07  0.3466  0.4591
-## sigma      1.4140 4.899e+00 8.776e-04  0.7314  2.0960
-## 
-## FOCUS Chi2 error levels in percent:
-##          err.min n.optim df
-## All data    2.53       4  2
-## parent      2.53       4  2
-## 
-## Estimated disappearance times:
-##          DT50  DT90 DT50back DT50_k1 DT50_k2
-## parent 0.5335 5.311    1.599 0.03084   2.058</code></pre>
-<p>Here, the DFOP model is clearly the best-fit model for dataset L2 based on the chi^2 error level criterion. However, the failure to calculate the covariance matrix indicates that the parameter estimates correlate excessively. Therefore, the FOMC model may be preferred for this dataset.</p>
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.L2.DFOP</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## mkin version used for fitting:    1.1.2 </span></span>
+<span><span class="co">## R version used for fitting:       4.2.1 </span></span>
+<span><span class="co">## Date of fit:     Wed Aug 10 15:28:19 2022 </span></span>
+<span><span class="co">## Date of summary: Wed Aug 10 15:28:19 2022 </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Equations:</span></span>
+<span><span class="co">## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *</span></span>
+<span><span class="co">##            time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))</span></span>
+<span><span class="co">##            * parent</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Model predictions using solution type analytical </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Fitted using 581 model solutions performed in 0.132 s</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Error model: Constant variance </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Error model algorithm: OLS </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Starting values for parameters to be optimised:</span></span>
+<span><span class="co">##          value   type</span></span>
+<span><span class="co">## parent_0 93.95  state</span></span>
+<span><span class="co">## k1        0.10 deparm</span></span>
+<span><span class="co">## k2        0.01 deparm</span></span>
+<span><span class="co">## g         0.50 deparm</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Starting values for the transformed parameters actually optimised:</span></span>
+<span><span class="co">##              value lower upper</span></span>
+<span><span class="co">## parent_0 93.950000  -Inf   Inf</span></span>
+<span><span class="co">## log_k1   -2.302585  -Inf   Inf</span></span>
+<span><span class="co">## log_k2   -4.605170  -Inf   Inf</span></span>
+<span><span class="co">## g_qlogis  0.000000  -Inf   Inf</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Fixed parameter values:</span></span>
+<span><span class="co">## None</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Results:</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">##        AIC      BIC    logLik</span></span>
+<span><span class="co">##   52.36695 54.79148 -21.18347</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Optimised, transformed parameters with symmetric confidence intervals:</span></span>
+<span><span class="co">##          Estimate Std. Error      Lower     Upper</span></span>
+<span><span class="co">## parent_0   93.950  9.998e-01    91.5900   96.3100</span></span>
+<span><span class="co">## log_k1      3.112  1.842e+03 -4353.0000 4359.0000</span></span>
+<span><span class="co">## log_k2     -1.088  6.285e-02    -1.2370   -0.9394</span></span>
+<span><span class="co">## g_qlogis   -0.399  9.946e-02    -0.6342   -0.1638</span></span>
+<span><span class="co">## sigma       1.414  2.886e-01     0.7314    2.0960</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Parameter correlation:</span></span>
+<span><span class="co">##            parent_0     log_k1     log_k2   g_qlogis      sigma</span></span>
+<span><span class="co">## parent_0  1.000e+00  6.783e-07 -3.390e-10  2.665e-01 -2.967e-10</span></span>
+<span><span class="co">## log_k1    6.783e-07  1.000e+00  1.116e-04 -2.196e-04 -1.031e-05</span></span>
+<span><span class="co">## log_k2   -3.390e-10  1.116e-04  1.000e+00 -7.903e-01  2.917e-09</span></span>
+<span><span class="co">## g_qlogis  2.665e-01 -2.196e-04 -7.903e-01  1.000e+00 -4.408e-09</span></span>
+<span><span class="co">## sigma    -2.967e-10 -1.031e-05  2.917e-09 -4.408e-09  1.000e+00</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Backtransformed parameters:</span></span>
+<span><span class="co">## Confidence intervals for internally transformed parameters are asymmetric.</span></span>
+<span><span class="co">## t-test (unrealistically) based on the assumption of normal distribution</span></span>
+<span><span class="co">## for estimators of untransformed parameters.</span></span>
+<span><span class="co">##          Estimate   t value    Pr(&gt;t)   Lower   Upper</span></span>
+<span><span class="co">## parent_0  93.9500 9.397e+01 2.036e-12 91.5900 96.3100</span></span>
+<span><span class="co">## k1        22.4800 5.553e-04 4.998e-01  0.0000     Inf</span></span>
+<span><span class="co">## k2         0.3369 1.591e+01 4.697e-07  0.2904  0.3909</span></span>
+<span><span class="co">## g          0.4016 1.680e+01 3.238e-07  0.3466  0.4591</span></span>
+<span><span class="co">## sigma      1.4140 4.899e+00 8.776e-04  0.7314  2.0960</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## FOCUS Chi2 error levels in percent:</span></span>
+<span><span class="co">##          err.min n.optim df</span></span>
+<span><span class="co">## All data    2.53       4  2</span></span>
+<span><span class="co">## parent      2.53       4  2</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Estimated disappearance times:</span></span>
+<span><span class="co">##          DT50  DT90 DT50back DT50_k1 DT50_k2</span></span>
+<span><span class="co">## parent 0.5335 5.311    1.599 0.03084   2.058</span></span></code></pre>
+<p>Here, the DFOP model is clearly the best-fit model for dataset L2 based on the chi^2 error level criterion.</p>
 </div>
 </div>
-<div id="laboratory-data-l3" class="section level1">
-<h1 class="hasAnchor">
-<a href="#laboratory-data-l3" class="anchor"></a>Laboratory Data L3</h1>
+<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">
-<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">data.frame</a></span><span class="op">(</span>
-  t <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">3</span>, <span class="fl">7</span>, <span class="fl">14</span>, <span class="fl">30</span>, <span class="fl">60</span>, <span class="fl">91</span>, <span class="fl">120</span><span class="op">)</span>,
-  parent <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="fl">97.8</span>, <span class="fl">60</span>, <span class="fl">51</span>, <span class="fl">43</span>, <span class="fl">35</span>, <span class="fl">22</span>, <span class="fl">15</span>, <span class="fl">12</span><span class="op">)</span><span class="op">)</span>
-<span class="va">FOCUS_2006_L3_mkin</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span><span class="op">(</span><span class="va">FOCUS_2006_L3</span><span class="op">)</span></code></pre></div>
-<div id="fit-multiple-models" class="section level2">
-<h2 class="hasAnchor">
-<a href="#fit-multiple-models" class="anchor"></a>Fit multiple models</h2>
+<code class="sourceCode R"><span><span class="va">FOCUS_2006_L3</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span></span>
+<span>  t <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">3</span>, <span class="fl">7</span>, <span class="fl">14</span>, <span class="fl">30</span>, <span class="fl">60</span>, <span class="fl">91</span>, <span class="fl">120</span><span class="op">)</span>,</span>
+<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></span>
+<span><span class="va">FOCUS_2006_L3_mkin</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span><span class="op">(</span><span class="va">FOCUS_2006_L3</span><span class="op">)</span></span></code></pre></div>
+<div class="section level3">
+<h3 id="fit-multiple-models">Fit multiple models<a class="anchor" aria-label="anchor" href="#fit-multiple-models"></a>
+</h3>
 <p>As of mkin version 0.9-39 (June 2015), we can fit several models to one or more datasets in one call to the function <code>mmkin</code>. The datasets have to be passed in a list, in this case a named list holding only the L3 dataset prepared above.</p>
 <div class="sourceCode" id="cb23"><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">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span><span class="op">)</span>, cores <span class="op">=</span> <span class="fl">1</span>,
-               <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="st">"FOCUS L3"</span> <span class="op">=</span> <span class="va">FOCUS_2006_L3_mkin</span><span class="op">)</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>
-<span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-method.html">plot</a></span><span class="op">(</span><span class="va">mm.L3</span><span class="op">)</span></code></pre></div>
+<code class="sourceCode R"><span><span class="co"># Only use one core here, not to offend the CRAN checks</span></span>
+<span><span class="va">mm.L3</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mmkin.html">mmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span><span class="op">)</span>, cores <span class="op">=</span> <span class="fl">1</span>,</span>
+<span>               <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="st">"FOCUS L3"</span> <span class="op">=</span> <span class="va">FOCUS_2006_L3_mkin</span><span class="op">)</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
+<span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">mm.L3</span><span class="op">)</span></span></code></pre></div>
 <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-12-1.png" width="700"></p>
 <p>The <span class="math inline">\(\chi^2\)</span> error level of 21% as well as the plot suggest that the SFO model does not fit very well. The FOMC model performs better, with an error level at which the <span class="math inline">\(\chi^2\)</span> test passes of 7%. Fitting the four parameter DFOP model further reduces the <span class="math inline">\(\chi^2\)</span> error level considerably.</p>
 </div>
-<div id="accessing-mmkin-objects" class="section level2">
-<h2 class="hasAnchor">
-<a href="#accessing-mmkin-objects" class="anchor"></a>Accessing mmkin objects</h2>
+<div class="section level3">
+<h3 id="accessing-mmkin-objects">Accessing mmkin objects<a class="anchor" aria-label="anchor" href="#accessing-mmkin-objects"></a>
+</h3>
 <p>The objects returned by mmkin are arranged like a matrix, with models as a row index and datasets as a column index.</p>
 <p>We can extract the summary and plot for <em>e.g.</em> the DFOP fit, using square brackets for indexing which will result in the use of the summary and plot functions working on mkinfit objects.</p>
 <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/summary-methods.html">summary</a></span><span class="op">(</span><span class="va">mm.L3</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="fl">1</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></code></pre></div>
-<pre><code>## mkin version used for fitting:    1.0.3.9000 
-## R version used for fitting:       4.0.3 
-## Date of fit:     Mon Feb 15 17:13:41 2021 
-## Date of summary: Mon Feb 15 17:13:42 2021 
-## 
-## Equations:
-## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
-##            time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
-##            * parent
-## 
-## Model predictions using solution type analytical 
-## 
-## Fitted using 376 model solutions performed in 0.082 s
-## 
-## Error model: Constant variance 
-## 
-## Error model algorithm: OLS 
-## 
-## Starting values for parameters to be optimised:
-##          value   type
-## parent_0 97.80  state
-## k1        0.10 deparm
-## k2        0.01 deparm
-## g         0.50 deparm
-## 
-## Starting values for the transformed parameters actually optimised:
-##              value lower upper
-## parent_0 97.800000  -Inf   Inf
-## log_k1   -2.302585  -Inf   Inf
-## log_k2   -4.605170  -Inf   Inf
-## g_qlogis  0.000000  -Inf   Inf
-## 
-## Fixed parameter values:
-## None
-## 
-## Results:
-## 
-##        AIC      BIC    logLik
-##   32.97732 33.37453 -11.48866
-## 
-## Optimised, transformed parameters with symmetric confidence intervals:
-##          Estimate Std. Error   Lower      Upper
-## parent_0  97.7500    1.01900 94.5000 101.000000
-## log_k1    -0.6612    0.10050 -0.9812  -0.341300
-## log_k2    -4.2860    0.04322 -4.4230  -4.148000
-## g_qlogis  -0.1739    0.05270 -0.3416  -0.006142
-## sigma      1.0170    0.25430  0.2079   1.827000
-## 
-## Parameter correlation:
-##            parent_0     log_k1     log_k2   g_qlogis      sigma
-## parent_0  1.000e+00  1.732e-01  2.282e-02  4.009e-01 -9.664e-08
-## log_k1    1.732e-01  1.000e+00  4.945e-01 -5.809e-01  7.147e-07
-## log_k2    2.282e-02  4.945e-01  1.000e+00 -6.812e-01  1.022e-06
-## g_qlogis  4.009e-01 -5.809e-01 -6.812e-01  1.000e+00 -7.926e-07
-## sigma    -9.664e-08  7.147e-07  1.022e-06 -7.926e-07  1.000e+00
-## 
-## Backtransformed parameters:
-## Confidence intervals for internally transformed parameters are asymmetric.
-## t-test (unrealistically) based on the assumption of normal distribution
-## for estimators of untransformed parameters.
-##          Estimate t value    Pr(&gt;t)    Lower     Upper
-## parent_0 97.75000  95.960 1.248e-06 94.50000 101.00000
-## k1        0.51620   9.947 1.081e-03  0.37490   0.71090
-## k2        0.01376  23.140 8.840e-05  0.01199   0.01579
-## g         0.45660  34.920 2.581e-05  0.41540   0.49850
-## sigma     1.01700   4.000 1.400e-02  0.20790   1.82700
-## 
-## FOCUS Chi2 error levels in percent:
-##          err.min n.optim df
-## All data   2.225       4  4
-## parent     2.225       4  4
-## 
-## Estimated disappearance times:
-##         DT50 DT90 DT50back DT50_k1 DT50_k2
-## parent 7.464  123    37.03   1.343   50.37
-## 
-## Data:
-##  time variable observed predicted residual
-##     0   parent     97.8     97.75  0.05396
-##     3   parent     60.0     60.45 -0.44933
-##     7   parent     51.0     49.44  1.56338
-##    14   parent     43.0     43.84 -0.83632
-##    30   parent     35.0     35.15 -0.14707
-##    60   parent     22.0     23.26 -1.25919
-##    91   parent     15.0     15.18 -0.18181
-##   120   parent     12.0     10.19  1.81395</code></pre>
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">mm.L3</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="fl">1</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## mkin version used for fitting:    1.1.2 </span></span>
+<span><span class="co">## R version used for fitting:       4.2.1 </span></span>
+<span><span class="co">## Date of fit:     Wed Aug 10 15:28:20 2022 </span></span>
+<span><span class="co">## Date of summary: Wed Aug 10 15:28:20 2022 </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Equations:</span></span>
+<span><span class="co">## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *</span></span>
+<span><span class="co">##            time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))</span></span>
+<span><span class="co">##            * parent</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Model predictions using solution type analytical </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Fitted using 376 model solutions performed in 0.079 s</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Error model: Constant variance </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Error model algorithm: OLS </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Starting values for parameters to be optimised:</span></span>
+<span><span class="co">##          value   type</span></span>
+<span><span class="co">## parent_0 97.80  state</span></span>
+<span><span class="co">## k1        0.10 deparm</span></span>
+<span><span class="co">## k2        0.01 deparm</span></span>
+<span><span class="co">## g         0.50 deparm</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Starting values for the transformed parameters actually optimised:</span></span>
+<span><span class="co">##              value lower upper</span></span>
+<span><span class="co">## parent_0 97.800000  -Inf   Inf</span></span>
+<span><span class="co">## log_k1   -2.302585  -Inf   Inf</span></span>
+<span><span class="co">## log_k2   -4.605170  -Inf   Inf</span></span>
+<span><span class="co">## g_qlogis  0.000000  -Inf   Inf</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Fixed parameter values:</span></span>
+<span><span class="co">## None</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Results:</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">##        AIC      BIC    logLik</span></span>
+<span><span class="co">##   32.97732 33.37453 -11.48866</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Optimised, transformed parameters with symmetric confidence intervals:</span></span>
+<span><span class="co">##          Estimate Std. Error   Lower      Upper</span></span>
+<span><span class="co">## parent_0  97.7500    1.01900 94.5000 101.000000</span></span>
+<span><span class="co">## log_k1    -0.6612    0.10050 -0.9812  -0.341300</span></span>
+<span><span class="co">## log_k2    -4.2860    0.04322 -4.4230  -4.148000</span></span>
+<span><span class="co">## g_qlogis  -0.1739    0.05270 -0.3416  -0.006142</span></span>
+<span><span class="co">## sigma      1.0170    0.25430  0.2079   1.827000</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Parameter correlation:</span></span>
+<span><span class="co">##            parent_0     log_k1     log_k2   g_qlogis      sigma</span></span>
+<span><span class="co">## parent_0  1.000e+00  1.732e-01  2.282e-02  4.009e-01 -9.664e-08</span></span>
+<span><span class="co">## log_k1    1.732e-01  1.000e+00  4.945e-01 -5.809e-01  7.147e-07</span></span>
+<span><span class="co">## log_k2    2.282e-02  4.945e-01  1.000e+00 -6.812e-01  1.022e-06</span></span>
+<span><span class="co">## g_qlogis  4.009e-01 -5.809e-01 -6.812e-01  1.000e+00 -7.926e-07</span></span>
+<span><span class="co">## sigma    -9.664e-08  7.147e-07  1.022e-06 -7.926e-07  1.000e+00</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Backtransformed parameters:</span></span>
+<span><span class="co">## Confidence intervals for internally transformed parameters are asymmetric.</span></span>
+<span><span class="co">## t-test (unrealistically) based on the assumption of normal distribution</span></span>
+<span><span class="co">## for estimators of untransformed parameters.</span></span>
+<span><span class="co">##          Estimate t value    Pr(&gt;t)    Lower     Upper</span></span>
+<span><span class="co">## parent_0 97.75000  95.960 1.248e-06 94.50000 101.00000</span></span>
+<span><span class="co">## k1        0.51620   9.947 1.081e-03  0.37490   0.71090</span></span>
+<span><span class="co">## k2        0.01376  23.140 8.840e-05  0.01199   0.01579</span></span>
+<span><span class="co">## g         0.45660  34.920 2.581e-05  0.41540   0.49850</span></span>
+<span><span class="co">## sigma     1.01700   4.000 1.400e-02  0.20790   1.82700</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## FOCUS Chi2 error levels in percent:</span></span>
+<span><span class="co">##          err.min n.optim df</span></span>
+<span><span class="co">## All data   2.225       4  4</span></span>
+<span><span class="co">## parent     2.225       4  4</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Estimated disappearance times:</span></span>
+<span><span class="co">##         DT50 DT90 DT50back DT50_k1 DT50_k2</span></span>
+<span><span class="co">## parent 7.464  123    37.03   1.343   50.37</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Data:</span></span>
+<span><span class="co">##  time variable observed predicted residual</span></span>
+<span><span class="co">##     0   parent     97.8     97.75  0.05396</span></span>
+<span><span class="co">##     3   parent     60.0     60.45 -0.44933</span></span>
+<span><span class="co">##     7   parent     51.0     49.44  1.56338</span></span>
+<span><span class="co">##    14   parent     43.0     43.84 -0.83632</span></span>
