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+
+      <h1>Example evaluation of FOCUS dataset Z</h1>
+                        <h4 data-toc-skip class="author">Johannes
+Ranke</h4>
+            
+            <h4 data-toc-skip class="date">Last change 16 January 2018
+(rebuilt 2025-02-14)</h4>
+      
+      <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/FOCUS_Z.rmd" class="external-link"><code>vignettes/web_only/FOCUS_Z.rmd</code></a></small>
+      <div class="d-none name"><code>FOCUS_Z.rmd</code></div>
+    </div>
+
+    
+    
+<p><a href="http://www.jrwb.de" class="external-link">Wissenschaftlicher Berater, Kronacher
+Str. 12, 79639 Grenzach-Wyhlen, Germany</a><br><a href="http://chem.uft.uni-bremen.de/ranke" class="external-link">Privatdozent at the
+University of Bremen</a></p>
+<div class="section level2">
+<h2 id="the-data">The data<a class="anchor" aria-label="anchor" href="#the-data"></a>
+</h2>
+<p>The following code defines the example dataset from Appendix 7 to the
+FOCUS kinetics report <span class="citation">(FOCUS Work Group on
+Degradation Kinetics 2014, 354)</span>.</p>
+<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="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">LOD</span> <span class="op">=</span> <span class="fl">0.5</span></span>
+<span><span class="va">FOCUS_2006_Z</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" 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">0.04</span>, <span class="fl">0.125</span>, <span class="fl">0.29</span>, <span class="fl">0.54</span>, <span class="fl">1</span>, <span class="fl">2</span>, <span class="fl">3</span>, <span class="fl">4</span>, <span class="fl">7</span>, <span class="fl">10</span>, <span class="fl">14</span>, <span class="fl">21</span>,</span>
+<span>        <span class="fl">42</span>, <span class="fl">61</span>, <span class="fl">96</span>, <span class="fl">124</span><span class="op">)</span>,</span>
+<span>  Z0 <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">100</span>, <span class="fl">81.7</span>, <span class="fl">70.4</span>, <span class="fl">51.1</span>, <span class="fl">41.2</span>, <span class="fl">6.6</span>, <span class="fl">4.6</span>, <span class="fl">3.9</span>, <span class="fl">4.6</span>, <span class="fl">4.3</span>, <span class="fl">6.8</span>,</span>
+<span>         <span class="fl">2.9</span>, <span class="fl">3.5</span>, <span class="fl">5.3</span>, <span class="fl">4.4</span>, <span class="fl">1.2</span>, <span class="fl">0.7</span><span class="op">)</span>,</span>
+<span>  Z1 <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">18.3</span>, <span class="fl">29.6</span>, <span class="fl">46.3</span>, <span class="fl">55.1</span>, <span class="fl">65.7</span>, <span class="fl">39.1</span>, <span class="fl">36</span>, <span class="fl">15.3</span>, <span class="fl">5.6</span>, <span class="fl">1.1</span>,</span>
+<span>         <span class="fl">1.6</span>, <span class="fl">0.6</span>, <span class="fl">0.5</span> <span class="op">*</span> <span class="va">LOD</span>, <span class="cn">NA</span>, <span class="cn">NA</span>, <span class="cn">NA</span><span class="op">)</span>,</span>
+<span>  Z2 <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="cn">NA</span>, <span class="fl">0.5</span> <span class="op">*</span> <span class="va">LOD</span>, <span class="fl">2.6</span>, <span class="fl">3.8</span>, <span class="fl">15.3</span>, <span class="fl">37.2</span>, <span class="fl">31.7</span>, <span class="fl">35.6</span>, <span class="fl">14.5</span>,</span>
+<span>         <span class="fl">0.8</span>, <span class="fl">2.1</span>, <span class="fl">1.9</span>, <span class="fl">0.5</span> <span class="op">*</span> <span class="va">LOD</span>, <span class="cn">NA</span>, <span class="cn">NA</span>, <span class="cn">NA</span><span class="op">)</span>,</span>
+<span>  Z3 <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="cn">NA</span>, <span class="cn">NA</span>, <span class="cn">NA</span>, <span class="cn">NA</span>, <span class="fl">0.5</span> <span class="op">*</span> <span class="va">LOD</span>, <span class="fl">9.2</span>, <span class="fl">13.1</span>, <span class="fl">22.3</span>, <span class="fl">28.4</span>, <span class="fl">32.5</span>,</span>
+<span>         <span class="fl">25.2</span>, <span class="fl">17.2</span>, <span class="fl">4.8</span>, <span class="fl">4.5</span>, <span class="fl">2.8</span>, <span class="fl">4.4</span><span class="op">)</span><span class="op">)</span></span>
+<span></span>
+<span><span class="va">FOCUS_2006_Z_mkin</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span><span class="op">(</span><span class="va">FOCUS_2006_Z</span><span class="op">)</span></span></code></pre></div>
+</div>
+<div class="section level2">
+<h2 id="parent-and-one-metabolite">Parent and one metabolite<a class="anchor" aria-label="anchor" href="#parent-and-one-metabolite"></a>
+</h2>
+<p>The next step is to set up the models used for the kinetic analysis.
+As the simultaneous fit of parent and the first metabolite is usually
+straightforward, Step 1 (SFO for parent only) is skipped here. We start
+with the model 2a, with formation and decline of metabolite Z1 and the
+pathway from parent directly to sink included (default in mkin).</p>
+<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">Z.2a</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z1"</span><span class="op">)</span>,</span>
+<span>                Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre>
+<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">m.Z.2a</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.2a</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Warning in mkinfit(Z.2a, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with</span></span>
+<span><span class="co">## value of zero were removed from the data</span></span></code></pre>
+<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.2a</span><span class="op">)</span></span></code></pre></div>
+<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png" width="700"></p>
+<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.2a</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></code></pre></div>
+<pre><code><span><span class="co">##            Estimate se_notrans t value     Pr(&gt;t)    Lower    Upper</span></span>
+<span><span class="co">## Z0_0       97.01488   3.301084 29.3888 3.2971e-21 91.66556 102.3642</span></span>
+<span><span class="co">## k_Z0        2.23601   0.207078 10.7979 3.3309e-11  1.95303   2.5600</span></span>
+<span><span class="co">## k_Z1        0.48212   0.063265  7.6207 2.8154e-08  0.40341   0.5762</span></span>
+<span><span class="co">## f_Z0_to_Z1  1.00000   0.094764 10.5525 5.3560e-11  0.00000   1.0000</span></span>
+<span><span class="co">## sigma       4.80411   0.635638  7.5579 3.2592e-08  3.52677   6.0815</span></span></code></pre>
+<p>As obvious from the parameter summary (the component of the summary),
+the kinetic rate constant from parent compound Z to sink is very small
+and the t-test for this parameter suggests that it is not significantly
+different from zero. This suggests, in agreement with the analysis in
+the FOCUS kinetics report, to simplify the model by removing the pathway
+to sink.</p>
+<p>A similar result can be obtained when formation fractions are used in
+the model formulation:</p>
+<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">Z.2a.ff</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z1"</span><span class="op">)</span>,</span>
+<span>                   Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span>
+<span>                   use_of_ff <span class="op">=</span> <span class="st">"max"</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre>
+<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">m.Z.2a.ff</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.2a.ff</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Warning in mkinfit(Z.2a.ff, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with</span></span>
+<span><span class="co">## value of zero were removed from the data</span></span></code></pre>
+<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.2a.ff</span><span class="op">)</span></span></code></pre></div>
+<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png" width="700"></p>
+<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.2a.ff</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></code></pre></div>
+<pre><code><span><span class="co">##            Estimate se_notrans t value     Pr(&gt;t)    Lower    Upper</span></span>
+<span><span class="co">## Z0_0       97.01488   3.301084 29.3888 3.2971e-21 91.66556 102.3642</span></span>
+<span><span class="co">## k_Z0        2.23601   0.207078 10.7979 3.3309e-11  1.95303   2.5600</span></span>
+<span><span class="co">## k_Z1        0.48212   0.063265  7.6207 2.8154e-08  0.40341   0.5762</span></span>
+<span><span class="co">## f_Z0_to_Z1  1.00000   0.094764 10.5525 5.3560e-11  0.00000   1.0000</span></span>
+<span><span class="co">## sigma       4.80411   0.635638  7.5579 3.2592e-08  3.52677   6.0815</span></span></code></pre>
+<p>Here, the ilr transformed formation fraction fitted in the model
+takes a very large value, and the backtransformed formation fraction
+from parent Z to Z1 is practically unity. Here, the covariance matrix
+used for the calculation of confidence intervals is not returned as the
+model is overparameterised.</p>
+<p>A simplified model is obtained by removing the pathway to the sink.
+</p>
+<p>In the following, we use the parameterisation with formation
+fractions in order to be able to compare with the results in the FOCUS
+guidance, and as it makes it easier to use parameters obtained in a
+previous fit when adding a further metabolite.</p>
+<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">Z.3</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
+<span>               Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>, use_of_ff <span class="op">=</span> <span class="st">"max"</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre>
+<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">m.Z.3</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.3</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Warning in mkinfit(Z.3, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with</span></span>
+<span><span class="co">## value of zero were removed from the data</span></span></code></pre>
+<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.3</span><span class="op">)</span></span></code></pre></div>
+<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png" width="700"></p>
+<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.3</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></code></pre></div>
+<pre><code><span><span class="co">##       Estimate se_notrans t value     Pr(&gt;t)    Lower    Upper</span></span>
+<span><span class="co">## Z0_0  97.01488   2.597342  37.352 2.0106e-24 91.67597 102.3538</span></span>
+<span><span class="co">## k_Z0   2.23601   0.146904  15.221 9.1477e-15  1.95354   2.5593</span></span>
+<span><span class="co">## k_Z1   0.48212   0.041727  11.554 4.8268e-12  0.40355   0.5760</span></span>
+<span><span class="co">## sigma  4.80411   0.620208   7.746 1.6110e-08  3.52925   6.0790</span></span></code></pre>
+<p>As there is only one transformation product for Z0 and no pathway to
+sink, the formation fraction is internally fixed to unity.</p>
+</div>
+<div class="section level2">
+<h2 id="metabolites-z2-and-z3">Metabolites Z2 and Z3<a class="anchor" aria-label="anchor" href="#metabolites-z2-and-z3"></a>
+</h2>
+<p>As suggested in the FOCUS report, the pathway to sink was removed for
+metabolite Z1 as well in the next step. While this step appears
+questionable on the basis of the above results, it is followed here for
+the purpose of comparison. Also, in the FOCUS report, it is assumed that
+there is additional empirical evidence that Z1 quickly and exclusively
+hydrolyses to Z2.</p>
+<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">Z.5</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
+<span>               Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
+<span>               Z2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>, use_of_ff <span class="op">=</span> <span class="st">"max"</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre>
+<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">m.Z.5</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.5</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Warning in mkinfit(Z.5, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with</span></span>
+<span><span class="co">## value of zero were removed from the data</span></span></code></pre>
+<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.5</span><span class="op">)</span></span></code></pre></div>
+<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png" width="700"></p>
+<p>Finally, metabolite Z3 is added to the model. We use the optimised
+differential equation parameter values from the previous fit in order to
+accelerate the optimization.</p>
+<div class="sourceCode" id="cb28"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">Z.FOCUS</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
+<span>                   Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
+<span>                   Z2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z3"</span><span class="op">)</span>,</span>
+<span>                   Z3 <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><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre>
+<div class="sourceCode" id="cb30"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">m.Z.FOCUS</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.FOCUS</span>, <span class="va">FOCUS_2006_Z_mkin</span>,</span>
+<span>                     parms.ini <span class="op">=</span> <span class="va">m.Z.5</span><span class="op">$</span><span class="va">bparms.ode</span>,</span>
+<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(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.5$bparms.ode, :</span></span>
+<span><span class="co">## Observations with value of zero were removed from the data</span></span></code></pre>
+<pre><code><span><span class="co">## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.5$bparms.ode, : Optimisation did not converge:</span></span>
+<span><span class="co">## false convergence (8)</span></span></code></pre>
+<div class="sourceCode" id="cb33"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.FOCUS</span><span class="op">)</span></span></code></pre></div>
+<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png" width="700"></p>
+<div class="sourceCode" id="cb34"><pre class="downlit sourceCode r">
+<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.Z.FOCUS</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></code></pre></div>
+<pre><code><span><span class="co">##             Estimate se_notrans t value     Pr(&gt;t)     Lower      Upper</span></span>
+<span><span class="co">## Z0_0       96.842440   1.994291 48.5598 4.0226e-42 92.830421 100.854459</span></span>
+<span><span class="co">## k_Z0        2.215425   0.118457 18.7023 1.0404e-23  1.989490   2.467019</span></span>
+<span><span class="co">## k_Z1        0.478307   0.028257 16.9272 6.2332e-22  0.424709   0.538669</span></span>
+<span><span class="co">## k_Z2        0.451642   0.042139 10.7178 1.6304e-14  0.374348   0.544894</span></span>
+<span><span class="co">## k_Z3        0.058692   0.015245  3.8499 1.7803e-04  0.034804   0.098975</span></span>
+<span><span class="co">## f_Z2_to_Z3  0.471483   0.058348  8.0806 9.6585e-11  0.357720   0.588287</span></span>
+<span><span class="co">## sigma       3.984431   0.383402 10.3923 4.5576e-14  3.213126   4.755737</span></span></code></pre>
+<div class="sourceCode" id="cb36"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">m.Z.FOCUS</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## $ff</span></span>
+<span><span class="co">##   Z2_Z3 Z2_sink </span></span>
+<span><span class="co">## 0.47148 0.52852 </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $distimes</span></span>
+<span><span class="co">##        DT50    DT90</span></span>
+<span><span class="co">## Z0  0.31287  1.0393</span></span>
+<span><span class="co">## Z1  1.44917  4.8140</span></span>
+<span><span class="co">## Z2  1.53473  5.0983</span></span>
+<span><span class="co">## Z3 11.80991 39.2317</span></span></code></pre>
+<p>This fit corresponds to the final result chosen in Appendix 7 of the
+FOCUS report. Confidence intervals returned by mkin are based on
+internally transformed parameters, however.</p>
+</div>
+<div class="section level2">
+<h2 id="using-the-sforb-model">Using the SFORB model<a class="anchor" aria-label="anchor" href="#using-the-sforb-model"></a>
+</h2>
+<p>As the FOCUS report states, there is a certain tailing of the time
+course of metabolite Z3. Also, the time course of the parent compound is
+not fitted very well using the SFO model, as residues at a certain low
+level remain.</p>
+<p>Therefore, an additional model is offered here, using the single
+first-order reversible binding (SFORB) model for metabolite Z3. As
+expected, the
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msup><mi>χ</mi><mn>2</mn></msup><annotation encoding="application/x-tex">\chi^2</annotation></semantics></math>
+error level is lower for metabolite Z3 using this model and the
+graphical fit for Z3 is improved. However, the covariance matrix is not
+returned.</p>
+<div class="sourceCode" id="cb38"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">Z.mkin.1</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
+<span>                    Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
+<span>                    Z2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z3"</span><span class="op">)</span>,</span>
+<span>                    Z3 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre>
+<div class="sourceCode" id="cb40"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">m.Z.mkin.1</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.mkin.1</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Warning in mkinfit(Z.mkin.1, FOCUS_2006_Z_mkin, quiet = TRUE): Observations</span></span>
+<span><span class="co">## with value of zero were removed from the data</span></span></code></pre>
+<div class="sourceCode" id="cb42"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.1</span><span class="op">)</span></span></code></pre></div>
+<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png" width="700"></p>
+<div class="sourceCode" id="cb43"><pre class="downlit sourceCode r">
+<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.Z.mkin.1</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">cov.unscaled</span></span></code></pre></div>
+<pre><code><span><span class="co">## NULL</span></span></code></pre>
+<p>Therefore, a further stepwise model building is performed starting
+from the stage of parent and two metabolites, starting from the
+assumption that the model fit for the parent compound can be improved by
+using the SFORB model.</p>
+<div class="sourceCode" id="cb45"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">Z.mkin.3</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span>, <span class="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
+<span>                    Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
+<span>                    Z2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre>
+<div class="sourceCode" id="cb47"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">m.Z.mkin.3</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.mkin.3</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Warning in mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE): Observations</span></span>
+<span><span class="co">## with value of zero were removed from the data</span></span></code></pre>
+<div class="sourceCode" id="cb49"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.3</span><span class="op">)</span></span></code></pre></div>
+<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png" width="700"></p>
+<p>This results in a much better representation of the behaviour of the
+parent compound Z0.</p>
+<p>Finally, Z3 is added as well. These models appear overparameterised
+(no covariance matrix returned) if the sink for Z1 is left in the
+models.</p>
+<div class="sourceCode" id="cb50"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">Z.mkin.4</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span>, <span class="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
+<span>                    Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
+<span>                    Z2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z3"</span><span class="op">)</span>,</span>
+<span>                    Z3 <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></code></pre></div>
+<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre>
+<div class="sourceCode" id="cb52"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">m.Z.mkin.4</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.mkin.4</span>, <span class="va">FOCUS_2006_Z_mkin</span>,</span>
+<span>                      parms.ini <span class="op">=</span> <span class="va">m.Z.mkin.3</span><span class="op">$</span><span class="va">bparms.ode</span>,</span>
+<span>                      quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Warning in mkinfit(Z.mkin.4, FOCUS_2006_Z_mkin, parms.ini =</span></span>
+<span><span class="co">## m.Z.mkin.3$bparms.ode, : Observations with value of zero were removed from the</span></span>
+<span><span class="co">## data</span></span></code></pre>
+<div class="sourceCode" id="cb54"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.4</span><span class="op">)</span></span></code></pre></div>
+<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png" width="700"></p>
+<p>The error level of the fit, but especially of metabolite Z3, can be
+improved if the SFORB model is chosen for this metabolite, as this model
+is capable of representing the tailing of the metabolite decline
+phase.</p>
+<div class="sourceCode" id="cb55"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">Z.mkin.5</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span>, <span class="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
+<span>                    Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
+<span>                    Z2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z3"</span><span class="op">)</span>,</span>
+<span>                    Z3 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre>
+<div class="sourceCode" id="cb57"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">m.Z.mkin.5</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.mkin.5</span>, <span class="va">FOCUS_2006_Z_mkin</span>,</span>
+<span>                      parms.ini <span class="op">=</span> <span class="va">m.Z.mkin.4</span><span class="op">$</span><span class="va">bparms.ode</span><span class="op">[</span><span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span>,</span>
+<span>                      quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini =</span></span>
+<span><span class="co">## m.Z.mkin.4$bparms.ode[1:4], : Observations with value of zero were removed from</span></span>
+<span><span class="co">## the data</span></span></code></pre>
+<div class="sourceCode" id="cb59"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.5</span><span class="op">)</span></span></code></pre></div>
+<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png" width="700"></p>
+<p>The summary view of the backtransformed parameters shows that we get
+no confidence intervals due to overparameterisation. As the optimized is
+excessively small, it seems reasonable to fix it to zero.</p>
+<div class="sourceCode" id="cb60"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">m.Z.mkin.5a</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.mkin.5</span>, <span class="va">FOCUS_2006_Z_mkin</span>,</span>
+<span>                       parms.ini <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="va">m.Z.mkin.5</span><span class="op">$</span><span class="va">bparms.ode</span><span class="op">[</span><span class="fl">1</span><span class="op">:</span><span class="fl">7</span><span class="op">]</span>,</span>
+<span>                                     k_Z3_bound_free <span class="op">=</span> <span class="fl">0</span><span class="op">)</span>,</span>
+<span>                       fixed_parms <span class="op">=</span> <span class="st">"k_Z3_bound_free"</span>,</span>
+<span>                       quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini =</span></span>
+<span><span class="co">## c(m.Z.mkin.5$bparms.ode[1:7], : Observations with value of zero were removed</span></span>
+<span><span class="co">## from the data</span></span></code></pre>
+<div class="sourceCode" id="cb62"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.5a</span><span class="op">)</span></span></code></pre></div>
+<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png" width="700"></p>
+<p>As expected, the residual plots for Z0 and Z3 are more random than in
+the case of the all SFO model for which they were shown above. In
+conclusion, the model is proposed as the best-fit model for the dataset
+from Appendix 7 of the FOCUS report.</p>
+<p>A graphical representation of the confidence intervals can finally be
+obtained.</p>
+<div class="sourceCode" id="cb63"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../../reference/mkinparplot.html">mkinparplot</a></span><span class="op">(</span><span class="va">m.Z.mkin.5a</span><span class="op">)</span></span></code></pre></div>
+<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png" width="700"></p>
+<p>The endpoints obtained with this model are</p>
+<div class="sourceCode" id="cb64"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">m.Z.mkin.5a</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## $ff</span></span>
+<span><span class="co">## Z0_free   Z2_Z3 Z2_sink Z3_free </span></span>
+<span><span class="co">## 1.00000 0.53656 0.46344 1.00000 </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $SFORB</span></span>
+<span><span class="co">##     Z0_b1     Z0_b2      Z0_g     Z3_b1     Z3_b2      Z3_g </span></span>
+<span><span class="co">## 2.4471342 0.0075124 0.9519866 0.0800071 0.0000000 0.9347816 </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $distimes</span></span>
+<span><span class="co">##      DT50   DT90 DT50back DT50_Z0_b1 DT50_Z0_b2 DT50_Z3_b1 DT50_Z3_b2</span></span>
+<span><span class="co">## Z0 0.3043 1.1848  0.35666    0.28325     92.267         NA         NA</span></span>
+<span><span class="co">## Z1 1.5148 5.0320       NA         NA         NA         NA         NA</span></span>
+<span><span class="co">## Z2 1.6414 5.4526       NA         NA         NA         NA         NA</span></span>
+<span><span class="co">## Z3     NA     NA       NA         NA         NA     8.6636        Inf</span></span></code></pre>
+<p>It is clear the degradation rate of Z3 towards the end of the
+experiment is very low as DT50_Z3_b2 (the second Eigenvalue of the
+system of two differential equations representing the SFORB system for
+Z3, corresponding to the slower rate constant of the DFOP model) is
+reported to be infinity. However, this appears to be a feature of the
+data.</p>
+</div>
+<div class="section level2">
+<h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a>
+</h2>
+<!-- vim: set foldmethod=syntax: -->
+<div id="refs" class="references csl-bib-body hanging-indent">
+<div id="ref-FOCUSkinetics2014" class="csl-entry">
+FOCUS Work Group on Degradation Kinetics. 2014. <em>Generic Guidance for
+Estimating Persistence and Degradation Kinetics from Environmental Fate
+Studies on Pesticides in EU Registration</em>. 1.1 ed. <a href="http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics" class="external-link">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>.
