Initialize dev docs

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/prebuilt
parent: b0f08271d1dae8ffaf57f557c27eba1314ece1d5 (diff)
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+
+      <h1>Testing hierarchical pathway kinetics with residue data on cyantraniliprole</h1>
+                        <h4 data-toc-skip class="author">Johannes
+Ranke</h4>
+            
+            <h4 data-toc-skip class="date">Last change on 13 February
+2023, last compiled on 14 Februar 2025</h4>
+      
+      <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/prebuilt/2022_cyan_pathway.rmd" class="external-link"><code>vignettes/prebuilt/2022_cyan_pathway.rmd</code></a></small>
+      <div class="d-none name"><code>2022_cyan_pathway.rmd</code></div>
+    </div>
+
+    
+    
+<div class="section level2">
+<h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#introduction"></a>
+</h2>
+<p>The purpose of this document is to test demonstrate how nonlinear
+hierarchical models (NLHM) based on the parent degradation models SFO,
+FOMC, DFOP and HS, with serial formation of two or more metabolites can
+be fitted with the mkin package.</p>
+<p>It was assembled in the course of work package 1.2 of Project Number
+173340 (Application of nonlinear hierarchical models to the kinetic
+evaluation of chemical degradation data) of the German Environment
+Agency carried out in 2022 and 2023.</p>
+<p>The mkin package is used in version 1.2.10 which is currently under
+development. The newly introduced functionality that is used here is a
+simplification of excluding random effects for a set of fits based on a
+related set of fits with a reduced model, and the documentation of the
+starting parameters of the fit, so that all starting parameters of
+<code>saem</code> fits are now listed in the summary. The
+<code>saemix</code> package is used as a backend for fitting the NLHM,
+but is also loaded to make the convergence plot function available.</p>
+<p>This document is processed with the <code>knitr</code> package, which
+also provides the <code>kable</code> function that is used to improve
+the display of tabular data in R markdown documents. For parallel
+processing, the <code>parallel</code> package is used.</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="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://yihui.org/knitr/" class="external-link">knitr</a></span><span class="op">)</span></span>
+<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="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">parallel</span><span class="op">)</span></span>
+<span><span class="va">n_cores</span> <span class="op">&lt;-</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>
+<span></span>
+<span><span class="co"># We need to start a new cluster after defining a compiled model that is</span></span>
+<span><span class="co"># saved as a DLL to the user directory, therefore we define a function</span></span>
+<span><span class="co"># This is used again after defining the pathway model</span></span>
+<span><span class="va">start_cluster</span> <span class="op">&lt;-</span> <span class="kw">function</span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span> <span class="op">{</span></span>
+<span>  <span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/Sys.info.html" class="external-link">Sys.info</a></span><span class="op">(</span><span class="op">)</span><span class="op">[</span><span class="st">"sysname"</span><span class="op">]</span> <span class="op">==</span> <span class="st">"Windows"</span><span class="op">)</span> <span class="op">{</span></span>
+<span>    <span class="va">ret</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makePSOCKcluster</a></span><span class="op">(</span><span class="va">n_cores</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">ret</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makeForkCluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span>
+<span>  <span class="op">}</span></span>
+<span>  <span class="kw"><a href="https://rdrr.io/r/base/function.html" class="external-link">return</a></span><span class="op">(</span><span class="va">ret</span><span class="op">)</span></span>
+<span><span class="op">}</span></span>
+<span><span class="va">cl</span> <span class="op">&lt;-</span> <span class="fu">start_cluster</span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span></code></pre></div>
+<div class="section level3">
+<h3 id="test-data">Test data<a class="anchor" aria-label="anchor" href="#test-data"></a>
+</h3>
+<p>The example data are taken from the final addendum to the DAR from
+2014 and are distributed with the mkin package. Residue data and time
+step normalisation factors are read in using the function
+<code>read_spreadsheet</code> from the mkin package. This function also
+performs the time step normalisation.</p>
+<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">data_file</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.file.html" class="external-link">system.file</a></span><span class="op">(</span></span>
+<span>  <span class="st">"testdata"</span>, <span class="st">"cyantraniliprole_soil_efsa_2014.xlsx"</span>,</span>
+<span>  package <span class="op">=</span> <span class="st">"mkin"</span><span class="op">)</span></span>
+<span><span class="va">cyan_ds</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/read_spreadsheet.html">read_spreadsheet</a></span><span class="op">(</span><span class="va">data_file</span>, parent_only <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div>
+<p>The following tables show the covariate data and the 5 datasets that
+were read in from the spreadsheet file.</p>
+<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">pH</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/attr.html" class="external-link">attr</a></span><span class="op">(</span><span class="va">cyan_ds</span>, <span class="st">"covariates"</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">pH</span>, caption <span class="op">=</span> <span class="st">"Covariate data"</span><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<caption>Covariate data</caption>
+<thead><tr class="header">
+<th align="left"></th>
+<th align="right">pH</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">Nambsheim</td>
+<td align="right">7.90</td>
+</tr>
+<tr class="even">
+<td align="left">Tama</td>
+<td align="right">6.20</td>
+</tr>
+<tr class="odd">
+<td align="left">Gross-Umstadt</td>
+<td align="right">7.04</td>
+</tr>
+<tr class="even">
+<td align="left">Sassafras</td>
+<td align="right">4.62</td>
+</tr>
+<tr class="odd">
+<td align="left">Lleida</td>
+<td align="right">8.05</td>
+</tr>
+</tbody>
+</table>
+<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="kw">for</span> <span class="op">(</span><span class="va">ds_name</span> <span class="kw">in</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">cyan_ds</span><span class="op">)</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>
+<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="fu"><a href="../../reference/mkin_long_to_wide.html">mkin_long_to_wide</a></span><span class="op">(</span><span class="va">cyan_ds</span><span class="op">[[</span><span class="va">ds_name</span><span class="op">]</span><span class="op">]</span><span class="op">)</span>,</span>
+<span>      caption <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">"Dataset"</span>, <span class="va">ds_name</span><span class="op">)</span>,</span>
+<span>      booktabs <span class="op">=</span> <span class="cn">TRUE</span>, row.names <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">)</span></span>
+<span>    <span class="fu"><a href="https://rdrr.io/r/base/cat.html" class="external-link">cat</a></span><span class="op">(</span><span class="st">"\n\\clearpage\n"</span><span class="op">)</span></span>
+<span><span class="op">}</span></span></code></pre></div>
+<table class="table">
+<caption>Dataset Nambsheim</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">cyan</th>
+<th align="right">JCZ38</th>
+<th align="right">J9C38</th>
+<th align="right">JSE76</th>
+<th align="right">J9Z38</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.000000</td>
+<td align="right">105.79</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+</tr>
+<tr class="even">
+<td align="right">3.210424</td>
+<td align="right">77.26</td>
+<td align="right">7.92</td>
+<td align="right">11.94</td>
+<td align="right">5.58</td>
+<td align="right">9.12</td>
+</tr>
+<tr class="odd">
+<td align="right">7.490988</td>
+<td align="right">57.13</td>
+<td align="right">15.46</td>
+<td align="right">16.58</td>
+<td align="right">12.59</td>
+<td align="right">11.74</td>
+</tr>
+<tr class="even">
+<td align="right">17.122259</td>
+<td align="right">37.74</td>
+<td align="right">15.98</td>
+<td align="right">13.36</td>
+<td align="right">26.05</td>
+<td align="right">10.77</td>
+</tr>
+<tr class="odd">
+<td align="right">23.543105</td>
+<td align="right">31.47</td>
+<td align="right">6.05</td>
+<td align="right">14.49</td>
+<td align="right">34.71</td>
+<td align="right">4.96</td>
+</tr>
+<tr class="even">
+<td align="right">43.875788</td>
+<td align="right">16.74</td>
+<td align="right">6.07</td>
+<td align="right">7.57</td>
+<td align="right">40.38</td>
+<td align="right">6.52</td>
+</tr>
+<tr class="odd">
+<td align="right">67.418893</td>
+<td align="right">8.85</td>
+<td align="right">10.34</td>
+<td align="right">6.39</td>
+<td align="right">30.71</td>
+<td align="right">8.90</td>
+</tr>
+<tr class="even">
+<td align="right">107.014116</td>
+<td align="right">5.19</td>
+<td align="right">9.61</td>
+<td align="right">1.95</td>
+<td align="right">20.41</td>
+<td align="right">12.93</td>
+</tr>
+<tr class="odd">
+<td align="right">129.487080</td>
+<td align="right">3.45</td>
+<td align="right">6.18</td>
+<td align="right">1.36</td>
+<td align="right">21.78</td>
+<td align="right">6.99</td>
+</tr>
+<tr class="even">
+<td align="right">195.835832</td>
+<td align="right">2.15</td>
+<td align="right">9.13</td>
+<td align="right">0.95</td>
+<td align="right">16.29</td>
+<td align="right">7.69</td>
+</tr>
+<tr class="odd">
+<td align="right">254.693596</td>
+<td align="right">1.92</td>
+<td align="right">6.92</td>
+<td align="right">0.20</td>
+<td align="right">13.57</td>
+<td align="right">7.16</td>
+</tr>
+<tr class="even">
+<td align="right">321.042348</td>
+<td align="right">2.26</td>
+<td align="right">7.02</td>
+<td align="right">NA</td>
+<td align="right">11.12</td>
+<td align="right">8.66</td>
+</tr>
+<tr class="odd">
+<td align="right">383.110535</td>
+<td align="right">NA</td>
+<td align="right">5.05</td>
+<td align="right">NA</td>
+<td align="right">10.64</td>
+<td align="right">5.56</td>
+</tr>
+<tr class="even">
+<td align="right">0.000000</td>
+<td align="right">105.57</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+</tr>
+<tr class="odd">
+<td align="right">3.210424</td>
+<td align="right">78.88</td>
+<td align="right">12.77</td>
+<td align="right">11.94</td>
+<td align="right">5.47</td>
+<td align="right">9.12</td>
+</tr>
+<tr class="even">
+<td align="right">7.490988</td>
+<td align="right">59.94</td>
+<td align="right">15.27</td>
+<td align="right">16.58</td>
+<td align="right">13.60</td>
+<td align="right">11.74</td>
+</tr>
+<tr class="odd">
+<td align="right">17.122259</td>
+<td align="right">39.67</td>
+<td align="right">14.26</td>
+<td align="right">13.36</td>
+<td align="right">29.44</td>
+<td align="right">10.77</td>
+</tr>
+<tr class="even">
+<td align="right">23.543105</td>
+<td align="right">30.21</td>
+<td align="right">16.07</td>
+<td align="right">14.49</td>
+<td align="right">35.90</td>
+<td align="right">4.96</td>
+</tr>
+<tr class="odd">
+<td align="right">43.875788</td>
+<td align="right">18.06</td>
+<td align="right">9.44</td>
+<td align="right">7.57</td>
+<td align="right">42.30</td>
+<td align="right">6.52</td>
+</tr>
+<tr class="even">
+<td align="right">67.418893</td>
+<td align="right">8.54</td>
+<td align="right">5.78</td>
+<td align="right">6.39</td>
+<td align="right">34.70</td>
+<td align="right">8.90</td>
+</tr>
+<tr class="odd">
+<td align="right">107.014116</td>
+<td align="right">7.26</td>
+<td align="right">4.54</td>
+<td align="right">1.95</td>
+<td align="right">23.33</td>
+<td align="right">12.93</td>
+</tr>
+<tr class="even">
+<td align="right">129.487080</td>
+<td align="right">3.60</td>
+<td align="right">4.22</td>
+<td align="right">1.36</td>
+<td align="right">23.56</td>
+<td align="right">6.99</td>
+</tr>
+<tr class="odd">
+<td align="right">195.835832</td>
+<td align="right">2.84</td>
+<td align="right">3.05</td>
+<td align="right">0.95</td>
+<td align="right">16.21</td>
+<td align="right">7.69</td>
+</tr>
+<tr class="even">
+<td align="right">254.693596</td>
+<td align="right">2.00</td>
+<td align="right">2.90</td>
+<td align="right">0.20</td>
+<td align="right">15.53</td>
+<td align="right">7.16</td>
+</tr>
+<tr class="odd">
+<td align="right">321.042348</td>
+<td align="right">1.79</td>
+<td align="right">0.94</td>
+<td align="right">NA</td>
+<td align="right">9.80</td>
+<td align="right">8.66</td>
+</tr>
+<tr class="even">
+<td align="right">383.110535</td>
+<td align="right">NA</td>
+<td align="right">1.82</td>
+<td align="right">NA</td>
+<td align="right">9.49</td>
+<td align="right">5.56</td>
+</tr>
+</tbody>
+</table>
+<table class="table">
+<caption>Dataset Tama</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">cyan</th>
+<th align="right">JCZ38</th>
+<th align="right">J9Z38</th>
+<th align="right">JSE76</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.000000</td>
+<td align="right">106.14</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+</tr>
+<tr class="even">
+<td align="right">2.400833</td>
+<td align="right">93.47</td>
+<td align="right">6.46</td>
+<td align="right">2.85</td>
+<td align="right">NA</td>
+</tr>
+<tr class="odd">
+<td align="right">5.601943</td>
+<td align="right">88.39</td>
+<td align="right">10.86</td>
+<td align="right">4.65</td>
+<td align="right">3.85</td>
+</tr>
+<tr class="even">
+<td align="right">12.804442</td>
+<td align="right">72.29</td>
+<td align="right">11.97</td>
+<td align="right">4.91</td>
+<td align="right">11.24</td>
+</tr>
+<tr class="odd">
+<td align="right">17.606108</td>
+<td align="right">65.79</td>
+<td align="right">13.11</td>
+<td align="right">6.63</td>
+<td align="right">13.79</td>
+</tr>
+<tr class="even">
+<td align="right">32.811382</td>
+<td align="right">53.16</td>
+<td align="right">11.24</td>
+<td align="right">8.90</td>
+<td align="right">23.40</td>
+</tr>
+<tr class="odd">