+<span><span class="co">##    30   parent     35.0     35.15 -0.14707</span></span>
+<span><span class="co">##    60   parent     22.0     23.26 -1.25919</span></span>
+<span><span class="co">##    91   parent     15.0     15.18 -0.18181</span></span>
+<span><span class="co">##   120   parent     12.0     10.19  1.81395</span></span></code></pre>
 <div class="sourceCode" id="cb26"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-method.html">plot</a></span><span class="op">(</span><span class="va">mm.L3</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="fl">1</span><span class="op">]</span><span class="op">]</span>, show_errmin <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></code></pre></div>
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">mm.L3</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="fl">1</span><span class="op">]</span><span class="op">]</span>, show_errmin <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
 <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-13-1.png" width="700"></p>
 <p>Here, a look to the model plot, the confidence intervals of the parameters and the correlation matrix suggest that the parameter estimates are reliable, and the DFOP model can be used as the best-fit model based on the <span class="math inline">\(\chi^2\)</span> error level criterion for laboratory data L3.</p>
 <p>This is also an example where the standard t-test for the parameter <code>g_ilr</code> is misleading, as it tests for a significant difference from zero. In this case, zero appears to be the correct value for this parameter, and the confidence interval for the backtransformed parameter <code>g</code> is quite narrow.</p>
 </div>
 </div>
-<div id="laboratory-data-l4" class="section level1">
-<h1 class="hasAnchor">
-<a href="#laboratory-data-l4" class="anchor"></a>Laboratory Data L4</h1>
+<div class="section level2">
+<h2 id="laboratory-data-l4">Laboratory Data L4<a class="anchor" aria-label="anchor" href="#laboratory-data-l4"></a>
+</h2>
 <p>The following code defines example dataset L4 from the FOCUS kinetics report, p. 293:</p>
 <div class="sourceCode" id="cb27"><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">data.frame</a></span><span class="op">(</span>
-  t <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">3</span>, <span class="fl">7</span>, <span class="fl">14</span>, <span class="fl">30</span>, <span class="fl">60</span>, <span class="fl">91</span>, <span class="fl">120</span><span class="op">)</span>,
-  parent <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="fl">96.6</span>, <span class="fl">96.3</span>, <span class="fl">94.3</span>, <span class="fl">88.8</span>, <span class="fl">74.9</span>, <span class="fl">59.9</span>, <span class="fl">53.5</span>, <span class="fl">49.0</span><span class="op">)</span><span class="op">)</span>
-<span class="va">FOCUS_2006_L4_mkin</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span><span class="op">(</span><span class="va">FOCUS_2006_L4</span><span class="op">)</span></code></pre></div>
+<code class="sourceCode R"><span><span class="va">FOCUS_2006_L4</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span></span>
+<span>  t <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">3</span>, <span class="fl">7</span>, <span class="fl">14</span>, <span class="fl">30</span>, <span class="fl">60</span>, <span class="fl">91</span>, <span class="fl">120</span><span class="op">)</span>,</span>
+<span>  parent <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">96.6</span>, <span class="fl">96.3</span>, <span class="fl">94.3</span>, <span class="fl">88.8</span>, <span class="fl">74.9</span>, <span class="fl">59.9</span>, <span class="fl">53.5</span>, <span class="fl">49.0</span><span class="op">)</span><span class="op">)</span></span>
+<span><span class="va">FOCUS_2006_L4_mkin</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span><span class="op">(</span><span class="va">FOCUS_2006_L4</span><span class="op">)</span></span></code></pre></div>
 <p>Fits of the SFO and FOMC models, plots and summaries are produced below:</p>
 <div class="sourceCode" id="cb28"><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">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"FOMC"</span><span class="op">)</span>, cores <span class="op">=</span> <span class="fl">1</span>,
-               <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="st">"FOCUS L4"</span> <span class="op">=</span> <span class="va">FOCUS_2006_L4_mkin</span><span class="op">)</span>,
-               quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>
-<span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-method.html">plot</a></span><span class="op">(</span><span class="va">mm.L4</span><span class="op">)</span></code></pre></div>
+<code class="sourceCode R"><span><span class="co"># Only use one core here, not to offend the CRAN checks</span></span>
+<span><span class="va">mm.L4</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mmkin.html">mmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"FOMC"</span><span class="op">)</span>, cores <span class="op">=</span> <span class="fl">1</span>,</span>
+<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>,</span>
+<span>               quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
+<span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">mm.L4</span><span class="op">)</span></span></code></pre></div>
 <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-15-1.png" width="700"></p>
 <p>The <span class="math inline">\(\chi^2\)</span> error level of 3.3% as well as the plot suggest that the SFO model fits very well. The error level at which the <span class="math inline">\(\chi^2\)</span> test passes is slightly lower for the FOMC model. However, the difference appears negligible.</p>
 <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">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>## mkin version used for fitting:    1.0.3.9000 
-## R version used for fitting:       4.0.3 
-## Date of fit:     Mon Feb 15 17:13:42 2021 
-## Date of summary: Mon Feb 15 17:13:42 2021 
-## 
-## Equations:
-## d_parent/dt = - k_parent * parent
-## 
-## Model predictions using solution type analytical 
-## 
-## Fitted using 142 model solutions performed in 0.03 s
-## 
-## Error model: Constant variance 
-## 
-## Error model algorithm: OLS 
-## 
-## Starting values for parameters to be optimised:
-##          value   type
-## parent_0  96.6  state
-## k_parent   0.1 deparm
-## 
-## Starting values for the transformed parameters actually optimised:
-##                  value lower upper
-## parent_0     96.600000  -Inf   Inf
-## log_k_parent -2.302585  -Inf   Inf
-## 
-## Fixed parameter values:
-## None
-## 
-## Results:
-## 
-##        AIC      BIC    logLik
-##   47.12133 47.35966 -20.56067
-## 
-## Optimised, transformed parameters with symmetric confidence intervals:
-##              Estimate Std. Error  Lower   Upper
-## parent_0       96.440    1.69900 92.070 100.800
-## log_k_parent   -5.030    0.07059 -5.211  -4.848
-## sigma           3.162    0.79050  1.130   5.194
-## 
-## Parameter correlation:
-##               parent_0 log_k_parent     sigma
-## parent_0     1.000e+00    5.938e-01 3.387e-07
-## log_k_parent 5.938e-01    1.000e+00 5.830e-07
-## sigma        3.387e-07    5.830e-07 1.000e+00
-## 
-## Backtransformed parameters:
-## Confidence intervals for internally transformed parameters are asymmetric.
-## t-test (unrealistically) based on the assumption of normal distribution
-## for estimators of untransformed parameters.
-##           Estimate t value    Pr(&gt;t)     Lower     Upper
-## parent_0 96.440000   56.77 1.604e-08 92.070000 1.008e+02
-## k_parent  0.006541   14.17 1.578e-05  0.005455 7.842e-03
-## sigma     3.162000    4.00 5.162e-03  1.130000 5.194e+00
-## 
-## FOCUS Chi2 error levels in percent:
-##          err.min n.optim df
-## All data   3.287       2  6
-## parent     3.287       2  6
-## 
-## Estimated disappearance times:
-##        DT50 DT90
-## parent  106  352</code></pre>
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">mm.L4</span><span class="op">[[</span><span class="st">"SFO"</span>, <span class="fl">1</span><span class="op">]</span><span class="op">]</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## mkin version used for fitting:    1.1.2 </span></span>
+<span><span class="co">## R version used for fitting:       4.2.1 </span></span>
+<span><span class="co">## Date of fit:     Wed Aug 10 15:28:21 2022 </span></span>
+<span><span class="co">## Date of summary: Wed Aug 10 15:28:21 2022 </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Equations:</span></span>
+<span><span class="co">## d_parent/dt = - k_parent * parent</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Model predictions using solution type analytical </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Fitted using 142 model solutions performed in 0.03 s</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Error model: Constant variance </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Error model algorithm: OLS </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Starting values for parameters to be optimised:</span></span>
+<span><span class="co">##          value   type</span></span>
+<span><span class="co">## parent_0  96.6  state</span></span>
+<span><span class="co">## k_parent   0.1 deparm</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Starting values for the transformed parameters actually optimised:</span></span>
+<span><span class="co">##                  value lower upper</span></span>
+<span><span class="co">## parent_0     96.600000  -Inf   Inf</span></span>
+<span><span class="co">## log_k_parent -2.302585  -Inf   Inf</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Fixed parameter values:</span></span>
+<span><span class="co">## None</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Results:</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">##        AIC      BIC    logLik</span></span>
+<span><span class="co">##   47.12133 47.35966 -20.56067</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Optimised, transformed parameters with symmetric confidence intervals:</span></span>
+<span><span class="co">##              Estimate Std. Error  Lower   Upper</span></span>
+<span><span class="co">## parent_0       96.440    1.69900 92.070 100.800</span></span>
+<span><span class="co">## log_k_parent   -5.030    0.07059 -5.211  -4.848</span></span>
+<span><span class="co">## sigma           3.162    0.79050  1.130   5.194</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Parameter correlation:</span></span>
+<span><span class="co">##               parent_0 log_k_parent     sigma</span></span>
+<span><span class="co">## parent_0     1.000e+00    5.938e-01 3.387e-07</span></span>
+<span><span class="co">## log_k_parent 5.938e-01    1.000e+00 5.830e-07</span></span>
+<span><span class="co">## sigma        3.387e-07    5.830e-07 1.000e+00</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Backtransformed parameters:</span></span>
+<span><span class="co">## Confidence intervals for internally transformed parameters are asymmetric.</span></span>
+<span><span class="co">## t-test (unrealistically) based on the assumption of normal distribution</span></span>
+<span><span class="co">## for estimators of untransformed parameters.</span></span>
+<span><span class="co">##           Estimate t value    Pr(&gt;t)     Lower     Upper</span></span>
+<span><span class="co">## parent_0 96.440000   56.77 1.604e-08 92.070000 1.008e+02</span></span>
+<span><span class="co">## k_parent  0.006541   14.17 1.578e-05  0.005455 7.842e-03</span></span>
+<span><span class="co">## sigma     3.162000    4.00 5.162e-03  1.130000 5.194e+00</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## FOCUS Chi2 error levels in percent:</span></span>
+<span><span class="co">##          err.min n.optim df</span></span>
+<span><span class="co">## All data   3.287       2  6</span></span>
+<span><span class="co">## parent     3.287       2  6</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Estimated disappearance times:</span></span>
+<span><span class="co">##        DT50 DT90</span></span>
+<span><span class="co">## parent  106  352</span></span></code></pre>
 <div class="sourceCode" id="cb31"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html">summary</a></span><span class="op">(</span><span class="va">mm.L4</span><span class="op">[[</span><span class="st">"FOMC"</span>, <span class="fl">1</span><span class="op">]</span><span class="op">]</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></code></pre></div>
-<pre><code>## mkin version used for fitting:    1.0.3.9000 
-## R version used for fitting:       4.0.3 
-## Date of fit:     Mon Feb 15 17:13:42 2021 
-## Date of summary: Mon Feb 15 17:13:42 2021 
-## 
-## Equations:
-## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
-## 
-## Model predictions using solution type analytical 
-## 
-## Fitted using 224 model solutions performed in 0.046 s
-## 
-## Error model: Constant variance 
-## 
-## Error model algorithm: OLS 
-## 
-## Starting values for parameters to be optimised:
-##          value   type
-## parent_0  96.6  state
-## alpha      1.0 deparm
-## beta      10.0 deparm
-## 
-## Starting values for the transformed parameters actually optimised:
-##               value lower upper
-## parent_0  96.600000  -Inf   Inf
-## log_alpha  0.000000  -Inf   Inf
-## log_beta   2.302585  -Inf   Inf
-## 
-## Fixed parameter values:
-## None
-## 
-## Results:
-## 
-##        AIC      BIC    logLik
-##   40.37255 40.69032 -16.18628
-## 
-## Optimised, transformed parameters with symmetric confidence intervals:
-##           Estimate Std. Error   Lower    Upper
-## parent_0   99.1400     1.2670 95.6300 102.7000
-## log_alpha  -0.3506     0.2616 -1.0770   0.3756
-## log_beta    4.1740     0.3938  3.0810   5.2670
-## sigma       1.8300     0.4575  0.5598   3.1000
-## 
-## Parameter correlation:
-##             parent_0  log_alpha   log_beta      sigma
-## parent_0   1.000e+00 -4.696e-01 -5.543e-01 -2.468e-07
-## log_alpha -4.696e-01  1.000e+00  9.889e-01  2.478e-08
-## log_beta  -5.543e-01  9.889e-01  1.000e+00  5.211e-08
-## sigma     -2.468e-07  2.478e-08  5.211e-08  1.000e+00
-## 
-## Backtransformed parameters:
-## Confidence intervals for internally transformed parameters are asymmetric.
-## t-test (unrealistically) based on the assumption of normal distribution
-## for estimators of untransformed parameters.
-##          Estimate t value    Pr(&gt;t)   Lower   Upper
-## parent_0  99.1400  78.250 7.993e-08 95.6300 102.700
-## alpha      0.7042   3.823 9.365e-03  0.3407   1.456
-## beta      64.9800   2.540 3.201e-02 21.7800 193.900
-## sigma      1.8300   4.000 8.065e-03  0.5598   3.100
-## 
-## FOCUS Chi2 error levels in percent:
-##          err.min n.optim df
-## All data   2.029       3  5
-## parent     2.029       3  5
-## 
-## Estimated disappearance times:
-##         DT50 DT90 DT50back
-## parent 108.9 1644    494.9</code></pre>
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">mm.L4</span><span class="op">[[</span><span class="st">"FOMC"</span>, <span class="fl">1</span><span class="op">]</span><span class="op">]</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## mkin version used for fitting:    1.1.2 </span></span>
+<span><span class="co">## R version used for fitting:       4.2.1 </span></span>
+<span><span class="co">## Date of fit:     Wed Aug 10 15:28:21 2022 </span></span>
+<span><span class="co">## Date of summary: Wed Aug 10 15:28:21 2022 </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Equations:</span></span>
+<span><span class="co">## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Model predictions using solution type analytical </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Fitted using 224 model solutions performed in 0.045 s</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Error model: Constant variance </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Error model algorithm: OLS </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Starting values for parameters to be optimised:</span></span>
+<span><span class="co">##          value   type</span></span>
+<span><span class="co">## parent_0  96.6  state</span></span>
+<span><span class="co">## alpha      1.0 deparm</span></span>
+<span><span class="co">## beta      10.0 deparm</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Starting values for the transformed parameters actually optimised:</span></span>
+<span><span class="co">##               value lower upper</span></span>
+<span><span class="co">## parent_0  96.600000  -Inf   Inf</span></span>
+<span><span class="co">## log_alpha  0.000000  -Inf   Inf</span></span>
+<span><span class="co">## log_beta   2.302585  -Inf   Inf</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Fixed parameter values:</span></span>
+<span><span class="co">## None</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Results:</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">##        AIC      BIC    logLik</span></span>
+<span><span class="co">##   40.37255 40.69032 -16.18628</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Optimised, transformed parameters with symmetric confidence intervals:</span></span>
+<span><span class="co">##           Estimate Std. Error   Lower    Upper</span></span>
+<span><span class="co">## parent_0   99.1400     1.2670 95.6300 102.7000</span></span>
+<span><span class="co">## log_alpha  -0.3506     0.2616 -1.0770   0.3756</span></span>
+<span><span class="co">## log_beta    4.1740     0.3938  3.0810   5.2670</span></span>
+<span><span class="co">## sigma       1.8300     0.4575  0.5598   3.1000</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Parameter correlation:</span></span>
+<span><span class="co">##             parent_0  log_alpha   log_beta      sigma</span></span>
+<span><span class="co">## parent_0   1.000e+00 -4.696e-01 -5.543e-01 -2.468e-07</span></span>
+<span><span class="co">## log_alpha -4.696e-01  1.000e+00  9.889e-01  2.478e-08</span></span>
+<span><span class="co">## log_beta  -5.543e-01  9.889e-01  1.000e+00  5.211e-08</span></span>
+<span><span class="co">## sigma     -2.468e-07  2.478e-08  5.211e-08  1.000e+00</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Backtransformed parameters:</span></span>
+<span><span class="co">## Confidence intervals for internally transformed parameters are asymmetric.</span></span>
+<span><span class="co">## t-test (unrealistically) based on the assumption of normal distribution</span></span>
+<span><span class="co">## for estimators of untransformed parameters.</span></span>
+<span><span class="co">##          Estimate t value    Pr(&gt;t)   Lower   Upper</span></span>
+<span><span class="co">## parent_0  99.1400  78.250 7.993e-08 95.6300 102.700</span></span>
+<span><span class="co">## alpha      0.7042   3.823 9.365e-03  0.3407   1.456</span></span>
+<span><span class="co">## beta      64.9800   2.540 3.201e-02 21.7800 193.900</span></span>
+<span><span class="co">## sigma      1.8300   4.000 8.065e-03  0.5598   3.100</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## FOCUS Chi2 error levels in percent:</span></span>
+<span><span class="co">##          err.min n.optim df</span></span>
+<span><span class="co">## All data   2.029       3  5</span></span>
+<span><span class="co">## parent     2.029       3  5</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Estimated disappearance times:</span></span>
+<span><span class="co">##         DT50 DT90 DT50back</span></span>
+<span><span class="co">## parent 108.9 1644    494.9</span></span></code></pre>
 </div>
-<div id="references" class="section level1 unnumbered">
-<h1 class="hasAnchor">
-<a href="#references" class="anchor"></a>References</h1>
+<div class="section level2">
+<h2 class="unnumbered" id="references">References<a class="anchor" aria-label="anchor" href="#references"></a>
+</h2>
 <div id="refs" class="references hanging-indent">
 <div id="ref-ranke2014">
 <p>Ranke, Johannes. 2014. “Prüfung und Validierung von Modellierungssoftware als Alternative zu ModelMaker 4.0.” Umweltbundesamt Projektnummer 27452.</p>
@@ -801,11 +806,13 @@
 