+</div>
+</div>
+</div>
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside>
+</div>
+
+
+
+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Johannes Ranke.</p>
+</div>
+
+<div class="pkgdown-footer-right">
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
+</div>
+
+    </footer>
+</div>
+
+
+
+
+
+  </body>
+</html>
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+    <li><a class="dropdown-item" href="../../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a></li>
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+    <li><h6 class="dropdown-header" data-toc-skip>Example evaluations with hierarchical models (nonlinear mixed-effects models)</h6></li>
+    <li><a class="dropdown-item" href="../../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a></li>
+    <li><a class="dropdown-item" href="../../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a></li>
+    <li><a class="dropdown-item" href="../../articles/prebuilt/2023_mesotrione_parent.html">Testing covariate modelling in hierarchical parent degradation kinetics with residue data on mesotrione</a></li>
+    <li><a class="dropdown-item" href="../../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a></li>
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+
+      <h1>Evaluation of example datasets from Attachment 1 to the US EPA SOP for the NAFTA guidance</h1>
+                        <h4 data-toc-skip class="author">Johannes
+Ranke</h4>
+            
+            <h4 data-toc-skip class="date">26 February 2019 (rebuilt
+2025-02-14)</h4>
+      
+      <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/NAFTA_examples.rmd" class="external-link"><code>vignettes/web_only/NAFTA_examples.rmd</code></a></small>
+      <div class="d-none name"><code>NAFTA_examples.rmd</code></div>
+    </div>
+
+    
+    
+<div class="section level2">
+<h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#introduction"></a>
+</h2>
+<p>In this document, the example evaluations provided in Attachment 1 to
+the SOP of US EPA for using the NAFTA guidance <span class="citation">(US EPA 2015)</span> are repeated using mkin. The
+original evaluations reported in the attachment were performed using
+PestDF in version 0.8.4. Note that PestDF 0.8.13 is the version
+distributed at the US EPA website today (2019-02-26).</p>
+<p>The datasets are now distributed with the mkin package.</p>
+</div>
+<div class="section level2">
+<h2 id="examples-where-dfop-did-not-converge-with-pestdf-0-8-4">Examples where DFOP did not converge with PestDF 0.8.4<a class="anchor" aria-label="anchor" href="#examples-where-dfop-did-not-converge-with-pestdf-0-8-4"></a>
+</h2>
+<p>In attachment 1, it is reported that the DFOP model does not converge
+for these datasets when PestDF 0.8.4 was used. For all four datasets,
+the DFOP model can be fitted with mkin (see below). The negative
+half-life given by PestDF 0.8.4 for these fits appears to be the result
+of a bug. The results for the other two models (SFO and IORE) are the
+same.</p>
+<div class="section level3">
+<h3 id="example-on-page-5-upper-panel">Example on page 5, upper panel<a class="anchor" aria-label="anchor" href="#example-on-page-5-upper-panel"></a>
+</h3>
+<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">p5a</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p5a"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre>
+<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre>
+<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p5a</span><span class="op">)</span></span></code></pre></div>
+<p><img src="NAFTA_examples_files/figure-html/p5a-1.png" width="700"></p>
+<div class="sourceCode" id="cb5"><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">p5a</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Sums of squares:</span></span>
+<span><span class="co">##       SFO      IORE      DFOP </span></span>
+<span><span class="co">## 465.21753  56.27506  32.06401 </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span>
+<span><span class="co">## [1] 64.4304</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Parameters:</span></span>
+<span><span class="co">## $SFO</span></span>
+<span><span class="co">##          Estimate   Pr(&gt;t)  Lower   Upper</span></span>
+<span><span class="co">## parent_0  95.8401 4.67e-21 92.245 99.4357</span></span>
+<span><span class="co">## k_parent   0.0102 3.92e-12  0.009  0.0117</span></span>
+<span><span class="co">## sigma      4.8230 3.81e-06  3.214  6.4318</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $IORE</span></span>
+<span><span class="co">##                Estimate Pr(&gt;t)    Lower    Upper</span></span>
+<span><span class="co">## parent_0       1.01e+02     NA 9.91e+01 1.02e+02</span></span>
+<span><span class="co">## k__iore_parent 1.54e-05     NA 4.08e-06 5.84e-05</span></span>
+<span><span class="co">## N_parent       2.57e+00     NA 2.25e+00 2.89e+00</span></span>
+<span><span class="co">## sigma          1.68e+00     NA 1.12e+00 2.24e+00</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $DFOP</span></span>
+<span><span class="co">##          Estimate   Pr(&gt;t)   Lower    Upper</span></span>
+<span><span class="co">## parent_0 9.99e+01 1.41e-26 98.8116 101.0810</span></span>
+<span><span class="co">## k1       2.67e-02 5.05e-06  0.0243   0.0295</span></span>
+<span><span class="co">## k2       3.41e-12 5.00e-01  0.0000      Inf</span></span>
+<span><span class="co">## g        6.47e-01 3.67e-06  0.6248   0.6677</span></span>
+<span><span class="co">## sigma    1.27e+00 8.91e-06  0.8395   1.6929</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## DTx values:</span></span>
+<span><span class="co">##      DT50     DT90 DT50_rep</span></span>
+<span><span class="co">## SFO  67.7 2.25e+02 6.77e+01</span></span>
+<span><span class="co">## IORE 58.2 1.07e+03 3.22e+02</span></span>
+<span><span class="co">## DFOP 55.5 3.70e+11 2.03e+11</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Representative half-life:</span></span>
+<span><span class="co">## [1] 321.51</span></span></code></pre>
+</div>
+<div class="section level3">
+<h3 id="example-on-page-5-lower-panel">Example on page 5, lower panel<a class="anchor" aria-label="anchor" href="#example-on-page-5-lower-panel"></a>
+</h3>
+<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">p5b</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p5b"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre>
+<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre>
+<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p5b</span><span class="op">)</span></span></code></pre></div>
+<p><img src="NAFTA_examples_files/figure-html/p5b-1.png" width="700"></p>
+<div class="sourceCode" id="cb11"><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">p5b</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Sums of squares:</span></span>
+<span><span class="co">##      SFO     IORE     DFOP </span></span>
+<span><span class="co">## 94.81123 10.10936  7.55871 </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span>
+<span><span class="co">## [1] 11.77879</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Parameters:</span></span>
+<span><span class="co">## $SFO</span></span>
+<span><span class="co">##          Estimate   Pr(&gt;t)    Lower    Upper</span></span>
+<span><span class="co">## parent_0   96.497 2.32e-24 94.85271 98.14155</span></span>
+<span><span class="co">## k_parent    0.008 3.42e-14  0.00737  0.00869</span></span>
+<span><span class="co">## sigma       2.295 1.22e-05  1.47976  3.11036</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $IORE</span></span>
+<span><span class="co">##                Estimate   Pr(&gt;t)    Lower    Upper</span></span>
+<span><span class="co">## parent_0       9.85e+01 1.17e-28 9.79e+01 9.92e+01</span></span>
+<span><span class="co">## k__iore_parent 1.53e-04 6.50e-03 7.21e-05 3.26e-04</span></span>
+<span><span class="co">## N_parent       1.94e+00 5.88e-13 1.76e+00 2.12e+00</span></span>
+<span><span class="co">## sigma          7.49e-01 1.63e-05 4.82e-01 1.02e+00</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $DFOP</span></span>
+<span><span class="co">##          Estimate   Pr(&gt;t)   Lower   Upper</span></span>
+<span><span class="co">## parent_0 9.84e+01 1.24e-27 97.8078 98.9187</span></span>
+<span><span class="co">## k1       1.55e-02 4.10e-04  0.0143  0.0167</span></span>
+<span><span class="co">## k2       9.07e-12 5.00e-01  0.0000     Inf</span></span>
+<span><span class="co">## g        6.89e-01 2.92e-03  0.6626  0.7142</span></span>
+<span><span class="co">## sigma    6.48e-01 2.38e-05  0.4147  0.8813</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## DTx values:</span></span>
+<span><span class="co">##      DT50     DT90 DT50_rep</span></span>
+<span><span class="co">## SFO  86.6 2.88e+02 8.66e+01</span></span>
+<span><span class="co">## IORE 85.5 7.17e+02 2.16e+02</span></span>
+<span><span class="co">## DFOP 83.6 1.25e+11 7.64e+10</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Representative half-life:</span></span>
+<span><span class="co">## [1] 215.87</span></span></code></pre>
+</div>
+<div class="section level3">
+<h3 id="example-on-page-6">Example on page 6<a class="anchor" aria-label="anchor" href="#example-on-page-6"></a>
+</h3>
+<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">p6</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p6"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre>
+<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre>
+<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p6</span><span class="op">)</span></span></code></pre></div>
+<p><img src="NAFTA_examples_files/figure-html/p6-1.png" width="700"></p>
+<div class="sourceCode" id="cb17"><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">p6</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Sums of squares:</span></span>
+<span><span class="co">##       SFO      IORE      DFOP </span></span>
+<span><span class="co">## 188.45361  51.00699  42.46931 </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span>
+<span><span class="co">## [1] 58.39888</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Parameters:</span></span>
+<span><span class="co">## $SFO</span></span>
+<span><span class="co">##          Estimate   Pr(&gt;t)   Lower   Upper</span></span>
+<span><span class="co">## parent_0  94.7759 7.29e-24 92.3478 97.2039</span></span>
+<span><span class="co">## k_parent   0.0179 8.02e-16  0.0166  0.0194</span></span>
+<span><span class="co">## sigma      3.0696 3.81e-06  2.0456  4.0936</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $IORE</span></span>
+<span><span class="co">##                Estimate   Pr(&gt;t)    Lower    Upper</span></span>
+<span><span class="co">## parent_0       97.12446 2.63e-26 95.62461 98.62431</span></span>
+<span><span class="co">## k__iore_parent  0.00252 1.95e-03  0.00134  0.00472</span></span>
+<span><span class="co">## N_parent        1.49587 4.07e-13  1.33896  1.65279</span></span>
+<span><span class="co">## sigma           1.59698 5.05e-06  1.06169  2.13227</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $DFOP</span></span>
+<span><span class="co">##          Estimate   Pr(&gt;t)   Lower   Upper</span></span>
+<span><span class="co">## parent_0 9.66e+01 1.57e-25 95.3476 97.8979</span></span>
+<span><span class="co">## k1       2.55e-02 7.33e-06  0.0233  0.0278</span></span>
+<span><span class="co">## k2       3.84e-11 5.00e-01  0.0000     Inf</span></span>
+<span><span class="co">## g        8.61e-01 7.55e-06  0.8314  0.8867</span></span>
+<span><span class="co">## sigma    1.46e+00 6.93e-06  0.9661  1.9483</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## DTx values:</span></span>
+<span><span class="co">##      DT50     DT90 DT50_rep</span></span>
+<span><span class="co">## SFO  38.6 1.28e+02 3.86e+01</span></span>
+<span><span class="co">## IORE 34.0 1.77e+02 5.32e+01</span></span>
+<span><span class="co">## DFOP 34.1 8.50e+09 1.80e+10</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Representative half-life:</span></span>
+<span><span class="co">## [1] 53.17</span></span></code></pre>
+</div>
+<div class="section level3">
+<h3 id="example-on-page-7">Example on page 7<a class="anchor" aria-label="anchor" href="#example-on-page-7"></a>
+</h3>
+<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">p7</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p7"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre>
+<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre>
+<div class="sourceCode" id="cb22"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p7</span><span class="op">)</span></span></code></pre></div>
+<p><img src="NAFTA_examples_files/figure-html/p7-1.png" width="700"></p>
+<div class="sourceCode" id="cb23"><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">p7</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Sums of squares:</span></span>
+<span><span class="co">##      SFO     IORE     DFOP </span></span>
+<span><span class="co">## 3661.661 3195.030 3174.145 </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span>
+<span><span class="co">## [1] 3334.194</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Parameters:</span></span>
+<span><span class="co">## $SFO</span></span>
+<span><span class="co">##          Estimate   Pr(&gt;t)    Lower    Upper</span></span>
+<span><span class="co">## parent_0 96.41796 4.80e-53 93.32245 99.51347</span></span>
+<span><span class="co">## k_parent  0.00735 7.64e-21  0.00641  0.00843</span></span>
+<span><span class="co">## sigma     7.94557 1.83e-15  6.46713  9.42401</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $IORE</span></span>
+<span><span class="co">##                Estimate Pr(&gt;t)    Lower    Upper</span></span>
+<span><span class="co">## parent_0       9.92e+01     NA 9.55e+01 1.03e+02</span></span>
+<span><span class="co">## k__iore_parent 1.60e-05     NA 1.45e-07 1.77e-03</span></span>
+<span><span class="co">## N_parent       2.45e+00     NA 1.35e+00 3.54e+00</span></span>
+<span><span class="co">## sigma          7.42e+00     NA 6.04e+00 8.80e+00</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $DFOP</span></span>
+<span><span class="co">##          Estimate   Pr(&gt;t)   Lower    Upper</span></span>
+<span><span class="co">## parent_0 9.89e+01 9.44e-49 95.4640 102.2573</span></span>
+<span><span class="co">## k1       1.81e-02 1.75e-01  0.0116   0.0281</span></span>
+<span><span class="co">## k2       3.62e-10 5.00e-01  0.0000      Inf</span></span>
+<span><span class="co">## g        6.06e-01 2.19e-01  0.4826   0.7178</span></span>
+<span><span class="co">## sigma    7.40e+00 2.97e-15  6.0201   8.7754</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## DTx values:</span></span>
+<span><span class="co">##      DT50     DT90 DT50_rep</span></span>
+<span><span class="co">## SFO  94.3 3.13e+02 9.43e+01</span></span>
+<span><span class="co">## IORE 96.7 1.51e+03 4.55e+02</span></span>
+<span><span class="co">## DFOP 96.4 3.79e+09 1.92e+09</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Representative half-life:</span></span>
+<span><span class="co">## [1] 454.55</span></span></code></pre>
+</div>
+</div>
+<div class="section level2">
+<h2 id="examples-where-the-representative-half-life-deviates-from-the-observed-dt50">Examples where the representative half-life deviates from the
+observed DT50<a class="anchor" aria-label="anchor" href="#examples-where-the-representative-half-life-deviates-from-the-observed-dt50"></a>
+</h2>
+<div class="section level3">
+<h3 id="example-on-page-8">Example on page 8<a class="anchor" aria-label="anchor" href="#example-on-page-8"></a>
+</h3>
+<p>For this dataset, the IORE fit does not converge when the default
+starting values used by mkin for the IORE model are used. Therefore, a
+lower value for the rate constant is used here.</p>
+<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">p8</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p8"</span><span class="op">]</span><span class="op">]</span>, parms.ini <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>k__iore_parent <span class="op">=</span> <span class="fl">1e-3</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre>
+<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre>
+<div class="sourceCode" id="cb28"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p8</span><span class="op">)</span></span></code></pre></div>
+<p><img src="NAFTA_examples_files/figure-html/p8-1.png" width="700"></p>
+<div class="sourceCode" id="cb29"><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">p8</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Sums of squares:</span></span>
+<span><span class="co">##       SFO      IORE      DFOP </span></span>
+<span><span class="co">## 1996.9408  444.9237  547.5616 </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span>
+<span><span class="co">## [1] 477.4924</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Parameters:</span></span>
+<span><span class="co">## $SFO</span></span>
+<span><span class="co">##          Estimate   Pr(&gt;t)    Lower    Upper</span></span>
+<span><span class="co">## parent_0 88.16549 6.53e-29 83.37344 92.95754</span></span>
+<span><span class="co">## k_parent  0.00803 1.67e-13  0.00674  0.00957</span></span>
+<span><span class="co">## sigma     7.44786 4.17e-10  5.66209  9.23363</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $IORE</span></span>
+<span><span class="co">##                Estimate   Pr(&gt;t)    Lower    Upper</span></span>
+<span><span class="co">## parent_0       9.77e+01 7.03e-35 9.44e+01 1.01e+02</span></span>
+<span><span class="co">## k__iore_parent 6.14e-05 3.20e-02 2.12e-05 1.78e-04</span></span>
+<span><span class="co">## N_parent       2.27e+00 4.23e-18 2.00e+00 2.54e+00</span></span>
+<span><span class="co">## sigma          3.52e+00 5.36e-10 2.67e+00 4.36e+00</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $DFOP</span></span>
+<span><span class="co">##          Estimate   Pr(&gt;t)    Lower    Upper</span></span>
+<span><span class="co">## parent_0 95.70619 8.99e-32 91.87941 99.53298</span></span>
+<span><span class="co">## k1        0.02500 5.25e-04  0.01422  0.04394</span></span>
+<span><span class="co">## k2        0.00273 6.84e-03  0.00125  0.00597</span></span>
+<span><span class="co">## g         0.58835 2.84e-06  0.36595  0.77970</span></span>
+<span><span class="co">## sigma     3.90001 6.94e-10  2.96260  4.83741</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## DTx values:</span></span>
+<span><span class="co">##      DT50 DT90 DT50_rep</span></span>
+<span><span class="co">## SFO  86.3  287     86.3</span></span>
+<span><span class="co">## IORE 53.4  668    201.0</span></span>
+<span><span class="co">## DFOP 55.6  517    253.0</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Representative half-life:</span></span>
+<span><span class="co">## [1] 201.03</span></span></code></pre>
+</div>
+</div>
+<div class="section level2">
+<h2 id="examples-where-sfo-was-not-selected-for-an-abiotic-study">Examples where SFO was not selected for an abiotic study<a class="anchor" aria-label="anchor" href="#examples-where-sfo-was-not-selected-for-an-abiotic-study"></a>
+</h2>
+<div class="section level3">
+<h3 id="example-on-page-9-upper-panel">Example on page 9, upper panel<a class="anchor" aria-label="anchor" href="#example-on-page-9-upper-panel"></a>
+</h3>
+<div class="sourceCode" id="cb31"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">p9a</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p9a"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre>
+<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre>
+<div class="sourceCode" id="cb34"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p9a</span><span class="op">)</span></span></code></pre></div>