+<td align="right">50.417490</td>
+<td align="right">44.01</td>
+<td align="right">11.34</td>
+<td align="right">9.98</td>
+<td align="right">29.56</td>
+</tr>
+<tr class="even">
+<td align="right">80.027761</td>
+<td align="right">33.23</td>
+<td align="right">8.82</td>
+<td align="right">11.31</td>
+<td align="right">35.63</td>
+</tr>
+<tr class="odd">
+<td align="right">96.833591</td>
+<td align="right">40.68</td>
+<td align="right">5.94</td>
+<td align="right">8.32</td>
+<td align="right">29.09</td>
+</tr>
+<tr class="even">
+<td align="right">146.450803</td>
+<td align="right">20.65</td>
+<td align="right">4.49</td>
+<td align="right">8.72</td>
+<td align="right">36.88</td>
+</tr>
+<tr class="odd">
+<td align="right">190.466072</td>
+<td align="right">17.71</td>
+<td align="right">4.66</td>
+<td align="right">11.10</td>
+<td align="right">40.97</td>
+</tr>
+<tr class="even">
+<td align="right">240.083284</td>
+<td align="right">14.86</td>
+<td align="right">2.27</td>
+<td align="right">11.62</td>
+<td align="right">40.11</td>
+</tr>
+<tr class="odd">
+<td align="right">286.499386</td>
+<td align="right">12.02</td>
+<td align="right">NA</td>
+<td align="right">10.73</td>
+<td align="right">42.58</td>
+</tr>
+<tr class="even">
+<td align="right">0.000000</td>
+<td align="right">109.11</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+</tr>
+<tr class="odd">
+<td align="right">2.400833</td>
+<td align="right">96.84</td>
+<td align="right">5.52</td>
+<td align="right">2.04</td>
+<td align="right">2.02</td>
+</tr>
+<tr class="even">
+<td align="right">5.601943</td>
+<td align="right">85.29</td>
+<td align="right">9.65</td>
+<td align="right">2.99</td>
+<td align="right">4.39</td>
+</tr>
+<tr class="odd">
+<td align="right">12.804442</td>
+<td align="right">73.68</td>
+<td align="right">12.48</td>
+<td align="right">5.05</td>
+<td align="right">11.47</td>
+</tr>
+<tr class="even">
+<td align="right">17.606108</td>
+<td align="right">64.89</td>
+<td align="right">12.44</td>
+<td align="right">6.29</td>
+<td align="right">15.00</td>
+</tr>
+<tr class="odd">
+<td align="right">32.811382</td>
+<td align="right">52.27</td>
+<td align="right">10.86</td>
+<td align="right">7.65</td>
+<td align="right">23.30</td>
+</tr>
+<tr class="even">
+<td align="right">50.417490</td>
+<td align="right">42.61</td>
+<td align="right">10.54</td>
+<td align="right">9.37</td>
+<td align="right">31.06</td>
+</tr>
+<tr class="odd">
+<td align="right">80.027761</td>
+<td align="right">34.29</td>
+<td align="right">10.02</td>
+<td align="right">9.04</td>
+<td align="right">37.87</td>
+</tr>
+<tr class="even">
+<td align="right">96.833591</td>
+<td align="right">30.50</td>
+<td align="right">6.34</td>
+<td align="right">8.14</td>
+<td align="right">33.97</td>
+</tr>
+<tr class="odd">
+<td align="right">146.450803</td>
+<td align="right">19.21</td>
+<td align="right">6.29</td>
+<td align="right">8.52</td>
+<td align="right">26.15</td>
+</tr>
+<tr class="even">
+<td align="right">190.466072</td>
+<td align="right">17.55</td>
+<td align="right">5.81</td>
+<td align="right">9.89</td>
+<td align="right">32.08</td>
+</tr>
+<tr class="odd">
+<td align="right">240.083284</td>
+<td align="right">13.22</td>
+<td align="right">5.99</td>
+<td align="right">10.79</td>
+<td align="right">40.66</td>
+</tr>
+<tr class="even">
+<td align="right">286.499386</td>
+<td align="right">11.09</td>
+<td align="right">6.05</td>
+<td align="right">8.82</td>
+<td align="right">42.90</td>
+</tr>
+</tbody>
+</table>
+<table class="table">
+<caption>Dataset Gross-Umstadt</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">cyan</th>
+<th align="right">JCZ38</th>
+<th align="right">J9Z38</th>
+<th align="right">JSE76</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.0000000</td>
+<td align="right">103.03</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+</tr>
+<tr class="even">
+<td align="right">2.1014681</td>
+<td align="right">87.85</td>
+<td align="right">4.79</td>
+<td align="right">3.26</td>
+<td align="right">0.62</td>
+</tr>
+<tr class="odd">
+<td align="right">4.9034255</td>
+<td align="right">77.35</td>
+<td align="right">8.05</td>
+<td align="right">9.89</td>
+<td align="right">1.32</td>
+</tr>
+<tr class="even">
+<td align="right">10.5073404</td>
+<td align="right">69.33</td>
+<td align="right">9.74</td>
+<td align="right">12.32</td>
+<td align="right">4.74</td>
+</tr>
+<tr class="odd">
+<td align="right">21.0146807</td>
+<td align="right">55.65</td>
+<td align="right">14.57</td>
+<td align="right">13.59</td>
+<td align="right">9.84</td>
+</tr>
+<tr class="even">
+<td align="right">31.5220211</td>
+<td align="right">49.03</td>
+<td align="right">14.66</td>
+<td align="right">16.71</td>
+<td align="right">12.32</td>
+</tr>
+<tr class="odd">
+<td align="right">42.0293615</td>
+<td align="right">41.86</td>
+<td align="right">15.97</td>
+<td align="right">13.64</td>
+<td align="right">15.53</td>
+</tr>
+<tr class="even">
+<td align="right">63.0440422</td>
+<td align="right">34.88</td>
+<td align="right">18.20</td>
+<td align="right">14.12</td>
+<td align="right">22.02</td>
+</tr>
+<tr class="odd">
+<td align="right">84.0587230</td>
+<td align="right">28.26</td>
+<td align="right">15.64</td>
+<td align="right">14.06</td>
+<td align="right">25.60</td>
+</tr>
+<tr class="even">
+<td align="right">0.0000000</td>
+<td align="right">104.05</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+</tr>
+<tr class="odd">
+<td align="right">2.1014681</td>
+<td align="right">85.25</td>
+<td align="right">2.68</td>
+<td align="right">7.32</td>
+<td align="right">0.69</td>
+</tr>
+<tr class="even">
+<td align="right">4.9034255</td>
+<td align="right">77.22</td>
+<td align="right">7.28</td>
+<td align="right">8.37</td>
+<td align="right">1.45</td>
+</tr>
+<tr class="odd">
+<td align="right">10.5073404</td>
+<td align="right">65.23</td>
+<td align="right">10.73</td>
+<td align="right">10.93</td>
+<td align="right">4.74</td>
+</tr>
+<tr class="even">
+<td align="right">21.0146807</td>
+<td align="right">57.78</td>
+<td align="right">12.29</td>
+<td align="right">14.80</td>
+<td align="right">9.05</td>
+</tr>
+<tr class="odd">
+<td align="right">31.5220211</td>
+<td align="right">54.83</td>
+<td align="right">14.05</td>
+<td align="right">12.01</td>
+<td align="right">11.05</td>
+</tr>
+<tr class="even">
+<td align="right">42.0293615</td>
+<td align="right">45.17</td>
+<td align="right">12.12</td>
+<td align="right">17.89</td>
+<td align="right">15.71</td>
+</tr>
+<tr class="odd">
+<td align="right">63.0440422</td>
+<td align="right">34.83</td>
+<td align="right">12.90</td>
+<td align="right">15.86</td>
+<td align="right">22.52</td>
+</tr>
+<tr class="even">
+<td align="right">84.0587230</td>
+<td align="right">26.59</td>
+<td align="right">14.28</td>
+<td align="right">14.91</td>
+<td align="right">28.48</td>
+</tr>
+<tr class="odd">
+<td align="right">0.0000000</td>
+<td align="right">104.62</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+</tr>
+<tr class="even">
+<td align="right">0.8145225</td>
+<td align="right">97.21</td>
+<td align="right">NA</td>
+<td align="right">4.00</td>
+<td align="right">NA</td>
+</tr>
+<tr class="odd">
+<td align="right">1.9005525</td>
+<td align="right">89.64</td>
+<td align="right">3.59</td>
+<td align="right">5.24</td>
+<td align="right">NA</td>
+</tr>
+<tr class="even">
+<td align="right">4.0726125</td>
+<td align="right">87.90</td>
+<td align="right">4.10</td>
+<td align="right">9.58</td>
+<td align="right">NA</td>
+</tr>
+<tr class="odd">
+<td align="right">8.1452251</td>
+<td align="right">86.90</td>
+<td align="right">5.96</td>
+<td align="right">9.45</td>
+<td align="right">NA</td>
+</tr>
+<tr class="even">
+<td align="right">12.2178376</td>
+<td align="right">74.74</td>
+<td align="right">7.83</td>
+<td align="right">15.03</td>
+<td align="right">5.33</td>
+</tr>
+<tr class="odd">
+<td align="right">16.2904502</td>
+<td align="right">74.13</td>
+<td align="right">8.84</td>
+<td align="right">14.41</td>
+<td align="right">5.10</td>
+</tr>
+<tr class="even">
+<td align="right">24.4356753</td>
+<td align="right">65.26</td>
+<td align="right">11.84</td>
+<td align="right">18.33</td>
+<td align="right">6.71</td>
+</tr>
+<tr class="odd">
+<td align="right">32.5809004</td>
+<td align="right">57.70</td>
+<td align="right">12.74</td>
+<td align="right">19.93</td>
+<td align="right">9.74</td>
+</tr>
+<tr class="even">
+<td align="right">0.0000000</td>
+<td align="right">101.94</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+</tr>
+<tr class="odd">
+<td align="right">0.8145225</td>
+<td align="right">99.94</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+</tr>
+<tr class="even">
+<td align="right">1.9005525</td>
+<td align="right">94.87</td>
+<td align="right">NA</td>
+<td align="right">4.56</td>
+<td align="right">NA</td>
+</tr>
+<tr class="odd">
+<td align="right">4.0726125</td>
+<td align="right">86.96</td>
+<td align="right">6.75</td>
+<td align="right">6.90</td>
+<td align="right">NA</td>
+</tr>
+<tr class="even">
+<td align="right">8.1452251</td>
+<td align="right">80.51</td>
+<td align="right">10.68</td>
+<td align="right">7.43</td>
+<td align="right">2.58</td>
+</tr>
+<tr class="odd">
+<td align="right">12.2178376</td>
+<td align="right">78.38</td>
+<td align="right">10.35</td>
+<td align="right">9.46</td>
+<td align="right">3.69</td>
+</tr>
+<tr class="even">
+<td align="right">16.2904502</td>
+<td align="right">70.05</td>
+<td align="right">13.73</td>
+<td align="right">9.27</td>
+<td align="right">7.18</td>
+</tr>
+<tr class="odd">
+<td align="right">24.4356753</td>
+<td align="right">61.28</td>
+<td align="right">12.57</td>
+<td align="right">13.28</td>
+<td align="right">13.19</td>
+</tr>
+<tr class="even">
+<td align="right">32.5809004</td>
+<td align="right">52.85</td>
+<td align="right">12.67</td>
+<td align="right">12.95</td>
+<td align="right">13.69</td>
+</tr>
+</tbody>
+</table>
+<table class="table">
+<caption>Dataset Sassafras</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">cyan</th>
+<th align="right">JCZ38</th>
+<th align="right">J9Z38</th>
+<th align="right">JSE76</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.000000</td>
+<td align="right">102.17</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+</tr>
+<tr class="even">
+<td align="right">2.216719</td>
+<td align="right">95.49</td>
+<td align="right">1.11</td>
+<td align="right">0.10</td>
+<td align="right">0.83</td>
+</tr>
+<tr class="odd">
+<td align="right">5.172343</td>
+<td align="right">83.35</td>
+<td align="right">6.43</td>
+<td align="right">2.89</td>
+<td align="right">3.30</td>
+</tr>
+<tr class="even">
+<td align="right">11.083593</td>
+<td align="right">78.18</td>
+<td align="right">10.00</td>
+<td align="right">5.59</td>
+<td align="right">0.81</td>
+</tr>
+<tr class="odd">
+<td align="right">22.167186</td>
+<td align="right">70.44</td>
+<td align="right">17.21</td>
+<td align="right">4.23</td>
+<td align="right">1.09</td>
+</tr>
+<tr class="even">
+<td align="right">33.250779</td>
+<td align="right">68.00</td>
+<td align="right">20.45</td>
+<td align="right">5.86</td>
+<td align="right">1.17</td>
+</tr>
+<tr class="odd">
+<td align="right">44.334371</td>
+<td align="right">59.64</td>
+<td align="right">24.64</td>
+<td align="right">3.17</td>
+<td align="right">2.72</td>
+</tr>
+<tr class="even">
+<td align="right">66.501557</td>
+<td align="right">50.73</td>
+<td align="right">27.50</td>
+<td align="right">6.19</td>
+<td align="right">1.27</td>
+</tr>
+<tr class="odd">
+<td align="right">88.668742</td>
+<td align="right">45.65</td>
+<td align="right">32.77</td>
+<td align="right">5.69</td>
+<td align="right">4.54</td>
+</tr>
+<tr class="even">
+<td align="right">0.000000</td>
+<td align="right">100.43</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+</tr>
+<tr class="odd">
+<td align="right">2.216719</td>
+<td align="right">95.34</td>
+<td align="right">3.21</td>
+<td align="right">0.14</td>
+<td align="right">0.46</td>
+</tr>
+<tr class="even">
+<td align="right">5.172343</td>
+<td align="right">84.38</td>
+<td align="right">5.73</td>
+<td align="right">4.75</td>
+<td align="right">0.62</td>
+</tr>
+<tr class="odd">
+<td align="right">11.083593</td>
+<td align="right">78.50</td>
+<td align="right">11.89</td>
+<td align="right">3.99</td>
+<td align="right">0.73</td>
+</tr>
+<tr class="even">
+<td align="right">22.167186</td>
+<td align="right">71.17</td>
+<td align="right">17.28</td>
+<td align="right">4.39</td>
+<td align="right">0.66</td>
+</tr>
+<tr class="odd">
+<td align="right">33.250779</td>
+<td align="right">59.41</td>
+<td align="right">18.73</td>
+<td align="right">11.85</td>
+<td align="right">2.65</td>
+</tr>
+<tr class="even">
+<td align="right">44.334371</td>
+<td align="right">64.57</td>
+<td align="right">22.93</td>
+<td align="right">5.13</td>
+<td align="right">2.01</td>
+</tr>
+<tr class="odd">
+<td align="right">66.501557</td>
+<td align="right">49.08</td>
+<td align="right">33.39</td>
+<td align="right">5.67</td>
+<td align="right">3.63</td>
+</tr>
+<tr class="even">
+<td align="right">88.668742</td>
+<td align="right">40.41</td>
+<td align="right">39.60</td>
+<td align="right">5.93</td>
+<td align="right">6.17</td>
+</tr>
+</tbody>
+</table>
+<table class="table">
+<caption>Dataset Lleida</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">cyan</th>
+<th align="right">JCZ38</th>
+<th align="right">J9Z38</th>
+<th align="right">JSE76</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.000000</td>
+<td align="right">102.71</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+</tr>
+<tr class="even">
+<td align="right">2.821051</td>
+<td align="right">79.11</td>
+<td align="right">5.70</td>
+<td align="right">8.07</td>
+<td align="right">0.97</td>
+</tr>
+<tr class="odd">
+<td align="right">6.582451</td>
+<td align="right">70.03</td>
+<td align="right">7.17</td>
+<td align="right">11.31</td>
+<td align="right">4.72</td>
+</tr>
+<tr class="even">
+<td align="right">14.105253</td>
+<td align="right">50.93</td>
+<td align="right">10.25</td>
+<td align="right">14.84</td>
+<td align="right">9.95</td>
+</tr>
+<tr class="odd">
+<td align="right">28.210505</td>
+<td align="right">33.43</td>
+<td align="right">10.40</td>
+<td align="right">14.82</td>
+<td align="right">24.06</td>
+</tr>
+<tr class="even">
+<td align="right">42.315758</td>
+<td align="right">24.69</td>
+<td align="right">9.75</td>
+<td align="right">16.38</td>
+<td align="right">29.38</td>
+</tr>
+<tr class="odd">
+<td align="right">56.421010</td>
+<td align="right">22.99</td>
+<td align="right">10.06</td>