 
       <footer><div class="copyright">
-  <p>Developed by Johannes Ranke.</p>
+  <p></p>
+<p>Developed by Johannes Ranke.</p>
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
+  <p></p>
+<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer>
@@ -814,5 +821,7 @@
   
 
 
+  
+
   </body>
 </html>
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--- a/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-5-1.png
+++ b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-5-1.png
diff --git a/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-6-1.png b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-6-1.png
index c0e08884..b6130527 100644
--- a/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-6-1.png
+++ b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-6-1.png
diff --git a/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-8-1.png b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-8-1.png
index 310b4f3b..dea51d58 100644
--- a/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-8-1.png
+++ b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-8-1.png
diff --git a/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-9-1.png b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-9-1.png
index 570f0026..05460304 100644
--- a/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-9-1.png
+++ b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-9-1.png
diff --git a/docs/dev/articles/index.html b/docs/dev/articles/index.html
index d1ca6668..526708a4 100644
--- a/docs/dev/articles/index.html
+++ b/docs/dev/articles/index.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">1.1.0</span>
+        <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">1.1.2</span>
       </span>
     </div>
 
@@ -26,7 +26,7 @@
   <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>
@@ -41,6 +41,9 @@
       <a href="../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a>
     </li>
     <li>
+      <a href="../articles/web_only/dimethenamid_2018.html">Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models</a>
+    </li>
+    <li>
       <a href="../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a>
     </li>
     <li>
@@ -109,7 +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> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/dev/articles/web_only/benchmarks.html b/docs/dev/articles/web_only/benchmarks.html
index a6d52649..3dbf2881 100644
--- a/docs/dev/articles/web_only/benchmarks.html
+++ b/docs/dev/articles/web_only/benchmarks.html
@@ -20,6 +20,8 @@
 <![endif]-->
 </head>
 <body data-spy="scroll" data-target="#toc">
+    
+
     <div class="container template-article">
       <header><div class="navbar navbar-default navbar-fixed-top" role="navigation">
   <div class="container">
@@ -32,7 +34,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../../index.html">mkin</a>
-        <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">1.0.3.9000</span>
+        <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">1.1.2</span>
       </span>
     </div>
 
@@ -42,7 +44,7 @@
   <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>
@@ -58,6 +60,9 @@
       <a href="../../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a>
     </li>
     <li>
+      <a href="../../articles/web_only/dimethenamid_2018.html">Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models</a>
+    </li>
+    <li>
       <a href="../../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a>
     </li>
     <li>
@@ -80,7 +85,7 @@
       </ul>
 <ul class="nav navbar-nav navbar-right">
 <li>
-  <a href="https://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/" class="external-link">
     <span class="fab fa-github fa-lg"></span>
      
   </a>
@@ -95,243 +100,442 @@
 
       
 
-      </header><script src="benchmarks_files/header-attrs-2.6/header-attrs.js"></script><script src="benchmarks_files/accessible-code-block-0.0.1/empty-anchor.js"></script><div class="row">
+      </header><script src="benchmarks_files/accessible-code-block-0.0.1/empty-anchor.js"></script><div class="row">
   <div class="col-md-9 contents">
     <div class="page-header toc-ignore">
       <h1 data-toc-skip>Benchmark timings for mkin</h1>
-                        <h4 class="author">Johannes Ranke</h4>
+                        <h4 data-toc-skip class="author">Johannes Ranke</h4>
             
-            <h4 class="date">Last change 13 May 2020 (rebuilt 2021-02-15)</h4>
+            <h4 data-toc-skip class="date">Last change 14 July 2022 (rebuilt 2022-08-10)</h4>
       
-      <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/master/vignettes/web_only/benchmarks.rmd"><code>vignettes/web_only/benchmarks.rmd</code></a></small>
+      <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>
 
     </div>
 
     
     