+<p><img src="NAFTA_examples_files/figure-html/p9a-1.png" width="700"></p>
+<div class="sourceCode" id="cb35"><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">p9a</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Sums of squares:</span></span>
+<span><span class="co">##       SFO      IORE      DFOP </span></span>
+<span><span class="co">## 839.35238  88.57064   9.93363 </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span>
+<span><span class="co">## [1] 105.5678</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Parameters:</span></span>
+<span><span class="co">## $SFO</span></span>
+<span><span class="co">##          Estimate   Pr(&gt;t)   Lower   Upper</span></span>
+<span><span class="co">## parent_0  88.1933 3.06e-12 79.9447 96.4419</span></span>
+<span><span class="co">## k_parent   0.0409 2.07e-07  0.0324  0.0516</span></span>
+<span><span class="co">## sigma      7.2429 3.92e-05  4.4768 10.0090</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $IORE</span></span>
+<span><span class="co">##                Estimate   Pr(&gt;t)    Lower    Upper</span></span>
+<span><span class="co">## parent_0       9.89e+01 1.12e-16 9.54e+01 1.02e+02</span></span>
+<span><span class="co">## k__iore_parent 1.93e-05 1.13e-01 3.49e-06 1.06e-04</span></span>
+<span><span class="co">## N_parent       2.91e+00 1.45e-09 2.50e+00 3.32e+00</span></span>
+<span><span class="co">## sigma          2.35e+00 5.31e-05 1.45e+00 3.26e+00</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $DFOP</span></span>
+<span><span class="co">##          Estimate   Pr(&gt;t)  Lower  Upper</span></span>
+<span><span class="co">## parent_0 9.85e+01 2.54e-20 97.390 99.672</span></span>
+<span><span class="co">## k1       1.38e-01 3.52e-05  0.131  0.146</span></span>
+<span><span class="co">## k2       9.02e-13 5.00e-01  0.000    Inf</span></span>
+<span><span class="co">## g        6.52e-01 8.13e-06  0.642  0.661</span></span>
+<span><span class="co">## sigma    7.88e-01 6.13e-02  0.481  1.095</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## DTx values:</span></span>
+<span><span class="co">##      DT50     DT90 DT50_rep</span></span>
+<span><span class="co">## SFO  16.9 5.63e+01 1.69e+01</span></span>
+<span><span class="co">## IORE 11.6 3.37e+02 1.01e+02</span></span>
+<span><span class="co">## DFOP 10.5 1.38e+12 7.68e+11</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Representative half-life:</span></span>
+<span><span class="co">## [1] 101.43</span></span></code></pre>
+<p>In this example, the residuals of the SFO indicate a lack of fit of
+this model, so even if it was an abiotic experiment, the data do not
+suggest a simple exponential decline.</p>
+</div>
+<div class="section level3">
+<h3 id="example-on-page-9-lower-panel">Example on page 9, lower panel<a class="anchor" aria-label="anchor" href="#example-on-page-9-lower-panel"></a>
+</h3>
+<div class="sourceCode" id="cb37"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">p9b</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p9b"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre>
+<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre>
+<div class="sourceCode" id="cb40"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p9b</span><span class="op">)</span></span></code></pre></div>
+<p><img src="NAFTA_examples_files/figure-html/p9b-1.png" width="700"></p>
+<div class="sourceCode" id="cb41"><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">p9b</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Sums of squares:</span></span>
+<span><span class="co">##      SFO     IORE     DFOP </span></span>
+<span><span class="co">## 35.64867 23.22334 35.64867 </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span>
+<span><span class="co">## [1] 28.54188</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Parameters:</span></span>
+<span><span class="co">## $SFO</span></span>
+<span><span class="co">##          Estimate   Pr(&gt;t)  Lower   Upper</span></span>
+<span><span class="co">## parent_0  94.7123 2.15e-19 93.178 96.2464</span></span>
+<span><span class="co">## k_parent   0.0389 4.47e-14  0.037  0.0408</span></span>
+<span><span class="co">## sigma      1.5957 1.28e-04  0.932  2.2595</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $IORE</span></span>
+<span><span class="co">##                Estimate   Pr(&gt;t)   Lower  Upper</span></span>
+<span><span class="co">## parent_0         93.863 2.32e-18 92.4565 95.269</span></span>
+<span><span class="co">## k__iore_parent    0.127 1.85e-02  0.0504  0.321</span></span>
+<span><span class="co">## N_parent          0.711 1.88e-05  0.4843  0.937</span></span>
+<span><span class="co">## sigma             1.288 1.76e-04  0.7456  1.830</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $DFOP</span></span>
+<span><span class="co">##          Estimate   Pr(&gt;t)   Lower   Upper</span></span>
+<span><span class="co">## parent_0  94.7123 1.61e-16 93.1355 96.2891</span></span>
+<span><span class="co">## k1         0.0389 1.08e-04  0.0266  0.0569</span></span>
+<span><span class="co">## k2         0.0389 2.24e-04  0.0255  0.0592</span></span>
+<span><span class="co">## g          0.5256 5.00e-01  0.0000  1.0000</span></span>
+<span><span class="co">## sigma      1.5957 2.50e-04  0.9135  2.2779</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## DTx values:</span></span>
+<span><span class="co">##      DT50 DT90 DT50_rep</span></span>
+<span><span class="co">## SFO  17.8 59.2     17.8</span></span>
+<span><span class="co">## IORE 18.4 49.2     14.8</span></span>
+<span><span class="co">## DFOP 17.8 59.2     17.8</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Representative half-life:</span></span>
+<span><span class="co">## [1] 14.8</span></span></code></pre>
+<p>Here, mkin gives a longer slow DT50 for the DFOP model (17.8 days)
+than PestDF (13.5 days). Presumably, this is related to the fact that
+PestDF gives a negative value for the proportion of the fast degradation
+which should be between 0 and 1, inclusive. This parameter is called f
+in PestDF and g in mkin. In mkin, it is restricted to the interval from
+0 to 1.</p>
+</div>
+<div class="section level3">
+<h3 id="example-on-page-10">Example on page 10<a class="anchor" aria-label="anchor" href="#example-on-page-10"></a>
+</h3>
+<div class="sourceCode" id="cb43"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">p10</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p10"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Warning in sqrt(diag(covar_notrans)): NaNs produced</span></span></code></pre>
+<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre>
+<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre>
+<div class="sourceCode" id="cb47"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p10</span><span class="op">)</span></span></code></pre></div>
+<p><img src="NAFTA_examples_files/figure-html/p10-1.png" width="700"></p>
+<div class="sourceCode" id="cb48"><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">p10</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Sums of squares:</span></span>
+<span><span class="co">##      SFO     IORE     DFOP </span></span>
+<span><span class="co">## 899.4089 336.4348 899.4089 </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span>
+<span><span class="co">## [1] 413.4841</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Parameters:</span></span>
+<span><span class="co">## $SFO</span></span>
+<span><span class="co">##          Estimate   Pr(&gt;t)   Lower    Upper</span></span>
+<span><span class="co">## parent_0 101.7315 6.42e-11 91.9259 111.5371</span></span>
+<span><span class="co">## k_parent   0.0495 1.70e-07  0.0404   0.0607</span></span>
+<span><span class="co">## sigma      8.0152 1.28e-04  4.6813  11.3491</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $IORE</span></span>
+<span><span class="co">##                Estimate   Pr(&gt;t)  Lower   Upper</span></span>
+<span><span class="co">## parent_0          96.86 3.32e-12 90.848 102.863</span></span>
+<span><span class="co">## k__iore_parent     2.96 7.91e-02  0.687  12.761</span></span>
+<span><span class="co">## N_parent           0.00 5.00e-01 -0.372   0.372</span></span>
+<span><span class="co">## sigma              4.90 1.77e-04  2.837   6.968</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $DFOP</span></span>
+<span><span class="co">##          Estimate   Pr(&gt;t)   Lower   Upper</span></span>
+<span><span class="co">## parent_0 101.7315 1.41e-09 91.6534 111.810</span></span>
+<span><span class="co">## k1         0.0495 3.04e-03  0.0188   0.131</span></span>
+<span><span class="co">## k2         0.0495 4.92e-04  0.0197   0.124</span></span>
+<span><span class="co">## g          0.4487      NaN  0.0000   1.000</span></span>
+<span><span class="co">## sigma      8.0152 2.50e-04  4.5886  11.442</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## DTx values:</span></span>
+<span><span class="co">##      DT50 DT90 DT50_rep</span></span>
+<span><span class="co">## SFO  14.0 46.5    14.00</span></span>
+<span><span class="co">## IORE 16.4 29.4     8.86</span></span>
+<span><span class="co">## DFOP 14.0 46.5    14.00</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Representative half-life:</span></span>
+<span><span class="co">## [1] 8.86</span></span></code></pre>
+<p>Here, a value below N is given for the IORE model, because the data
+suggests a faster decline towards the end of the experiment, which
+appears physically rather unlikely in the case of a photolysis study. It
+seems PestDF does not constrain N to values above zero, thus the slight
+difference in IORE model parameters between PestDF and mkin.</p>
+</div>
+</div>
+<div class="section level2">
+<h2 id="the-dt50-was-not-observed-during-the-study">The DT50 was not observed during the study<a class="anchor" aria-label="anchor" href="#the-dt50-was-not-observed-during-the-study"></a>
+</h2>
+<div class="section level3">
+<h3 id="example-on-page-11">Example on page 11<a class="anchor" aria-label="anchor" href="#example-on-page-11"></a>
+</h3>
+<div class="sourceCode" id="cb50"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">p11</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p11"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre>
+<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre>
+<div class="sourceCode" id="cb53"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p11</span><span class="op">)</span></span></code></pre></div>
+<p><img src="NAFTA_examples_files/figure-html/p11-1.png" width="700"></p>
+<div class="sourceCode" id="cb54"><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">p11</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Sums of squares:</span></span>
+<span><span class="co">##      SFO     IORE     DFOP </span></span>
+<span><span class="co">## 579.6805 204.7932 144.7783 </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span>
+<span><span class="co">## [1] 251.6944</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Parameters:</span></span>
+<span><span class="co">## $SFO</span></span>
+<span><span class="co">##          Estimate   Pr(&gt;t)    Lower    Upper</span></span>
+<span><span class="co">## parent_0 96.15820 4.83e-13 90.24934 1.02e+02</span></span>
+<span><span class="co">## k_parent  0.00321 4.71e-05  0.00222 4.64e-03</span></span>
+<span><span class="co">## sigma     6.43473 1.28e-04  3.75822 9.11e+00</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $IORE</span></span>
+<span><span class="co">##                Estimate Pr(&gt;t)    Lower    Upper</span></span>
+<span><span class="co">## parent_0       1.05e+02     NA 9.90e+01 1.10e+02</span></span>
+<span><span class="co">## k__iore_parent 3.11e-17     NA 1.35e-20 7.18e-14</span></span>
+<span><span class="co">## N_parent       8.36e+00     NA 6.62e+00 1.01e+01</span></span>
+<span><span class="co">## sigma          3.82e+00     NA 2.21e+00 5.44e+00</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $DFOP</span></span>
+<span><span class="co">##          Estimate   Pr(&gt;t)    Lower    Upper</span></span>
+<span><span class="co">## parent_0 1.05e+02 9.47e-13  99.9990 109.1224</span></span>
+<span><span class="co">## k1       4.41e-02 5.95e-03   0.0296   0.0658</span></span>
+<span><span class="co">## k2       9.94e-13 5.00e-01   0.0000      Inf</span></span>
+<span><span class="co">## g        3.22e-01 1.45e-03   0.2814   0.3650</span></span>
+<span><span class="co">## sigma    3.22e+00 3.52e-04   1.8410   4.5906</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## DTx values:</span></span>
+<span><span class="co">##          DT50     DT90 DT50_rep</span></span>
+<span><span class="co">## SFO  2.16e+02 7.18e+02 2.16e+02</span></span>
+<span><span class="co">## IORE 9.73e+02 1.37e+08 4.11e+07</span></span>
+<span><span class="co">## DFOP 3.07e+11 1.93e+12 6.98e+11</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Representative half-life:</span></span>
+<span><span class="co">## [1] 41148169</span></span></code></pre>
+<p>In this case, the DFOP fit reported for PestDF resulted in a negative
+value for the slower rate constant, which is not possible in mkin. The
+other results are in agreement.</p>
+</div>
+</div>
+<div class="section level2">
+<h2 id="n-is-less-than-1-and-the-dfop-rate-constants-are-like-the-sfo-rate-constant">N is less than 1 and the DFOP rate constants are like the SFO rate
+constant<a class="anchor" aria-label="anchor" href="#n-is-less-than-1-and-the-dfop-rate-constants-are-like-the-sfo-rate-constant"></a>
+</h2>
+<p>In the following three examples, the same results are obtained with
+mkin as reported for PestDF. As in the case on page 10, the N values
+below 1 are deemed unrealistic and appear to be the result of an
+overparameterisation.</p>
+<div class="section level3">
+<h3 id="example-on-page-12-upper-panel">Example on page 12, upper panel<a class="anchor" aria-label="anchor" href="#example-on-page-12-upper-panel"></a>
+</h3>
+<div class="sourceCode" id="cb56"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">p12a</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p12a"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Warning in summary.mkinfit(x): Could not calculate correlation; no covariance</span></span>
+<span><span class="co">## matrix</span></span></code></pre>
+<pre><code><span><span class="co">## Warning in sqrt(diag(covar_notrans)): NaNs produced</span></span></code></pre>
+<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre>
+<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre>
+<div class="sourceCode" id="cb61"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p12a</span><span class="op">)</span></span></code></pre></div>
+<p><img src="NAFTA_examples_files/figure-html/p12a-1.png" width="700"></p>
+<div class="sourceCode" id="cb62"><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">p12a</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Sums of squares:</span></span>
+<span><span class="co">##      SFO     IORE     DFOP </span></span>
+<span><span class="co">## 695.4440 220.0685 695.4440 </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span>
+<span><span class="co">## [1] 270.4679</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Parameters:</span></span>
+<span><span class="co">## $SFO</span></span>
+<span><span class="co">##          Estimate   Pr(&gt;t)  Lower   Upper</span></span>
+<span><span class="co">## parent_0  100.521 8.75e-12 92.461 108.581</span></span>
+<span><span class="co">## k_parent    0.124 3.61e-08  0.104   0.148</span></span>
+<span><span class="co">## sigma       7.048 1.28e-04  4.116   9.980</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $IORE</span></span>
+<span><span class="co">##                Estimate Pr(&gt;t) Lower Upper</span></span>
+<span><span class="co">## parent_0         96.823     NA    NA    NA</span></span>
+<span><span class="co">## k__iore_parent    2.436     NA    NA    NA</span></span>
+<span><span class="co">## N_parent          0.263     NA    NA    NA</span></span>
+<span><span class="co">## sigma             3.965     NA    NA    NA</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $DFOP</span></span>
+<span><span class="co">##          Estimate   Pr(&gt;t)   Lower   Upper</span></span>
+<span><span class="co">## parent_0  100.521 2.74e-10 92.2366 108.805</span></span>
+<span><span class="co">## k1          0.124 2.53e-05  0.0908   0.170</span></span>
+<span><span class="co">## k2          0.124 2.52e-02  0.0456   0.339</span></span>
+<span><span class="co">## g           0.793      NaN  0.0000   1.000</span></span>
+<span><span class="co">## sigma       7.048 2.50e-04  4.0349  10.061</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## DTx values:</span></span>
+<span><span class="co">##      DT50 DT90 DT50_rep</span></span>
+<span><span class="co">## SFO  5.58 18.5     5.58</span></span>
+<span><span class="co">## IORE 6.49 13.2     3.99</span></span>
+<span><span class="co">## DFOP 5.58 18.5     5.58</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Representative half-life:</span></span>
+<span><span class="co">## [1] 3.99</span></span></code></pre>
+</div>
+<div class="section level3">
+<h3 id="example-on-page-12-lower-panel">Example on page 12, lower panel<a class="anchor" aria-label="anchor" href="#example-on-page-12-lower-panel"></a>
+</h3>
+<div class="sourceCode" id="cb64"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">p12b</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p12b"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></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 qt(alpha/2, rdf): NaNs produced</span></span></code></pre>
+<pre><code><span><span class="co">## Warning in qt(1 - alpha/2, rdf): NaNs produced</span></span></code></pre>
+<pre><code><span><span class="co">## Warning in pt(abs(tval), rdf, lower.tail = FALSE): NaNs produced</span></span></code></pre>
+<pre><code><span><span class="co">## Warning in cov2cor(ans$covar): diag(V) had non-positive or NA entries; the</span></span>
+<span><span class="co">## non-finite result may be dubious</span></span></code></pre>
+<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre>
+<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre>
+<div class="sourceCode" id="cb72"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p12b</span><span class="op">)</span></span></code></pre></div>
+<p><img src="NAFTA_examples_files/figure-html/p12b-1.png" width="700"></p>
+<div class="sourceCode" id="cb73"><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">p12b</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Sums of squares:</span></span>
+<span><span class="co">##      SFO     IORE     DFOP </span></span>
+<span><span class="co">## 58.90242 19.06353 58.90242 </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span>
+<span><span class="co">## [1] 51.51756</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Parameters:</span></span>
+<span><span class="co">## $SFO</span></span>
+<span><span class="co">##          Estimate  Pr(&gt;t)   Lower    Upper</span></span>
+<span><span class="co">## parent_0  97.6840 0.00039 85.9388 109.4292</span></span>
+<span><span class="co">## k_parent   0.0589 0.00261  0.0431   0.0805</span></span>
+<span><span class="co">## sigma      3.4323 0.04356 -1.2377   8.1023</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $IORE</span></span>
+<span><span class="co">##                Estimate Pr(&gt;t)     Lower  Upper</span></span>
+<span><span class="co">## parent_0         95.523 0.0055 74.539157 116.51</span></span>
+<span><span class="co">## k__iore_parent    0.333 0.1433  0.000717 154.57</span></span>
+<span><span class="co">## N_parent          0.568 0.0677 -0.989464   2.13</span></span>