+<td align="right">15.51</td>
+<td align="right">29.25</td>
+</tr>
+<tr class="even">
+<td align="right">84.631516</td>
+<td align="right">14.63</td>
+<td align="right">5.63</td>
+<td align="right">14.74</td>
+<td align="right">31.04</td>
+</tr>
+<tr class="odd">
+<td align="right">112.842021</td>
+<td align="right">12.43</td>
+<td align="right">4.17</td>
+<td align="right">13.53</td>
+<td align="right">33.28</td>
+</tr>
+<tr class="even">
+<td align="right">0.000000</td>
+<td align="right">99.31</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+</tr>
+<tr class="odd">
+<td align="right">2.821051</td>
+<td align="right">82.07</td>
+<td align="right">6.55</td>
+<td align="right">5.60</td>
+<td align="right">1.12</td>
+</tr>
+<tr class="even">
+<td align="right">6.582451</td>
+<td align="right">70.65</td>
+<td align="right">7.61</td>
+<td align="right">8.01</td>
+<td align="right">3.21</td>
+</tr>
+<tr class="odd">
+<td align="right">14.105253</td>
+<td align="right">53.52</td>
+<td align="right">11.48</td>
+<td align="right">10.82</td>
+<td align="right">12.24</td>
+</tr>
+<tr class="even">
+<td align="right">28.210505</td>
+<td align="right">35.60</td>
+<td align="right">11.19</td>
+<td align="right">15.43</td>
+<td align="right">23.53</td>
+</tr>
+<tr class="odd">
+<td align="right">42.315758</td>
+<td align="right">34.26</td>
+<td align="right">11.09</td>
+<td align="right">13.26</td>
+<td align="right">27.42</td>
+</tr>
+<tr class="even">
+<td align="right">56.421010</td>
+<td align="right">21.79</td>
+<td align="right">4.80</td>
+<td align="right">18.30</td>
+<td align="right">30.20</td>
+</tr>
+<tr class="odd">
+<td align="right">84.631516</td>
+<td align="right">14.06</td>
+<td align="right">6.30</td>
+<td align="right">16.35</td>
+<td align="right">32.32</td>
+</tr>
+<tr class="even">
+<td align="right">112.842021</td>
+<td align="right">11.51</td>
+<td align="right">5.57</td>
+<td align="right">12.64</td>
+<td align="right">32.51</td>
+</tr>
+</tbody>
+</table>
+</div>
+</div>
+<div class="section level2">
+<h2 id="parent-only-evaluations">Parent only evaluations<a class="anchor" aria-label="anchor" href="#parent-only-evaluations"></a>
+</h2>
+<p>As the pathway fits have very long run times, evaluations of the
+parent data are performed first, in order to determine for each
+hierarchical parent degradation model which random effects on the
+degradation model parameters are ill-defined.</p>
+<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">cyan_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="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">"SFORB"</span>, <span class="st">"HS"</span><span class="op">)</span>,</span>
+<span>  <span class="va">cyan_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">cyan_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">cyan_sep_const</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span>
+<span><span class="va">cyan_saem_full</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mhmkin.html">mhmkin</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">cyan_sep_const</span>, <span class="va">cyan_sep_tc</span><span class="op">)</span><span class="op">)</span></span>
+<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">cyan_saem_full</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><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="left">const</th>
+<th align="left">tc</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">SFO</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">FOMC</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="odd">
+<td align="left">DFOP</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">SFORB</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="odd">
+<td align="left">HS</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+</tbody>
+</table>
+<p>All fits converged successfully.</p>
+<div class="sourceCode" id="cb6"><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">cyan_saem_full</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><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="left">const</th>
+<th align="left">tc</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">SFO</td>
+<td align="left">sd(cyan_0)</td>
+<td align="left">sd(cyan_0)</td>
+</tr>
+<tr class="even">
+<td align="left">FOMC</td>
+<td align="left">sd(log_beta)</td>
+<td align="left">sd(cyan_0)</td>
+</tr>
+<tr class="odd">
+<td align="left">DFOP</td>
+<td align="left">sd(cyan_0)</td>
+<td align="left">sd(cyan_0), sd(log_k1)</td>
+</tr>
+<tr class="even">
+<td align="left">SFORB</td>
+<td align="left">sd(cyan_free_0)</td>
+<td align="left">sd(cyan_free_0), sd(log_k_cyan_free_bound)</td>
+</tr>
+<tr class="odd">
+<td align="left">HS</td>
+<td align="left">sd(cyan_0)</td>
+<td align="left">sd(cyan_0)</td>
+</tr>
+</tbody>
+</table>
+<p>In almost all models, the random effect for the initial concentration
+of the parent compound is ill-defined. For the biexponential models DFOP
+and SFORB, the random effect of one additional parameter is ill-defined
+when the two-component error model is used.</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">cyan_saem_full</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">833.9</td>
+<td align="right">832.0</td>
+<td align="right">-412.0</td>
+</tr>
+<tr class="even">
+<td align="left">SFO tc</td>
+<td align="right">6</td>
+<td align="right">831.6</td>
+<td align="right">829.3</td>
+<td align="right">-409.8</td>
+</tr>
+<tr class="odd">
+<td align="left">FOMC const</td>
+<td align="right">7</td>
+<td align="right">709.1</td>
+<td align="right">706.4</td>
+<td align="right">-347.6</td>
+</tr>
+<tr class="even">
+<td align="left">FOMC tc</td>
+<td align="right">8</td>
+<td align="right">689.2</td>
+<td align="right">686.1</td>
+<td align="right">-336.6</td>
+</tr>
+<tr class="odd">
+<td align="left">DFOP const</td>
+<td align="right">9</td>
+<td align="right">703.0</td>
+<td align="right">699.5</td>
+<td align="right">-342.5</td>
+</tr>
+<tr class="even">
+<td align="left">SFORB const</td>
+<td align="right">9</td>
+<td align="right">701.3</td>
+<td align="right">697.8</td>
+<td align="right">-341.7</td>
+</tr>
+<tr class="odd">
+<td align="left">HS const</td>
+<td align="right">9</td>
+<td align="right">718.6</td>
+<td align="right">715.1</td>
+<td align="right">-350.3</td>
+</tr>
+<tr class="even">
+<td align="left">DFOP tc</td>
+<td align="right">10</td>
+<td align="right">703.1</td>
+<td align="right">699.2</td>
+<td align="right">-341.6</td>
+</tr>
+<tr class="odd">
+<td align="left">SFORB tc</td>
+<td align="right">10</td>
+<td align="right">700.0</td>
+<td align="right">696.1</td>
+<td align="right">-340.0</td>
+</tr>
+<tr class="even">
+<td align="left">HS tc</td>
+<td align="right">10</td>
+<td align="right">716.7</td>
+<td align="right">712.8</td>
+<td align="right">-348.3</td>
+</tr>
+</tbody>
+</table>
+<p>Model comparison based on AIC and BIC indicates that the
+two-component error model is preferable for all parent models with the
+exception of DFOP. The lowest AIC and BIC values are are obtained with
+the FOMC model, followed by SFORB and DFOP.</p>
+<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">stopCluster</a></span><span class="op">(</span><span class="va">cl</span><span class="op">)</span></span></code></pre></div>
+</div>
+<div class="section level2">
+<h2 id="pathway-fits">Pathway fits<a class="anchor" aria-label="anchor" href="#pathway-fits"></a>
+</h2>
+<div class="section level3">
+<h3 id="evaluations-with-pathway-established-previously">Evaluations with pathway established previously<a class="anchor" aria-label="anchor" href="#evaluations-with-pathway-established-previously"></a>
+</h3>
+<p>To test the technical feasibility of coupling the relevant parent
+degradation models with different transformation pathway models, a list
+of <code>mkinmod</code> models is set up below. As in the EU evaluation,
+parallel formation of metabolites JCZ38 and J9Z38 and secondary
+formation of metabolite JSE76 from JCZ38 is used.</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="op">!</span><span class="fu"><a href="https://rdrr.io/r/base/files2.html" class="external-link">dir.exists</a></span><span class="op">(</span><span class="st">"cyan_dlls"</span><span class="op">)</span><span class="op">)</span> <span class="fu"><a href="https://rdrr.io/r/base/files2.html" class="external-link">dir.create</a></span><span class="op">(</span><span class="st">"cyan_dlls"</span><span class="op">)</span></span>
+<span><span class="va">cyan_path_1</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>  sfo_path_1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span>
+<span>    cyan <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="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"JCZ38"</span>, <span class="st">"J9Z38"</span><span class="op">)</span><span class="op">)</span>,</span>
+<span>    JCZ38 <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">"JSE76"</span><span class="op">)</span>,</span>
+<span>    J9Z38 <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>    JSE76 <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>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span>
+<span>    name <span class="op">=</span> <span class="st">"sfo_path_1"</span>, dll_dir <span class="op">=</span> <span class="st">"cyan_dlls"</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,</span>
+<span>  fomc_path_1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span>
+<span>    cyan <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="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"JCZ38"</span>, <span class="st">"J9Z38"</span><span class="op">)</span><span class="op">)</span>,</span>
+<span>    JCZ38 <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">"JSE76"</span><span class="op">)</span>,</span>
+<span>    J9Z38 <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>    JSE76 <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>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span>
+<span>    name <span class="op">=</span> <span class="st">"fomc_path_1"</span>, dll_dir <span class="op">=</span> <span class="st">"cyan_dlls"</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,</span>
+<span>  dfop_path_1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span>
+<span>    cyan <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">"JCZ38"</span>, <span class="st">"J9Z38"</span><span class="op">)</span><span class="op">)</span>,</span>
+<span>    JCZ38 <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">"JSE76"</span><span class="op">)</span>,</span>
+<span>    J9Z38 <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>    JSE76 <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>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span>
+<span>    name <span class="op">=</span> <span class="st">"dfop_path_1"</span>, dll_dir <span class="op">=</span> <span class="st">"cyan_dlls"</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,</span>
+<span>  sforb_path_1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span>
+<span>    cyan <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">"JCZ38"</span>, <span class="st">"J9Z38"</span><span class="op">)</span><span class="op">)</span>,</span>
+<span>    JCZ38 <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">"JSE76"</span><span class="op">)</span>,</span>
+<span>    J9Z38 <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>    JSE76 <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>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span>
+<span>    name <span class="op">=</span> <span class="st">"sforb_path_1"</span>, dll_dir <span class="op">=</span> <span class="st">"cyan_dlls"</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,</span>
+<span>  hs_path_1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span>
+<span>    cyan <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"HS"</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">"JCZ38"</span>, <span class="st">"J9Z38"</span><span class="op">)</span><span class="op">)</span>,</span>
+<span>    JCZ38 <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">"JSE76"</span><span class="op">)</span>,</span>
+<span>    J9Z38 <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>    JSE76 <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>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span>
+<span>    name <span class="op">=</span> <span class="st">"hs_path_1"</span>, dll_dir <span class="op">=</span> <span class="st">"cyan_dlls"</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
+<span><span class="op">)</span></span>
+<span><span class="va">cl_path_1</span> <span class="op">&lt;-</span> <span class="fu">start_cluster</span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span></code></pre></div>
+<p>To obtain suitable starting values for the NLHM fits, separate
+pathway fits are performed for all datasets.</p>
+<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">f_sep_1_const</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span></span>
+<span>  <span class="va">cyan_path_1</span>,</span>
+<span>  <span class="va">cyan_ds</span>,</span>
+<span>  error_model <span class="op">=</span> <span class="st">"const"</span>,</span>
+<span>  cluster <span class="op">=</span> <span class="va">cl_path_1</span>,</span>
+<span>  quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
+<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_1_const</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><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="left">Nambsheim</th>
+<th align="left">Tama</th>
+<th align="left">Gross-Umstadt</th>
+<th align="left">Sassafras</th>
+<th align="left">Lleida</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">sfo_path_1</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">fomc_path_1</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="odd">
+<td align="left">dfop_path_1</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">sforb_path_1</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="odd">
+<td align="left">hs_path_1</td>
+<td align="left">C</td>
+<td align="left">C</td>
+<td align="left">C</td>
+<td align="left">C</td>
+<td align="left">C</td>
+</tr>
+</tbody>
+</table>
+<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">f_sep_1_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">f_sep_1_const</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span>
+<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_1_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><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="left">Nambsheim</th>