-<p>Each system is characterized by its CPU type, the operating system type and the mkin version. Currently only values for one system are available. A compiler was available, so if no analytical solution was available, compiled ODE models are used.</p>
-<div id="test-cases" class="section level2">
-<h2 class="hasAnchor">
-<a href="#test-cases" class="anchor"></a>Test cases</h2>
-<p>Parent only:</p>
+<p>Each system is characterized by the operating system type, the CPU type, the mkin version, and, as in June 2022 the current R version lead to worse performance, the R version. A compiler was available, so if no analytical solution was available, compiled ODE models are used.</p>
+<p>Every fit is only performed once, so the accuracy of the benchmarks is limited.</p>
+<p>The following wrapper function for <code>mmkin</code> is used because the way the error model is specified was changed in mkin version 0.9.49.1.</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">subset</a></span><span class="op">(</span><span class="va">FOCUS_2006_D</span>, <span class="va">value</span> <span class="op">!=</span> <span class="fl">0</span><span class="op">)</span>
-<span class="va">parent_datasets</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">FOCUS_C</span>, <span class="va">FOCUS_D</span><span class="op">)</span>
-
-<span class="va">t1</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>, <span class="st">"HS"</span><span class="op">)</span>, <span class="va">parent_datasets</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span>
-<span class="va">t2</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>, <span class="st">"HS"</span><span class="op">)</span>, <span class="va">parent_datasets</span>,
-    error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></code></pre></div>
-<p>One metabolite:</p>
+<code class="sourceCode R"><span><span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/utils/packageDescription.html" class="external-link">packageVersion</a></span><span class="op">(</span><span class="st">"mkin"</span><span class="op">)</span> <span class="op">&gt;</span> <span class="st">"0.9.48.1"</span><span class="op">)</span> <span class="op">{</span></span>
+<span>  <span class="va">mmkin_bench</span> <span class="op">&lt;-</span> <span class="kw">function</span><span class="op">(</span><span class="va">models</span>, <span class="va">datasets</span>, <span class="va">error_model</span> <span class="op">=</span> <span class="st">"const"</span><span class="op">)</span> <span class="op">{</span></span>
+<span>    <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span><span class="va">models</span>, <span class="va">datasets</span>, error_model <span class="op">=</span> <span class="va">error_model</span>, cores <span class="op">=</span> <span class="fl">1</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
+<span>  <span class="op">}</span></span>
+<span><span class="op">}</span> <span class="kw">else</span> <span class="op">{</span></span>
+<span>  <span class="va">mmkin_bench</span> <span class="op">&lt;-</span> <span class="kw">function</span><span class="op">(</span><span class="va">models</span>, <span class="va">datasets</span>, <span class="va">error_model</span> <span class="op">=</span> <span class="cn">NULL</span><span class="op">)</span> <span class="op">{</span></span>
+<span>    <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span><span class="va">models</span>, <span class="va">datasets</span>, reweight.method <span class="op">=</span> <span class="va">error_model</span>, cores <span class="op">=</span> <span class="fl">1</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
+<span>  <span class="op">}</span></span>
+<span><span class="op">}</span></span></code></pre></div>
+<div class="section level2">
+<h2 id="test-cases">Test cases<a class="anchor" aria-label="anchor" href="#test-cases"></a>
+</h2>
+<p>Parent only:</p>
 <div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span class="va">SFO_SFO</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>
-  parent <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"m1"</span><span class="op">)</span>,
-  m1 <span class="op">=</span> <span class="fu"><a href="../../reference/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">FOMC_SFO</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>
-  parent <span class="op">=</span> <span class="fu"><a href="../../reference/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">DFOP_SFO</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>
-  parent <span class="op">=</span> <span class="fu"><a href="../../reference/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">t3</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOMC_SFO</span>, <span class="va">DFOP_SFO</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">FOCUS_D</span><span class="op">)</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span>
-<span class="va">t4</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOMC_SFO</span>, <span class="va">DFOP_SFO</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">FOCUS_D</span><span class="op">)</span>,
-    error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span>
-<span class="va">t5</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOMC_SFO</span>, <span class="va">DFOP_SFO</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">FOCUS_D</span><span class="op">)</span>,
-    error_model <span class="op">=</span> <span class="st">"obs"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></code></pre></div>
-<p>Two metabolites, synthetic data:</p>
+<code class="sourceCode R"><span><span class="va">FOCUS_C</span> <span class="op">&lt;-</span> <span class="va">FOCUS_2006_C</span></span>
+<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>
+<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>
+<span></span>
+<span></span>
+<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></span>
+<span><span class="va">t2</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>
+<span>    error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span></code></pre></div>
+<p>One metabolite:</p>
 <div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span class="va">m_synth_SFO_lin</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>parent <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M1"</span><span class="op">)</span>,
-                           M1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M2"</span><span class="op">)</span>,
-                           M2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,
-                           use_of_ff <span class="op">=</span> <span class="st">"max"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>
-
-<span class="va">m_synth_DFOP_par</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>parent <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"DFOP"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="st">"M1"</span>, <span class="st">"M2"</span><span class="op">)</span><span class="op">)</span>,
-                           M1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,
-                           M2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,
-                           use_of_ff <span class="op">=</span> <span class="st">"max"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>
-
-<span class="va">SFO_lin_a</span> <span class="op">&lt;-</span> <span class="va">synthetic_data_for_UBA_2014</span><span class="op">[[</span><span class="fl">1</span><span class="op">]</span><span class="op">]</span><span class="op">$</span><span class="va">data</span>
-
-<span class="va">DFOP_par_c</span> <span class="op">&lt;-</span> <span class="va">synthetic_data_for_UBA_2014</span><span class="op">[[</span><span class="fl">12</span><span class="op">]</span><span class="op">]</span><span class="op">$</span><span class="va">data</span>
-
-<span class="va">t6</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">m_synth_SFO_lin</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">SFO_lin_a</span><span class="op">)</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span>
-<span class="va">t7</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">m_synth_DFOP_par</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">DFOP_par_c</span><span class="op">)</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span>
-
-<span class="va">t8</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">m_synth_SFO_lin</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">SFO_lin_a</span><span class="op">)</span>,
-    error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span>
-<span class="va">t9</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">m_synth_DFOP_par</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">DFOP_par_c</span><span class="op">)</span>,
-    error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span>
-
-<span class="va">t10</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">m_synth_SFO_lin</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">SFO_lin_a</span><span class="op">)</span>,
-    error_model <span class="op">=</span> <span class="st">"obs"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span>
-<span class="va">t11</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">m_synth_DFOP_par</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">DFOP_par_c</span><span class="op">)</span>,
-    error_model <span class="op">=</span> <span class="st">"obs"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></code></pre></div>
+<code class="sourceCode R"><span><span class="va">SFO_SFO</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span>
+<span>  parent <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">"m1"</span><span class="op">)</span>,</span>
+<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>
+<span><span class="va">FOMC_SFO</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span>
+<span>  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>,</span>
+<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>
+<span><span class="va">DFOP_SFO</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span>
+<span>  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>,</span>
+<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>
+<span><span class="va">t3</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/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOMC_SFO</span>, <span class="va">DFOP_SFO</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">FOCUS_D</span><span class="op">)</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span>
+<span><span class="va">t4</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/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOMC_SFO</span>, <span class="va">DFOP_SFO</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">FOCUS_D</span><span class="op">)</span>,</span>
+<span>    error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span>
+<span><span class="va">t5</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/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOMC_SFO</span>, <span class="va">DFOP_SFO</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">FOCUS_D</span><span class="op">)</span>,</span>
+<span>    error_model <span class="op">=</span> <span class="st">"obs"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span></code></pre></div>
+<p>Two metabolites, synthetic data:</p>
 <div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span class="va">mkin_benchmarks</span><span class="op">[</span><span class="va">system_string</span>, <span class="fu"><a href="https://rdrr.io/r/base/paste.html">paste0</a></span><span class="op">(</span><span class="st">"t"</span>, <span class="fl">1</span><span class="op">:</span><span class="fl">11</span><span class="op">)</span><span class="op">]</span> <span class="op">&lt;-</span>
-  <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="va">t1</span>, <span class="va">t2</span>, <span class="va">t3</span>, <span class="va">t4</span>, <span class="va">t5</span>, <span class="va">t6</span>, <span class="va">t7</span>, <span class="va">t8</span>, <span class="va">t9</span>, <span class="va">t10</span>, <span class="va">t11</span><span class="op">)</span>
-<span class="fu"><a href="https://rdrr.io/r/base/save.html">save</a></span><span class="op">(</span><span class="va">mkin_benchmarks</span>, file <span class="op">=</span> <span class="st">"~/git/mkin/vignettes/web_only/mkin_benchmarks.rda"</span><span class="op">)</span></code></pre></div>
+<code class="sourceCode R"><span><span class="va">m_synth_SFO_lin</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>parent <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M1"</span><span class="op">)</span>,</span>
+<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="st">"M2"</span><span class="op">)</span>,</span>
+<span>                           M2 <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>
+<span>                           use_of_ff <span class="op">=</span> <span class="st">"max"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
+<span></span>
+<span><span class="va">m_synth_DFOP_par</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>parent <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"DFOP"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"M1"</span>, <span class="st">"M2"</span><span class="op">)</span><span class="op">)</span>,</span>
+<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>
+<span>                           M2 <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>
+<span>                           use_of_ff <span class="op">=</span> <span class="st">"max"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
+<span></span>
+<span><span class="va">SFO_lin_a</span> <span class="op">&lt;-</span> <span class="va">synthetic_data_for_UBA_2014</span><span class="op">[[</span><span class="fl">1</span><span class="op">]</span><span class="op">]</span><span class="op">$</span><span class="va">data</span></span>
+<span></span>
+<span><span class="va">DFOP_par_c</span> <span class="op">&lt;-</span> <span class="va">synthetic_data_for_UBA_2014</span><span class="op">[[</span><span class="fl">12</span><span class="op">]</span><span class="op">]</span><span class="op">$</span><span class="va">data</span></span>
+<span></span>
+<span><span class="va">t6</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/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">m_synth_SFO_lin</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">SFO_lin_a</span><span class="op">)</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span>
+<span><span class="va">t7</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/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">m_synth_DFOP_par</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">DFOP_par_c</span><span class="op">)</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span>
+<span></span>
+<span><span class="va">t8</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/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">m_synth_SFO_lin</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">SFO_lin_a</span><span class="op">)</span>,</span>
+<span>    error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span>
+<span><span class="va">t9</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/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">m_synth_DFOP_par</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">DFOP_par_c</span><span class="op">)</span>,</span>
+<span>    error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span>
+<span></span>
+<span><span class="va">t10</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/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">m_synth_SFO_lin</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">SFO_lin_a</span><span class="op">)</span>,</span>
+<span>    error_model <span class="op">=</span> <span class="st">"obs"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span>
+<span><span class="va">t11</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/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">m_synth_DFOP_par</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">DFOP_par_c</span><span class="op">)</span>,</span>
+<span>    error_model <span class="op">=</span> <span class="st">"obs"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span></code></pre></div>
 </div>
-<div id="results" class="section level2">
-<h2 class="hasAnchor">
-<a href="#results" class="anchor"></a>Results</h2>
-<p>Currently, we only have benchmark information on one system, therefore only the mkin version is shown with the results below. Timings are in seconds, shorter is better. All results were obtained by serial, i.e. not using multiple computing cores.</p>
-<p>Benchmarks for all available error models are shown.</p>
-<div id="parent-only" class="section level3">
-<h3 class="hasAnchor">
-<a href="#parent-only" class="anchor"></a>Parent only</h3>
+<div class="section level2">
+<h2 id="results">Results<a class="anchor" aria-label="anchor" href="#results"></a>
+</h2>
+<p>Benchmarks for all available error models are shown. They are intended for improving mkin, not for comparing CPUs or operating systems. All trademarks belong to their respective owners.</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">
 <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">OS</th>
+<th align="left">CPU</th>
+<th align="left">R</th>
+<th align="left">mkin</th>
+<th align="right">t1</th>
+<th align="right">t2</th>
 </tr></thead>
 <tbody>
 <tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">NA</td>
 <td align="left">0.9.48.1</td>
 <td align="right">3.610</td>
 <td align="right">11.019</td>
 </tr>
 <tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">NA</td>
 <td align="left">0.9.49.1</td>
 <td align="right">8.184</td>
 <td align="right">22.889</td>
 </tr>
 <tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">NA</td>
 <td align="left">0.9.49.2</td>
 <td align="right">7.064</td>
 <td align="right">12.558</td>
 </tr>
 <tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">NA</td>
 <td align="left">0.9.49.3</td>
 <td align="right">7.296</td>
 <td align="right">21.239</td>
 </tr>
 <tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">NA</td>
 <td align="left">0.9.49.4</td>
 <td align="right">5.936</td>
 <td align="right">20.545</td>
 </tr>
 <tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">NA</td>
 <td align="left">0.9.50.2</td>
 <td align="right">1.714</td>
 <td align="right">3.971</td>
 </tr>
 <tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">NA</td>
 <td align="left">0.9.50.3</td>
 <td align="right">1.752</td>
 <td align="right">4.156</td>
 </tr>
 <tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">NA</td>
 <td align="left">0.9.50.4</td>
 <td align="right">1.786</td>
 <td align="right">3.729</td>
 </tr>
 <tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">NA</td>
 <td align="left">1.0.3</td>
-<td align="right">1.722</td>
-<td align="right">3.419</td>
+<td align="right">1.881</td>
+<td align="right">3.504</td>
 </tr>
 <tr class="even">
-<td align="left">1.0.3.9000</td>
-<td align="right">2.770</td>
-<td align="right">3.458</td>
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">NA</td>
+<td align="left">1.0.4</td>
+<td align="right">1.867</td>
+<td align="right">3.450</td>
+</tr>
+<tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">4.1.3</td>
+<td align="left">1.1.0</td>
+<td align="right">1.791</td>
+<td align="right">3.289</td>
+</tr>
+<tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">4.2.1</td>
+<td align="left">1.1.0</td>
+<td align="right">1.842</td>
+<td align="right">3.453</td>
+</tr>
+<tr class="odd">
+<td align="left">Linux</td>
+<td align="left">i7-4710MQ</td>
+<td align="left">4.2.1</td>
+<td align="left">1.1.0</td>
+<td align="right">1.959</td>
+<td align="right">4.116</td>
+</tr>
+<tr class="even">
+<td align="left">Linux</td>
+<td align="left">i7-4710MQ</td>
+<td align="left">4.1.3</td>
+<td align="left">1.1.0</td>
+<td align="right">1.877</td>
+<td align="right">3.906</td>
+</tr>
+<tr class="odd">
+<td align="left">Linux</td>
+<td align="left">i7-4710MQ</td>
+<td align="left">4.2.1</td>
+<td align="left">1.1.1</td>
+<td align="right">1.644</td>
+<td align="right">3.172</td>
+</tr>
+<tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">4.2.1</td>
+<td align="left">1.1.1</td>
+<td align="right">1.770</td>
+<td align="right">3.377</td>
+</tr>
+<tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">4.2.1</td>
+<td align="left">1.1.2</td>
+<td align="right">1.940</td>
+<td align="right">3.619</td>
 </tr>
 </tbody>
 </table>
 </div>
-<div id="one-metabolite" class="section level3">
-<h3 class="hasAnchor">
-<a href="#one-metabolite" class="anchor"></a>One metabolite</h3>
+<div class="section level3">
+<h3 id="one-metabolite">One metabolite<a class="anchor" aria-label="anchor" href="#one-metabolite"></a>
+</h3>
 <p>Constant variance (t3), two-component error model (t4), and variance by variable (t5) for three models fitted to one dataset, i.e. three fits for each test.</p>
 <table class="table">
 <thead><tr class="header">
-<th align="left">mkin version</th>
-<th align="right">t3 [s]</th>
-<th align="right">t4 [s]</th>
-<th align="right">t5 [s]</th>
+<th align="left">OS</th>
+<th align="left">CPU</th>
+<th align="left">R</th>
+<th align="left">mkin</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">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">NA</td>
 <td align="left">0.9.48.1</td>
 <td align="right">3.764</td>
 <td align="right">14.347</td>
 <td align="right">9.495</td>
 </tr>
 <tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">NA</td>
 <td align="left">0.9.49.1</td>
 <td align="right">4.649</td>
 <td align="right">13.789</td>
 <td align="right">6.395</td>
 </tr>
 <tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">NA</td>
 <td align="left">0.9.49.2</td>
 <td align="right">4.786</td>
 <td align="right">8.461</td>
 <td align="right">5.675</td>
 </tr>
 <tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">NA</td>
 <td align="left">0.9.49.3</td>
 <td align="right">4.510</td>
 <td align="right">13.805</td>
 <td align="right">7.386</td>
 </tr>
 <tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">NA</td>
 <td align="left">0.9.49.4</td>
 <td align="right">4.446</td>
 <td align="right">15.335</td>
 <td align="right">6.002</td>
 </tr>
 <tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">NA</td>
 <td align="left">0.9.50.2</td>
 <td align="right">1.402</td>
 <td align="right">6.174</td>
 <td align="right">2.764</td>
 </tr>
 <tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">NA</td>
 <td align="left">0.9.50.3</td>
 <td align="right">1.430</td>
 <td align="right">6.615</td>
 <td align="right">2.878</td>
 </tr>
 <tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">NA</td>
 <td align="left">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">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">NA</td>
 <td align="left">1.0.3</td>
-<td align="right">1.402</td>
-<td align="right">6.343</td>
-<td align="right">2.802</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">1.0.3.9000</td>
-<td align="right">1.405</td>
-<td align="right">6.417</td>
-<td align="right">2.824</td>
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">NA</td>
+<td align="left">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">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">4.1.3</td>
+<td align="left">1.1.0</td>
+<td align="right">1.310</td>
+<td align="right">6.279</td>
+<td align="right">2.681</td>
+</tr>
+<tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">4.2.1</td>
+<td align="left">1.1.0</td>
+<td align="right">3.802</td>
+<td align="right">21.247</td>
+<td align="right">8.461</td>
+</tr>
+<tr class="odd">
+<td align="left">Linux</td>
+<td align="left">i7-4710MQ</td>
+<td align="left">4.2.1</td>
+<td align="left">1.1.0</td>
+<td align="right">3.334</td>
+<td align="right">19.521</td>
+<td align="right">7.565</td>
+</tr>
+<tr class="even">
+<td align="left">Linux</td>
+<td align="left">i7-4710MQ</td>
+<td align="left">4.1.3</td>
+<td align="left">1.1.0</td>
+<td align="right">1.578</td>
+<td align="right">8.058</td>
+<td align="right">3.339</td>
+</tr>
+<tr class="odd">
+<td align="left">Linux</td>
+<td align="left">i7-4710MQ</td>
+<td align="left">4.2.1</td>
+<td align="left">1.1.1</td>
+<td align="right">1.230</td>
+<td align="right">5.839</td>
+<td align="right">2.444</td>
+</tr>
+<tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">4.2.1</td>
+<td align="left">1.1.1</td>
+<td align="right">1.308</td>
+<td align="right">5.758</td>
+<td align="right">2.558</td>
+</tr>
+<tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">4.2.1</td>
+<td align="left">1.1.2</td>
+<td align="right">1.490</td>
+<td align="right">6.035</td>
+<td align="right">2.799</td>
 </tr>
 </tbody>
 </table>
 </div>
-<div id="two-metabolites" class="section level3">
-<h3 class="hasAnchor">
-<a href="#two-metabolites" class="anchor"></a>Two metabolites</h3>
+<div class="section level3">
+<h3 id="two-metabolites">Two metabolites<a class="anchor" aria-label="anchor" href="#two-metabolites"></a>
+</h3>
 <p>Constant variance (t6 and t7), two-component error model (t8 and t9), and variance by variable (t10 and t11) for one model fitted to one dataset, i.e. one fit for each test.</p>
 <table class="table">
 <thead><tr class="header">
-<th align="left">mkin version</th>
-<th align="right">t6 [s]</th>
-<th align="right">t7 [s]</th>
-<th align="right">t8 [s]</th>
-<th align="right">t9 [s]</th>
-<th align="right">t10 [s]</th>
-<th align="right">t11 [s]</th>
+<th align="left">OS</th>
+<th align="left">CPU</th>
+<th align="left">R</th>
+<th align="left">mkin</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">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">NA</td>
 <td align="left">0.9.48.1</td>
 <td align="right">2.623</td>
 <td align="right">4.587</td>
@@ -341,6 +545,9 @@
 <td align="right">31.267</td>
 </tr>
 <tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">NA</td>
 <td align="left">0.9.49.1</td>
 <td align="right">2.542</td>
 <td align="right">4.128</td>
@@ -350,6 +557,9 @@
 <td align="right">5.636</td>
 </tr>
 <tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">NA</td>
 <td align="left">0.9.49.2</td>
 <td align="right">2.723</td>
 <td align="right">4.478</td>
@@ -359,6 +569,9 @@
 <td align="right">5.574</td>
 </tr>
 <tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">NA</td>
 <td align="left">0.9.49.3</td>
 <td align="right">2.643</td>
 <td align="right">4.374</td>
@@ -368,6 +581,9 @@
 <td align="right">7.365</td>
 </tr>
 <tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">NA</td>
 <td align="left">0.9.49.4</td>
 <td align="right">2.635</td>
 <td align="right">4.259</td>
@@ -377,6 +593,9 @@
 <td align="right">5.626</td>
 </tr>
 <tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">NA</td>
 <td align="left">0.9.50.2</td>
 <td align="right">0.777</td>
 <td align="right">1.236</td>
@@ -386,6 +605,9 @@
 <td align="right">2.987</td>
 </tr>
 <tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">NA</td>
 <td align="left">0.9.50.3</td>
 <td align="right">0.858</td>
 <td align="right">1.264</td>
@@ -395,6 +617,9 @@
 <td align="right">3.073</td>
 </tr>
 <tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">NA</td>
 <td align="left">0.9.50.4</td>
 <td align="right">0.783</td>
 <td align="right">1.282</td>
@@ -404,22 +629,112 @@
 <td align="right">3.105</td>
 </tr>
 <tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">NA</td>
 <td align="left">1.0.3</td>
-<td align="right">0.771</td>
-<td align="right">1.251</td>
-<td align="right">1.464</td>
-<td align="right">3.074</td>
-<td align="right">1.940</td>
-<td align="right">2.831</td>
+<td align="right">0.763</td>
+<td align="right">1.244</td>
+<td align="right">1.457</td>
+<td align="right">3.054</td>
+<td align="right">1.923</td>
+<td align="right">2.839</td>
 </tr>
 <tr class="even">
-<td align="left">1.0.3.9000</td>
-<td align="right">0.772</td>
-<td align="right">1.263</td>
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">NA</td>
+<td align="left">1.0.4</td>
+<td align="right">0.785</td>
+<td align="right">1.252</td>
+<td align="right">1.466</td>
+<td align="right">3.091</td>
+<td align="right">1.936</td>
+<td align="right">2.826</td>
+</tr>
+<tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">4.1.3</td>
+<td align="left">1.1.0</td>
+<td align="right">0.744</td>
+<td align="right">1.227</td>
+<td align="right">1.288</td>
+<td align="right">3.553</td>
+<td align="right">1.895</td>
+<td align="right">2.738</td>
+</tr>
+<tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">4.2.1</td>
+<td align="left">1.1.0</td>
+<td align="right">3.018</td>
+<td align="right">4.165</td>
+<td align="right">5.036</td>
+<td align="right">10.844</td>
+<td align="right">6.623</td>
+<td align="right">9.722</td>
+</tr>
+<tr class="odd">
+<td align="left">Linux</td>
+<td align="left">i7-4710MQ</td>
+<td align="left">4.2.1</td>
+<td align="left">1.1.0</td>
+<td align="right">2.522</td>
+<td align="right">3.792</td>
+<td align="right">4.143</td>
+<td align="right">11.268</td>
+<td align="right">5.935</td>
+<td align="right">8.728</td>
+</tr>
+<tr class="even">
+<td align="left">Linux</td>
+<td align="left">i7-4710MQ</td>
+<td align="left">4.1.3</td>
+<td align="left">1.1.0</td>
+<td align="right">0.907</td>
+<td align="right">1.535</td>
+<td align="right">1.589</td>
+<td align="right">4.544</td>
+<td align="right">2.302</td>
+<td align="right">3.463</td>
+</tr>
+<tr class="odd">
+<td align="left">Linux</td>
+<td align="left">i7-4710MQ</td>
+<td align="left">4.2.1</td>
+<td align="left">1.1.1</td>
+<td align="right">0.678</td>
+<td align="right">1.095</td>
+<td align="right">1.149</td>
+<td align="right">3.247</td>
+<td align="right">1.658</td>
+<td align="right">2.472</td>
+</tr>
+<tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">4.2.1</td>
+<td align="left">1.1.1</td>
+<td align="right">0.696</td>
+<td align="right">1.124</td>
+<td align="right">1.321</td>
+<td align="right">2.786</td>
+<td align="right">1.744</td>
+<td align="right">2.566</td>
+</tr>
+<tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">4.2.1</td>
+<td align="left">1.1.2</td>
+<td align="right">0.857</td>
+<td align="right">1.295</td>
 <td align="right">1.483</td>
-<td align="right">3.101</td>
-<td align="right">1.958</td>
-<td align="right">2.843</td>
+<td align="right">2.989</td>
+<td align="right">1.919</td>
+<td align="right">2.766</td>
 </tr>
 </tbody>
 </table>
@@ -438,11 +753,13 @@
 