+<span><span class="co">## sigma             1.953 0.0975 -5.893100   9.80</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $DFOP</span></span>
+<span><span class="co">##          Estimate Pr(&gt;t) Lower Upper</span></span>
+<span><span class="co">## parent_0  97.6840    NaN   NaN   NaN</span></span>
+<span><span class="co">## k1         0.0589    NaN    NA    NA</span></span>
+<span><span class="co">## k2         0.0589    NaN    NA    NA</span></span>
+<span><span class="co">## g          0.6473    NaN    NA    NA</span></span>
+<span><span class="co">## sigma      3.4323    NaN   NaN   NaN</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## DTx values:</span></span>
+<span><span class="co">##      DT50 DT90 DT50_rep</span></span>
+<span><span class="co">## SFO  11.8 39.1    11.80</span></span>
+<span><span class="co">## IORE 12.9 31.4     9.46</span></span>
+<span><span class="co">## DFOP 11.8 39.1    11.80</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Representative half-life:</span></span>
+<span><span class="co">## [1] 9.46</span></span></code></pre>
+</div>
+<div class="section level3">
+<h3 id="example-on-page-13">Example on page 13<a class="anchor" aria-label="anchor" href="#example-on-page-13"></a>
+</h3>
+<div class="sourceCode" id="cb75"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">p13</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p13"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre>
+<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre>
+<div class="sourceCode" id="cb78"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p13</span><span class="op">)</span></span></code></pre></div>
+<p><img src="NAFTA_examples_files/figure-html/p13-1.png" width="700"></p>
+<div class="sourceCode" id="cb79"><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">p13</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Sums of squares:</span></span>
+<span><span class="co">##      SFO     IORE     DFOP </span></span>
+<span><span class="co">## 174.5971 142.3951 174.5971 </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span>
+<span><span class="co">## [1] 172.131</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Parameters:</span></span>
+<span><span class="co">## $SFO</span></span>
+<span><span class="co">##          Estimate   Pr(&gt;t)    Lower    Upper</span></span>
+<span><span class="co">## parent_0 92.73500 5.99e-17 89.61936 95.85065</span></span>
+<span><span class="co">## k_parent  0.00258 2.42e-09  0.00223  0.00299</span></span>
+<span><span class="co">## sigma     3.41172 7.07e-05  2.05455  4.76888</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $IORE</span></span>
+<span><span class="co">##                Estimate   Pr(&gt;t)    Lower  Upper</span></span>
+<span><span class="co">## parent_0        91.6016 6.34e-16 88.53086 94.672</span></span>
+<span><span class="co">## k__iore_parent   0.0396 2.36e-01  0.00207  0.759</span></span>
+<span><span class="co">## N_parent         0.3541 1.46e-01 -0.35153  1.060</span></span>
+<span><span class="co">## sigma            3.0811 9.64e-05  1.84296  4.319</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $DFOP</span></span>
+<span><span class="co">##          Estimate Pr(&gt;t)    Lower    Upper</span></span>
+<span><span class="co">## parent_0 92.73500     NA 8.95e+01 95.92118</span></span>
+<span><span class="co">## k1        0.00258     NA 4.18e-04  0.01592</span></span>
+<span><span class="co">## k2        0.00258     NA 1.75e-03  0.00381</span></span>
+<span><span class="co">## g         0.16452     NA 0.00e+00  1.00000</span></span>
+<span><span class="co">## sigma     3.41172     NA 2.02e+00  4.79960</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## DTx values:</span></span>
+<span><span class="co">##      DT50 DT90 DT50_rep</span></span>
+<span><span class="co">## SFO   269  892      269</span></span>
+<span><span class="co">## IORE  261  560      169</span></span>
+<span><span class="co">## DFOP  269  892      269</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Representative half-life:</span></span>
+<span><span class="co">## [1] 168.51</span></span></code></pre>
+</div>
+</div>
+<div class="section level2">
+<h2 id="dt50-not-observed-in-the-study-and-dfop-problems-in-pestdf">DT50 not observed in the study and DFOP problems in PestDF<a class="anchor" aria-label="anchor" href="#dt50-not-observed-in-the-study-and-dfop-problems-in-pestdf"></a>
+</h2>
+<div class="sourceCode" id="cb81"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">p14</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p14"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></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 cov2cor(ans$covar): diag(V) had non-positive or NA entries; the</span></span>
+<span><span class="co">## non-finite result may be dubious</span></span></code></pre>
+<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre>
+<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre>
+<div class="sourceCode" id="cb86"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p14</span><span class="op">)</span></span></code></pre></div>
+<p><img src="NAFTA_examples_files/figure-html/p14-1.png" width="700"></p>
+<div class="sourceCode" id="cb87"><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">p14</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Sums of squares:</span></span>
+<span><span class="co">##      SFO     IORE     DFOP </span></span>
+<span><span class="co">## 48.43249 28.67746 27.26248 </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span>
+<span><span class="co">## [1] 32.83337</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Parameters:</span></span>
+<span><span class="co">## $SFO</span></span>
+<span><span class="co">##          Estimate   Pr(&gt;t)    Lower    Upper</span></span>
+<span><span class="co">## parent_0 99.47124 2.06e-30 98.42254 1.01e+02</span></span>
+<span><span class="co">## k_parent  0.00279 3.75e-15  0.00256 3.04e-03</span></span>
+<span><span class="co">## sigma     1.55616 3.81e-06  1.03704 2.08e+00</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $IORE</span></span>
+<span><span class="co">##                Estimate Pr(&gt;t) Lower Upper</span></span>
+<span><span class="co">## parent_0       1.00e+02     NA   NaN   NaN</span></span>
+<span><span class="co">## k__iore_parent 9.44e-08     NA   NaN   NaN</span></span>
+<span><span class="co">## N_parent       3.31e+00     NA   NaN   NaN</span></span>
+<span><span class="co">## sigma          1.20e+00     NA 0.796   1.6</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $DFOP</span></span>
+<span><span class="co">##          Estimate   Pr(&gt;t)    Lower    Upper</span></span>
+<span><span class="co">## parent_0 1.00e+02 2.96e-28 99.40280 101.2768</span></span>
+<span><span class="co">## k1       9.53e-03 1.20e-01  0.00638   0.0143</span></span>
+<span><span class="co">## k2       5.21e-12 5.00e-01  0.00000      Inf</span></span>
+<span><span class="co">## g        3.98e-01 2.19e-01  0.30481   0.4998</span></span>
+<span><span class="co">## sigma    1.17e+00 7.68e-06  0.77406   1.5610</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## DTx values:</span></span>
+<span><span class="co">##          DT50     DT90 DT50_rep</span></span>
+<span><span class="co">## SFO  2.48e+02 8.25e+02 2.48e+02</span></span>
+<span><span class="co">## IORE 4.34e+02 2.22e+04 6.70e+03</span></span>
+<span><span class="co">## DFOP 3.55e+10 3.44e+11 1.33e+11</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Representative half-life:</span></span>
+<span><span class="co">## [1] 6697.44</span></span></code></pre>
+<p>The slower rate constant reported by PestDF is negative, which is not
+physically realistic, and not possible in mkin. The other fits give the
+same results in mkin and PestDF.</p>
+</div>
+<div class="section level2">
+<h2 id="n-is-less-than-1-and-dfop-fraction-parameter-is-below-zero">N is less than 1 and DFOP fraction parameter is below zero<a class="anchor" aria-label="anchor" href="#n-is-less-than-1-and-dfop-fraction-parameter-is-below-zero"></a>
+</h2>
+<div class="sourceCode" id="cb89"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">p15a</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p15a"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></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 cov2cor(ans$covar): diag(V) had non-positive or NA entries; the</span></span>
+<span><span class="co">## non-finite result may be dubious</span></span></code></pre>
+<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre>
+<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre>
+<div class="sourceCode" id="cb94"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p15a</span><span class="op">)</span></span></code></pre></div>
+<p><img src="NAFTA_examples_files/figure-html/p15a-1.png" width="700"></p>
+<div class="sourceCode" id="cb95"><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">p15a</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Sums of squares:</span></span>
+<span><span class="co">##      SFO     IORE     DFOP </span></span>
+<span><span class="co">## 245.5248 135.0132 245.5248 </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span>
+<span><span class="co">## [1] 165.9335</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Parameters:</span></span>
+<span><span class="co">## $SFO</span></span>
+<span><span class="co">##          Estimate   Pr(&gt;t)    Lower   Upper</span></span>
+<span><span class="co">## parent_0 97.96751 2.00e-15 94.32049 101.615</span></span>
+<span><span class="co">## k_parent  0.00952 4.93e-09  0.00824   0.011</span></span>
+<span><span class="co">## sigma     4.18778 1.28e-04  2.44588   5.930</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $IORE</span></span>
+<span><span class="co">##                Estimate   Pr(&gt;t)  Lower  Upper</span></span>
+<span><span class="co">## parent_0         95.874 2.94e-15 92.937 98.811</span></span>
+<span><span class="co">## k__iore_parent    0.629 2.11e-01  0.044  8.982</span></span>
+<span><span class="co">## N_parent          0.000 5.00e-01 -0.642  0.642</span></span>
+<span><span class="co">## sigma             3.105 1.78e-04  1.795  4.416</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $DFOP</span></span>
+<span><span class="co">##          Estimate   Pr(&gt;t)    Lower    Upper</span></span>
+<span><span class="co">## parent_0 97.96751 2.85e-13 94.21913 101.7159</span></span>
+<span><span class="co">## k1        0.00952 6.28e-02  0.00260   0.0349</span></span>
+<span><span class="co">## k2        0.00952 1.27e-04  0.00652   0.0139</span></span>
+<span><span class="co">## g         0.21241 5.00e-01       NA       NA</span></span>
+<span><span class="co">## sigma     4.18778 2.50e-04  2.39747   5.9781</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## DTx values:</span></span>
+<span><span class="co">##      DT50 DT90 DT50_rep</span></span>
+<span><span class="co">## SFO  72.8  242     72.8</span></span>
+<span><span class="co">## IORE 76.3  137     41.3</span></span>
+<span><span class="co">## DFOP 72.8  242     72.8</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Representative half-life:</span></span>
+<span><span class="co">## [1] 41.33</span></span></code></pre>
+<div class="sourceCode" id="cb97"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">p15b</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p15b"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Warning in summary.mkinfit(x): Could not calculate correlation; no covariance</span></span>
+<span><span class="co">## matrix</span></span></code></pre>
+<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre>
+<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre>
+<div class="sourceCode" id="cb101"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p15b</span><span class="op">)</span></span></code></pre></div>
+<p><img src="NAFTA_examples_files/figure-html/p15b-1.png" width="700"></p>
+<div class="sourceCode" id="cb102"><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">p15b</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Sums of squares:</span></span>
+<span><span class="co">##       SFO      IORE      DFOP </span></span>
+<span><span class="co">## 106.91629  68.55574 106.91629 </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span>
+<span><span class="co">## [1] 84.25618</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Parameters:</span></span>
+<span><span class="co">## $SFO</span></span>
+<span><span class="co">##          Estimate   Pr(&gt;t)    Lower    Upper</span></span>
+<span><span class="co">## parent_0 1.01e+02 3.06e-17 98.31594 1.03e+02</span></span>
+<span><span class="co">## k_parent 4.86e-03 2.48e-10  0.00435 5.42e-03</span></span>
+<span><span class="co">## sigma    2.76e+00 1.28e-04  1.61402 3.91e+00</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $IORE</span></span>
+<span><span class="co">##                Estimate   Pr(&gt;t)    Lower  Upper</span></span>
+<span><span class="co">## parent_0          99.83 1.81e-16 97.51348 102.14</span></span>
+<span><span class="co">## k__iore_parent     0.38 3.22e-01  0.00352  41.05</span></span>
+<span><span class="co">## N_parent           0.00 5.00e-01 -1.07696   1.08</span></span>
+<span><span class="co">## sigma              2.21 2.57e-04  1.23245   3.19</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $DFOP</span></span>
+<span><span class="co">##          Estimate Pr(&gt;t) Lower Upper</span></span>
+<span><span class="co">## parent_0 1.01e+02     NA    NA    NA</span></span>
+<span><span class="co">## k1       4.86e-03     NA    NA    NA</span></span>
+<span><span class="co">## k2       4.86e-03     NA    NA    NA</span></span>
+<span><span class="co">## g        1.88e-01     NA    NA    NA</span></span>
+<span><span class="co">## sigma    2.76e+00     NA    NA    NA</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## DTx values:</span></span>
+<span><span class="co">##      DT50 DT90 DT50_rep</span></span>
+<span><span class="co">## SFO   143  474    143.0</span></span>
+<span><span class="co">## IORE  131  236     71.2</span></span>
+<span><span class="co">## DFOP  143  474    143.0</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Representative half-life:</span></span>
+<span><span class="co">## [1] 71.18</span></span></code></pre>
+<p>In mkin, only the IORE fit is affected (deemed unrealistic), as the
+fraction parameter of the DFOP model is restricted to the interval
+between 0 and 1 in mkin. The SFO fits give the same results for both
+mkin and PestDF.</p>
+</div>
+<div class="section level2">
+<h2 id="the-dfop-fraction-parameter-is-greater-than-1">The DFOP fraction parameter is greater than 1<a class="anchor" aria-label="anchor" href="#the-dfop-fraction-parameter-is-greater-than-1"></a>
+</h2>
+<div class="sourceCode" id="cb104"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">p16</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p16"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre>
+<pre><code><span><span class="co">## The representative half-life of the IORE model is longer than the one corresponding</span></span></code></pre>
+<pre><code><span><span class="co">## to the terminal degradation rate found with the DFOP model.</span></span></code></pre>
+<pre><code><span><span class="co">## The representative half-life obtained from the DFOP model may be used</span></span></code></pre>
+<div class="sourceCode" id="cb109"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p16</span><span class="op">)</span></span></code></pre></div>
+<p><img src="NAFTA_examples_files/figure-html/p16-1.png" width="700"></p>
+<div class="sourceCode" id="cb110"><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">p16</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Sums of squares:</span></span>
+<span><span class="co">##      SFO     IORE     DFOP </span></span>
+<span><span class="co">## 3831.804 2062.008 1550.980 </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span>
+<span><span class="co">## [1] 2247.348</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Parameters:</span></span>
+<span><span class="co">## $SFO</span></span>
+<span><span class="co">##          Estimate   Pr(&gt;t)  Lower Upper</span></span>
+<span><span class="co">## parent_0   71.953 2.33e-13 60.509 83.40</span></span>
+<span><span class="co">## k_parent    0.159 4.86e-05  0.102  0.25</span></span>
+<span><span class="co">## sigma      11.302 1.25e-08  8.308 14.30</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $IORE</span></span>
+<span><span class="co">##                Estimate   Pr(&gt;t)    Lower    Upper</span></span>
+<span><span class="co">## parent_0       8.74e+01 2.48e-16 7.72e+01 97.52972</span></span>
+<span><span class="co">## k__iore_parent 4.55e-04 2.16e-01 3.48e-05  0.00595</span></span>
+<span><span class="co">## N_parent       2.70e+00 1.21e-08 1.99e+00  3.40046</span></span>
+<span><span class="co">## sigma          8.29e+00 1.61e-08 6.09e+00 10.49062</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## $DFOP</span></span>
+<span><span class="co">##          Estimate   Pr(&gt;t)   Lower  Upper</span></span>
+<span><span class="co">## parent_0  88.5333 7.40e-18 79.9836 97.083</span></span>
+<span><span class="co">## k1        18.8461 5.00e-01  0.0000    Inf</span></span>
+<span><span class="co">## k2         0.0776 1.41e-05  0.0518  0.116</span></span>
+<span><span class="co">## g          0.4733 1.41e-09  0.3674  0.582</span></span>
+<span><span class="co">## sigma      7.1902 2.11e-08  5.2785  9.102</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## DTx values:</span></span>
+<span><span class="co">##      DT50 DT90 DT50_rep</span></span>
+<span><span class="co">## SFO  4.35 14.4     4.35</span></span>
+<span><span class="co">## IORE 1.48 32.1     9.67</span></span>
+<span><span class="co">## DFOP 0.67 21.4     8.93</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">## Representative half-life:</span></span>
+<span><span class="co">## [1] 8.93</span></span></code></pre>
+<p>In PestDF, the DFOP fit seems to have stuck in a local minimum, as
+mkin finds a solution with a much lower
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msup><mi>χ</mi><mn>2</mn></msup><annotation encoding="application/x-tex">\chi^2</annotation></semantics></math>
+error level. As the half-life from the slower rate constant of the DFOP
+model is larger than the IORE derived half-life, the NAFTA
+recommendation obtained with mkin is to use the DFOP representative
+half-life of 8.9 days.</p>
+</div>
+<div class="section level2">
+<h2 id="conclusions">Conclusions<a class="anchor" aria-label="anchor" href="#conclusions"></a>
+</h2>
+<p>The results obtained with mkin deviate from the results obtained with
+PestDF either in cases where one of the interpretive rules would apply,
+i.e. the IORE parameter N is less than one or the DFOP k values obtained
+with PestDF are equal to the SFO k values, or in cases where the DFOP
+model did not converge, which often lead to negative rate constants
+returned by PestDF.</p>
+<p>Therefore, mkin appears to suitable for kinetic evaluations according
+to the NAFTA guidance.</p>
+</div>
+<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 csl-bib-body hanging-indent">
+<div id="ref-usepa2015" class="csl-entry">
+US EPA. 2015. <span>“Standard Operating Procedure for Using the NAFTA
+Guidance to Calculate Representative Half-Life Values and Characterizing
+Pesticide Degradation.”</span> <a href="https://www.epa.gov/pesticide-science-and-assessing-pesticide-risks/standard-operating-procedure-using-nafta-guidance" class="external-link">https://www.epa.gov/pesticide-science-and-assessing-pesticide-risks/standard-operating-procedure-using-nafta-guidance</a>.