+<th align="left">Tama</th>
+<th align="left">Gross-Umstadt</th>
+<th align="left">Sassafras</th>
+<th align="left">Lleida</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">sfo_path_1</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">fomc_path_1</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="odd">
+<td align="left">dfop_path_1</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">sforb_path_1</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="odd">
+<td align="left">hs_path_1</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+</tr>
+</tbody>
+</table>
+<p>Most separate fits converged successfully. The biggest convergence
+problems are seen when using the HS model with constant variance.</p>
+<p>For the hierarchical pathway fits, those random effects that could
+not be quantified in the corresponding parent data analyses are
+excluded.</p>
+<p>In the code below, the output of the <code>illparms</code> function
+for the parent only fits is used as an argument
+<code>no_random_effect</code> to the <code>mhmkin</code> function. The
+possibility to do so was introduced in mkin version <code>1.2.2</code>
+which is currently under development.</p>
+<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">f_saem_1</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mhmkin.html">mhmkin</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_sep_1_const</span>, <span class="va">f_sep_1_tc</span><span class="op">)</span>,</span>
+<span>  no_random_effect <span class="op">=</span> <span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">cyan_saem_full</span><span class="op">)</span>,</span>
+<span>  cluster <span class="op">=</span> <span class="va">cl_path_1</span><span class="op">)</span></span></code></pre></div>
+<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_saem_1</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><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="left">const</th>
+<th align="left">tc</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">sfo_path_1</td>
+<td align="left">FO</td>
+<td align="left">Fth, FO</td>
+</tr>
+<tr class="even">
+<td align="left">fomc_path_1</td>
+<td align="left">OK</td>
+<td align="left">Fth, FO</td>
+</tr>
+<tr class="odd">
+<td align="left">dfop_path_1</td>
+<td align="left">Fth, FO</td>
+<td align="left">Fth, FO</td>
+</tr>
+<tr class="even">
+<td align="left">sforb_path_1</td>
+<td align="left">Fth, FO</td>
+<td align="left">Fth, FO</td>
+</tr>
+<tr class="odd">
+<td align="left">hs_path_1</td>
+<td align="left">FO</td>
+<td align="left">E</td>
+</tr>
+</tbody>
+</table>
+<p>The status information from the individual fits shows that all fits
+completed successfully. The matrix entries Fth and FO indicate that the
+Fisher Information Matrix could not be inverted for the fixed effects
+(theta) and the random effects (Omega), respectively. For the affected
+fits, ill-defined parameters cannot be determined using the
+<code>illparms</code> function, because it relies on the Fisher
+Information Matrix.</p>
+<div class="sourceCode" id="cb14"><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">f_saem_1</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><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<colgroup>
+<col width="18%">
+<col width="77%">
+<col width="4%">
+</colgroup>
+<thead><tr class="header">
+<th align="left"></th>
+<th align="left">const</th>
+<th align="left">tc</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">sfo_path_1</td>
+<td align="left">NA</td>
+<td align="left">NA</td>
+</tr>
+<tr class="even">
+<td align="left">fomc_path_1</td>
+<td align="left">sd(log_k_J9Z38), sd(f_cyan_ilr_2),
+sd(f_JCZ38_qlogis)</td>
+<td align="left">NA</td>
+</tr>
+<tr class="odd">
+<td align="left">dfop_path_1</td>
+<td align="left">NA</td>
+<td align="left">NA</td>
+</tr>
+<tr class="even">
+<td align="left">sforb_path_1</td>
+<td align="left">NA</td>
+<td align="left">NA</td>
+</tr>
+<tr class="odd">
+<td align="left">hs_path_1</td>
+<td align="left">NA</td>
+<td align="left">E</td>
+</tr>
+</tbody>
+</table>
+<p>The model comparisons below suggest that the pathway fits using DFOP
+or SFORB for the parent compound provide the best fit.</p>
+<div class="sourceCode" id="cb15"><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_1</span><span class="op">[</span>, <span class="st">"const"</span><span class="op">]</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_path_1 const</td>
+<td align="right">16</td>
+<td align="right">2693.0</td>
+<td align="right">2686.8</td>
+<td align="right">-1330.5</td>
+</tr>
+<tr class="even">
+<td align="left">fomc_path_1 const</td>
+<td align="right">18</td>
+<td align="right">2427.9</td>
+<td align="right">2420.9</td>
+<td align="right">-1196.0</td>
+</tr>
+<tr class="odd">
+<td align="left">dfop_path_1 const</td>
+<td align="right">20</td>
+<td align="right">2403.2</td>
+<td align="right">2395.4</td>
+<td align="right">-1181.6</td>
+</tr>
+<tr class="even">
+<td align="left">sforb_path_1 const</td>
+<td align="right">20</td>
+<td align="right">2401.4</td>
+<td align="right">2393.6</td>
+<td align="right">-1180.7</td>
+</tr>
+<tr class="odd">
+<td align="left">hs_path_1 const</td>
+<td align="right">20</td>
+<td align="right">2427.2</td>
+<td align="right">2419.4</td>
+<td align="right">-1193.6</td>
+</tr>
+</tbody>
+</table>
+<div class="sourceCode" id="cb16"><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_1</span><span class="op">[</span><span class="fl">1</span><span class="op">:</span><span class="fl">4</span>, <span class="op">]</span><span class="op">)</span> <span class="op">|&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_path_1 const</td>
+<td align="right">16</td>
+<td align="right">2693.0</td>
+<td align="right">2686.8</td>
+<td align="right">-1330.5</td>
+</tr>
+<tr class="even">
+<td align="left">sfo_path_1 tc</td>
+<td align="right">17</td>
+<td align="right">2657.6</td>
+<td align="right">2651.0</td>
+<td align="right">-1311.8</td>
+</tr>
+<tr class="odd">
+<td align="left">fomc_path_1 const</td>
+<td align="right">18</td>
+<td align="right">2427.9</td>
+<td align="right">2420.9</td>
+<td align="right">-1196.0</td>
+</tr>
+<tr class="even">
+<td align="left">fomc_path_1 tc</td>
+<td align="right">19</td>
+<td align="right">2423.6</td>
+<td align="right">2416.2</td>
+<td align="right">-1192.8</td>
+</tr>
+<tr class="odd">
+<td align="left">dfop_path_1 const</td>
+<td align="right">20</td>
+<td align="right">2403.2</td>
+<td align="right">2395.4</td>
+<td align="right">-1181.6</td>
+</tr>
+<tr class="even">
+<td align="left">sforb_path_1 const</td>
+<td align="right">20</td>
+<td align="right">2401.4</td>
+<td align="right">2393.6</td>
+<td align="right">-1180.7</td>
+</tr>
+<tr class="odd">
+<td align="left">dfop_path_1 tc</td>
+<td align="right">20</td>
+<td align="right">2398.0</td>
+<td align="right">2390.1</td>
+<td align="right">-1179.0</td>
+</tr>
+<tr class="even">
+<td align="left">sforb_path_1 tc</td>
+<td align="right">20</td>
+<td align="right">2399.9</td>
+<td align="right">2392.1</td>
+<td align="right">-1180.0</td>
+</tr>
+</tbody>
+</table>
+<p>For these two parent model, successful fits are shown below. Plots of
+the fits with the other parent models are shown in the Appendix.</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/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">[[</span><span class="st">"dfop_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
+<div class="figure" style="text-align: center">
+<img src="2022_cyan_pathway_files/figure-html/unnamed-chunk-7-1.png" alt="DFOP pathway fit with two-component error" width="700"><p class="caption">
+DFOP pathway fit with two-component error
+</p>
+</div>
+<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/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">[[</span><span class="st">"sforb_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
+<div class="figure" style="text-align: center">
+<img src="2022_cyan_pathway_files/figure-html/unnamed-chunk-8-1.png" alt="SFORB pathway fit with two-component error" width="700"><p class="caption">
+SFORB pathway fit with two-component error
+</p>
+</div>
+<p>A closer graphical analysis of these Figures shows that the residues
+of transformation product JCZ38 in the soils Tama and Nambsheim observed
+at later time points are strongly and systematically underestimated.</p>
+<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">stopCluster</a></span><span class="op">(</span><span class="va">cl_path_1</span><span class="op">)</span></span></code></pre></div>
+</div>
+<div class="section level3">
+<h3 id="alternative-pathway-fits">Alternative pathway fits<a class="anchor" aria-label="anchor" href="#alternative-pathway-fits"></a>
+</h3>
+<p>To improve the fit for JCZ38, a back-reaction from JSE76 to JCZ38 was
+introduced in an alternative version of the transformation pathway, in
+analogy to the back-reaction from K5A78 to K5A77. Both pairs of
+transformation products are pairs of an organic acid with its
+corresponding amide (Addendum 2014, p. 109). As FOMC provided the best
+fit for the parent, and the biexponential models DFOP and SFORB provided
+the best initial pathway fits, these three parent models are used in the
+alternative pathway fits.</p>
+<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">cyan_path_2</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>  fomc_path_2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span>
+<span>    cyan <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="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"JCZ38"</span>, <span class="st">"J9Z38"</span><span class="op">)</span><span class="op">)</span>,</span>
+<span>    JCZ38 <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">"JSE76"</span><span class="op">)</span>,</span>
+<span>    J9Z38 <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>    JSE76 <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">"JCZ38"</span><span class="op">)</span>,</span>
+<span>    name <span class="op">=</span> <span class="st">"fomc_path_2"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span>
+<span>    dll_dir <span class="op">=</span> <span class="st">"cyan_dlls"</span>,</span>
+<span>    overwrite <span class="op">=</span> <span class="cn">TRUE</span></span>
+<span>  <span class="op">)</span>,</span>
+<span>  dfop_path_2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span>
+<span>    cyan <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">"JCZ38"</span>, <span class="st">"J9Z38"</span><span class="op">)</span><span class="op">)</span>,</span>
+<span>    JCZ38 <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">"JSE76"</span><span class="op">)</span>,</span>
+<span>    J9Z38 <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>    JSE76 <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">"JCZ38"</span><span class="op">)</span>,</span>
+<span>    name <span class="op">=</span> <span class="st">"dfop_path_2"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span>
+<span>    dll_dir <span class="op">=</span> <span class="st">"cyan_dlls"</span>,</span>
+<span>    overwrite <span class="op">=</span> <span class="cn">TRUE</span></span>
+<span>  <span class="op">)</span>,</span>
+<span>  sforb_path_2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span>
+<span>    cyan <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">"JCZ38"</span>, <span class="st">"J9Z38"</span><span class="op">)</span><span class="op">)</span>,</span>
+<span>    JCZ38 <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">"JSE76"</span><span class="op">)</span>,</span>
+<span>    J9Z38 <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>    JSE76 <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">"JCZ38"</span><span class="op">)</span>,</span>
+<span>    name <span class="op">=</span> <span class="st">"sforb_path_2"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span>
+<span>    dll_dir <span class="op">=</span> <span class="st">"cyan_dlls"</span>,</span>
+<span>    overwrite <span class="op">=</span> <span class="cn">TRUE</span></span>
+<span>  <span class="op">)</span></span>
+<span><span class="op">)</span></span>
+<span></span>
+<span><span class="va">cl_path_2</span> <span class="op">&lt;-</span> <span class="fu">start_cluster</span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span>
+<span><span class="va">f_sep_2_const</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span></span>
+<span>  <span class="va">cyan_path_2</span>,</span>
+<span>  <span class="va">cyan_ds</span>,</span>
+<span>  error_model <span class="op">=</span> <span class="st">"const"</span>,</span>
+<span>  cluster <span class="op">=</span> <span class="va">cl_path_2</span>,</span>
+<span>  quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
+<span></span>
+<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_2_const</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><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="left">Nambsheim</th>
+<th align="left">Tama</th>
+<th align="left">Gross-Umstadt</th>
+<th align="left">Sassafras</th>
+<th align="left">Lleida</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">fomc_path_2</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">dfop_path_2</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+</tr>
+<tr class="odd">
+<td align="left">sforb_path_2</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+</tbody>
+</table>
+<p>Using constant variance, separate fits converge with the exception of
+the fits to the Sassafras soil data.</p>
+<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">f_sep_2_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">f_sep_2_const</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span>
+<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_2_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><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="left">Nambsheim</th>
+<th align="left">Tama</th>
+<th align="left">Gross-Umstadt</th>
+<th align="left">Sassafras</th>
+<th align="left">Lleida</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">fomc_path_2</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">dfop_path_2</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+</tr>
+<tr class="odd">
+<td align="left">sforb_path_2</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+</tr>
+</tbody>
+</table>
+<p>Using the two-component error model, all separate fits converge with
+the exception of the alternative pathway fit with DFOP used for the