 
       <footer><div class="copyright">
-  <p>Developed by Johannes Ranke.</p>
+  <p></p>
+<p>Developed by Johannes Ranke.</p>
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
+  <p></p>
+<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer>
@@ -451,5 +768,7 @@
   
 
 
+  
+
   </body>
 </html>
diff --git a/docs/dev/articles/web_only/dimethenamid_2018.html b/docs/dev/articles/web_only/dimethenamid_2018.html
index 6b5c8c4e..81b15cb9 100644
--- a/docs/dev/articles/web_only/dimethenamid_2018.html
+++ b/docs/dev/articles/web_only/dimethenamid_2018.html
@@ -34,7 +34,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../../index.html">mkin</a>
-        <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">1.1.0</span>
+        <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">1.1.2</span>
       </span>
     </div>
 
@@ -44,7 +44,7 @@
   <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>
@@ -60,6 +60,9 @@
       <a href="../../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a>
     </li>
     <li>
+      <a href="../../articles/web_only/dimethenamid_2018.html">Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models</a>
+    </li>
+    <li>
       <a href="../../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a>
     </li>
     <li>
@@ -103,7 +106,7 @@
       <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 10 February 2022, built on 28 Feb 2022</h4>
+            <h4 data-toc-skip class="date">Last change 1 July 2022, built on 10 Aug 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>
@@ -116,8 +119,8 @@
 <div class="section level2">
 <h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#introduction"></a>
 </h2>
-<p>During the preparation of the journal article on nonlinear mixed-effects models in degradation kinetics <span class="citation">(Ranke et al. 2021)</span> and the analysis of the dimethenamid degradation data analysed therein, a need for a more detailed analysis using not only nlme and saemix, but also nlmixr for fitting the mixed-effects models was identified, as many model variants do not converge when fitted with nlme, and not all relevant error models can be fitted with saemix.</p>
-<p>This vignette is an attempt to satisfy this need.</p>
+<p>A first analysis of the data analysed here was presented in a recent journal article on nonlinear mixed-effects models in degradation kinetics <span class="citation">(Ranke et al. 2021)</span>. That analysis was based on the <code>nlme</code> package and a development version of the <code>saemix</code> package that was unpublished at the time. Meanwhile, version 3.0 of the <code>saemix</code> package is available from the CRAN repository. Also, it turned out that there was an error in the handling of the Borstel data in the mkin package at the time, leading to the duplication of a few data points from that soil. The dataset in the mkin package has been corrected, and the interface to <code>saemix</code> in the mkin package has been updated to use the released version.</p>
+<p>This vignette is intended to present an up to date analysis of the data, using the corrected dataset and released versions of <code>mkin</code> and <code>saemix</code>.</p>
 </div>
 <div class="section level2">
 <h2 id="data">Data<a class="anchor" aria-label="anchor" href="#data"></a>
@@ -126,17 +129,17 @@
 <p>The data are <a href="https://pkgdown.jrwb.de/mkin/reference/dimethenamid_2018.html">available in the mkin package</a>. The following code (hidden by default, please use the button to the right to show it) treats the data available for the racemic mixture dimethenamid (DMTA) and its enantiomer dimethenamid-P (DMTAP) in the same way, as no difference between their degradation behaviour was identified in the EU risk assessment. The observation times of each dataset are multiplied with the corresponding normalisation factor also available in the dataset, in order to make it possible to describe all datasets with a single set of parameters.</p>
 <p>Also, datasets observed in the same soil are merged, resulting in dimethenamid (DMTA) data from six soils.</p>
 <div class="sourceCode" id="cb1"><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"><a href="https://pkgdown.jrwb.de/mkin/">mkin</a></span>, quietly <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>
-<span class="va">dmta_ds</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">lapply</a></span><span class="op">(</span><span class="fl">1</span><span class="op">:</span><span class="fl">7</span>, <span class="kw">function</span><span class="op">(</span><span class="va">i</span><span class="op">)</span> <span class="op">{</span>
-  <span class="va">ds_i</span> <span class="op">&lt;-</span> <span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">ds</span><span class="op">[[</span><span class="va">i</span><span class="op">]</span><span class="op">]</span><span class="op">$</span><span class="va">data</span>
-  <span class="va">ds_i</span><span class="op">[</span><span class="va">ds_i</span><span class="op">$</span><span class="va">name</span> <span class="op">==</span> <span class="st">"DMTAP"</span>, <span class="st">"name"</span><span class="op">]</span> <span class="op">&lt;-</span>  <span class="st">"DMTA"</span>
-  <span class="va">ds_i</span><span class="op">$</span><span class="va">time</span> <span class="op">&lt;-</span> <span class="va">ds_i</span><span class="op">$</span><span class="va">time</span> <span class="op">*</span> <span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">f_time_norm</span><span class="op">[</span><span class="va">i</span><span class="op">]</span>
-  <span class="va">ds_i</span>
-<span class="op">}</span><span class="op">)</span>
-<span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">)</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</span><span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">ds</span>, <span class="kw">function</span><span class="op">(</span><span class="va">ds</span><span class="op">)</span> <span class="va">ds</span><span class="op">$</span><span class="va">title</span><span class="op">)</span>
-<span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot"</span><span class="op">]</span><span class="op">]</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/cbind.html" class="external-link">rbind</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 1"</span><span class="op">]</span><span class="op">]</span>, <span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 2"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span>
-<span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 1"</span><span class="op">]</span><span class="op">]</span> <span class="op">&lt;-</span> <span class="cn">NULL</span>
-<span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 2"</span><span class="op">]</span><span class="op">]</span> <span class="op">&lt;-</span> <span class="cn">NULL</span></code></pre></div>
+<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://pkgdown.jrwb.de/mkin/">mkin</a></span>, quietly <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
+<span><span class="va">dmta_ds</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">lapply</a></span><span class="op">(</span><span class="fl">1</span><span class="op">:</span><span class="fl">7</span>, <span class="kw">function</span><span class="op">(</span><span class="va">i</span><span class="op">)</span> <span class="op">{</span></span>
+<span>  <span class="va">ds_i</span> <span class="op">&lt;-</span> <span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">ds</span><span class="op">[[</span><span class="va">i</span><span class="op">]</span><span class="op">]</span><span class="op">$</span><span class="va">data</span></span>
+<span>  <span class="va">ds_i</span><span class="op">[</span><span class="va">ds_i</span><span class="op">$</span><span class="va">name</span> <span class="op">==</span> <span class="st">"DMTAP"</span>, <span class="st">"name"</span><span class="op">]</span> <span class="op">&lt;-</span>  <span class="st">"DMTA"</span></span>
+<span>  <span class="va">ds_i</span><span class="op">$</span><span class="va">time</span> <span class="op">&lt;-</span> <span class="va">ds_i</span><span class="op">$</span><span class="va">time</span> <span class="op">*</span> <span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">f_time_norm</span><span class="op">[</span><span class="va">i</span><span class="op">]</span></span>
+<span>  <span class="va">ds_i</span></span>
+<span><span class="op">}</span><span class="op">)</span></span>
+<span><span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">)</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</span><span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">ds</span>, <span class="kw">function</span><span class="op">(</span><span class="va">ds</span><span class="op">)</span> <span class="va">ds</span><span class="op">$</span><span class="va">title</span><span class="op">)</span></span>
+<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot"</span><span class="op">]</span><span class="op">]</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/cbind.html" class="external-link">rbind</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 1"</span><span class="op">]</span><span class="op">]</span>, <span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 2"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span>
+<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 1"</span><span class="op">]</span><span class="op">]</span> <span class="op">&lt;-</span> <span class="cn">NULL</span></span>
+<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 2"</span><span class="op">]</span><span class="op">]</span> <span class="op">&lt;-</span> <span class="cn">NULL</span></span></code></pre></div>
 </div>
 <div class="section level2">
 <h2 id="parent-degradation">Parent degradation<a class="anchor" aria-label="anchor" href="#parent-degradation"></a>
@@ -147,30 +150,30 @@
 </h3>
 <p>As a first step, to get a visual impression of the fit of the different models, we do separate evaluations for each soil using the mmkin function from the mkin package:</p>
 <div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span class="va">f_parent_mkin_const</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">"DFOP"</span><span class="op">)</span>, <span class="va">dmta_ds</span>,
-  error_model <span class="op">=</span> <span class="st">"const"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>
-<span class="va">f_parent_mkin_tc</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">"DFOP"</span><span class="op">)</span>, <span class="va">dmta_ds</span>,
-  error_model <span class="op">=</span> <span class="st">"tc"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></code></pre></div>
+<code class="sourceCode R"><span><span class="va">f_parent_mkin_const</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">"DFOP"</span><span class="op">)</span>, <span class="va">dmta_ds</span>,</span>
+<span>  error_model <span class="op">=</span> <span class="st">"const"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
+<span><span class="va">f_parent_mkin_tc</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">"DFOP"</span><span class="op">)</span>, <span class="va">dmta_ds</span>,</span>
+<span>  error_model <span class="op">=</span> <span class="st">"tc"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
 <p>The plot of the individual SFO fits shown below suggests that at least in some datasets the degradation slows down towards later time points, and that the scatter of the residuals error is smaller for smaller values (panel to the right):</p>
 <div class="sourceCode" id="cb3"><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="fu"><a href="../../reference/mixed.html">mixed</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><span class="op">)</span><span class="op">)</span></code></pre></div>
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="fu"><a href="../../reference/mixed.html">mixed</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><span class="op">)</span><span class="op">)</span></span></code></pre></div>
 <p><img src="dimethenamid_2018_files/figure-html/f_parent_mkin_sfo_const-1.png" width="700"></p>
 <p>Using biexponential decline (DFOP) results in a slightly more random scatter of the residuals:</p>
 <div class="sourceCode" id="cb4"><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="fu"><a href="../../reference/mixed.html">mixed</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><span class="op">)</span><span class="op">)</span></code></pre></div>
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="fu"><a href="../../reference/mixed.html">mixed</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><span class="op">)</span><span class="op">)</span></span></code></pre></div>
 <p><img src="dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const-1.png" width="700"></p>
 <p>The population curve (bold line) in the above plot results from taking the mean of the individual transformed parameters, i.e. of log k1 and log k2, as well as of the logit of the g parameter of the DFOP model). Here, this procedure does not result in parameters that represent the degradation well, because in some datasets the fitted value for k2 is extremely close to zero, leading to a log k2 value that dominates the average. This is alleviated if only rate constants that pass the t-test for significant difference from zero (on the untransformed scale) are considered in the averaging:</p>
 <div class="sourceCode" id="cb5"><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="fu"><a href="../../reference/mixed.html">mixed</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><span class="op">)</span>, test_log_parms <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></code></pre></div>
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="fu"><a href="../../reference/mixed.html">mixed</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><span class="op">)</span>, test_log_parms <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
 <p><img src="dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const_test-1.png" width="700"></p>
 <p>While this is visually much more satisfactory, such an average procedure could introduce a bias, as not all results from the individual fits enter the population curve with the same weight. This is where nonlinear mixed-effects models can help out by treating all datasets with equally by fitting a parameter distribution model together with the degradation model and the error model (see below).</p>
 <p>The remaining trend of the residuals to be higher for higher predicted residues is reduced by using the two-component error model:</p>
 <div class="sourceCode" id="cb6"><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="fu"><a href="../../reference/mixed.html">mixed</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>, test_log_parms <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></code></pre></div>
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="fu"><a href="../../reference/mixed.html">mixed</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>, test_log_parms <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
 <p><img src="dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_tc_test-1.png" width="700"></p>
 <p>However, note that in the case of using this error model, the fits to the Flaach and BBA 2.3 datasets appear to be ill-defined, indicated by the fact that they did not converge:</p>
 <div class="sourceCode" id="cb7"><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_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span><span class="op">)</span></code></pre></div>
+<code class="sourceCode R"><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">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span><span class="op">)</span></span></code></pre></div>
 <pre><code>&lt;mmkin&gt; object
 Status of individual fits:
 