+</div>
+</div>
+</div>
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside>
+</div>
+
+
+
+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Johannes Ranke.</p>
+</div>
+
+<div class="pkgdown-footer-right">
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
+</div>
+
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+</div>
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@@ -0,0 +1,1133 @@
+<!DOCTYPE html>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en">
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+<li><a class="dropdown-item" href="../../articles/mkin.html">Introduction to mkin</a></li>
+    <li><hr class="dropdown-divider"></li>
+    <li><h6 class="dropdown-header" data-toc-skip>Example evaluations with (generalised) nonlinear least squares</h6></li>
+    <li><a class="dropdown-item" href="../../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a></li>
+    <li><a class="dropdown-item" href="../../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a></li>
+    <li><a class="dropdown-item" href="../../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a></li>
+    <li><hr class="dropdown-divider"></li>
+    <li><h6 class="dropdown-header" data-toc-skip>Example evaluations with hierarchical models (nonlinear mixed-effects models)</h6></li>
+    <li><a class="dropdown-item" href="../../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a></li>
+    <li><a class="dropdown-item" href="../../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a></li>
+    <li><a class="dropdown-item" href="../../articles/prebuilt/2023_mesotrione_parent.html">Testing covariate modelling in hierarchical parent degradation kinetics with residue data on mesotrione</a></li>
+    <li><a class="dropdown-item" href="../../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a></li>
+    <li><a class="dropdown-item" href="../../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a></li>
+    <li><a class="dropdown-item" href="../../articles/web_only/multistart.html">Short demo of the multistart method</a></li>
+    <li><hr class="dropdown-divider"></li>
+    <li><h6 class="dropdown-header" data-toc-skip>Performance</h6></li>
+    <li><a class="dropdown-item" href="../../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a></li>
+    <li><a class="dropdown-item" href="../../articles/web_only/benchmarks.html">Benchmark timings for mkin</a></li>
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+    <li><a class="dropdown-item" href="../../articles/twa.html">Calculation of time weighted average concentrations with mkin</a></li>
+    <li><a class="dropdown-item" href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a></li>
+  </ul>
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+
+      <h1>Benchmark timings for mkin</h1>
+                        <h4 data-toc-skip class="author">Johannes
+Ranke</h4>
+            
+            <h4 data-toc-skip class="date">Last change 17 February 2023
+(rebuilt 2025-02-14)</h4>
+      
+      <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/benchmarks.rmd" class="external-link"><code>vignettes/web_only/benchmarks.rmd</code></a></small>
+      <div class="d-none name"><code>benchmarks.rmd</code></div>
+    </div>
+
+    
+    
+<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><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><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><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 class="co"># erroneously used FOMC twice, not fixed for consistency</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><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 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 style="width:100%;" class="table">
+<colgroup>
+<col width="8%">
+<col width="54%">
+<col width="8%">
+<col width="12%">
+<col width="8%">
+<col width="9%">
+</colgroup>
+<thead><tr class="header">
+<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">1.881</td>
+<td align="right">3.504</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">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">1.957</td>
+<td align="right">3.633</td>
+</tr>
+<tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">4.2.2</td>
+<td align="left">1.2.0</td>
+<td align="right">2.140</td>
+<td align="right">3.774</td>
+</tr>
+<tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">4.2.2</td>
+<td align="left">1.2.2</td>
+<td align="right">2.187</td>
+<td align="right">3.851</td>
+</tr>
+<tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">4.2.2</td>
+<td align="left">1.2.0</td>
+<td align="right">1.288</td>
+<td align="right">1.794</td>
+</tr>
+<tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">4.2.2</td>
+<td align="left">1.2.2</td>
+<td align="right">1.276</td>
+<td align="right">1.804</td>
+</tr>
+<tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">4.2.2</td>
+<td align="left">1.2.3</td>
+<td align="right">1.370</td>
+<td align="right">1.883</td>
+</tr>
+<tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">4.2.3</td>
+<td align="left">1.2.3</td>
+<td align="right">1.406</td>
+<td align="right">1.948</td>
+</tr>
+<tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">4.3.0</td>
+<td align="left">1.2.4</td>
+<td align="right">1.386</td>
+<td align="right">1.960</td>
+</tr>
+<tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Intel(R) Xeon(R) Gold 6134 CPU @ 3.20GHz</td>
+<td align="left">4.3.1</td>
+<td align="left">1.2.5</td>
+<td align="right">2.369</td>
+<td align="right">3.632</td>
+</tr>
+<tr class="even">
+<td align="left">Linux</td>
+<td align="left">Intel(R) Xeon(R) Gold 6134 CPU @ 3.20GHz</td>
+<td align="left">4.3.1</td>
+<td align="left">1.2.6</td>
+<td align="right">2.856</td>
+<td align="right">4.960</td>
+</tr>
+<tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">4.3.2</td>
+<td align="left">1.2.6</td>
+<td align="right">1.408</td>
+<td align="right">2.041</td>
+</tr>
+<tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">4.4.2</td>
+<td align="left">1.2.9</td>
+<td align="right">1.323</td>
+<td align="right">1.925</td>
+</tr>
+<tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">4.4.2</td>
+<td align="left">1.2.10</td>
+<td align="right">1.371</td>
+<td align="right">1.980</td>
+</tr>
+</tbody>
+</table>
+</div>
+<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">
+<colgroup>
+<col width="7%">
+<col width="50%">
+<col width="7%">
+<col width="11%">
+<col width="7%">
+<col width="8%">
+<col width="7%">
+</colgroup>
+<thead><tr class="header">
+<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">1.430</td>
+<td align="right">6.344</td>
+<td align="right">2.798</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">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">1.503</td>
+<td align="right">6.147</td>
+<td align="right">2.803</td>
+</tr>
+<tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">4.2.2</td>
+<td align="left">1.2.0</td>
+<td align="right">1.554</td>
+<td align="right">6.193</td>
+<td align="right">2.843</td>
+</tr>
+<tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">4.2.2</td>
+<td align="left">1.2.2</td>
+<td align="right">1.585</td>
+<td align="right">6.335</td>
+<td align="right">3.003</td>
+</tr>
+<tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">4.2.2</td>
+<td align="left">1.2.0</td>
+<td align="right">0.792</td>
+<td align="right">2.378</td>
+<td align="right">1.245</td>
+</tr>
+<tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">4.2.2</td>
+<td align="left">1.2.2</td>
+<td align="right">0.784</td>
+<td align="right">2.355</td>
+<td align="right">1.233</td>
+</tr>
+<tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">4.2.2</td>
+<td align="left">1.2.3</td>
+<td align="right">0.770</td>
+<td align="right">2.011</td>
+<td align="right">1.123</td>
+</tr>
+<tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">4.2.3</td>
+<td align="left">1.2.3</td>
+<td align="right">0.793</td>
+<td align="right">2.109</td>
+<td align="right">1.178</td>
+</tr>
+<tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">4.3.0</td>
+<td align="left">1.2.4</td>
+<td align="right">0.779</td>
+<td align="right">2.080</td>
+<td align="right">1.106</td>
+</tr>
+<tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Intel(R) Xeon(R) Gold 6134 CPU @ 3.20GHz</td>
+<td align="left">4.3.1</td>
+<td align="left">1.2.5</td>
+<td align="right">1.823</td>
+<td align="right">5.555</td>
+<td align="right">2.404</td>
+</tr>
+<tr class="even">
+<td align="left">Linux</td>
+<td align="left">Intel(R) Xeon(R) Gold 6134 CPU @ 3.20GHz</td>
+<td align="left">4.3.1</td>
+<td align="left">1.2.6</td>
+<td align="right">1.761</td>
+<td align="right">5.405</td>
+<td align="right">2.462</td>
+</tr>
+<tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">4.3.2</td>
+<td align="left">1.2.6</td>
+<td align="right">0.795</td>
+<td align="right">2.228</td>
+<td align="right">1.178</td>
+</tr>
+<tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">4.4.2</td>
+<td align="left">1.2.9</td>
+<td align="right">0.754</td>
+<td align="right">2.153</td>
+<td align="right">1.139</td>
+</tr>
+<tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">4.4.2</td>
+<td align="left">1.2.10</td>
+<td align="right">0.762</td>
+<td align="right">2.179</td>
+<td align="right">1.131</td>
+</tr>
+</tbody>
+</table>
+</div>
+<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 style="width:100%;" class="table">
+<colgroup>
+<col width="5%">
+<col width="40%">
+<col width="5%">
+<col width="8%">
+<col width="5%">
+<col width="5%">
+<col width="5%">
+<col width="6%">
+<col width="5%">
+<col width="6%">
+</colgroup>
+<thead><tr class="header">
+<th align="left">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>
+<td align="right">7.525</td>
+<td align="right">16.621</td>
+<td align="right">8.576</td>
+<td align="right">31.267</td>
+</tr>
+<tr class="even">
+<td align="left">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>
+<td align="right">4.632</td>
+<td align="right">8.171</td>
+<td align="right">3.676</td>
+<td align="right">5.636</td>
+</tr>
+<tr class="odd">
+<td align="left">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>
+<td align="right">4.862</td>
+<td align="right">7.618</td>
+<td align="right">3.579</td>
+<td align="right">5.574</td>
+</tr>
+<tr class="even">
+<td align="left">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>
+<td align="right">7.020</td>
+<td align="right">11.124</td>
+<td align="right">5.388</td>
+<td align="right">7.365</td>
+</tr>
+<tr class="odd">
+<td align="left">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>
+<td align="right">4.737</td>
+<td align="right">7.763</td>
+<td align="right">3.427</td>
+<td align="right">5.626</td>
+</tr>
+<tr class="even">
+<td align="left">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>
+<td align="right">1.332</td>
+<td align="right">2.872</td>
+<td align="right">2.069</td>
+<td align="right">2.987</td>
+</tr>
+<tr class="odd">
+<td align="left">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>
+<td align="right">1.333</td>
+<td align="right">2.984</td>
+<td align="right">2.113</td>
+<td align="right">3.073</td>
+</tr>
+<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>
+<td align="right">1.486</td>
+<td align="right">3.815</td>
+<td align="right">1.958</td>
+<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">0.763</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">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">0.861</td>
+<td align="right">1.295</td>
+<td align="right">1.507</td>
+<td align="right">3.102</td>
+<td align="right">1.961</td>
+<td align="right">2.852</td>
+</tr>
+<tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">4.2.2</td>
+<td align="left">1.2.0</td>
+<td align="right">0.913</td>
+<td align="right">1.345</td>
+<td align="right">1.539</td>
+<td align="right">3.011</td>
+<td align="right">1.987</td>
+<td align="right">2.802</td>
+</tr>
+<tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Ryzen 7 1700</td>
+<td align="left">4.2.2</td>
+<td align="left">1.2.2</td>
+<td align="right">0.935</td>
+<td align="right">1.381</td>
+<td align="right">1.551</td>
+<td align="right">3.209</td>
+<td align="right">1.976</td>
+<td align="right">3.013</td>
+</tr>
+<tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">4.2.2</td>
+<td align="left">1.2.0</td>
+<td align="right">0.445</td>
+<td align="right">0.591</td>
+<td align="right">0.660</td>
+<td align="right">1.190</td>
+<td align="right">0.814</td>
+<td align="right">1.100</td>
+</tr>
+<tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">4.2.2</td>
+<td align="left">1.2.2</td>
+<td align="right">0.443</td>
+<td align="right">0.586</td>
+<td align="right">0.661</td>
+<td align="right">1.176</td>
+<td align="right">0.803</td>
+<td align="right">1.097</td>
+</tr>
+<tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">4.2.2</td>
+<td align="left">1.2.3</td>
+<td align="right">0.418</td>
+<td align="right">0.530</td>
+<td align="right">0.591</td>
+<td align="right">1.006</td>
+<td align="right">0.716</td>
+<td align="right">0.949</td>
+</tr>
+<tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">4.2.3</td>
+<td align="left">1.2.3</td>
+<td align="right">0.432</td>
+<td align="right">0.549</td>
+<td align="right">0.609</td>
+<td align="right">1.052</td>
+<td align="right">0.743</td>
+<td align="right">0.989</td>
+</tr>
+<tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">4.3.0</td>
+<td align="left">1.2.4</td>
+<td align="right">0.410</td>
+<td align="right">0.526</td>
+<td align="right">0.553</td>
+<td align="right">1.249</td>
+<td align="right">0.712</td>
+<td align="right">0.948</td>
+</tr>
+<tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Intel(R) Xeon(R) Gold 6134 CPU @ 3.20GHz</td>
+<td align="left">4.3.1</td>
+<td align="left">1.2.5</td>
+<td align="right">0.798</td>
+<td align="right">1.096</td>
+<td align="right">1.217</td>
+<td align="right">3.173</td>
+<td align="right">1.634</td>
+<td align="right">2.271</td>
+</tr>
+<tr class="even">
+<td align="left">Linux</td>
+<td align="left">Intel(R) Xeon(R) Gold 6134 CPU @ 3.20GHz</td>
+<td align="left">4.3.1</td>
+<td align="left">1.2.6</td>
+<td align="right">0.813</td>
+<td align="right">1.136</td>
+<td align="right">1.220</td>
+<td align="right">3.114</td>
+<td align="right">1.598</td>
+<td align="right">2.255</td>
+</tr>
+<tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">4.3.2</td>
+<td align="left">1.2.6</td>
+<td align="right">0.439</td>
+<td align="right">0.557</td>
+<td align="right">0.585</td>
+<td align="right">1.338</td>
+<td align="right">0.749</td>
+<td align="right">0.999</td>
+</tr>
+<tr class="even">
+<td align="left">Linux</td>
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">4.4.2</td>
+<td align="left">1.2.9</td>
+<td align="right">0.424</td>
+<td align="right">0.534</td>
+<td align="right">0.560</td>
+<td align="right">1.298</td>
+<td align="right">0.735</td>
+<td align="right">0.981</td>
+</tr>
+<tr class="odd">
+<td align="left">Linux</td>
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">4.4.2</td>
+<td align="left">1.2.10</td>
+<td align="right">0.426</td>
+<td align="right">0.533</td>
+<td align="right">0.565</td>
+<td align="right">1.296</td>
+<td align="right">0.728</td>
+<td align="right">0.978</td>
+</tr>
+</tbody>
+</table>
+</div>
+</div>
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside>
+</div>
+
+
+
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+  <p>Developed by Johannes Ranke.</p>
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diff --git a/docs/dev/articles/web_only/compiled_models.html b/docs/dev/articles/web_only/compiled_models.html
new file mode 100644
index 00000000..113f7b67
--- /dev/null
+++ b/docs/dev/articles/web_only/compiled_models.html
@@ -0,0 +1,231 @@
+<!DOCTYPE html>
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+    <li><h6 class="dropdown-header" data-toc-skip>Example evaluations with (generalised) nonlinear least squares</h6></li>
+    <li><a class="dropdown-item" href="../../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a></li>
+    <li><a class="dropdown-item" href="../../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a></li>
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+    <li><hr class="dropdown-divider"></li>
+    <li><h6 class="dropdown-header" data-toc-skip>Example evaluations with hierarchical models (nonlinear mixed-effects models)</h6></li>
+    <li><a class="dropdown-item" href="../../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a></li>
+    <li><a class="dropdown-item" href="../../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a></li>
+    <li><a class="dropdown-item" href="../../articles/prebuilt/2023_mesotrione_parent.html">Testing covariate modelling in hierarchical parent degradation kinetics with residue data on mesotrione</a></li>
+    <li><a class="dropdown-item" href="../../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a></li>
+    <li><a class="dropdown-item" href="../../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a></li>
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+    <li><h6 class="dropdown-header" data-toc-skip>Performance</h6></li>
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+
+      <h1>Performance benefit by using compiled model definitions in mkin</h1>
+                        <h4 data-toc-skip class="author">Johannes
+Ranke</h4>
+            
+            <h4 data-toc-skip class="date">2025-02-14</h4>
+      
+      <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/compiled_models.rmd" class="external-link"><code>vignettes/web_only/compiled_models.rmd</code></a></small>
+      <div class="d-none name"><code>compiled_models.rmd</code></div>
+    </div>
+
+    
+    
+<div class="section level2">
+<h2 id="how-to-benefit-from-compiled-models">How to benefit from compiled models<a class="anchor" aria-label="anchor" href="#how-to-benefit-from-compiled-models"></a>
+</h2>
+<p>When using an mkin version equal to or greater than 0.9-36 and a C
+compiler is available, you will see a message that the model is being
+compiled from autogenerated C code when defining a model using mkinmod.