+parent and the Sassafras dataset.</p>
+<div class="sourceCode" id="cb22"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">f_saem_2</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mhmkin.html">mhmkin</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_sep_2_const</span>, <span class="va">f_sep_2_tc</span><span class="op">)</span>,</span>
+<span>  no_random_effect <span class="op">=</span> <span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">cyan_saem_full</span><span class="op">[</span><span class="fl">2</span><span class="op">:</span><span class="fl">4</span>, <span class="op">]</span><span class="op">)</span>,</span>
+<span>  cluster <span class="op">=</span> <span class="va">cl_path_2</span><span class="op">)</span></span></code></pre></div>
+<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_saem_2</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><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="left">const</th>
+<th align="left">tc</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">fomc_path_2</td>
+<td align="left">E</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">dfop_path_2</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="odd">
+<td align="left">sforb_path_2</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+</tbody>
+</table>
+<p>The hierarchical fits for the alternative pathway completed
+successfully, with the exception of the model using FOMC for the parent
+compound and constant variance as the error model.</p>
+<div class="sourceCode" id="cb24"><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">f_saem_2</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><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<colgroup>
+<col width="14%">
+<col width="42%">
+<col width="42%">
+</colgroup>
+<thead><tr class="header">
+<th align="left"></th>
+<th align="left">const</th>
+<th align="left">tc</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">fomc_path_2</td>
+<td align="left">E</td>
+<td align="left">sd(f_JSE76_qlogis)</td>
+</tr>
+<tr class="even">
+<td align="left">dfop_path_2</td>
+<td align="left">sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)</td>
+<td align="left">sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)</td>
+</tr>
+<tr class="odd">
+<td align="left">sforb_path_2</td>
+<td align="left">sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)</td>
+<td align="left">sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)</td>
+</tr>
+</tbody>
+</table>
+<p>In all biphasic fits (DFOP or SFORB for the parent compound), the
+random effects for the formation fractions for the pathways from JCZ38
+to JSE76, and for the reverse pathway from JSE76 to JCZ38 are
+ill-defined.</p>
+<div class="sourceCode" id="cb25"><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_2</span><span class="op">[</span>, <span class="st">"tc"</span><span class="op">]</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">fomc_path_2 tc</td>
+<td align="right">21</td>
+<td align="right">2249.0</td>
+<td align="right">2240.8</td>
+<td align="right">-1103.5</td>
+</tr>
+<tr class="even">
+<td align="left">dfop_path_2 tc</td>
+<td align="right">22</td>
+<td align="right">2234.4</td>
+<td align="right">2225.8</td>
+<td align="right">-1095.2</td>
+</tr>
+<tr class="odd">
+<td align="left">sforb_path_2 tc</td>
+<td align="right">22</td>
+<td align="right">2239.7</td>
+<td align="right">2231.1</td>
+<td align="right">-1097.9</td>
+</tr>
+</tbody>
+</table>
+<div class="sourceCode" id="cb26"><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_2</span><span class="op">[</span><span class="fl">2</span><span class="op">:</span><span class="fl">3</span>,<span class="op">]</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">dfop_path_2 const</td>
+<td align="right">22</td>
+<td align="right">2288.4</td>
+<td align="right">2279.8</td>
+<td align="right">-1122.2</td>
+</tr>
+<tr class="even">
+<td align="left">sforb_path_2 const</td>
+<td align="right">22</td>
+<td align="right">2283.3</td>
+<td align="right">2274.7</td>
+<td align="right">-1119.7</td>
+</tr>
+<tr class="odd">
+<td align="left">dfop_path_2 tc</td>
+<td align="right">22</td>
+<td align="right">2234.4</td>
+<td align="right">2225.8</td>
+<td align="right">-1095.2</td>
+</tr>
+<tr class="even">
+<td align="left">sforb_path_2 tc</td>
+<td align="right">22</td>
+<td align="right">2239.7</td>
+<td align="right">2231.1</td>
+<td align="right">-1097.9</td>
+</tr>
+</tbody>
+</table>
+<p>The variants using the biexponential models DFOP and SFORB for the
+parent compound and the two-component error model give the lowest AIC
+and BIC values and are plotted below. Compared with the original
+pathway, the AIC and BIC values indicate a large improvement. This is
+confirmed by the plots, which show that the metabolite JCZ38 is fitted
+much better with this model.</p>
+<div class="sourceCode" id="cb27"><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_saem_2</span><span class="op">[[</span><span class="st">"fomc_path_2"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
+<div class="figure" style="text-align: center">
+<img src="2022_cyan_pathway_files/figure-html/unnamed-chunk-13-1.png" alt="FOMC pathway fit with two-component error, alternative pathway" width="700"><p class="caption">
+FOMC pathway fit with two-component error, alternative pathway
+</p>
+</div>
+<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">f_saem_2</span><span class="op">[[</span><span class="st">"dfop_path_2"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
+<div class="figure" style="text-align: center">
+<img src="2022_cyan_pathway_files/figure-html/unnamed-chunk-14-1.png" alt="DFOP pathway fit with two-component error, alternative pathway" width="700"><p class="caption">
+DFOP pathway fit with two-component error, alternative pathway
+</p>
+</div>
+<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/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"sforb_path_2"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
+<div class="figure" style="text-align: center">
+<img src="2022_cyan_pathway_files/figure-html/unnamed-chunk-15-1.png" alt="SFORB pathway fit with two-component error, alternative pathway" width="700"><p class="caption">
+SFORB pathway fit with two-component error, alternative pathway
+</p>
+</div>
+</div>
+<div class="section level3">
+<h3 id="refinement-of-alternative-pathway-fits">Refinement of alternative pathway fits<a class="anchor" aria-label="anchor" href="#refinement-of-alternative-pathway-fits"></a>
+</h3>
+<p>All ill-defined random effects that were identified in the parent
+only fits and in the above pathway fits, are excluded for the final
+evaluations below. For this purpose, a list of character vectors is
+created below that can be indexed by row and column indices, and which
+contains the degradation parameter names for which random effects should
+be excluded for each of the hierarchical fits contained in
+<code>f_saem_2</code>.</p>
+<div class="sourceCode" id="cb30"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">no_ranef</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/matrix.html" class="external-link">matrix</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="op">)</span>, nrow <span class="op">=</span> <span class="fl">3</span>, ncol <span class="op">=</span> <span class="fl">2</span>, dimnames <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/dimnames.html" class="external-link">dimnames</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">)</span><span class="op">)</span></span>
+<span><span class="va">no_ranef</span><span class="op">[[</span><span class="st">"fomc_path_2"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"log_beta"</span>, <span class="st">"f_JCZ38_qlogis"</span>, <span class="st">"f_JSE76_qlogis"</span><span class="op">)</span></span>
+<span><span class="va">no_ranef</span><span class="op">[[</span><span class="st">"fomc_path_2"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"cyan_0"</span>, <span class="st">"f_JCZ38_qlogis"</span>, <span class="st">"f_JSE76_qlogis"</span><span class="op">)</span></span>
+<span><span class="va">no_ranef</span><span class="op">[[</span><span class="st">"dfop_path_2"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"cyan_0"</span>, <span class="st">"f_JCZ38_qlogis"</span>, <span class="st">"f_JSE76_qlogis"</span><span class="op">)</span></span>
+<span><span class="va">no_ranef</span><span class="op">[[</span><span class="st">"dfop_path_2"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"cyan_0"</span>, <span class="st">"log_k1"</span>, <span class="st">"f_JCZ38_qlogis"</span>, <span class="st">"f_JSE76_qlogis"</span><span class="op">)</span></span>
+<span><span class="va">no_ranef</span><span class="op">[[</span><span class="st">"sforb_path_2"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"cyan_free_0"</span>,</span>
+<span>  <span class="st">"f_JCZ38_qlogis"</span>, <span class="st">"f_JSE76_qlogis"</span><span class="op">)</span></span>
+<span><span class="va">no_ranef</span><span class="op">[[</span><span class="st">"sforb_path_2"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"cyan_free_0"</span>, <span class="st">"log_k_cyan_free_bound"</span>,</span>
+<span>  <span class="st">"f_JCZ38_qlogis"</span>, <span class="st">"f_JSE76_qlogis"</span><span class="op">)</span></span>
+<span><span class="fu"><a href="https://rdrr.io/r/parallel/clusterApply.html" class="external-link">clusterExport</a></span><span class="op">(</span><span class="va">cl_path_2</span>, <span class="st">"no_ranef"</span><span class="op">)</span></span>
+<span></span>
+<span><span class="va">f_saem_3</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">f_saem_2</span>,</span>
+<span>  no_random_effect <span class="op">=</span> <span class="va">no_ranef</span>,</span>
+<span>  cluster <span class="op">=</span> <span class="va">cl_path_2</span><span class="op">)</span></span></code></pre></div>
+<div class="sourceCode" id="cb31"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_saem_3</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><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="left">const</th>
+<th align="left">tc</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">fomc_path_2</td>
+<td align="left">E</td>
+<td align="left">Fth</td>
+</tr>
+<tr class="even">
+<td align="left">dfop_path_2</td>
+<td align="left">Fth</td>
+<td align="left">Fth</td>
+</tr>
+<tr class="odd">
+<td align="left">sforb_path_2</td>
+<td align="left">Fth</td>
+<td align="left">Fth</td>
+</tr>
+</tbody>
+</table>
+<p>With the exception of the FOMC pathway fit with constant variance,
+all updated fits completed successfully. However, the Fisher Information
+Matrix for the fixed effects (Fth) could not be inverted, so no
+confidence intervals for the optimised parameters are available.</p>
+<div class="sourceCode" id="cb32"><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">f_saem_3</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><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="left">const</th>
+<th align="left">tc</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">fomc_path_2</td>
+<td align="left">E</td>
+<td align="left"></td>
+</tr>
+<tr class="even">
+<td align="left">dfop_path_2</td>
+<td align="left"></td>
+<td align="left"></td>
+</tr>
+<tr class="odd">
+<td align="left">sforb_path_2</td>
+<td align="left"></td>
+<td align="left"></td>
+</tr>
+</tbody>
+</table>
+<div class="sourceCode" id="cb33"><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_3</span><span class="op">[</span>, <span class="st">"tc"</span><span class="op">]</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">fomc_path_2 tc</td>
+<td align="right">19</td>
+<td align="right">2249.1</td>
+<td align="right">2241.6</td>
+<td align="right">-1105.5</td>
+</tr>
+<tr class="even">
+<td align="left">dfop_path_2 tc</td>
+<td align="right">20</td>
+<td align="right">2237.3</td>
+<td align="right">2229.5</td>
+<td align="right">-1098.6</td>
+</tr>
+<tr class="odd">
+<td align="left">sforb_path_2 tc</td>
+<td align="right">20</td>
+<td align="right">2241.3</td>
+<td align="right">2233.5</td>
+<td align="right">-1100.7</td>
+</tr>
+</tbody>
+</table>
+<div class="sourceCode" id="cb34"><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_3</span><span class="op">[</span><span class="fl">2</span><span class="op">:</span><span class="fl">3</span>,<span class="op">]</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">dfop_path_2 const</td>
+<td align="right">20</td>
+<td align="right">2282.2</td>
+<td align="right">2274.4</td>
+<td align="right">-1121.1</td>
+</tr>
+<tr class="even">
+<td align="left">sforb_path_2 const</td>
+<td align="right">20</td>
+<td align="right">2279.7</td>
+<td align="right">2271.9</td>
+<td align="right">-1119.9</td>
+</tr>
+<tr class="odd">
+<td align="left">dfop_path_2 tc</td>
+<td align="right">20</td>
+<td align="right">2237.3</td>
+<td align="right">2229.5</td>
+<td align="right">-1098.6</td>
+</tr>
+<tr class="even">
+<td align="left">sforb_path_2 tc</td>
+<td align="right">20</td>
+<td align="right">2241.3</td>
+<td align="right">2233.5</td>
+<td align="right">-1100.7</td>
+</tr>
+</tbody>
+</table>
+<p>While the AIC and BIC values of the best fit (DFOP pathway fit with
+two-component error) are lower than in the previous fits with the
+alternative pathway, the practical value of these refined evaluations is
+limited as no confidence intervals are obtained.</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/parallel/makeCluster.html" class="external-link">stopCluster</a></span><span class="op">(</span><span class="va">cl_path_2</span><span class="op">)</span></span></code></pre></div>
+</div>
+</div>
+<div class="section level2">
+<h2 id="conclusion">Conclusion<a class="anchor" aria-label="anchor" href="#conclusion"></a>
+</h2>
+<p>It was demonstrated that a relatively complex transformation pathway
+with parallel formation of two primary metabolites and one secondary
+metabolite can be fitted even if the data in the individual datasets are
+quite different and partly only cover the formation phase.</p>
+<p>The run times of the pathway fits were several hours, limiting the
+practical feasibility of iterative refinements based on ill-defined
+parameters and of alternative checks of parameter identifiability based
+on multistart runs.</p>
+</div>
+<div class="section level2">
+<h2 id="acknowledgements">Acknowledgements<a class="anchor" aria-label="anchor" href="#acknowledgements"></a>
+</h2>
+<p>The helpful comments by Janina Wöltjen of the German Environment