@@ -178,9 +181,9 @@ Status of individual fits:
 model  Calke Borstel Flaach BBA 2.2 BBA 2.3 Elliot
   DFOP OK    OK      C      OK      C       OK    
 
-OK: No warnings
 C: Optimisation did not converge:
-iteration limit reached without convergence (10)</code></pre>
+iteration limit reached without convergence (10)
+OK: No warnings</code></pre>
 </div>
 <div class="section level3">
 <h3 id="nonlinear-mixed-effects-models">Nonlinear mixed-effects models<a class="anchor" aria-label="anchor" href="#nonlinear-mixed-effects-models"></a>
@@ -191,92 +194,146 @@ iteration limit reached without convergence (10)</code></pre>
 </h4>
 <p>The nlme package was the first R extension providing facilities to fit nonlinear mixed-effects models. We would like to do model selection from all four combinations of degradation models and error models based on the AIC. However, fitting the DFOP model with constant variance and using default control parameters results in an error, signalling that the maximum number of 50 iterations was reached, potentially indicating overparameterisation. Nevertheless, the algorithm converges when the two-component error model is used in combination with the DFOP model. This can be explained by the fact that the smaller residues observed at later sampling times get more weight when using the two-component error model which will counteract the tendency of the algorithm to try parameter combinations unsuitable for fitting these data.</p>
 <div class="sourceCode" id="cb9"><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"><a href="https://svn.r-project.org/R-packages/trunk/nlme/" class="external-link">nlme</a></span><span class="op">)</span>
-<span class="va">f_parent_nlme_sfo_const</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlme/man/nlme.html" class="external-link">nlme</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><span class="op">)</span>
-<span class="co"># f_parent_nlme_dfop_const &lt;- nlme(f_parent_mkin_const["DFOP", ])</span>
-<span class="va">f_parent_nlme_sfo_tc</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlme/man/nlme.html" class="external-link">nlme</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><span class="op">)</span>
-<span class="va">f_parent_nlme_dfop_tc</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlme/man/nlme.html" class="external-link">nlme</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></code></pre></div>
+<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://svn.r-project.org/R-packages/trunk/nlme/" class="external-link">nlme</a></span><span class="op">)</span></span>
+<span><span class="va">f_parent_nlme_sfo_const</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlme/man/nlme.html" class="external-link">nlme</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><span class="op">)</span></span>
+<span><span class="co"># f_parent_nlme_dfop_const &lt;- nlme(f_parent_mkin_const["DFOP", ])</span></span>
+<span><span class="va">f_parent_nlme_sfo_tc</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlme/man/nlme.html" class="external-link">nlme</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><span class="op">)</span></span>
+<span><span class="va">f_parent_nlme_dfop_tc</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlme/man/nlme.html" class="external-link">nlme</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></code></pre></div>
 <p>Note that a certain degree of overparameterisation is also indicated by a warning obtained when fitting DFOP with the two-component error model (‘false convergence’ in the ‘LME step’ in iteration 3). However, as this warning does not occur in later iterations, and specifically not in the last of the 6 iterations, we can ignore this warning.</p>
 <p>The model comparison function of the nlme package can directly be applied to these fits showing a much lower AIC for the DFOP model fitted with the two-component error model. Also, the likelihood ratio test indicates that this difference is significant as the p-value is below 0.0001.</p>
 <div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span>
-  <span class="va">f_parent_nlme_sfo_const</span>, <span class="va">f_parent_nlme_sfo_tc</span>, <span class="va">f_parent_nlme_dfop_tc</span>
-<span class="op">)</span></code></pre></div>
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span></span>
+<span>  <span class="va">f_parent_nlme_sfo_const</span>, <span class="va">f_parent_nlme_sfo_tc</span>, <span class="va">f_parent_nlme_dfop_tc</span></span>
+<span><span class="op">)</span></span></code></pre></div>
 <pre><code>                        Model df    AIC    BIC  logLik   Test L.Ratio p-value
 f_parent_nlme_sfo_const     1  5 796.60 811.82 -393.30                       
 f_parent_nlme_sfo_tc        2  6 798.60 816.86 -393.30 1 vs 2    0.00   0.998
 f_parent_nlme_dfop_tc       3 10 671.91 702.34 -325.96 2 vs 3  134.69  &lt;.0001</code></pre>
 <p>In addition to these fits, attempts were also made to include correlations between random effects by using the log Cholesky parameterisation of the matrix specifying them. The code used for these attempts can be made visible below.</p>
 <div class="sourceCode" id="cb12"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span class="va">f_parent_nlme_sfo_const_logchol</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlme/man/nlme.html" class="external-link">nlme</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>,
-  random <span class="op">=</span> <span class="fu">nlme</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/nlme/man/pdLogChol.html" class="external-link">pdLogChol</a></span><span class="op">(</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">DMTA_0</span> <span class="op">~</span> <span class="fl">1</span>, <span class="va">log_k_DMTA</span> <span class="op">~</span> <span class="fl">1</span><span class="op">)</span><span class="op">)</span><span class="op">)</span>
-<span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_parent_nlme_sfo_const</span>, <span class="va">f_parent_nlme_sfo_const_logchol</span><span class="op">)</span>
-<span class="va">f_parent_nlme_sfo_tc_logchol</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlme/man/nlme.html" class="external-link">nlme</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>,
-  random <span class="op">=</span> <span class="fu">nlme</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/nlme/man/pdLogChol.html" class="external-link">pdLogChol</a></span><span class="op">(</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">DMTA_0</span> <span class="op">~</span> <span class="fl">1</span>, <span class="va">log_k_DMTA</span> <span class="op">~</span> <span class="fl">1</span><span class="op">)</span><span class="op">)</span><span class="op">)</span>
-<span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_parent_nlme_sfo_tc</span>, <span class="va">f_parent_nlme_sfo_tc_logchol</span><span class="op">)</span>
-<span class="va">f_parent_nlme_dfop_tc_logchol</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlme/man/nlme.html" class="external-link">nlme</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>,
-  random <span class="op">=</span> <span class="fu">nlme</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/nlme/man/pdLogChol.html" class="external-link">pdLogChol</a></span><span class="op">(</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">DMTA_0</span> <span class="op">~</span> <span class="fl">1</span>, <span class="va">log_k1</span> <span class="op">~</span> <span class="fl">1</span>, <span class="va">log_k2</span> <span class="op">~</span> <span class="fl">1</span>, <span class="va">g_qlogis</span> <span class="op">~</span> <span class="fl">1</span><span class="op">)</span><span class="op">)</span><span class="op">)</span>
-<span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_parent_nlme_dfop_tc</span>, <span class="va">f_parent_nlme_dfop_tc_logchol</span><span class="op">)</span></code></pre></div>
+<code class="sourceCode R"><span><span class="va">f_parent_nlme_sfo_const_logchol</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlme/man/nlme.html" class="external-link">nlme</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>,</span>
+<span>  random <span class="op">=</span> <span class="fu">nlme</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/nlme/man/pdLogChol.html" class="external-link">pdLogChol</a></span><span class="op">(</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">DMTA_0</span> <span class="op">~</span> <span class="fl">1</span>, <span class="va">log_k_DMTA</span> <span class="op">~</span> <span class="fl">1</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span>
+<span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_parent_nlme_sfo_const</span>, <span class="va">f_parent_nlme_sfo_const_logchol</span><span class="op">)</span></span>
+<span><span class="va">f_parent_nlme_sfo_tc_logchol</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlme/man/nlme.html" class="external-link">nlme</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>,</span>
+<span>  random <span class="op">=</span> <span class="fu">nlme</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/nlme/man/pdLogChol.html" class="external-link">pdLogChol</a></span><span class="op">(</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">DMTA_0</span> <span class="op">~</span> <span class="fl">1</span>, <span class="va">log_k_DMTA</span> <span class="op">~</span> <span class="fl">1</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span>
+<span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_parent_nlme_sfo_tc</span>, <span class="va">f_parent_nlme_sfo_tc_logchol</span><span class="op">)</span></span>
+<span><span class="va">f_parent_nlme_dfop_tc_logchol</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlme/man/nlme.html" class="external-link">nlme</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>,</span>
+<span>  random <span class="op">=</span> <span class="fu">nlme</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/nlme/man/pdLogChol.html" class="external-link">pdLogChol</a></span><span class="op">(</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">DMTA_0</span> <span class="op">~</span> <span class="fl">1</span>, <span class="va">log_k1</span> <span class="op">~</span> <span class="fl">1</span>, <span class="va">log_k2</span> <span class="op">~</span> <span class="fl">1</span>, <span class="va">g_qlogis</span> <span class="op">~</span> <span class="fl">1</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span>
+<span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_parent_nlme_dfop_tc</span>, <span class="va">f_parent_nlme_dfop_tc_logchol</span><span class="op">)</span></span></code></pre></div>
 <p>While the SFO variants converge fast, the additional parameters introduced by this lead to convergence warnings for the DFOP model. The model comparison clearly show that adding correlations between random effects does not improve the fits.</p>
 <p>The selected model (DFOP with two-component error) fitted to the data assuming no correlations between random effects is shown below.</p>
 <div class="sourceCode" id="cb13"><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_nlme_dfop_tc</span><span class="op">)</span></code></pre></div>
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_parent_nlme_dfop_tc</span><span class="op">)</span></span></code></pre></div>
 <p><img src="dimethenamid_2018_files/figure-html/plot_parent_nlme-1.png" width="700"></p>
 </div>
 <div class="section level4">
 <h4 id="saemix">saemix<a class="anchor" aria-label="anchor" href="#saemix"></a>
 </h4>
 <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. As we will compare the SAEM implementation of saemix to the results obtained using the nlmixr package later, we define control settings that work well for all the parent data fits shown in this vignette.</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>,
-    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>
+<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">saemix</span><span class="op">)</span></span>
+<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>,</span>
+<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>
+<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>,</span>
+<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>
+<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>,</span>
+<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></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">
-<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">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></code></pre></div>
+<code class="sourceCode R"><span><span class="va">f_parent_saemix_sfo_const</span> <span class="op">&lt;-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span>
+<span>  control <span class="op">=</span> <span class="va">saemix_control</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span></span>
+<span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_parent_saemix_sfo_const</span><span class="op">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></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 default number of iterations is sufficient to reach convergence. This can also be said for the SFO fit using the two-component error model.</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">
-<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">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></code></pre></div>
+<code class="sourceCode R"><span><span class="va">f_parent_saemix_sfo_tc</span> <span class="op">&lt;-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span>
+<span>  control <span class="op">=</span> <span class="va">saemix_control</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span></span>
+<span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_parent_saemix_sfo_tc</span><span class="op">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></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">
-<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">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></code></pre></div>
+<code class="sourceCode R"><span><span class="va">f_parent_saemix_dfop_const</span> <span class="op">&lt;-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span>
+<span>  control <span class="op">=</span> <span class="va">saemix_control</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span></span>
+<span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_const</span><span class="op">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></span></code></pre></div>
 <p><img src="dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_const-1.png" width="700"></p>
-<p>This is improved when the DFOP model is fitted with the two-component error model. Convergence of the variance of k2 is enhanced, it remains more or less stable already after 200 iterations of the first phase.</p>
 <div class="sourceCode" id="cb18"><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>
+<code class="sourceCode R"><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">f_parent_saemix_dfop_const</span><span class="op">)</span></span></code></pre></div>
+<pre><code>Kinetic nonlinear mixed-effects model fit by SAEM
+Structural model:
+d_DMTA/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+           time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+           * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Likelihood computed by importance sampling
+  AIC BIC logLik
+  706 704   -344
+
+Fitted parameters:
+          estimate    lower   upper
+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
+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>
+<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">
+<code class="sourceCode R"><span><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>,</span>
+<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>
+<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>,</span>
+<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>
+<span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">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></span></code></pre></div>
 <p><img src="dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc-1.png" width="700"></p>
-<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. This 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>
+<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><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">f_parent_saemix_dfop_tc</span><span class="op">)</span></span></code></pre></div>
+<pre><code>Kinetic nonlinear mixed-effects model fit by SAEM
+Structural model:
+d_DMTA/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+           time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+           * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Likelihood computed by importance sampling
+  AIC BIC logLik
+  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>
+<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="cb19"><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>,
-  <span class="va">f_parent_saemix_dfop_const</span><span class="op">$</span><span class="va">so</span>,
-  <span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span>,
-  <span class="va">f_parent_saemix_dfop_tc_moreiter</span><span class="op">$</span><span class="va">so</span><span class="op">)</span></code></pre></div>
+<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">AIC_parent_saemix</span> <span class="op">&lt;-</span> <span class="fu">saemix</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/compare.saemix.html" class="external-link">compare.saemix</a></span><span class="op">(</span></span>
+<span>  <span class="va">f_parent_saemix_sfo_const</span><span class="op">$</span><span class="va">so</span>,</span>
+<span>  <span class="va">f_parent_saemix_sfo_tc</span><span class="op">$</span><span class="va">so</span>,</span>
+<span>  <span class="va">f_parent_saemix_dfop_const</span><span class="op">$</span><span class="va">so</span>,</span>
+<span>  <span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span>,</span>
+<span>  <span class="va">f_parent_saemix_dfop_tc_moreiter</span><span class="op">$</span><span class="va">so</span><span class="op">)</span></span></code></pre></div>
 <pre><code>Likelihoods calculated by importance sampling</code></pre>
-<div class="sourceCode" id="cb21"><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>
+<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><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>
+<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>
+<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></span></code></pre></div>
 <pre><code>                           AIC    BIC
 SFO const               796.38 795.34
 SFO tc                  798.38 797.13
@@ -284,149 +341,57 @@ DFOP const              705.75 703.88
 DFOP tc                 665.65 663.57
 DFOP tc more iterations 665.88 663.80</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="cb23"><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>
-  is <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/AIC.html" class="external-link">AIC</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span>, method <span class="op">=</span> <span class="st">"is"</span><span class="op">)</span>,
-  gq <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/AIC.html" class="external-link">AIC</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span>, method <span class="op">=</span> <span class="st">"gq"</span><span class="op">)</span>,
-  lin <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/AIC.html" class="external-link">AIC</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span>, method <span class="op">=</span> <span class="st">"lin"</span><span class="op">)</span>
-<span class="op">)</span>
-<span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">AIC_parent_saemix_methods</span><span class="op">)</span></code></pre></div>
+<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span> <span class="op">&lt;-</span></span>
+<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">$</span><span class="va">so</span><span class="op">)</span></span>
+<span><span class="va">AIC_parent_saemix_methods</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span></span>
+<span>  is <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/AIC.html" class="external-link">AIC</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span>, method <span class="op">=</span> <span class="st">"is"</span><span class="op">)</span>,</span>
+<span>  gq <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/AIC.html" class="external-link">AIC</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span>, method <span class="op">=</span> <span class="st">"gq"</span><span class="op">)</span>,</span>
+<span>  lin <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/AIC.html" class="external-link">AIC</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span>, method <span class="op">=</span> <span class="st">"lin"</span><span class="op">)</span></span>
+<span><span class="op">)</span></span>
+<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></span></code></pre></div>
 <pre><code>    is     gq    lin 
 665.65 665.68 665.11 </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="cb25"><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>
-<span class="va">AIC_parent_saemix_methods_defaults</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>
-  is <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/AIC.html" class="external-link">AIC</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc_defaults</span><span class="op">$</span><span class="va">so</span>, method <span class="op">=</span> <span class="st">"is"</span><span class="op">)</span>,
-  gq <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/AIC.html" class="external-link">AIC</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc_defaults</span><span class="op">$</span><span class="va">so</span>, method <span class="op">=</span> <span class="st">"gq"</span><span class="op">)</span>,
-  lin <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/AIC.html" class="external-link">AIC</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc_defaults</span><span class="op">$</span><span class="va">so</span>, method <span class="op">=</span> <span class="st">"lin"</span><span class="op">)</span>
-<span class="op">)</span>
-<span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">AIC_parent_saemix_methods_defaults</span><span class="op">)</span></code></pre></div>
+<p>The AIC values based on importance sampling and Gaussian quadrature are very similar. Using linearisation is known to be less accurate, but still gives a similar value.</p>
+<p>In order to illustrate that the comparison of the three method depends on the degree of convergence obtained in the fit, the same comparison is shown below for the fit using the defaults for the number of iterations and the number of MCMC chains.</p>
+<p>When using OpenBlas for linear algebra, there is a large difference in the values obtained with Gaussian quadrature, so the larger number of iterations makes a lot of difference. When using the LAPACK version coming with Debian Bullseye, the AIC based on Gaussian quadrature is almost the same as the one obtained with the other methods, also when using defaults for the fit.</p>
+<div class="sourceCode" id="cb29"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">f_parent_saemix_dfop_tc_defaults</span> <span class="op">&lt;-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span><span class="op">)</span></span>
+<span><span class="va">f_parent_saemix_dfop_tc_defaults</span><span class="op">$</span><span class="va">so</span> <span class="op">&lt;-</span></span>
+<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">$</span><span class="va">so</span><span class="op">)</span></span>
+<span><span class="va">AIC_parent_saemix_methods_defaults</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span></span>
+<span>  is <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/AIC.html" class="external-link">AIC</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc_defaults</span><span class="op">$</span><span class="va">so</span>, method <span class="op">=</span> <span class="st">"is"</span><span class="op">)</span>,</span>
+<span>  gq <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/AIC.html" class="external-link">AIC</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc_defaults</span><span class="op">$</span><span class="va">so</span>, method <span class="op">=</span> <span class="st">"gq"</span><span class="op">)</span>,</span>
+<span>  lin <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/AIC.html" class="external-link">AIC</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc_defaults</span><span class="op">$</span><span class="va">so</span>, method <span class="op">=</span> <span class="st">"lin"</span><span class="op">)</span></span>
+<span><span class="op">)</span></span>
+<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></span></code></pre></div>
 <pre><code>    is     gq    lin 
 668.27 718.36 666.49 </code></pre>
 </div>
-<div class="section level4">