+Starting from version 0.9.49.9, the <code><a href="../../reference/mkinmod.html">mkinmod()</a></code> function
+checks for presence of a compiler using</p>
+<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu">pkgbuild</span><span class="fu">::</span><span class="fu"><a href="https://pkgbuild.r-lib.org/reference/has_compiler.html" class="external-link">has_compiler</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
+<p>In previous versions, it used <code>Sys.which("gcc")</code> for this
+check.</p>
+<p>On Linux, you need to have the essential build tools like make and
+gcc or clang installed. On Debian based linux distributions, these will
+be pulled in by installing the build-essential package.</p>
+<p>On MacOS, which I do not use personally, I have had reports that a
+compiler is available by default.</p>
+<p>On Windows, you need to install Rtools and have the path to its bin
+directory in your PATH variable. You do not need to modify the PATH
+variable when installing Rtools. Instead, I would recommend to put the
+line</p>
+<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/Sys.setenv.html" class="external-link">Sys.setenv</a></span><span class="op">(</span>PATH <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste</a></span><span class="op">(</span><span class="st">"C:/Rtools/bin"</span>, <span class="fu"><a href="https://rdrr.io/r/base/Sys.getenv.html" class="external-link">Sys.getenv</a></span><span class="op">(</span><span class="st">"PATH"</span><span class="op">)</span>, sep<span class="op">=</span><span class="st">";"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<p>into your .Rprofile startup file. This is just a text file with some
+R code that is executed when your R session starts. It has to be named
+.Rprofile and has to be located in your home directory, which will
+generally be your Documents folder. You can check the location of the
+home directory used by R by issuing</p>
+<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/Sys.getenv.html" class="external-link">Sys.getenv</a></span><span class="op">(</span><span class="st">"HOME"</span><span class="op">)</span></span></code></pre></div>
+</div>
+<div class="section level2">
+<h2 id="comparison-with-other-solution-methods">Comparison with other solution methods<a class="anchor" aria-label="anchor" href="#comparison-with-other-solution-methods"></a>
+</h2>
+<p>First, we build a simple degradation model for a parent compound with
+one metabolite, and we remove zero values from the dataset.</p>
+<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="st"><a href="https://pkgdown.jrwb.de/mkin/">"mkin"</a></span>, quietly <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
+<span><span class="va">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></code></pre></div>
+<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre>
+<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><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></code></pre></div>
+<p>We can compare the performance of the Eigenvalue based solution
+against the compiled version and the R implementation of the
+differential equations using the benchmark package. In the output of
+below code, the warnings about zero being removed from the FOCUS D
+dataset are suppressed. Since mkin version 0.9.49.11, an analytical
+solution is also implemented, which is included in the tests below.</p>
+<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="kw">if</span> <span class="op">(</span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">require</a></span><span class="op">(</span><span class="va"><a href="http://rbenchmark.googlecode.com" class="external-link">rbenchmark</a></span><span class="op">)</span><span class="op">)</span> <span class="op">{</span></span>
+<span>  <span class="va">b.1</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/rbenchmark/man/benchmark.html" class="external-link">benchmark</a></span><span class="op">(</span></span>
+<span>    <span class="st">"deSolve, not compiled"</span> <span class="op">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOCUS_D</span>,</span>
+<span>       solution_type <span class="op">=</span> <span class="st">"deSolve"</span>,</span>
+<span>       use_compiled <span class="op">=</span> <span class="cn">FALSE</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,</span>
+<span>    <span class="st">"Eigenvalue based"</span> <span class="op">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOCUS_D</span>,</span>
+<span>       solution_type <span class="op">=</span> <span class="st">"eigen"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,</span>
+<span>    <span class="st">"deSolve, compiled"</span> <span class="op">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOCUS_D</span>,</span>
+<span>       solution_type <span class="op">=</span> <span class="st">"deSolve"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,</span>
+<span>    <span class="st">"analytical"</span> <span class="op">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOCUS_D</span>,</span>
+<span>       solution_type <span class="op">=</span> <span class="st">"analytical"</span>,</span>
+<span>       use_compiled <span class="op">=</span> <span class="cn">FALSE</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,</span>
+<span>    replications <span class="op">=</span> <span class="fl">1</span>, order <span class="op">=</span> <span class="st">"relative"</span>,</span>
+<span>    columns <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">"test"</span>, <span class="st">"replications"</span>, <span class="st">"relative"</span>, <span class="st">"elapsed"</span><span class="op">)</span><span class="op">)</span></span>
+<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">b.1</span><span class="op">)</span></span>
+<span><span class="op">}</span> <span class="kw">else</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="st">"R package rbenchmark is not available"</span><span class="op">)</span></span>
+<span><span class="op">}</span></span></code></pre></div>
+<pre><code><span><span class="co">##                    test replications relative elapsed</span></span>
+<span><span class="co">## 4            analytical            1    1.000   0.102</span></span>
+<span><span class="co">## 3     deSolve, compiled            1    1.324   0.135</span></span>
+<span><span class="co">## 2      Eigenvalue based            1    1.706   0.174</span></span>
+<span><span class="co">## 1 deSolve, not compiled            1   22.627   2.308</span></span></code></pre>
+<p>We see that using the compiled model is by more than a factor of 10
+faster than using deSolve without compiled code.</p>
+</div>
+<div class="section level2">
+<h2 id="model-without-analytical-solution">Model without analytical solution<a class="anchor" aria-label="anchor" href="#model-without-analytical-solution"></a>
+</h2>
+<p>This evaluation is also taken from the example section of mkinfit. No
+analytical solution is available for this system, and now Eigenvalue
+based solution is possible, so only deSolve using with or without
+compiled code is available.</p>
+<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="kw">if</span> <span class="op">(</span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">require</a></span><span class="op">(</span><span class="va"><a href="http://rbenchmark.googlecode.com" class="external-link">rbenchmark</a></span><span class="op">)</span><span class="op">)</span> <span class="op">{</span></span>
+<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>
+<span>  <span class="va">b.2</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/rbenchmark/man/benchmark.html" class="external-link">benchmark</a></span><span class="op">(</span></span>
+<span>    <span class="st">"deSolve, not compiled"</span> <span class="op">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">FOMC_SFO</span>, <span class="va">FOCUS_D</span>,</span>
+<span>                                      use_compiled <span class="op">=</span> <span class="cn">FALSE</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,</span>
+<span>    <span class="st">"deSolve, compiled"</span> <span class="op">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">FOMC_SFO</span>, <span class="va">FOCUS_D</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,</span>
+<span>    replications <span class="op">=</span> <span class="fl">1</span>, order <span class="op">=</span> <span class="st">"relative"</span>,</span>
+<span>    columns <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">"test"</span>, <span class="st">"replications"</span>, <span class="st">"relative"</span>, <span class="st">"elapsed"</span><span class="op">)</span><span class="op">)</span></span>
+<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">b.2</span><span class="op">)</span></span>
+<span>  <span class="va">factor_FOMC_SFO</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/Round.html" class="external-link">round</a></span><span class="op">(</span><span class="va">b.2</span><span class="op">[</span><span class="st">"1"</span>, <span class="st">"relative"</span><span class="op">]</span><span class="op">)</span></span>
+<span><span class="op">}</span> <span class="kw">else</span> <span class="op">{</span></span>
+<span>  <span class="va">factor_FOMC_SFO</span> <span class="op">&lt;-</span> <span class="cn">NA</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="st">"R package benchmark is not available"</span><span class="op">)</span></span>
+<span><span class="op">}</span></span></code></pre></div>
+<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre>
+<pre><code><span><span class="co">##                    test replications relative elapsed</span></span>
+<span><span class="co">## 2     deSolve, compiled            1    1.000   0.170</span></span>
+<span><span class="co">## 1 deSolve, not compiled            1   23.865   4.057</span></span></code></pre>
+<p>Here we get a performance benefit of a factor of 24 using the version
+of the differential equation model compiled from C code!</p>
+<p>This vignette was built with mkin 1.2.10 on</p>
+<pre><code><span><span class="co">## R version 4.4.2 (2024-10-31)</span></span>
+<span><span class="co">## Platform: x86_64-pc-linux-gnu</span></span>
+<span><span class="co">## Running under: Debian GNU/Linux 12 (bookworm)</span></span></code></pre>
+<pre><code><span><span class="co">## CPU model: AMD Ryzen 9 7950X 16-Core Processor</span></span></code></pre>
+</div>
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside>
+</div>
+
+
+
+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Johannes Ranke.</p>
+</div>
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+<div class="pkgdown-footer-right">
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
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diff --git a/docs/dev/articles/web_only/dimethenamid_2018.html b/docs/dev/articles/web_only/dimethenamid_2018.html
new file mode 100644
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+++ b/docs/dev/articles/web_only/dimethenamid_2018.html
@@ -0,0 +1,651 @@
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+
+      <h1>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 1 July 2022,
+built on 14 Feb 2025</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="d-none name"><code>dimethenamid_2018.rmd</code></div>
+    </div>
+
+    
+    
+<p><a href="http://www.jrwb.de" class="external-link">Wissenschaftlicher Berater, Kronacher
+Str. 12, 79639 Grenzach-Wyhlen, Germany</a></p>
+<div class="section level2">
+<h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#introduction"></a>
+</h2>
+<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>
+</h2>
+<p>Residue data forming the basis for the endpoints derived in the
+conclusion on the peer review of the pesticide risk assessment of
+dimethenamid-P published by the European Food Safety Authority (EFSA) in
+2018 <span class="citation">(EFSA 2018)</span> were transcribed from the
+risk assessment report <span class="citation">(Rapporteur Member State
+Germany, Co-Rapporteur Member State Bulgaria 2018)</span> which can be
+downloaded from the Open EFSA repository <a href="https://open.efsa.europa.eu" class="external-link">https://open.efsa.europa.eu/study-inventory/EFSA-Q-2014-00716</a>.</p>
+<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><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>
+</h2>
+<p>We evaluate the observed degradation of the parent compound using
+simple exponential decline (SFO) and biexponential decline (DFOP), using
+constant variance (const) and a two-component variance (tc) as error
+models.</p>
+<div class="section level3">
+<h3 id="separate-evaluations">Separate evaluations<a class="anchor" aria-label="anchor" href="#separate-evaluations"></a>
+</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><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><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><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><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><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><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:
+
+      dataset
+model  Calke Borstel Flaach BBA 2.2 BBA 2.3 Elliot
+  DFOP OK    OK      OK     OK      C       OK    
+
+C: Optimisation did not converge:
+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>
+</h3>
+<p>Instead of taking a model selection decision for each of the
+individual fits, we fit nonlinear mixed-effects models (using different
+fitting algorithms as implemented in different packages) and do model
+selection using all available data at the same time. In order to make
+sure that these decisions are not unduly influenced by the type of
+algorithm used, by implementation details or by the use of wrong control
+parameters, we compare the model selection results obtained with
+different R packages, with different algorithms and checking control
+parameters.</p>
+<div class="section level4">
+<h4 id="nlme">nlme<a class="anchor" aria-label="anchor" href="#nlme"></a>
+</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><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 5 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><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 -325.95 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><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><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. 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><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><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 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><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">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></span></code></pre></div>
+<p><img src="dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_tc-1.png" width="700"></p>
+<p>When fitting the DFOP model with constant variance (see below),
+parameter convergence is not as unambiguous.</p>
+<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">f_parent_saemix_dfop_const</span> <span class="op">&lt;-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span>
+<span>  control <span class="op">=</span> <span class="va">saemix_control</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span></span>
+<span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_const</span><span class="op">$</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>
+<div class="sourceCode" id="cb18"><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_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  1.60516  2.0377
+SD.DMTA_0  1.64787  0.45729  2.8384
+SD.k1      0.57439  0.24731  0.9015
+SD.k2      0.03296 -2.50524  2.5712
+SD.g       1.10266  0.32354  1.8818</code></pre>
+<p>While the other parameters converge to credible values, the variance
+of k2 (<code>omega2.k2</code>) converges to a very small value. The
+printout of the <code>saem.mmkin</code> model shows that the estimated
+standard deviation of k2 across the population of soils
+(<code>SD.k2</code>) is ill-defined, indicating overparameterisation of
+this model.</p>
+<p>When the DFOP model is fitted with the two-component error model, we
+also observe that the estimated variance of k2 becomes very small, while
+being ill-defined, as illustrated by the excessive confidence interval
+of <code>SD.k2</code>.</p>
+<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r">
+<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>
+<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    98.24165  96.29190 100.1914
+k1         0.06421   0.03352   0.0949
+k2         0.00866   0.00617   0.0111
+g          0.95340   0.91218   0.9946
+a.1        1.06463   0.87979   1.2495
+b.1        0.02964   0.02266   0.0366
+SD.DMTA_0  2.03611   0.40361   3.6686
+SD.k1      0.59534   0.25692   0.9338
+SD.k2      0.00042 -73.00540  73.0062
+SD.g       1.04234   0.37189   1.7128</code></pre>
+<p>Doubling the number of iterations in the first phase of the algorithm
+leads to a slightly lower likelihood, and therefore to slightly higher
+AIC and BIC values. With even more iterations, the algorithm stops with
+an error message. This is related to the variance of k2 approximating
+zero and has been submitted as a <a href="https://github.com/saemixdevelopment/saemixextension/issues/29" class="external-link">bug
+to the saemix package</a>, as the algorithm does not converge in this
+case.</p>
+<p>An alternative way to fit DFOP in combination with the two-component
+error model is to use the model formulation with transformed parameters
+as used per default in mkin. When using this option, convergence is
+slower, but eventually the algorithm stops as well with the same error
+message.</p>
+<p>The four combinations (SFO/const, SFO/tc, DFOP/const and DFOP/tc) and
+the version with increased iterations can be compared using the model
+comparison function of the saemix package:</p>
+<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r">
+<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="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
+DFOP const              705.75 703.88
+DFOP tc                 665.67 663.59
+DFOP tc more iterations 665.85 663.76</code></pre>
+<p>In order to check the influence of the likelihood calculation
+algorithms implemented in saemix, the likelihood from Gaussian
+quadrature is added to the best fit, and the AIC values obtained from
+the three methods are compared.</p>
+<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r">
+<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">$</span><span class="va">so</span>, method <span class="op">=</span> <span class="st">"lin"</span><span class="op">)</span></span>
+<span><span class="op">)</span></span>
+<span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">AIC_parent_saemix_methods</span><span class="op">)</span></span></code></pre></div>
+<pre><code>    is     gq    lin 
+665.67 665.74 665.13 </code></pre>
+<p>The AIC values based on importance sampling and Gaussian quadrature
+are very similar. Using linearisation is known to be less accurate, but
+still gives a similar value.</p>
+<p>In order to illustrate that the comparison of the three method
+depends on the degree of convergence obtained in the fit, the same
+comparison is shown below for the fit using the defaults for the number
+of iterations and the number of MCMC chains.</p>
+<p>When using OpenBlas for linear algebra, there is a large difference
+in the values obtained with Gaussian quadrature, so the larger number of
+iterations makes a lot of difference. When using the LAPACK version
+coming with Debian Bullseye, the AIC based on Gaussian quadrature is
+almost the same as the one obtained with the other methods, also when
+using defaults for the fit.</p>
+<div class="sourceCode" id="cb29"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">f_parent_saemix_dfop_tc_defaults</span> <span class="op">&lt;-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span><span class="op">)</span></span>
+<span><span class="va">f_parent_saemix_dfop_tc_defaults</span><span class="op">$</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 
+670.09 669.37 671.29 </code></pre>
+</div>
+</div>
+<div class="section level3">
+<h3 id="comparison">Comparison<a class="anchor" aria-label="anchor" href="#comparison"></a>
+</h3>
+<p>The following table gives the AIC values obtained with both backend
+packages using the same control parameters (800 iterations burn-in, 300
+iterations second phase, 15 chains).</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"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></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">saemix_lin</th>
+<th align="right">saemix_is</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">SFO</td>
+<td align="left">const</td>
+<td align="right">796.60</td>
+<td align="right">796.60</td>
+<td align="right">796.38</td>
+</tr>
+<tr class="even">
+<td align="left">SFO</td>
+<td align="left">tc</td>
+<td align="right">798.60</td>
+<td align="right">798.60</td>
+<td align="right">798.38</td>
+</tr>
+<tr class="odd">
+<td align="left">DFOP</td>
+<td align="left">const</td>
+<td align="right">NA</td>
+<td align="right">704.95</td>
+<td align="right">705.75</td>
+</tr>
+<tr class="even">
+<td align="left">DFOP</td>
+<td align="left">tc</td>
+<td align="right">671.91</td>
+<td align="right">665.13</td>
+<td align="right">665.67</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 4.4.2 (2024-10-31)
+Platform: x86_64-pc-linux-gnu
+Running under: Debian GNU/Linux 12 (bookworm)
+
+Matrix products: default
+BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.11.0 
+LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.11.0
+
+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       
+
+time zone: Europe/Berlin
+tzcode source: system (glibc)
+
+attached base packages:
+[1] stats     graphics  grDevices utils     datasets  methods   base     
+
+other attached packages:
+[1] saemix_3.3   npde_3.5     nlme_3.1-166 mkin_1.2.10  knitr_1.49  
+
+loaded via a namespace (and not attached):
+ [1] gtable_0.3.6      jsonlite_1.8.9    dplyr_1.1.4       compiler_4.4.2   
+ [5] tidyselect_1.2.1  parallel_4.4.2    gridExtra_2.3     jquerylib_0.1.4  
+ [9] systemfonts_1.1.0 scales_1.3.0      textshaping_0.4.1 yaml_2.3.10      
+[13] fastmap_1.2.0     lattice_0.22-6    ggplot2_3.5.1     R6_2.5.1         
+[17] generics_0.1.3    lmtest_0.9-40     MASS_7.3-61       htmlwidgets_1.6.4
+[21] tibble_3.2.1      desc_1.4.3        munsell_0.5.1     bslib_0.8.0      
+[25] pillar_1.9.0      rlang_1.1.4       utf8_1.2.4        cachem_1.1.0     
+[29] xfun_0.49         fs_1.6.5          sass_0.4.9        cli_3.6.3        
+[33] pkgdown_2.1.1     magrittr_2.0.3    digest_0.6.37     grid_4.4.2       
+[37] mclust_6.1.1      lifecycle_1.0.4   vctrs_0.6.5       evaluate_1.0.1   
+[41] glue_1.8.0        codetools_0.2-20  ragg_1.3.3        zoo_1.8-12       
+[45] fansi_1.0.6       colorspace_2.1-1  rmarkdown_2.29    pkgconfig_2.0.3  
+[49] tools_4.4.2       htmltools_0.5.8.1</code></pre>
+</div>
+<div class="section level2">
+<h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a>
+</h2>
+<!-- vim: set foldmethod=syntax: -->
+<div id="refs" class="references csl-bib-body hanging-indent">
+<div id="ref-efsa_2018_dimethenamid" class="csl-entry">
+EFSA. 2018. <span>“Peer Review of the Pesticide Risk Assessment of the
+Active Substance Dimethenamid-p.”</span> <em>EFSA Journal</em> 16: 5211.