+Agency are gratefully acknowledged.</p>
+</div>
+<div class="section level2">
+<h2 id="appendix">Appendix<a class="anchor" aria-label="anchor" href="#appendix"></a>
+</h2>
+<div class="section level3">
+<h3 id="plots-of-fits-that-were-not-refined-further">Plots of fits that were not refined further<a class="anchor" aria-label="anchor" href="#plots-of-fits-that-were-not-refined-further"></a>
+</h3>
+<div class="sourceCode" id="cb36"><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_saem_1</span><span class="op">[[</span><span class="st">"sfo_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
+<div class="figure" style="text-align: center">
+<img src="2022_cyan_pathway_files/figure-html/unnamed-chunk-20-1.png" alt="SFO pathway fit with two-component error" width="700"><p class="caption">
+SFO pathway fit with two-component error
+</p>
+</div>
+<div class="sourceCode" id="cb37"><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_saem_1</span><span class="op">[[</span><span class="st">"fomc_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
+<div class="figure" style="text-align: center">
+<img src="2022_cyan_pathway_files/figure-html/unnamed-chunk-21-1.png" alt="FOMC pathway fit with two-component error" width="700"><p class="caption">
+FOMC pathway fit with two-component error
+</p>
+</div>
+<div class="sourceCode" id="cb38"><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_saem_1</span><span class="op">[[</span><span class="st">"sforb_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
+<div class="figure" style="text-align: center">
+<img src="2022_cyan_pathway_files/figure-html/unnamed-chunk-22-1.png" alt="HS pathway fit with two-component error" width="700"><p class="caption">
+HS pathway fit with two-component error
+</p>
+</div>
+</div>
+<div class="section level3">
+<h3 id="hierarchical-fit-listings">Hierarchical fit listings<a class="anchor" aria-label="anchor" href="#hierarchical-fit-listings"></a>
+</h3>
+<div class="section level4">
+<h4 id="pathway-1">Pathway 1<a class="anchor" aria-label="anchor" href="#pathway-1"></a>
+</h4>
+<caption>
+Hierarchical SFO path 1 fit with constant variance
+</caption>
+<pre><code>
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 07:42:26 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan/dt = - k_cyan * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * k_cyan * cyan - k_JCZ38 * JCZ38
+d_J9Z38/dt = + f_cyan_to_J9Z38 * k_cyan * cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 437.151 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+        cyan_0     log_k_cyan    log_k_JCZ38    log_k_J9Z38    log_k_JSE76 
+       95.3304        -3.8459        -3.1305        -5.0678        -5.3196 
+  f_cyan_ilr_1   f_cyan_ilr_2 f_JCZ38_qlogis 
+        0.8158        23.5335        11.8774 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_cyan log_k_JCZ38 log_k_J9Z38 log_k_JSE76
+cyan_0          4.797     0.0000       0.000       0.000      0.0000
+log_k_cyan      0.000     0.9619       0.000       0.000      0.0000
+log_k_JCZ38     0.000     0.0000       2.139       0.000      0.0000
+log_k_J9Z38     0.000     0.0000       0.000       1.639      0.0000
+log_k_JSE76     0.000     0.0000       0.000       0.000      0.7894
+f_cyan_ilr_1    0.000     0.0000       0.000       0.000      0.0000
+f_cyan_ilr_2    0.000     0.0000       0.000       0.000      0.0000
+f_JCZ38_qlogis  0.000     0.0000       0.000       0.000      0.0000
+               f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis
+cyan_0               0.0000        0.000           0.00
+log_k_cyan           0.0000        0.000           0.00
+log_k_JCZ38          0.0000        0.000           0.00
+log_k_J9Z38          0.0000        0.000           0.00
+log_k_JSE76          0.0000        0.000           0.00
+f_cyan_ilr_1         0.7714        0.000           0.00
+f_cyan_ilr_2         0.0000        9.247           0.00
+f_JCZ38_qlogis       0.0000        0.000          16.61
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2693 2687  -1331
+
+Optimised parameters:
+                     est.      lower      upper
+cyan_0            95.1279  9.354e+01  9.671e+01
+log_k_cyan        -3.8527 -4.367e+00 -3.338e+00
+log_k_JCZ38       -3.0381 -4.187e+00 -1.889e+00
+log_k_J9Z38       -5.0095 -5.623e+00 -4.396e+00
+log_k_JSE76       -5.3357 -6.025e+00 -4.646e+00
+f_cyan_ilr_1       0.8050  5.174e-01  1.093e+00
+f_cyan_ilr_2      12.4820 -1.050e+06  1.051e+06
+f_JCZ38_qlogis     1.2912  3.561e-01  2.226e+00
+a.1                4.8393         NA         NA
+SD.log_k_cyan      0.5840         NA         NA
+SD.log_k_JCZ38     1.2740         NA         NA
+SD.log_k_J9Z38     0.3172         NA         NA
+SD.log_k_JSE76     0.5677         NA         NA
+SD.f_cyan_ilr_1    0.2623         NA         NA
+SD.f_cyan_ilr_2    1.3724         NA         NA
+SD.f_JCZ38_qlogis  0.1464         NA         NA
+
+Correlation is not available
+
+Random effects:
+                    est. lower upper
+SD.log_k_cyan     0.5840    NA    NA
+SD.log_k_JCZ38    1.2740    NA    NA
+SD.log_k_J9Z38    0.3172    NA    NA
+SD.log_k_JSE76    0.5677    NA    NA
+SD.f_cyan_ilr_1   0.2623    NA    NA
+SD.f_cyan_ilr_2   1.3724    NA    NA
+SD.f_JCZ38_qlogis 0.1464    NA    NA
+
+Variance model:
+     est. lower upper
+a.1 4.839    NA    NA
+
+Backtransformed parameters:
+                      est.     lower     upper
+cyan_0           95.127935 93.542456 96.713413
+k_cyan            0.021221  0.012687  0.035497
+k_JCZ38           0.047924  0.015189  0.151213
+k_J9Z38           0.006674  0.003612  0.012332
+k_JSE76           0.004817  0.002417  0.009601
+f_cyan_to_JCZ38   0.757402        NA        NA
+f_cyan_to_J9Z38   0.242597        NA        NA
+f_JCZ38_to_JSE76  0.784347  0.588098  0.902582
+
+Resulting formation fractions:
+                   ff
+cyan_JCZ38  7.574e-01
+cyan_J9Z38  2.426e-01
+cyan_sink   9.839e-08
+JCZ38_JSE76 7.843e-01
+JCZ38_sink  2.157e-01
+
+Estimated disappearance times:
+        DT50   DT90
+cyan   32.66 108.50
+JCZ38  14.46  48.05
+J9Z38 103.86 345.00
+JSE76 143.91 478.04
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical SFO path 1 fit with two-component error
+</caption>
+<pre><code>
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 07:42:06 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan/dt = - k_cyan * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * k_cyan * cyan - k_JCZ38 * JCZ38
+d_J9Z38/dt = + f_cyan_to_J9Z38 * k_cyan * cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 417.143 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+        cyan_0     log_k_cyan    log_k_JCZ38    log_k_J9Z38    log_k_JSE76 
+       96.0039        -3.8907        -3.1276        -5.0069        -4.9367 
+  f_cyan_ilr_1   f_cyan_ilr_2 f_JCZ38_qlogis 
+        0.7937        22.3422        17.8932 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_cyan log_k_JCZ38 log_k_J9Z38 log_k_JSE76
+cyan_0          4.859      0.000        0.00        0.00      0.0000
+log_k_cyan      0.000      0.962        0.00        0.00      0.0000
+log_k_JCZ38     0.000      0.000        2.04        0.00      0.0000
+log_k_J9Z38     0.000      0.000        0.00        1.72      0.0000
+log_k_JSE76     0.000      0.000        0.00        0.00      0.9076
+f_cyan_ilr_1    0.000      0.000        0.00        0.00      0.0000
+f_cyan_ilr_2    0.000      0.000        0.00        0.00      0.0000
+f_JCZ38_qlogis  0.000      0.000        0.00        0.00      0.0000
+               f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis
+cyan_0               0.0000        0.000           0.00
+log_k_cyan           0.0000        0.000           0.00
+log_k_JCZ38          0.0000        0.000           0.00
+log_k_J9Z38          0.0000        0.000           0.00
+log_k_JSE76          0.0000        0.000           0.00
+f_cyan_ilr_1         0.7598        0.000           0.00
+f_cyan_ilr_2         0.0000        8.939           0.00
+f_JCZ38_qlogis       0.0000        0.000          14.49
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2658 2651  -1312
+
+Optimised parameters:
+                      est. lower upper
+cyan_0            94.81681    NA    NA
+log_k_cyan        -3.91558    NA    NA
+log_k_JCZ38       -3.12715    NA    NA
+log_k_J9Z38       -5.04840    NA    NA
+log_k_JSE76       -5.10443    NA    NA
+f_cyan_ilr_1       0.80760    NA    NA
+f_cyan_ilr_2      48.66960    NA    NA
+f_JCZ38_qlogis     3.03397    NA    NA
+a.1                3.93879    NA    NA
+b.1                0.08057    NA    NA
+SD.log_k_cyan      0.58921    NA    NA
+SD.log_k_JCZ38     1.29813    NA    NA
+SD.log_k_J9Z38     0.68372    NA    NA
+SD.log_k_JSE76     0.35128    NA    NA
+SD.f_cyan_ilr_1    0.38352    NA    NA
+SD.f_cyan_ilr_2    4.98884    NA    NA
+SD.f_JCZ38_qlogis  1.75636    NA    NA
+
+Correlation is not available
+
+Random effects:
+                    est. lower upper
+SD.log_k_cyan     0.5892    NA    NA
+SD.log_k_JCZ38    1.2981    NA    NA
+SD.log_k_J9Z38    0.6837    NA    NA
+SD.log_k_JSE76    0.3513    NA    NA
+SD.f_cyan_ilr_1   0.3835    NA    NA
+SD.f_cyan_ilr_2   4.9888    NA    NA
+SD.f_JCZ38_qlogis 1.7564    NA    NA
+
+Variance model:
+       est. lower upper
+a.1 3.93879    NA    NA
+b.1 0.08057    NA    NA
+
+Backtransformed parameters:
+                     est. lower upper
+cyan_0           94.81681    NA    NA
+k_cyan            0.01993    NA    NA
+k_JCZ38           0.04384    NA    NA
+k_J9Z38           0.00642    NA    NA
+k_JSE76           0.00607    NA    NA
+f_cyan_to_JCZ38   0.75807    NA    NA
+f_cyan_to_J9Z38   0.24193    NA    NA
+f_JCZ38_to_JSE76  0.95409    NA    NA
+
+Resulting formation fractions:
+                 ff
+cyan_JCZ38  0.75807
+cyan_J9Z38  0.24193
+cyan_sink   0.00000
+JCZ38_JSE76 0.95409
+JCZ38_sink  0.04591
+
+Estimated disappearance times:
+        DT50   DT90
+cyan   34.78 115.54
+JCZ38  15.81  52.52
+J9Z38 107.97 358.68
+JSE76 114.20 379.35
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical FOMC path 1 fit with constant variance
+</caption>
+<pre><code>
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 07:42:57 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * (alpha/beta) * 1/((time/beta) + 1) *
+           cyan - k_JCZ38 * JCZ38
+d_J9Z38/dt = + f_cyan_to_J9Z38 * (alpha/beta) * 1/((time/beta) + 1) *
+           cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 468.609 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+      101.2314        -3.3680        -5.1108        -5.9416         0.7144 
+  f_cyan_ilr_2 f_JCZ38_qlogis      log_alpha       log_beta 
+        7.0229        14.9234        -0.1791         2.9811 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          5.416       0.000         0.0       0.000       0.0000
+log_k_JCZ38     0.000       2.439         0.0       0.000       0.0000
+log_k_J9Z38     0.000       0.000         1.7       0.000       0.0000
+log_k_JSE76     0.000       0.000         0.0       1.856       0.0000
+f_cyan_ilr_1    0.000       0.000         0.0       0.000       0.7164
+f_cyan_ilr_2    0.000       0.000         0.0       0.000       0.0000
+f_JCZ38_qlogis  0.000       0.000         0.0       0.000       0.0000
+log_alpha       0.000       0.000         0.0       0.000       0.0000
+log_beta        0.000       0.000         0.0       0.000       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis log_alpha log_beta
+cyan_0                 0.00           0.00    0.0000   0.0000
+log_k_JCZ38            0.00           0.00    0.0000   0.0000
+log_k_J9Z38            0.00           0.00    0.0000   0.0000
+log_k_JSE76            0.00           0.00    0.0000   0.0000
+f_cyan_ilr_1           0.00           0.00    0.0000   0.0000
+f_cyan_ilr_2          11.57           0.00    0.0000   0.0000
+f_JCZ38_qlogis         0.00          18.81    0.0000   0.0000
+log_alpha              0.00           0.00    0.4144   0.0000
+log_beta               0.00           0.00    0.0000   0.5077
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2428 2421  -1196
+
+Optimised parameters:
+                      est.    lower    upper
+cyan_0            101.1664 98.51265 103.8202
+log_k_JCZ38        -3.3883 -4.78250  -1.9941
+log_k_J9Z38        -5.3087 -5.91564  -4.7017
+log_k_JSE76        -6.1313 -7.30061  -4.9619
+f_cyan_ilr_1        0.7456  0.43782   1.0534
+f_cyan_ilr_2        0.8181  0.24956   1.3866
+f_JCZ38_qlogis      2.0467  0.61165   3.4817
+log_alpha          -0.2391 -0.62806   0.1499
+log_beta            2.8739  2.67664   3.0711
+a.1                 3.4160  3.17960   3.6525
+SD.cyan_0           2.4355  0.40399   4.4671
+SD.log_k_JCZ38      1.5654  0.57311   2.5576
+SD.log_k_J9Z38      0.4645 -0.06533   0.9943
+SD.log_k_JSE76      0.9841  0.10738   1.8609
+SD.f_cyan_ilr_1     0.3285  0.10546   0.5515
+SD.f_cyan_ilr_2     0.2276 -0.38711   0.8424
+SD.f_JCZ38_qlogis   0.8340 -0.20970   1.8777
+SD.log_alpha        0.4250  0.16017   0.6898
+
+Correlation: 
+               cyan_0  l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 log_lph
+log_k_JCZ38    -0.0159                                                        
+log_k_J9Z38    -0.0546  0.0080                                                
+log_k_JSE76    -0.0337  0.0016  0.0074                                        
+f_cyan_ilr_1   -0.0095  0.0194 -0.1573  0.0003                                
+f_cyan_ilr_2   -0.2733  0.0799  0.3059  0.0263  0.0125                        
+f_JCZ38_qlogis  0.0755 -0.0783 -0.0516  0.1222 -0.1155 -0.5231                
+log_alpha      -0.0567  0.0120  0.0351  0.0189  0.0040  0.0829 -0.0502        
+log_beta       -0.2980  0.0461  0.1382  0.0758  0.0209  0.4079 -0.2053  0.2759
+
+Random effects:
+                    est.    lower  upper
+SD.cyan_0         2.4355  0.40399 4.4671
+SD.log_k_JCZ38    1.5654  0.57311 2.5576
+SD.log_k_J9Z38    0.4645 -0.06533 0.9943
+SD.log_k_JSE76    0.9841  0.10738 1.8609
+SD.f_cyan_ilr_1   0.3285  0.10546 0.5515
+SD.f_cyan_ilr_2   0.2276 -0.38711 0.8424
+SD.f_JCZ38_qlogis 0.8340 -0.20970 1.8777
+SD.log_alpha      0.4250  0.16017 0.6898
+
+Variance model:
+     est. lower upper
+a.1 3.416  3.18 3.652
+
+Backtransformed parameters:
+                      est.     lower     upper
+cyan_0           1.012e+02 9.851e+01 103.82023
+k_JCZ38          3.377e-02 8.375e-03   0.13614
+k_J9Z38          4.948e-03 2.697e-03   0.00908
+k_JSE76          2.174e-03 6.751e-04   0.00700
+f_cyan_to_JCZ38  6.389e-01        NA        NA
+f_cyan_to_J9Z38  2.226e-01        NA        NA
+f_JCZ38_to_JSE76 8.856e-01 6.483e-01   0.97016
+alpha            7.873e-01 5.336e-01   1.16166