-<h4 id="nlmixr">nlmixr<a class="anchor" aria-label="anchor" href="#nlmixr"></a>
-</h4>
-<p>In the last years, a lot of effort has been put into the nlmixr package which is designed for pharmacokinetics, where nonlinear mixed-effects models are routinely used, but which can also be used for related data like chemical degradation data. A current development branch of the mkin package provides an interface between mkin and nlmixr. Here, we check if we get equivalent results when using a refined version of the First Order Conditional Estimation (FOCE) algorithm used in nlme, namely the First Order Conditional Estimation with Interaction (FOCEI), and the SAEM algorithm as implemented in nlmixr.</p>
-<p>First, the focei algorithm is used for the four model combinations.</p>
-<div class="sourceCode" id="cb27"><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"><a href="https://github.com/nlmixrdevelopment/nlmixr" class="external-link">nlmixr</a></span><span class="op">)</span>
-<span class="va">f_parent_nlmixr_focei_sfo_const</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/nlmixr.html" class="external-link">nlmixr</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>, est <span class="op">=</span> <span class="st">"focei"</span><span class="op">)</span>
-<span class="va">f_parent_nlmixr_focei_sfo_tc</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/nlmixr.html" class="external-link">nlmixr</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>, est <span class="op">=</span> <span class="st">"focei"</span><span class="op">)</span>
-<span class="va">f_parent_nlmixr_focei_dfop_const</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/nlmixr.html" class="external-link">nlmixr</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>, est <span class="op">=</span> <span class="st">"focei"</span><span class="op">)</span>
-<span class="va">f_parent_nlmixr_focei_dfop_tc</span><span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/nlmixr.html" class="external-link">nlmixr</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>, est <span class="op">=</span> <span class="st">"focei"</span><span class="op">)</span></code></pre></div>
-<p>For the SFO model with constant variance, the AIC values are the same, for the DFOP model, there are significant differences between the AIC values. These may be caused by different solutions that are found, but also by the fact that the AIC values for the nlmixr fits are calculated based on Gaussian quadrature, not on linearisation.</p>
-<div class="sourceCode" id="cb28"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span class="va">aic_nlmixr_focei</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</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">f_parent_nlmixr_focei_sfo_const</span><span class="op">$</span><span class="va">nm</span>, <span class="va">f_parent_nlmixr_focei_sfo_tc</span><span class="op">$</span><span class="va">nm</span>,
-    <span class="va">f_parent_nlmixr_focei_dfop_const</span><span class="op">$</span><span class="va">nm</span>, <span class="va">f_parent_nlmixr_focei_dfop_tc</span><span class="op">$</span><span class="va">nm</span><span class="op">)</span>,
-  <span class="va">AIC</span><span class="op">)</span>
-<span class="va">aic_nlme</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</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">f_parent_nlme_sfo_const</span>, <span class="cn">NA</span>, <span class="va">f_parent_nlme_sfo_tc</span>, <span class="va">f_parent_nlme_dfop_tc</span><span class="op">)</span>,
-  <span class="kw">function</span><span class="op">(</span><span class="va">x</span><span class="op">)</span> <span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/NA.html" class="external-link">is.na</a></span><span class="op">(</span><span class="va">x</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span><span class="op">)</span><span class="op">)</span> <span class="cn">NA</span> <span class="kw">else</span> <span class="fu"><a href="https://rdrr.io/r/stats/AIC.html" class="external-link">AIC</a></span><span class="op">(</span><span class="va">x</span><span class="op">)</span><span class="op">)</span>
-<span class="va">aic_nlme_nlmixr_focei</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>
-  <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>,
-  <span class="st">"Error model"</span> <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="st">"constant variance"</span>, <span class="st">"two-component"</span><span class="op">)</span>, <span class="fl">2</span><span class="op">)</span>,
-  <span class="st">"AIC (nlme)"</span> <span class="op">=</span> <span class="va">aic_nlme</span>,
-  <span class="st">"AIC (nlmixr with FOCEI)"</span> <span class="op">=</span> <span class="va">aic_nlmixr_focei</span>,
-  check.names <span class="op">=</span> <span class="cn">FALSE</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_nlme_nlmixr_focei</span><span class="op">)</span></code></pre></div>
-<pre><code>  Degradation model       Error model AIC (nlme) AIC (nlmixr with FOCEI)
-1               SFO constant variance     796.60                  796.60
-2               SFO     two-component         NA                  798.64
-3              DFOP constant variance     798.60                  745.87
-4              DFOP     two-component     671.91                  740.42</code></pre>
-<p>Secondly, we use the SAEM estimation routine and check the convergence plots. The control parameters, which were also used for the saemix fits, are defined beforehand.</p>
-<div class="sourceCode" id="cb30"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span class="va">nlmixr_saem_control_800</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/saemControl.html" class="external-link">saemControl</a></span><span class="op">(</span>logLik <span class="op">=</span> <span class="cn">TRUE</span>,
-  nBurn <span class="op">=</span> <span class="fl">800</span>, nEm <span class="op">=</span> <span class="fl">300</span>, nmc <span class="op">=</span> <span class="fl">15</span><span class="op">)</span>
-<span class="va">nlmixr_saem_control_moreiter</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/saemControl.html" class="external-link">saemControl</a></span><span class="op">(</span>logLik <span class="op">=</span> <span class="cn">TRUE</span>,
-  nBurn <span class="op">=</span> <span class="fl">1600</span>, nEm <span class="op">=</span> <span class="fl">300</span>, nmc <span class="op">=</span> <span class="fl">15</span><span class="op">)</span>
-<span class="va">nlmixr_saem_control_10k</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/saemControl.html" class="external-link">saemControl</a></span><span class="op">(</span>logLik <span class="op">=</span> <span class="cn">TRUE</span>,
-  nBurn <span class="op">=</span> <span class="fl">10000</span>, nEm <span class="op">=</span> <span class="fl">1000</span>, nmc <span class="op">=</span> <span class="fl">15</span><span class="op">)</span></code></pre></div>
-<p>Then we fit SFO with constant variance</p>
-<div class="sourceCode" id="cb31"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span class="va">f_parent_nlmixr_saem_sfo_const</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/nlmixr.html" class="external-link">nlmixr</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>, est <span class="op">=</span> <span class="st">"saem"</span>,
-  control <span class="op">=</span> <span class="va">nlmixr_saem_control_800</span><span class="op">)</span>
-<span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/traceplot.html" class="external-link">traceplot</a></span><span class="op">(</span><span class="va">f_parent_nlmixr_saem_sfo_const</span><span class="op">$</span><span class="va">nm</span><span class="op">)</span></code></pre></div>
-<p><img src="dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_sfo_const-1.png" width="700"></p>
-<p>and SFO with two-component error.</p>
-<div class="sourceCode" id="cb32"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span class="va">f_parent_nlmixr_saem_sfo_tc</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/nlmixr.html" class="external-link">nlmixr</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span>, est <span class="op">=</span> <span class="st">"saem"</span>,
-  control <span class="op">=</span> <span class="va">nlmixr_saem_control_800</span><span class="op">)</span>
-<span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/traceplot.html" class="external-link">traceplot</a></span><span class="op">(</span><span class="va">f_parent_nlmixr_saem_sfo_tc</span><span class="op">$</span><span class="va">nm</span><span class="op">)</span></code></pre></div>
-<p><img src="dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_sfo_tc-1.png" width="700"></p>
-<p>For DFOP with constant variance, the convergence plots show considerable instability of the fit, which indicates overparameterisation which was already observed above for this model combination. Also note that the variance of k2 approximates zero, which was already observed in the saemix fits of the DFOP model.</p>
-<div class="sourceCode" id="cb33"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span class="va">f_parent_nlmixr_saem_dfop_const</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/nlmixr.html" class="external-link">nlmixr</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>, est <span class="op">=</span> <span class="st">"saem"</span>,
-  control <span class="op">=</span> <span class="va">nlmixr_saem_control_800</span><span class="op">)</span>
-<span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/traceplot.html" class="external-link">traceplot</a></span><span class="op">(</span><span class="va">f_parent_nlmixr_saem_dfop_const</span><span class="op">$</span><span class="va">nm</span><span class="op">)</span></code></pre></div>
-<p><img src="dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_dfop_const-1.png" width="700"></p>
-<p>For DFOP with two-component error, a less erratic convergence is seen, but the variance of k2 again approximates zero.</p>
-<div class="sourceCode" id="cb34"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span class="va">f_parent_nlmixr_saem_dfop_tc</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/nlmixr.html" class="external-link">nlmixr</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, est <span class="op">=</span> <span class="st">"saem"</span>,
-  control <span class="op">=</span> <span class="va">nlmixr_saem_control_800</span><span class="op">)</span>
-<span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/traceplot.html" class="external-link">traceplot</a></span><span class="op">(</span><span class="va">f_parent_nlmixr_saem_dfop_tc</span><span class="op">$</span><span class="va">nm</span><span class="op">)</span></code></pre></div>
-<p><img src="dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_dfop_tc-1.png" width="700"></p>
-<p>To check if an increase in the number of iterations improves the fit, we repeat the fit with 1000 iterations for the burn in phase and 300 iterations for the second phase.</p>
-<div class="sourceCode" id="cb35"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span class="va">f_parent_nlmixr_saem_dfop_tc_moreiter</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/nlmixr.html" class="external-link">nlmixr</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>, est <span class="op">=</span> <span class="st">"saem"</span>,
-  control <span class="op">=</span> <span class="va">nlmixr_saem_control_moreiter</span><span class="op">)</span>
-<span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/traceplot.html" class="external-link">traceplot</a></span><span class="op">(</span><span class="va">f_parent_nlmixr_saem_dfop_tc_moreiter</span><span class="op">$</span><span class="va">nm</span><span class="op">)</span></code></pre></div>
-<p><img src="dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_dfop_tc_1k-1.png" width="700"></p>
-<p>Here the fit looks very similar, but we will see below that it shows a higher AIC than the fit with 800 iterations in the burn in phase. Next we choose 10 000 iterations for the burn in phase and 1000 iterations for the second phase for comparison with saemix.</p>
-<div class="sourceCode" id="cb36"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span class="va">f_parent_nlmixr_saem_dfop_tc_10k</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/nlmixr.html" class="external-link">nlmixr</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, est <span class="op">=</span> <span class="st">"saem"</span>,
-  control <span class="op">=</span> <span class="va">nlmixr_saem_control_10k</span><span class="op">)</span>
-<span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/traceplot.html" class="external-link">traceplot</a></span><span class="op">(</span><span class="va">f_parent_nlmixr_saem_dfop_tc_10k</span><span class="op">$</span><span class="va">nm</span><span class="op">)</span></code></pre></div>
-<p><img src="dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_dfop_tc_10k-1.png" width="700"></p>
-<p>The AIC values are internally calculated using Gaussian quadrature.</p>
-<div class="sourceCode" id="cb37"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/stats/AIC.html" class="external-link">AIC</a></span><span class="op">(</span><span class="va">f_parent_nlmixr_saem_sfo_const</span><span class="op">$</span><span class="va">nm</span>, <span class="va">f_parent_nlmixr_saem_sfo_tc</span><span class="op">$</span><span class="va">nm</span>,
-  <span class="va">f_parent_nlmixr_saem_dfop_const</span><span class="op">$</span><span class="va">nm</span>, <span class="va">f_parent_nlmixr_saem_dfop_tc</span><span class="op">$</span><span class="va">nm</span>,
-  <span class="va">f_parent_nlmixr_saem_dfop_tc_moreiter</span><span class="op">$</span><span class="va">nm</span>,
-  <span class="va">f_parent_nlmixr_saem_dfop_tc_10k</span><span class="op">$</span><span class="va">nm</span><span class="op">)</span></code></pre></div>
-<pre><code>                                         df     AIC
-f_parent_nlmixr_saem_sfo_const$nm         5  798.71
-f_parent_nlmixr_saem_sfo_tc$nm            6  808.64
-f_parent_nlmixr_saem_dfop_const$nm        9 1995.96
-f_parent_nlmixr_saem_dfop_tc$nm          10  664.96
-f_parent_nlmixr_saem_dfop_tc_moreiter$nm 10 4464.93
-f_parent_nlmixr_saem_dfop_tc_10k$nm      10     Inf</code></pre>
-<p>We can see that again, the DFOP/tc model shows the best goodness of fit. However, increasing the number of burn-in iterations from 800 to 1600 results in a higher AIC. If we further increase the number of iterations to 10 000 (burn-in) and 1000 (second phase), the AIC cannot be calculated for the nlmixr/saem fit, confirming that this fit does not converge properly with the SAEM algorithm.</p>
 </div>
-<div class="section level4">
-<h4 id="comparison">Comparison<a class="anchor" aria-label="anchor" href="#comparison"></a>
-</h4>
-<p>The following table gives the AIC values obtained with the three packages using the same control parameters (800 iterations burn-in, 300 iterations second phase, 15 chains).</p>
-<div class="sourceCode" id="cb39"><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>,
-  <span class="st">"Error 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">"const"</span>, <span class="st">"tc"</span>, <span class="st">"const"</span>, <span class="st">"tc"</span><span class="op">)</span>,
-  nlme <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="fu"><a href="https://rdrr.io/r/stats/AIC.html" class="external-link">AIC</a></span><span class="op">(</span><span class="va">f_parent_nlme_sfo_const</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/stats/AIC.html" class="external-link">AIC</a></span><span class="op">(</span><span class="va">f_parent_nlme_sfo_tc</span><span class="op">)</span>, <span class="cn">NA</span>, <span class="fu"><a href="https://rdrr.io/r/stats/AIC.html" class="external-link">AIC</a></span><span class="op">(</span><span class="va">f_parent_nlme_dfop_tc</span><span class="op">)</span><span class="op">)</span>,
-  nlmixr_focei <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</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">f_parent_nlmixr_focei_sfo_const</span><span class="op">$</span><span class="va">nm</span>, <span class="va">f_parent_nlmixr_focei_sfo_tc</span><span class="op">$</span><span class="va">nm</span>,
-  <span class="va">f_parent_nlmixr_focei_dfop_const</span><span class="op">$</span><span class="va">nm</span>, <span class="va">f_parent_nlmixr_focei_dfop_tc</span><span class="op">$</span><span class="va">nm</span><span class="op">)</span>, <span class="va">AIC</span><span class="op">)</span>,
-  saemix <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</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">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>,
-    <span class="va">f_parent_saemix_dfop_const</span><span class="op">$</span><span class="va">so</span>, <span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span><span class="op">)</span>, <span class="va">AIC</span><span class="op">)</span>,
-  nlmixr_saem <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</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">f_parent_nlmixr_saem_sfo_const</span><span class="op">$</span><span class="va">nm</span>, <span class="va">f_parent_nlmixr_saem_sfo_tc</span><span class="op">$</span><span class="va">nm</span>,
-  <span class="va">f_parent_nlmixr_saem_dfop_const</span><span class="op">$</span><span class="va">nm</span>, <span class="va">f_parent_nlmixr_saem_dfop_tc</span><span class="op">$</span><span class="va">nm</span><span class="op">)</span>, <span class="va">AIC</span><span class="op">)</span>
-<span class="op">)</span>
-<span class="fu">kable</span><span class="op">(</span><span class="va">AIC_all</span><span class="op">)</span></code></pre></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).</p>
+<div class="sourceCode" id="cb31"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><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></span>
+<span>  check.names <span class="op">=</span> <span class="cn">FALSE</span>,</span>
+<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>,</span>
+<span>  <span class="st">"Error 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">"const"</span>, <span class="st">"tc"</span>, <span class="st">"const"</span>, <span class="st">"tc"</span><span class="op">)</span>,</span>
+<span>  nlme <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="fu"><a href="https://rdrr.io/r/stats/AIC.html" class="external-link">AIC</a></span><span class="op">(</span><span class="va">f_parent_nlme_sfo_const</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/stats/AIC.html" class="external-link">AIC</a></span><span class="op">(</span><span class="va">f_parent_nlme_sfo_tc</span><span class="op">)</span>, <span class="cn">NA</span>, <span class="fu"><a href="https://rdrr.io/r/stats/AIC.html" class="external-link">AIC</a></span><span class="op">(</span><span class="va">f_parent_nlme_dfop_tc</span><span class="op">)</span><span class="op">)</span>,</span>
+<span>  saemix_lin <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</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">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>,</span>
+<span>    <span class="va">f_parent_saemix_dfop_const</span><span class="op">$</span><span class="va">so</span>, <span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span><span class="op">)</span>, <span class="va">AIC</span>, method <span class="op">=</span> <span class="st">"lin"</span><span class="op">)</span>,</span>
+<span>  saemix_is <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</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">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>,</span>
+<span>    <span class="va">f_parent_saemix_dfop_const</span><span class="op">$</span><span class="va">so</span>, <span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span><span class="op">)</span>, <span class="va">AIC</span>, method <span class="op">=</span> <span class="st">"is"</span><span class="op">)</span></span>
+<span><span class="op">)</span></span>
+<span><span class="fu">kable</span><span class="op">(</span><span class="va">AIC_all</span><span class="op">)</span></span></code></pre></div>
 <table class="table">
 <thead><tr class="header">
 <th align="left">Degradation model</th>
 <th align="left">Error model</th>
 <th align="right">nlme</th>
-<th align="right">nlmixr_focei</th>
-<th align="right">saemix</th>
-<th align="right">nlmixr_saem</th>
+<th align="right">saemix_lin</th>
+<th align="right">saemix_is</th>
 </tr></thead>
 <tbody>
 <tr class="odd">
@@ -435,36 +400,81 @@ f_parent_nlmixr_saem_dfop_tc_10k$nm      10     Inf</code></pre>
 <td align="right">796.60</td>
 <td align="right">796.60</td>
 <td align="right">796.38</td>
-<td align="right">798.71</td>
 </tr>
 <tr class="even">
 <td align="left">SFO</td>
 <td align="left">tc</td>
 <td align="right">798.60</td>
-<td align="right">798.64</td>
+<td align="right">798.60</td>
 <td align="right">798.38</td>
-<td align="right">808.64</td>
 </tr>
 <tr class="odd">
 <td align="left">DFOP</td>
 <td align="left">const</td>
 <td align="right">NA</td>
-<td align="right">745.87</td>
+<td align="right">671.98</td>
 <td align="right">705.75</td>
-<td align="right">1995.96</td>
 </tr>
 <tr class="even">
 <td align="left">DFOP</td>
 <td align="left">tc</td>
 <td align="right">671.91</td>
-<td align="right">740.42</td>
+<td align="right">665.11</td>
 <td align="right">665.65</td>
-<td align="right">664.96</td>
 </tr>
 </tbody>
 </table>
 </div>
 </div>
+<div class="section level2">
+<h2 id="conclusion">Conclusion<a class="anchor" aria-label="anchor" href="#conclusion"></a>
+</h2>
+<p>A more detailed analysis of the dimethenamid dataset confirmed that the DFOP model provides the most appropriate description of the decline of the parent compound in these data. On the other hand, closer inspection of the results revealed that the variability of the k2 parameter across the population of soils is ill-defined. This coincides with the observation that this parameter cannot robustly be quantified for some of the soils.</p>
+<p>Regarding the regulatory use of these data, it is claimed that an improved characterisation of the mean parameter values across the population is obtained using the nonlinear mixed-effects models presented here. However, attempts to quantify the variability of the slower rate constant of the biphasic decline of dimethenamid indicate that the data are not sufficient to characterise this variability to a satisfactory precision.</p>
+</div>
+<div class="section level2">
+<h2 id="session-info">Session Info<a class="anchor" aria-label="anchor" href="#session-info"></a>
+</h2>
+<div class="sourceCode" id="cb32"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/utils/sessionInfo.html" class="external-link">sessionInfo</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
+<pre><code>R version 4.2.1 (2022-06-23)
+Platform: x86_64-pc-linux-gnu (64-bit)
+Running under: Debian GNU/Linux 11 (bullseye)
+
+Matrix products: default
+BLAS:   /usr/lib/x86_64-linux-gnu/openblas-serial/libblas.so.3
+LAPACK: /usr/lib/x86_64-linux-gnu/openblas-serial/libopenblas-r0.3.13.so
+
+locale:
+ [1] LC_CTYPE=de_DE.UTF-8       LC_NUMERIC=C              
+ [3] LC_TIME=C                  LC_COLLATE=de_DE.UTF-8    
+ [5] LC_MONETARY=de_DE.UTF-8    LC_MESSAGES=de_DE.UTF-8   
+ [7] LC_PAPER=de_DE.UTF-8       LC_NAME=C                 
+ [9] LC_ADDRESS=C               LC_TELEPHONE=C            
+[11] LC_MEASUREMENT=de_DE.UTF-8 LC_IDENTIFICATION=C       
+
+attached base packages:
+[1] stats     graphics  grDevices utils     datasets  methods   base     
+
+other attached packages:
+[1] saemix_3.1   npde_3.2     nlme_3.1-158 mkin_1.1.2   knitr_1.39  
+
+loaded via a namespace (and not attached):
+ [1] deSolve_1.33      zoo_1.8-10        tidyselect_1.1.2  xfun_0.31        
+ [5] bslib_0.4.0       purrr_0.3.4       lattice_0.20-45   colorspace_2.0-3 
+ [9] vctrs_0.4.1       generics_0.1.3    htmltools_0.5.3   yaml_2.3.5       
+[13] utf8_1.2.2        rlang_1.0.4       pkgdown_2.0.6     jquerylib_0.1.4  
+[17] pillar_1.8.0      glue_1.6.2        DBI_1.1.3         lifecycle_1.0.1  
+[21] stringr_1.4.0     munsell_0.5.0     gtable_0.3.0      ragg_1.2.2       
+[25] codetools_0.2-18  memoise_2.0.1     evaluate_0.15     fastmap_1.1.0    
+[29] lmtest_0.9-40     parallel_4.2.1    fansi_1.0.3       highr_0.9        
+[33] scales_1.2.0      cachem_1.0.6      desc_1.4.1        jsonlite_1.8.0   
+[37] systemfonts_1.0.4 fs_1.5.2          textshaping_0.3.6 gridExtra_2.3    
+[41] ggplot2_3.3.6     digest_0.6.29     stringi_1.7.8     dplyr_1.0.9      
+[45] grid_4.2.1        rprojroot_2.0.3   cli_3.3.0         tools_4.2.1      
+[49] magrittr_2.0.3    sass_0.4.2        tibble_3.1.8      pkgconfig_2.0.3  
+[53] assertthat_0.2.1  rmarkdown_2.14.3  R6_2.5.1          mclust_5.4.10    
+[57] compiler_4.2.1   </code></pre>
 </div>
 <div class="section level2">
 <h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a>
@@ -501,7 +511,7 @@ f_parent_nlmixr_saem_dfop_tc_10k$nm      10     Inf</code></pre>
 