+</div>
+<div id="ref-ranke2021" class="csl-entry">
+Ranke, Johannes, Janina Wöltjen, Jana Schmidt, and Emmanuelle Comets.
+2021. <span>“Taking Kinetic Evaluations of Degradation Data to the Next
+Level with Nonlinear Mixed-Effects Models.”</span> <em>Environments</em>
+8 (8). <a href="https://doi.org/10.3390/environments8080071" class="external-link">https://doi.org/10.3390/environments8080071</a>.
+</div>
+<div id="ref-dimethenamid_rar_2018_b8" class="csl-entry">
+Rapporteur Member State Germany, Co-Rapporteur Member State Bulgaria.
+2018. <span>“<span class="nocase">Renewal Assessment Report
+Dimethenamid-P Volume 3 - B.8 Environmental fate and behaviour, Rev. 2 -
+November 2017</span>.”</span> <a href="https://open.efsa.europa.eu/study-inventory/EFSA-Q-2014-00716" class="external-link">https://open.efsa.europa.eu/study-inventory/EFSA-Q-2014-00716</a>.
+</div>
+</div>
+</div>
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside>
+</div>
+
+
+
+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Johannes Ranke.</p>
+</div>
+
+<div class="pkgdown-footer-right">
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
+</div>
+
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+</html>
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
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diff --git a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_const-1.png b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_const-1.png
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diff --git a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_const-1.png b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_const-1.png
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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
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diff --git a/docs/dev/articles/web_only/multistart.html b/docs/dev/articles/web_only/multistart.html
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@@ -0,0 +1,179 @@
+<!DOCTYPE html>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en">
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+<li><a class="dropdown-item" href="../../articles/mkin.html">Introduction to mkin</a></li>
+    <li><hr class="dropdown-divider"></li>
+    <li><h6 class="dropdown-header" data-toc-skip>Example evaluations with (generalised) nonlinear least squares</h6></li>
+    <li><a class="dropdown-item" href="../../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a></li>
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+    <li><a class="dropdown-item" href="../../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a></li>
+    <li><a class="dropdown-item" href="../../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a></li>
+    <li><a class="dropdown-item" href="../../articles/prebuilt/2023_mesotrione_parent.html">Testing covariate modelling in hierarchical parent degradation kinetics with residue data on mesotrione</a></li>
+    <li><a class="dropdown-item" href="../../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a></li>
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+
+      <h1>Short demo of the multistart method</h1>
+                        <h4 data-toc-skip class="author">Johannes
+Ranke</h4>
+            
+            <h4 data-toc-skip class="date">Last change 20 April 2023
+(rebuilt 2025-02-14)</h4>
+      
+      <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/multistart.rmd" class="external-link"><code>vignettes/web_only/multistart.rmd</code></a></small>
+      <div class="d-none name"><code>multistart.rmd</code></div>
+    </div>
+
+    
+    
+<p>The dimethenamid data from 2018 from seven soils is used as example
+data in this vignette.</p>
+<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://pkgdown.jrwb.de/mkin/">mkin</a></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="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>
+<p>First, we check the DFOP model with the two-component error model and
+random effects for all degradation parameters.</p>
+<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">f_mmkin</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span><span class="st">"DFOP"</span>, <span class="va">dmta_ds</span>, error_model <span class="op">=</span> <span class="st">"tc"</span>, cores <span class="op">=</span> <span class="fl">7</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
+<span><span class="va">f_saem_full</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_mmkin</span><span class="op">)</span></span>
+<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_full</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## [1] "sd(log_k2)"</span></span></code></pre>
+<p>We see that not all variability parameters are identifiable. The
+<code>illparms</code> function tells us that the confidence interval for
+the standard deviation of ‘log_k2’ includes zero. We check this
+assessment using multiple runs with different starting values.</p>
+<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">f_saem_full_multi</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/multistart.html">multistart</a></span><span class="op">(</span><span class="va">f_saem_full</span>, n <span class="op">=</span> <span class="fl">16</span>, cores <span class="op">=</span> <span class="fl">16</span><span class="op">)</span></span>
+<span><span class="fu"><a href="../../reference/parplot.html">parplot</a></span><span class="op">(</span><span class="va">f_saem_full_multi</span>, lpos <span class="op">=</span> <span class="st">"topleft"</span><span class="op">)</span></span></code></pre></div>
+<p><img src="multistart_files/figure-html/unnamed-chunk-3-1.png" width="700"></p>
+<p>This confirms that the variance of k2 is the most problematic
+parameter, so we reduce the parameter distribution model by removing the
+intersoil variability for k2.</p>
+<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">f_saem_reduced</span> <span class="op">&lt;-</span> <span class="fu">stats</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_saem_full</span>, no_random_effect <span class="op">=</span> <span class="st">"log_k2"</span><span class="op">)</span></span>
+<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_reduced</span><span class="op">)</span></span>
+<span><span class="va">f_saem_reduced_multi</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/multistart.html">multistart</a></span><span class="op">(</span><span class="va">f_saem_reduced</span>, n <span class="op">=</span> <span class="fl">16</span>, cores <span class="op">=</span> <span class="fl">16</span><span class="op">)</span></span>
+<span><span class="fu"><a href="../../reference/parplot.html">parplot</a></span><span class="op">(</span><span class="va">f_saem_reduced_multi</span>, lpos <span class="op">=</span> <span class="st">"topright"</span>, ylim <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">0.5</span>, <span class="fl">2</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<p><img src="multistart_files/figure-html/unnamed-chunk-4-1.png" width="700"></p>
+<p>The results confirm that all remaining parameters can be determined
+with sufficient certainty.</p>
+<p>We can also analyse the log-likelihoods obtained in the multiple
+runs:</p>
+<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../../reference/llhist.html">llhist</a></span><span class="op">(</span><span class="va">f_saem_reduced_multi</span><span class="op">)</span></span></code></pre></div>
+<p><img src="multistart_files/figure-html/unnamed-chunk-5-1.png" width="700"></p>
+<p>We can use the <code>anova</code> method to compare the models.</p>
+<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
+<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 class="va">f_saem_full</span>, <span class="fu"><a href="../../reference/multistart.html">best</a></span><span class="op">(</span><span class="va">f_saem_full_multi</span><span class="op">)</span>,</span>
+<span>  <span class="va">f_saem_reduced</span>, <span class="fu"><a href="../../reference/multistart.html">best</a></span><span class="op">(</span><span class="va">f_saem_reduced_multi</span><span class="op">)</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Data: 155 observations of 1 variable(s) grouped in 6 datasets</span></span>
+<span><span class="co">## </span></span>
+<span><span class="co">##                            npar    AIC    BIC     Lik  Chisq Df Pr(&gt;Chisq)</span></span>
+<span><span class="co">## f_saem_reduced                9 663.67 661.80 -322.84                     </span></span>
+<span><span class="co">## best(f_saem_reduced_multi)    9 663.65 661.78 -322.82 0.0219  0           </span></span>
+<span><span class="co">## f_saem_full                  10 670.09 668.01 -325.05 0.0000  1          1</span></span>
+<span><span class="co">## best(f_saem_full_multi)      10 665.61 663.52 -322.80 4.4870  0</span></span></code></pre>
+<p>The reduced model results in lower AIC and BIC values, so it is
+clearly preferable. Using multiple starting values gives a large
+improvement in case of the full model, because it is less well-defined,
+which impedes convergence. For the reduced model, using multiple
+starting values only results in a small improvement of the model
+fit.</p>
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside>
+</div>
+
+
+
+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Johannes Ranke.</p>
+</div>
+
+<div class="pkgdown-footer-right">
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
+</div>
+
+    </footer>
+</div>
+
+
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+  </body>
+</html>
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new file mode 100644
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+++ b/docs/dev/articles/web_only/saem_benchmarks.html
@@ -0,0 +1,789 @@
+<!DOCTYPE html>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en">
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+<title>Benchmark timings for saem.mmkin • mkin</title>
+<script src="../../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
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+    <small class="nav-text text-info me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="In-development version">1.2.10</small>
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+<li><a class="dropdown-item" href="../../articles/mkin.html">Introduction to mkin</a></li>
+    <li><hr class="dropdown-divider"></li>
+    <li><h6 class="dropdown-header" data-toc-skip>Example evaluations with (generalised) nonlinear least squares</h6></li>
+    <li><a class="dropdown-item" href="../../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a></li>
+    <li><a class="dropdown-item" href="../../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a></li>
+    <li><a class="dropdown-item" href="../../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a></li>
+    <li><hr class="dropdown-divider"></li>
+    <li><h6 class="dropdown-header" data-toc-skip>Example evaluations with hierarchical models (nonlinear mixed-effects models)</h6></li>
+    <li><a class="dropdown-item" href="../../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a></li>
+    <li><a class="dropdown-item" href="../../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a></li>
+    <li><a class="dropdown-item" href="../../articles/prebuilt/2023_mesotrione_parent.html">Testing covariate modelling in hierarchical parent degradation kinetics with residue data on mesotrione</a></li>
+    <li><a class="dropdown-item" href="../../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a></li>
+    <li><a class="dropdown-item" href="../../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a></li>
+    <li><a class="dropdown-item" href="../../articles/web_only/multistart.html">Short demo of the multistart method</a></li>
+    <li><hr class="dropdown-divider"></li>
+    <li><h6 class="dropdown-header" data-toc-skip>Performance</h6></li>
+    <li><a class="dropdown-item" href="../../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a></li>
+    <li><a class="dropdown-item" href="../../articles/web_only/benchmarks.html">Benchmark timings for mkin</a></li>
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+    <li><a class="dropdown-item" href="../../articles/twa.html">Calculation of time weighted average concentrations with mkin</a></li>
+    <li><a class="dropdown-item" href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a></li>
+  </ul>
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+<div class="row">
+  <main id="main" class="col-md-9"><div class="page-header">
+
+      <h1>Benchmark timings for saem.mmkin</h1>
+                        <h4 data-toc-skip class="author">Johannes
+Ranke</h4>
+            
+            <h4 data-toc-skip class="date">Last change 17 February 2023
+(rebuilt 2025-02-14)</h4>
+      
+      <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/saem_benchmarks.rmd" class="external-link"><code>vignettes/web_only/saem_benchmarks.rmd</code></a></small>
+      <div class="d-none name"><code>saem_benchmarks.rmd</code></div>
+    </div>
+
+    
+    
+<p>Each system is characterized by operating system type, CPU type, mkin
+version, saemix version and 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>For the initial mmkin fits, we use all available cores.</p>
+<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">n_cores</span> <span class="op">&lt;-</span> <span class="fu">parallel</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/r/parallel/detectCores.html" class="external-link">detectCores</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
+<div class="section level2">
+<h2 id="test-data">Test data<a class="anchor" aria-label="anchor" href="#test-data"></a>
+</h2>
+<p>Please refer to the vignette <code>dimethenamid_2018</code> for an
+explanation of the following preprocessing.</p>
+<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><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="test-cases">Test cases<a class="anchor" aria-label="anchor" href="#test-cases"></a>
+</h2>
+<div class="section level3">
+<h3 id="parent-only">Parent only<a class="anchor" aria-label="anchor" href="#parent-only"></a>
+</h3>
+<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">parent_mods</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"</span>, <span class="st">"DFOP"</span>, <span class="st">"SFORB"</span>, <span class="st">"HS"</span><span class="op">)</span></span>
+<span><span class="va">parent_sep_const</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span><span class="va">parent_mods</span>, <span class="va">dmta_ds</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>, cores <span class="op">=</span> <span class="va">n_cores</span><span class="op">)</span></span>
+<span><span class="va">parent_sep_tc</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">parent_sep_const</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</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="va">sfo_const</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">parent_sep_const</span><span class="op">[</span><span class="st">"SFO"</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">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="va">dfop_const</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">parent_sep_const</span><span class="op">[</span><span class="st">"DFOP"</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">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="va">sforb_const</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">parent_sep_const</span><span class="op">[</span><span class="st">"SFORB"</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="va">hs_const</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">parent_sep_const</span><span class="op">[</span><span class="st">"HS"</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">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="va">sfo_tc</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">parent_sep_tc</span><span class="op">[</span><span class="st">"SFO"</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">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="va">dfop_tc</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">parent_sep_tc</span><span class="op">[</span><span class="st">"DFOP"</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="va">sforb_tc</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">parent_sep_tc</span><span class="op">[</span><span class="st">"SFORB"</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">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="va">hs_tc</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">parent_sep_tc</span><span class="op">[</span><span class="st">"HS"</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></code></pre></div>
+<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
+<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">sfo_const</span>, <span class="va">dfop_const</span>, <span class="va">sforb_const</span>, <span class="va">hs_const</span>,</span>
+<span>  <span class="va">sfo_tc</span>, <span class="va">dfop_tc</span>, <span class="va">sforb_tc</span>, <span class="va">hs_tc</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>, digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="right">npar</th>
+<th align="right">AIC</th>
+<th align="right">BIC</th>
+<th align="right">Lik</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">sfo_const</td>
+<td align="right">5</td>
+<td align="right">796.3</td>
+<td align="right">795.3</td>
+<td align="right">-393.2</td>
+</tr>
+<tr class="even">
+<td align="left">sfo_tc</td>
+<td align="right">6</td>
+<td align="right">798.3</td>
+<td align="right">797.1</td>
+<td align="right">-393.2</td>
+</tr>
+<tr class="odd">
+<td align="left">dfop_const</td>
+<td align="right">9</td>
+<td align="right">709.4</td>
+<td align="right">707.5</td>
+<td align="right">-345.7</td>
+</tr>
+<tr class="even">
+<td align="left">sforb_const</td>
+<td align="right">9</td>
+<td align="right">710.0</td>
+<td align="right">708.1</td>
+<td align="right">-346.0</td>
+</tr>
+<tr class="odd">
+<td align="left">hs_const</td>
+<td align="right">9</td>
+<td align="right">713.7</td>
+<td align="right">711.8</td>
+<td align="right">-347.8</td>
+</tr>
+<tr class="even">
+<td align="left">dfop_tc</td>
+<td align="right">10</td>
+<td align="right">670.1</td>
+<td align="right">668.0</td>
+<td align="right">-325.0</td>
+</tr>
+<tr class="odd">
+<td align="left">sforb_tc</td>
+<td align="right">10</td>
+<td align="right">662.9</td>
+<td align="right">660.8</td>
+<td align="right">-321.4</td>
+</tr>
+<tr class="even">