+beta             1.771e+01 1.454e+01  21.56509
+
+Resulting formation fractions:
+                ff
+cyan_JCZ38  0.6389
+cyan_J9Z38  0.2226
+cyan_sink   0.1385
+JCZ38_JSE76 0.8856
+JCZ38_sink  0.1144
+
+Estimated disappearance times:
+        DT50    DT90 DT50back
+cyan   25.00  312.06    93.94
+JCZ38  20.53   68.19       NA
+J9Z38 140.07  465.32       NA
+JSE76 318.86 1059.22       NA
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical FOMC path 1 fit with two-component error
+</caption>
+<pre><code>
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 07:42:50 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * (alpha/beta) * 1/((time/beta) + 1) *
+           cyan - k_JCZ38 * JCZ38
+d_J9Z38/dt = + f_cyan_to_J9Z38 * (alpha/beta) * 1/((time/beta) + 1) *
+           cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 460.309 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+     101.13294       -3.32499       -5.09097       -5.93566        0.71359 
+  f_cyan_ilr_2 f_JCZ38_qlogis      log_alpha       log_beta 
+      10.30315       14.62272       -0.09633        3.10634 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          5.649       0.000        0.00        0.00       0.0000
+log_k_JCZ38     0.000       2.319        0.00        0.00       0.0000
+log_k_J9Z38     0.000       0.000        1.73        0.00       0.0000
+log_k_JSE76     0.000       0.000        0.00        1.86       0.0000
+f_cyan_ilr_1    0.000       0.000        0.00        0.00       0.7183
+f_cyan_ilr_2    0.000       0.000        0.00        0.00       0.0000
+f_JCZ38_qlogis  0.000       0.000        0.00        0.00       0.0000
+log_alpha       0.000       0.000        0.00        0.00       0.0000
+log_beta        0.000       0.000        0.00        0.00       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis log_alpha log_beta
+cyan_0                 0.00           0.00    0.0000   0.0000
+log_k_JCZ38            0.00           0.00    0.0000   0.0000
+log_k_J9Z38            0.00           0.00    0.0000   0.0000
+log_k_JSE76            0.00           0.00    0.0000   0.0000
+f_cyan_ilr_1           0.00           0.00    0.0000   0.0000
+f_cyan_ilr_2          12.85           0.00    0.0000   0.0000
+f_JCZ38_qlogis         0.00          18.54    0.0000   0.0000
+log_alpha              0.00           0.00    0.3142   0.0000
+log_beta               0.00           0.00    0.0000   0.7333
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2424 2416  -1193
+
+Optimised parameters:
+                       est. lower upper
+cyan_0            100.65667    NA    NA
+log_k_JCZ38        -3.45782    NA    NA
+log_k_J9Z38        -5.23476    NA    NA
+log_k_JSE76        -5.71827    NA    NA
+f_cyan_ilr_1        0.68389    NA    NA
+f_cyan_ilr_2        0.61027    NA    NA
+f_JCZ38_qlogis    116.27482    NA    NA
+log_alpha          -0.14484    NA    NA
+log_beta            3.03220    NA    NA
+a.1                 3.11051    NA    NA
+b.1                 0.04508    NA    NA
+SD.log_k_JCZ38      1.39961    NA    NA
+SD.log_k_J9Z38      0.57920    NA    NA
+SD.log_k_JSE76      0.68364    NA    NA
+SD.f_cyan_ilr_1     0.31477    NA    NA
+SD.f_cyan_ilr_2     0.37716    NA    NA
+SD.f_JCZ38_qlogis   5.52695    NA    NA
+SD.log_alpha        0.22823    NA    NA
+SD.log_beta         0.39161    NA    NA
+
+Correlation is not available
+
+Random effects:
+                    est. lower upper
+SD.log_k_JCZ38    1.3996    NA    NA
+SD.log_k_J9Z38    0.5792    NA    NA
+SD.log_k_JSE76    0.6836    NA    NA
+SD.f_cyan_ilr_1   0.3148    NA    NA
+SD.f_cyan_ilr_2   0.3772    NA    NA
+SD.f_JCZ38_qlogis 5.5270    NA    NA
+SD.log_alpha      0.2282    NA    NA
+SD.log_beta       0.3916    NA    NA
+
+Variance model:
+       est. lower upper
+a.1 3.11051    NA    NA
+b.1 0.04508    NA    NA
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.007e+02    NA    NA
+k_JCZ38          3.150e-02    NA    NA
+k_J9Z38          5.328e-03    NA    NA
+k_JSE76          3.285e-03    NA    NA
+f_cyan_to_JCZ38  5.980e-01    NA    NA
+f_cyan_to_J9Z38  2.273e-01    NA    NA
+f_JCZ38_to_JSE76 1.000e+00    NA    NA
+alpha            8.652e-01    NA    NA
+beta             2.074e+01    NA    NA
+
+Resulting formation fractions:
+                ff
+cyan_JCZ38  0.5980
+cyan_J9Z38  0.2273
+cyan_sink   0.1746
+JCZ38_JSE76 1.0000
+JCZ38_sink  0.0000
+
+Estimated disappearance times:
+        DT50  DT90 DT50back
+cyan   25.48 276.2    83.15
+JCZ38  22.01  73.1       NA
+J9Z38 130.09 432.2       NA
+JSE76 210.98 700.9       NA
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical DFOP path 1 fit with constant variance
+</caption>
+<pre><code>
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 07:43:33 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+           time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+           * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38
+d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 504.014 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+      102.0643        -3.4008        -5.0024        -5.8612         0.6855 
+  f_cyan_ilr_2 f_JCZ38_qlogis         log_k1         log_k2       g_qlogis 
+        1.2366        13.6901        -1.8641        -4.5063        -0.6468 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          4.466       0.000       0.000       0.000       0.0000
+log_k_JCZ38     0.000       2.382       0.000       0.000       0.0000
+log_k_J9Z38     0.000       0.000       1.595       0.000       0.0000
+log_k_JSE76     0.000       0.000       0.000       1.245       0.0000
+f_cyan_ilr_1    0.000       0.000       0.000       0.000       0.6852
+f_cyan_ilr_2    0.000       0.000       0.000       0.000       0.0000
+f_JCZ38_qlogis  0.000       0.000       0.000       0.000       0.0000
+log_k1          0.000       0.000       0.000       0.000       0.0000
+log_k2          0.000       0.000       0.000       0.000       0.0000
+g_qlogis        0.000       0.000       0.000       0.000       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 g_qlogis
+cyan_0                 0.00           0.00 0.0000 0.0000    0.000
+log_k_JCZ38            0.00           0.00 0.0000 0.0000    0.000
+log_k_J9Z38            0.00           0.00 0.0000 0.0000    0.000
+log_k_JSE76            0.00           0.00 0.0000 0.0000    0.000
+f_cyan_ilr_1           0.00           0.00 0.0000 0.0000    0.000
+f_cyan_ilr_2           1.28           0.00 0.0000 0.0000    0.000
+f_JCZ38_qlogis         0.00          16.08 0.0000 0.0000    0.000
+log_k1                 0.00           0.00 0.9866 0.0000    0.000
+log_k2                 0.00           0.00 0.0000 0.5953    0.000
+g_qlogis               0.00           0.00 0.0000 0.0000    1.583
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2403 2395  -1182
+
+Optimised parameters:
+                      est. lower upper
+cyan_0            102.5565    NA    NA
+log_k_JCZ38        -3.4729    NA    NA
+log_k_J9Z38        -5.1533    NA    NA
+log_k_JSE76        -5.6669    NA    NA
+f_cyan_ilr_1        0.6665    NA    NA
+f_cyan_ilr_2        0.5191    NA    NA
+f_JCZ38_qlogis     37.0113    NA    NA
+log_k1             -1.8497    NA    NA
+log_k2             -4.4931    NA    NA
+g_qlogis           -0.6383    NA    NA
+a.1                 3.2397    NA    NA
+SD.log_k_JCZ38      1.4286    NA    NA
+SD.log_k_J9Z38      0.5312    NA    NA
+SD.log_k_JSE76      0.6627    NA    NA
+SD.f_cyan_ilr_1     0.3013    NA    NA
+SD.f_cyan_ilr_2     0.2980    NA    NA
+SD.f_JCZ38_qlogis   0.1637    NA    NA
+SD.log_k1           0.5069    NA    NA
+SD.log_k2           0.3828    NA    NA
+SD.g_qlogis         0.8641    NA    NA
+
+Correlation is not available
+
+Random effects:
+                    est. lower upper
+SD.log_k_JCZ38    1.4286    NA    NA
+SD.log_k_J9Z38    0.5312    NA    NA
+SD.log_k_JSE76    0.6627    NA    NA
+SD.f_cyan_ilr_1   0.3013    NA    NA
+SD.f_cyan_ilr_2   0.2980    NA    NA
+SD.f_JCZ38_qlogis 0.1637    NA    NA
+SD.log_k1         0.5069    NA    NA
+SD.log_k2         0.3828    NA    NA
+SD.g_qlogis       0.8641    NA    NA
+
+Variance model:
+    est. lower upper
+a.1 3.24    NA    NA
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.026e+02    NA    NA
+k_JCZ38          3.103e-02    NA    NA
+k_J9Z38          5.780e-03    NA    NA
+k_JSE76          3.459e-03    NA    NA
+f_cyan_to_JCZ38  5.813e-01    NA    NA
+f_cyan_to_J9Z38  2.265e-01    NA    NA
+f_JCZ38_to_JSE76 1.000e+00    NA    NA
+k1               1.573e-01    NA    NA
+k2               1.119e-02    NA    NA
+g                3.456e-01    NA    NA
+
+Resulting formation fractions:
+                ff
+cyan_JCZ38  0.5813
+cyan_J9Z38  0.2265
+cyan_sink   0.1922
+JCZ38_JSE76 1.0000
+JCZ38_sink  0.0000
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   25.23 167.94    50.55   4.407   61.97
+JCZ38  22.34  74.22       NA      NA      NA
+J9Z38 119.92 398.36       NA      NA      NA
+JSE76 200.41 665.76       NA      NA      NA
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical DFOP path 1 fit with two-component error
+</caption>
+<pre><code>
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 07:46:07 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+           time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+           * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38
+d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 658.043 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+      101.3964        -3.3626        -4.9792        -5.8727         0.6814 
+  f_cyan_ilr_2 f_JCZ38_qlogis         log_k1         log_k2       g_qlogis 
+        6.8713        13.6901        -1.9222        -4.5035        -0.7172 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          5.317       0.000       0.000       0.000       0.0000
+log_k_JCZ38     0.000       2.272       0.000       0.000       0.0000
+log_k_J9Z38     0.000       0.000       1.633       0.000       0.0000
+log_k_JSE76     0.000       0.000       0.000       1.271       0.0000
+f_cyan_ilr_1    0.000       0.000       0.000       0.000       0.6839
+f_cyan_ilr_2    0.000       0.000       0.000       0.000       0.0000
+f_JCZ38_qlogis  0.000       0.000       0.000       0.000       0.0000
+log_k1          0.000       0.000       0.000       0.000       0.0000
+log_k2          0.000       0.000       0.000       0.000       0.0000
+g_qlogis        0.000       0.000       0.000       0.000       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 g_qlogis
+cyan_0                 0.00           0.00 0.0000 0.0000    0.000
+log_k_JCZ38            0.00           0.00 0.0000 0.0000    0.000
+log_k_J9Z38            0.00           0.00 0.0000 0.0000    0.000
+log_k_JSE76            0.00           0.00 0.0000 0.0000    0.000
+f_cyan_ilr_1           0.00           0.00 0.0000 0.0000    0.000
+f_cyan_ilr_2          11.95           0.00 0.0000 0.0000    0.000
+f_JCZ38_qlogis         0.00          16.08 0.0000 0.0000    0.000
+log_k1                 0.00           0.00 0.9496 0.0000    0.000
+log_k2                 0.00           0.00 0.0000 0.5846    0.000
+g_qlogis               0.00           0.00 0.0000 0.0000    1.719
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2398 2390  -1179
+
+Optimised parameters:
+                       est. lower upper
+cyan_0            100.69709    NA    NA
+log_k_JCZ38        -3.46669    NA    NA
+log_k_J9Z38        -5.05076    NA    NA
+log_k_JSE76        -5.55558    NA    NA
+f_cyan_ilr_1        0.66045    NA    NA
+f_cyan_ilr_2        0.84275    NA    NA
+f_JCZ38_qlogis     64.22404    NA    NA
+log_k1             -2.17715    NA    NA
+log_k2             -4.55002    NA    NA
+g_qlogis           -0.55920    NA    NA
+a.1                 2.95785    NA    NA
+b.1                 0.04456    NA    NA
+SD.log_k_JCZ38      1.39881    NA    NA
+SD.log_k_J9Z38      0.67788    NA    NA
+SD.log_k_JSE76      0.52603    NA    NA
+SD.f_cyan_ilr_1     0.32490    NA    NA
+SD.f_cyan_ilr_2     0.53923    NA    NA
+SD.f_JCZ38_qlogis   2.75576    NA    NA
+SD.log_k2           0.30694    NA    NA
+SD.g_qlogis         0.83619    NA    NA
+
+Correlation is not available
+
+Random effects:
+                    est. lower upper
+SD.log_k_JCZ38    1.3988    NA    NA
+SD.log_k_J9Z38    0.6779    NA    NA
+SD.log_k_JSE76    0.5260    NA    NA
+SD.f_cyan_ilr_1   0.3249    NA    NA
+SD.f_cyan_ilr_2   0.5392    NA    NA
+SD.f_JCZ38_qlogis 2.7558    NA    NA
+SD.log_k2         0.3069    NA    NA
+SD.g_qlogis       0.8362    NA    NA
+
+Variance model:
+       est. lower upper
+a.1 2.95785    NA    NA
+b.1 0.04456    NA    NA
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.007e+02    NA    NA
+k_JCZ38          3.122e-02    NA    NA
+k_J9Z38          6.404e-03    NA    NA
+k_JSE76          3.866e-03    NA    NA
+f_cyan_to_JCZ38  6.187e-01    NA    NA
+f_cyan_to_J9Z38  2.431e-01    NA    NA
+f_JCZ38_to_JSE76 1.000e+00    NA    NA
+k1               1.134e-01    NA    NA
+k2               1.057e-02    NA    NA
+g                3.637e-01    NA    NA
+
+Resulting formation fractions:
+                ff
+cyan_JCZ38  0.6187
+cyan_J9Z38  0.2431
+cyan_sink   0.1382
+JCZ38_JSE76 1.0000
+JCZ38_sink  0.0000
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   26.35 175.12    52.72   6.114    65.6
+JCZ38  22.20  73.75       NA      NA      NA
+J9Z38 108.23 359.53       NA      NA      NA
+JSE76 179.30 595.62       NA      NA      NA
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical SFORB path 1 fit with constant variance
+</caption>
+<pre><code>
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 07:43:36 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
+           cyan_free + k_cyan_bound_free * cyan_bound
+d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free *
+           cyan_bound
+d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38
+           * JCZ38
+d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38
+           * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 507.042 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+          cyan_free_0       log_k_cyan_free log_k_cyan_free_bound 
+             102.0643               -2.8987               -2.7077 
+log_k_cyan_bound_free           log_k_JCZ38           log_k_J9Z38 
+              -3.4717               -3.4008               -5.0024 
+          log_k_JSE76          f_cyan_ilr_1          f_cyan_ilr_2 
+              -5.8613                0.6855                1.2366 
+       f_JCZ38_qlogis 
+              13.7395 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+                      cyan_free_0 log_k_cyan_free log_k_cyan_free_bound