 <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> 2.0.6.</p>
 </div>
 
       </footer>
diff --git a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const-1.png b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const-1.png
index 950abf27..4999e72c 100644
--- a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const-1.png
+++ b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const-1.png
diff --git a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const_test-1.png b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const_test-1.png
index 66481bc1..b59764b1 100644
--- a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const_test-1.png
+++ b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const_test-1.png
diff --git a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_tc_test-1.png b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_tc_test-1.png
index 557ccc45..da7ceeb6 100644
--- a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_tc_test-1.png
+++ b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_tc_test-1.png
diff --git a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_sfo_const-1.png b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_sfo_const-1.png
index 089ab64d..467c3c1a 100644
--- a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_sfo_const-1.png
+++ b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_sfo_const-1.png
diff --git a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/plot_parent_nlme-1.png b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/plot_parent_nlme-1.png
index 849296d9..4d2dc94e 100644
--- a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/plot_parent_nlme-1.png
+++ b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/plot_parent_nlme-1.png
author	Johannes Ranke <jranke@uni-bremen.de>	2022-08-10 15:38:17 +0200
committer	Johannes Ranke <jranke@uni-bremen.de>	2022-08-10 15:38:17 +0200
commit	6178249bbb5e9de7cb7f34287ee7de28a68fed6c (patch)
tree	537dcc31245b02adba4a293ce6c90b23b202df25 /docs/dev/articles
parent	307e77e5bf81c7422055493cee7f073b57069c6c (diff)