+<td align="left">hs_tc</td>
+<td align="right">10</td>
+<td align="right">667.2</td>
+<td align="right">665.1</td>
+<td align="right">-323.6</td>
+</tr>
+</tbody>
+</table>
+<p>The above model comparison suggests to use the SFORB model with
+two-component error. For comparison, we keep the DFOP model with
+two-component error, as it competes with SFORB for biphasic curves.</p>
+<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">dfop_tc</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## [1] "sd(log_k2)"</span></span></code></pre>
+<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">sforb_tc</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## [1] "sd(log_k_DMTA_bound_free)"</span></span></code></pre>
+<p>For these two models, random effects for the transformed parameters
+<code>k2</code> and <code>k_DMTA_bound_free</code> could not be
+quantified.</p>
+</div>
+<div class="section level3">
+<h3 id="one-metabolite">One metabolite<a class="anchor" aria-label="anchor" href="#one-metabolite"></a>
+</h3>
+<p>We remove parameters that were found to be ill-defined in the parent
+only fits.</p>
+<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">one_met_mods</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>
+<span>  DFOP_SFO <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span>
+<span>    DMTA <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="st">"M23"</span><span class="op">)</span>,</span>
+<span>    M23 <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>  SFORB_SFO <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span>
+<span>    DMTA <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span>, <span class="st">"M23"</span><span class="op">)</span>,</span>
+<span>    M23 <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="op">)</span></span>
+<span></span>
+<span><span class="va">one_met_sep_const</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span><span class="va">one_met_mods</span>, <span class="va">dmta_ds</span>, error_model <span class="op">=</span> <span class="st">"const"</span>,</span>
+<span>  cores <span class="op">=</span> <span class="va">n_cores</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
+<span><span class="va">one_met_sep_tc</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span><span class="va">one_met_mods</span>, <span class="va">dmta_ds</span>, error_model <span class="op">=</span> <span class="st">"tc"</span>,</span>
+<span>  cores <span class="op">=</span> <span class="va">n_cores</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
+<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="va">dfop_sfo_tc</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">one_met_sep_tc</span><span class="op">[</span><span class="st">"DFOP_SFO"</span>, <span class="op">]</span>,</span>
+<span>    no_random_effect <span class="op">=</span> <span class="st">"log_k2"</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">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="va">sforb_sfo_tc</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">one_met_sep_tc</span><span class="op">[</span><span class="st">"SFORB_SFO"</span>, <span class="op">]</span>,</span>
+<span>    no_random_effect <span class="op">=</span> <span class="st">"log_k_DMTA_bound_free"</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 class="section level3">
+<h3 id="three-metabolites">Three metabolites<a class="anchor" aria-label="anchor" href="#three-metabolites"></a>
+</h3>
+<p>For the case of three metabolites, we only keep the SFORB model in
+order to limit the time for compiling this vignette, and as fitting in
+parallel may disturb the benchmark. Again, we do not include random
+effects that were ill-defined in previous fits of subsets of the
+degradation model.</p>
+<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">sforb_sfo_tc</span><span class="op">)</span></span></code></pre></div>
+<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">three_met_mods</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>
+<span>  SFORB_SFO3_plus <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span>
+<span>    DMTA <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"M23"</span>, <span class="st">"M27"</span>, <span class="st">"M31"</span><span class="op">)</span><span class="op">)</span>,</span>
+<span>    M23 <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>    M27 <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>    M31 <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">"M27"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span>
+<span></span>
+<span><span class="va">three_met_sep_tc</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span><span class="va">three_met_mods</span>, <span class="va">dmta_ds</span>, error_model <span class="op">=</span> <span class="st">"tc"</span>,</span>
+<span>  cores <span class="op">=</span> <span class="va">n_cores</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
+<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="va">sforb_sfo3_plus_const</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">three_met_sep_tc</span><span class="op">[</span><span class="st">"SFORB_SFO3_plus"</span>, <span class="op">]</span>,</span>
+<span>    no_random_effect <span class="op">=</span> <span class="st">"log_k_DMTA_bound_free"</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>
+<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-1">Parent only<a class="anchor" aria-label="anchor" href="#parent-only-1"></a>
+</h3>
+<p>Constant variance for SFO, DFOP, SFORB and HS.</p>
+<table class="table">
+<colgroup>
+<col width="48%">
+<col width="7%">
+<col width="8%">
+<col width="8%">
+<col width="7%">
+<col width="7%">
+<col width="7%">
+<col width="7%">
+</colgroup>
+<thead><tr class="header">
+<th align="left">CPU</th>
+<th align="left">OS</th>
+<th align="left">mkin</th>
+<th align="left">saemix</th>
+<th align="right">t1</th>
+<th align="right">t2</th>
+<th align="right">t3</th>
+<th align="right">t4</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">Ryzen 7 1700</td>
+<td align="left">Linux</td>
+<td align="left">1.2.0</td>
+<td align="left">3.2</td>
+<td align="right">2.140</td>
+<td align="right">4.626</td>
+<td align="right">4.328</td>
+<td align="right">4.998</td>
+</tr>
+<tr class="even">
+<td align="left">Ryzen 7 1700</td>
+<td align="left">Linux</td>
+<td align="left">1.2.2</td>
+<td align="left">3.2</td>
+<td align="right">2.427</td>
+<td align="right">4.550</td>
+<td align="right">4.217</td>
+<td align="right">4.851</td>
+</tr>
+<tr class="odd">
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">Linux</td>
+<td align="left">1.2.1</td>
+<td align="left">3.2</td>
+<td align="right">1.352</td>
+<td align="right">2.813</td>
+<td align="right">2.401</td>
+<td align="right">2.074</td>
+</tr>
+<tr class="even">
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">Linux</td>
+<td align="left">1.2.2</td>
+<td align="left">3.2</td>
+<td align="right">1.328</td>
+<td align="right">2.738</td>
+<td align="right">2.336</td>
+<td align="right">2.023</td>
+</tr>
+<tr class="odd">
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">Linux</td>
+<td align="left">1.2.3</td>
+<td align="left">3.2</td>
+<td align="right">1.118</td>
+<td align="right">2.036</td>
+<td align="right">2.010</td>
+<td align="right">2.088</td>
+</tr>
+<tr class="even">
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">Linux</td>
+<td align="left">1.2.3</td>
+<td align="left">3.2</td>
+<td align="right">1.419</td>
+<td align="right">2.374</td>
+<td align="right">1.926</td>
+<td align="right">2.398</td>
+</tr>
+<tr class="odd">
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">Linux</td>
+<td align="left">1.2.4</td>
+<td align="left">3.2</td>
+<td align="right">0.972</td>
+<td align="right">2.550</td>
+<td align="right">1.987</td>
+<td align="right">2.055</td>
+</tr>
+<tr class="even">
+<td align="left">Intel(R) Xeon(R) Gold 6134 CPU @ 3.20GHz</td>
+<td align="left">Linux</td>
+<td align="left">1.2.6</td>
+<td align="left">3.2</td>
+<td align="right">2.998</td>
+<td align="right">6.523</td>
+<td align="right">6.126</td>
+<td align="right">4.721</td>
+</tr>
+<tr class="odd">
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">Linux</td>
+<td align="left">1.2.6</td>
+<td align="left">3.2</td>
+<td align="right">1.135</td>
+<td align="right">2.025</td>
+<td align="right">2.406</td>
+<td align="right">2.478</td>
+</tr>
+<tr class="even">
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">Linux</td>
+<td align="left">1.2.9</td>
+<td align="left">3.3</td>
+<td align="right">1.086</td>
+<td align="right">1.991</td>
+<td align="right">1.949</td>
+<td align="right">2.411</td>
+</tr>
+<tr class="odd">
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">Linux</td>
+<td align="left">1.2.10</td>
+<td align="left">3.3</td>
+<td align="right">1.115</td>
+<td align="right">2.277</td>
+<td align="right">1.945</td>
+<td align="right">2.134</td>
+</tr>
+</tbody>
+</table>
+<p>Two-component error fits for SFO, DFOP, SFORB and HS.</p>
+<table class="table">
+<colgroup>
+<col width="48%">
+<col width="7%">
+<col width="8%">
+<col width="8%">
+<col width="7%">
+<col width="7%">
+<col width="7%">
+<col width="7%">
+</colgroup>
+<thead><tr class="header">
+<th align="left">CPU</th>
+<th align="left">OS</th>
+<th align="left">mkin</th>
+<th align="left">saemix</th>
+<th align="right">t5</th>
+<th align="right">t6</th>
+<th align="right">t7</th>
+<th align="right">t8</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">Ryzen 7 1700</td>
+<td align="left">Linux</td>
+<td align="left">1.2.0</td>
+<td align="left">3.2</td>
+<td align="right">5.678</td>
+<td align="right">7.441</td>
+<td align="right">8.000</td>
+<td align="right">7.980</td>
+</tr>
+<tr class="even">
+<td align="left">Ryzen 7 1700</td>
+<td align="left">Linux</td>
+<td align="left">1.2.2</td>
+<td align="left">3.2</td>
+<td align="right">5.352</td>
+<td align="right">7.201</td>
+<td align="right">8.174</td>
+<td align="right">8.401</td>
+</tr>
+<tr class="odd">
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">Linux</td>
+<td align="left">1.2.1</td>
+<td align="left">3.2</td>
+<td align="right">2.388</td>
+<td align="right">3.033</td>
+<td align="right">3.532</td>
+<td align="right">3.310</td>
+</tr>
+<tr class="even">
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">Linux</td>
+<td align="left">1.2.2</td>
+<td align="left">3.2</td>
+<td align="right">2.341</td>
+<td align="right">2.968</td>
+<td align="right">3.465</td>
+<td align="right">3.341</td>
+</tr>
+<tr class="odd">
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">Linux</td>
+<td align="left">1.2.3</td>
+<td align="left">3.2</td>
+<td align="right">2.159</td>
+<td align="right">3.584</td>
+<td align="right">3.307</td>
+<td align="right">3.460</td>
+</tr>
+<tr class="even">
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">Linux</td>
+<td align="left">1.2.3</td>
+<td align="left">3.2</td>
+<td align="right">2.348</td>
+<td align="right">3.134</td>
+<td align="right">3.253</td>
+<td align="right">3.530</td>
+</tr>
+<tr class="odd">
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">Linux</td>
+<td align="left">1.2.4</td>
+<td align="left">3.2</td>
+<td align="right">2.127</td>
+<td align="right">3.587</td>
+<td align="right">3.433</td>
+<td align="right">3.595</td>
+</tr>
+<tr class="even">
+<td align="left">Intel(R) Xeon(R) Gold 6134 CPU @ 3.20GHz</td>
+<td align="left">Linux</td>
+<td align="left">1.2.6</td>
+<td align="left">3.2</td>
+<td align="right">5.070</td>
+<td align="right">8.464</td>
+<td align="right">8.525</td>
+<td align="right">7.599</td>
+</tr>
+<tr class="odd">
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">Linux</td>
+<td align="left">1.2.6</td>
+<td align="left">3.2</td>
+<td align="right">2.161</td>
+<td align="right">3.325</td>
+<td align="right">3.669</td>
+<td align="right">3.153</td>
+</tr>
+<tr class="even">
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">Linux</td>
+<td align="left">1.2.9</td>
+<td align="left">3.3</td>
+<td align="right">2.426</td>
+<td align="right">3.196</td>
+<td align="right">3.256</td>
+<td align="right">3.322</td>
+</tr>
+<tr class="odd">
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">Linux</td>
+<td align="left">1.2.10</td>
+<td align="left">3.3</td>
+<td align="right">2.372</td>
+<td align="right">3.137</td>
+<td align="right">3.100</td>
+<td align="right">3.281</td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="section level3">
+<h3 id="one-metabolite-1">One metabolite<a class="anchor" aria-label="anchor" href="#one-metabolite-1"></a>
+</h3>
+<p>Two-component error for DFOP-SFO and SFORB-SFO.</p>
+<table style="width:100%;" class="table">
+<colgroup>
+<col width="53%">
+<col width="7%">
+<col width="9%">
+<col width="9%">
+<col width="9%">
+<col width="10%">
+</colgroup>
+<thead><tr class="header">
+<th align="left">CPU</th>
+<th align="left">OS</th>
+<th align="left">mkin</th>
+<th align="left">saemix</th>
+<th align="right">t9</th>
+<th align="right">t10</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">Ryzen 7 1700</td>
+<td align="left">Linux</td>
+<td align="left">1.2.0</td>
+<td align="left">3.2</td>
+<td align="right">24.465</td>
+<td align="right">800.266</td>
+</tr>
+<tr class="even">
+<td align="left">Ryzen 7 1700</td>
+<td align="left">Linux</td>
+<td align="left">1.2.2</td>
+<td align="left">3.2</td>
+<td align="right">25.193</td>
+<td align="right">798.580</td>
+</tr>
+<tr class="odd">
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">Linux</td>
+<td align="left">1.2.1</td>
+<td align="left">3.2</td>
+<td align="right">11.247</td>
+<td align="right">285.216</td>
+</tr>
+<tr class="even">
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">Linux</td>
+<td align="left">1.2.2</td>
+<td align="left">3.2</td>
+<td align="right">11.242</td>
+<td align="right">284.258</td>
+</tr>
+<tr class="odd">
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">Linux</td>
+<td align="left">1.2.3</td>
+<td align="left">3.2</td>
+<td align="right">11.796</td>
+<td align="right">216.012</td>
+</tr>
+<tr class="even">
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">Linux</td>
+<td align="left">1.2.3</td>
+<td align="left">3.2</td>
+<td align="right">12.841</td>
+<td align="right">292.688</td>
+</tr>
+<tr class="odd">
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">Linux</td>
+<td align="left">1.2.4</td>
+<td align="left">3.2</td>
+<td align="right">12.160</td>
+<td align="right">265.934</td>
+</tr>
+<tr class="even">
+<td align="left">Intel(R) Xeon(R) Gold 6134 CPU @ 3.20GHz</td>
+<td align="left">Linux</td>
+<td align="left">1.2.6</td>
+<td align="left">3.2</td>
+<td align="right">30.168</td>
+<td align="right">748.675</td>
+</tr>
+<tr class="odd">
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">Linux</td>
+<td align="left">1.2.6</td>
+<td align="left">3.2</td>
+<td align="right">12.007</td>
+<td align="right">286.757</td>
+</tr>
+<tr class="even">
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">Linux</td>
+<td align="left">1.2.9</td>
+<td align="left">3.3</td>
+<td align="right">12.420</td>
+<td align="right">289.338</td>
+</tr>
+<tr class="odd">
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">Linux</td>
+<td align="left">1.2.10</td>
+<td align="left">3.3</td>
+<td align="right">11.590</td>
+<td align="right">279.782</td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="section level3">
+<h3 id="three-metabolites-1">Three metabolites<a class="anchor" aria-label="anchor" href="#three-metabolites-1"></a>
+</h3>
+<p>Two-component error for SFORB-SFO3-plus</p>
+<table class="table">
+<colgroup>
+<col width="58%">
+<col width="8%">
+<col width="10%">
+<col width="10%">
+<col width="12%">
+</colgroup>
+<thead><tr class="header">
+<th align="left">CPU</th>
+<th align="left">OS</th>
+<th align="left">mkin</th>
+<th align="left">saemix</th>
+<th align="right">t11</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">Ryzen 7 1700</td>
+<td align="left">Linux</td>
+<td align="left">1.2.0</td>
+<td align="left">3.2</td>
+<td align="right">1289.198</td>
+</tr>
+<tr class="even">
+<td align="left">Ryzen 7 1700</td>
+<td align="left">Linux</td>
+<td align="left">1.2.2</td>
+<td align="left">3.2</td>
+<td align="right">1312.445</td>
+</tr>
+<tr class="odd">
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">Linux</td>
+<td align="left">1.2.1</td>
+<td align="left">3.2</td>
+<td align="right">489.939</td>
+</tr>
+<tr class="even">
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">Linux</td>
+<td align="left">1.2.2</td>
+<td align="left">3.2</td>
+<td align="right">482.970</td>
+</tr>
+<tr class="odd">
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">Linux</td>
+<td align="left">1.2.3</td>
+<td align="left">3.2</td>
+<td align="right">392.364</td>
+</tr>
+<tr class="even">
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">Linux</td>
+<td align="left">1.2.3</td>
+<td align="left">3.2</td>
+<td align="right">483.027</td>
+</tr>
+<tr class="odd">
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">Linux</td>
+<td align="left">1.2.4</td>
+<td align="left">3.2</td>
+<td align="right">456.252</td>
+</tr>
+<tr class="even">
+<td align="left">Intel(R) Xeon(R) Gold 6134 CPU @ 3.20GHz</td>
+<td align="left">Linux</td>
+<td align="left">1.2.6</td>
+<td align="left">3.2</td>
+<td align="right">1235.028</td>
+</tr>
+<tr class="odd">
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">Linux</td>
+<td align="left">1.2.6</td>
+<td align="left">3.2</td>
+<td align="right">480.577</td>
+</tr>
+<tr class="even">
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">Linux</td>
+<td align="left">1.2.9</td>
+<td align="left">3.3</td>
+<td align="right">485.836</td>
+</tr>
+<tr class="odd">
+<td align="left">Ryzen 9 7950X</td>
+<td align="left">Linux</td>
+<td align="left">1.2.10</td>
+<td align="left">3.3</td>
+<td align="right">469.036</td>
+</tr>
+</tbody>
+</table>
+</div>
+</div>
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside>
+</div>
+
+
+
+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Johannes Ranke.</p>
+</div>
+
+<div class="pkgdown-footer-right">
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p>
+</div>
+
+    </footer>
+</div>
+
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+
+
+  </body>
+</html>
author	Johannes Ranke <johannes.ranke@jrwb.de>	2025-02-14 09:15:20 +0100
committer	Johannes Ranke <johannes.ranke@jrwb.de>	2025-02-14 09:15:20 +0100
commit	91a5834dd701211f929fd25419dc34561ce3b4e7 (patch)
tree	860862d680fea23581d08b2948c5ac3e922a8447 /docs/dev/articles/web_only
parent	b0f08271d1dae8ffaf57f557c27eba1314ece1d5 (diff)