+cyan_free_0                 4.466          0.0000                 0.000
+log_k_cyan_free             0.000          0.6158                 0.000
+log_k_cyan_free_bound       0.000          0.0000                 1.463
+log_k_cyan_bound_free       0.000          0.0000                 0.000
+log_k_JCZ38                 0.000          0.0000                 0.000
+log_k_J9Z38                 0.000          0.0000                 0.000
+log_k_JSE76                 0.000          0.0000                 0.000
+f_cyan_ilr_1                0.000          0.0000                 0.000
+f_cyan_ilr_2                0.000          0.0000                 0.000
+f_JCZ38_qlogis              0.000          0.0000                 0.000
+                      log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76
+cyan_free_0                           0.000       0.000       0.000       0.000
+log_k_cyan_free                       0.000       0.000       0.000       0.000
+log_k_cyan_free_bound                 0.000       0.000       0.000       0.000
+log_k_cyan_bound_free                 1.058       0.000       0.000       0.000
+log_k_JCZ38                           0.000       2.382       0.000       0.000
+log_k_J9Z38                           0.000       0.000       1.595       0.000
+log_k_JSE76                           0.000       0.000       0.000       1.245
+f_cyan_ilr_1                          0.000       0.000       0.000       0.000
+f_cyan_ilr_2                          0.000       0.000       0.000       0.000
+f_JCZ38_qlogis                        0.000       0.000       0.000       0.000
+                      f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis
+cyan_free_0                 0.0000         0.00           0.00
+log_k_cyan_free             0.0000         0.00           0.00
+log_k_cyan_free_bound       0.0000         0.00           0.00
+log_k_cyan_bound_free       0.0000         0.00           0.00
+log_k_JCZ38                 0.0000         0.00           0.00
+log_k_J9Z38                 0.0000         0.00           0.00
+log_k_JSE76                 0.0000         0.00           0.00
+f_cyan_ilr_1                0.6852         0.00           0.00
+f_cyan_ilr_2                0.0000         1.28           0.00
+f_JCZ38_qlogis              0.0000         0.00          16.13
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2401 2394  -1181
+
+Optimised parameters:
+                             est. lower upper
+cyan_free_0              102.8136    NA    NA
+log_k_cyan_free           -2.7935    NA    NA
+log_k_cyan_free_bound     -2.5440    NA    NA
+log_k_cyan_bound_free     -3.4303    NA    NA
+log_k_JCZ38               -3.5010    NA    NA
+log_k_J9Z38               -5.1226    NA    NA
+log_k_JSE76               -5.6314    NA    NA
+f_cyan_ilr_1               0.6609    NA    NA
+f_cyan_ilr_2               0.5085    NA    NA
+f_JCZ38_qlogis            44.0153    NA    NA
+a.1                        3.2318    NA    NA
+SD.log_k_cyan_free         0.3211    NA    NA
+SD.log_k_cyan_free_bound   0.8408    NA    NA
+SD.log_k_cyan_bound_free   0.5724    NA    NA
+SD.log_k_JCZ38             1.4925    NA    NA
+SD.log_k_J9Z38             0.5816    NA    NA
+SD.log_k_JSE76             0.6037    NA    NA
+SD.f_cyan_ilr_1            0.3115    NA    NA
+SD.f_cyan_ilr_2            0.3436    NA    NA
+SD.f_JCZ38_qlogis          4.8937    NA    NA
+
+Correlation is not available
+
+Random effects:
+                           est. lower upper
+SD.log_k_cyan_free       0.3211    NA    NA
+SD.log_k_cyan_free_bound 0.8408    NA    NA
+SD.log_k_cyan_bound_free 0.5724    NA    NA
+SD.log_k_JCZ38           1.4925    NA    NA
+SD.log_k_J9Z38           0.5816    NA    NA
+SD.log_k_JSE76           0.6037    NA    NA
+SD.f_cyan_ilr_1          0.3115    NA    NA
+SD.f_cyan_ilr_2          0.3436    NA    NA
+SD.f_JCZ38_qlogis        4.8937    NA    NA
+
+Variance model:
+     est. lower upper
+a.1 3.232    NA    NA
+
+Backtransformed parameters:
+                          est. lower upper
+cyan_free_0          1.028e+02    NA    NA
+k_cyan_free          6.120e-02    NA    NA
+k_cyan_free_bound    7.855e-02    NA    NA
+k_cyan_bound_free    3.238e-02    NA    NA
+k_JCZ38              3.017e-02    NA    NA
+k_J9Z38              5.961e-03    NA    NA
+k_JSE76              3.584e-03    NA    NA
+f_cyan_free_to_JCZ38 5.784e-01    NA    NA
+f_cyan_free_to_J9Z38 2.271e-01    NA    NA
+f_JCZ38_to_JSE76     1.000e+00    NA    NA
+
+Estimated Eigenvalues of SFORB model(s):
+cyan_b1 cyan_b2  cyan_g 
+0.15973 0.01241 0.33124 
+
+Resulting formation fractions:
+                    ff
+cyan_free_JCZ38 0.5784
+cyan_free_J9Z38 0.2271
+cyan_free_sink  0.1945
+cyan_free       1.0000
+JCZ38_JSE76     1.0000
+JCZ38_sink      0.0000
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_cyan_b1 DT50_cyan_b2
+cyan   24.51 153.18    46.11         4.34        55.87
+JCZ38  22.98  76.33       NA           NA           NA
+J9Z38 116.28 386.29       NA           NA           NA
+JSE76 193.42 642.53       NA           NA           NA
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical SFORB path 1 fit with two-component error
+</caption>
+<pre><code>
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 07:46:14 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
+           cyan_free + k_cyan_bound_free * cyan_bound
+d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free *
+           cyan_bound
+d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38
+           * JCZ38
+d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38
+           * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 664.11 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+          cyan_free_0       log_k_cyan_free log_k_cyan_free_bound 
+             101.3964               -2.9881               -2.7949 
+log_k_cyan_bound_free           log_k_JCZ38           log_k_J9Z38 
+              -3.4376               -3.3626               -4.9792 
+          log_k_JSE76          f_cyan_ilr_1          f_cyan_ilr_2 
+              -5.8727                0.6814                6.7399 
+       f_JCZ38_qlogis 
+              13.7395 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+                      cyan_free_0 log_k_cyan_free log_k_cyan_free_bound
+cyan_free_0                 5.317          0.0000                 0.000
+log_k_cyan_free             0.000          0.7301                 0.000
+log_k_cyan_free_bound       0.000          0.0000                 1.384
+log_k_cyan_bound_free       0.000          0.0000                 0.000
+log_k_JCZ38                 0.000          0.0000                 0.000
+log_k_J9Z38                 0.000          0.0000                 0.000
+log_k_JSE76                 0.000          0.0000                 0.000
+f_cyan_ilr_1                0.000          0.0000                 0.000
+f_cyan_ilr_2                0.000          0.0000                 0.000
+f_JCZ38_qlogis              0.000          0.0000                 0.000
+                      log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76
+cyan_free_0                           0.000       0.000       0.000       0.000
+log_k_cyan_free                       0.000       0.000       0.000       0.000
+log_k_cyan_free_bound                 0.000       0.000       0.000       0.000
+log_k_cyan_bound_free                 1.109       0.000       0.000       0.000
+log_k_JCZ38                           0.000       2.272       0.000       0.000
+log_k_J9Z38                           0.000       0.000       1.633       0.000
+log_k_JSE76                           0.000       0.000       0.000       1.271
+f_cyan_ilr_1                          0.000       0.000       0.000       0.000
+f_cyan_ilr_2                          0.000       0.000       0.000       0.000
+f_JCZ38_qlogis                        0.000       0.000       0.000       0.000
+                      f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis
+cyan_free_0                 0.0000         0.00           0.00
+log_k_cyan_free             0.0000         0.00           0.00
+log_k_cyan_free_bound       0.0000         0.00           0.00
+log_k_cyan_bound_free       0.0000         0.00           0.00
+log_k_JCZ38                 0.0000         0.00           0.00
+log_k_J9Z38                 0.0000         0.00           0.00
+log_k_JSE76                 0.0000         0.00           0.00
+f_cyan_ilr_1                0.6838         0.00           0.00
+f_cyan_ilr_2                0.0000        11.69           0.00
+f_JCZ38_qlogis              0.0000         0.00          16.13
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2400 2392  -1180
+
+Optimised parameters:
+                              est. lower upper
+cyan_free_0              100.56004    NA    NA
+log_k_cyan_free           -3.12657    NA    NA
+log_k_cyan_free_bound     -3.16825    NA    NA
+log_k_cyan_bound_free     -3.66003    NA    NA
+log_k_JCZ38               -3.47278    NA    NA
+log_k_J9Z38               -5.06823    NA    NA
+log_k_JSE76               -5.54327    NA    NA
+f_cyan_ilr_1               0.66631    NA    NA
+f_cyan_ilr_2               0.82898    NA    NA
+f_JCZ38_qlogis            38.31115    NA    NA
+a.1                        2.98352    NA    NA
+b.1                        0.04388    NA    NA
+SD.log_k_cyan_free         0.49145    NA    NA
+SD.log_k_cyan_bound_free   0.27347    NA    NA
+SD.log_k_JCZ38             1.41193    NA    NA
+SD.log_k_J9Z38             0.66073    NA    NA
+SD.log_k_JSE76             0.55885    NA    NA
+SD.f_cyan_ilr_1            0.33020    NA    NA
+SD.f_cyan_ilr_2            0.51367    NA    NA
+SD.f_JCZ38_qlogis          5.52122    NA    NA
+
+Correlation is not available
+
+Random effects:
+                           est. lower upper
+SD.log_k_cyan_free       0.4914    NA    NA
+SD.log_k_cyan_bound_free 0.2735    NA    NA
+SD.log_k_JCZ38           1.4119    NA    NA
+SD.log_k_J9Z38           0.6607    NA    NA
+SD.log_k_JSE76           0.5589    NA    NA
+SD.f_cyan_ilr_1          0.3302    NA    NA
+SD.f_cyan_ilr_2          0.5137    NA    NA
+SD.f_JCZ38_qlogis        5.5212    NA    NA
+
+Variance model:
+       est. lower upper
+a.1 2.98352    NA    NA
+b.1 0.04388    NA    NA
+
+Backtransformed parameters:
+                          est. lower upper
+cyan_free_0          1.006e+02    NA    NA
+k_cyan_free          4.387e-02    NA    NA
+k_cyan_free_bound    4.208e-02    NA    NA
+k_cyan_bound_free    2.573e-02    NA    NA
+k_JCZ38              3.103e-02    NA    NA
+k_J9Z38              6.294e-03    NA    NA
+k_JSE76              3.914e-03    NA    NA
+f_cyan_free_to_JCZ38 6.188e-01    NA    NA
+f_cyan_free_to_J9Z38 2.412e-01    NA    NA
+f_JCZ38_to_JSE76     1.000e+00    NA    NA
+
+Estimated Eigenvalues of SFORB model(s):
+cyan_b1 cyan_b2  cyan_g 
+0.10044 0.01124 0.36580 
+
+Resulting formation fractions:
+                    ff
+cyan_free_JCZ38 0.6188
+cyan_free_J9Z38 0.2412
+cyan_free_sink  0.1400
+cyan_free       1.0000
+JCZ38_JSE76     1.0000
+JCZ38_sink      0.0000
+
+Estimated disappearance times:
+        DT50  DT90 DT50back DT50_cyan_b1 DT50_cyan_b2
+cyan   26.05 164.4    49.48        6.901        61.67
+JCZ38  22.34  74.2       NA           NA           NA
+J9Z38 110.14 365.9       NA           NA           NA
+JSE76 177.11 588.3       NA           NA           NA
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical HS path 1 fit with constant variance
+</caption>
+<pre><code>
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 07:43:42 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan/dt = - ifelse(time &lt;= tb, k1, k2) * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * ifelse(time &lt;= tb, k1, k2) * cyan -
+           k_JCZ38 * JCZ38
+d_J9Z38/dt = + f_cyan_to_J9Z38 * ifelse(time &lt;= tb, k1, k2) * cyan -
+           k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 512.818 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+      102.8845        -3.4495        -4.9355        -5.6040         0.6468 
+  f_cyan_ilr_2 f_JCZ38_qlogis         log_k1         log_k2         log_tb 
+        1.2396         9.7220        -2.9079        -4.1810         1.7813 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          5.406        0.00        0.00       0.000       0.0000
+log_k_JCZ38     0.000        2.33        0.00       0.000       0.0000
+log_k_J9Z38     0.000        0.00        1.59       0.000       0.0000
+log_k_JSE76     0.000        0.00        0.00       1.013       0.0000
+f_cyan_ilr_1    0.000        0.00        0.00       0.000       0.6367
+f_cyan_ilr_2    0.000        0.00        0.00       0.000       0.0000
+f_JCZ38_qlogis  0.000        0.00        0.00       0.000       0.0000
+log_k1          0.000        0.00        0.00       0.000       0.0000
+log_k2          0.000        0.00        0.00       0.000       0.0000
+log_tb          0.000        0.00        0.00       0.000       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 log_tb
+cyan_0                0.000           0.00 0.0000 0.0000 0.0000
+log_k_JCZ38           0.000           0.00 0.0000 0.0000 0.0000
+log_k_J9Z38           0.000           0.00 0.0000 0.0000 0.0000
+log_k_JSE76           0.000           0.00 0.0000 0.0000 0.0000
+f_cyan_ilr_1          0.000           0.00 0.0000 0.0000 0.0000
+f_cyan_ilr_2          2.038           0.00 0.0000 0.0000 0.0000
+f_JCZ38_qlogis        0.000          10.33 0.0000 0.0000 0.0000
+log_k1                0.000           0.00 0.7006 0.0000 0.0000
+log_k2                0.000           0.00 0.0000 0.8928 0.0000
+log_tb                0.000           0.00 0.0000 0.0000 0.6773
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2427 2419  -1194
+
+Optimised parameters:
+                      est.      lower      upper
+cyan_0            101.9660  1.005e+02  1.035e+02
+log_k_JCZ38        -3.4698 -4.716e+00 -2.224e+00
+log_k_J9Z38        -5.0947 -5.740e+00 -4.450e+00
+log_k_JSE76        -5.5977 -6.321e+00 -4.875e+00
+f_cyan_ilr_1        0.6595  3.734e-01  9.456e-01
+f_cyan_ilr_2        0.5905  1.664e-01  1.015e+00
+f_JCZ38_qlogis     25.8627 -4.224e+05  4.225e+05
+log_k1             -3.0884 -3.453e+00 -2.723e+00
+log_k2             -4.3877 -4.778e+00 -3.998e+00
+log_tb              2.3057  1.715e+00  2.896e+00
+a.1                 3.3228         NA         NA
+SD.log_k_JCZ38      1.4071         NA         NA
+SD.log_k_J9Z38      0.5774         NA         NA
+SD.log_k_JSE76      0.6214         NA         NA
+SD.f_cyan_ilr_1     0.3058         NA         NA
+SD.f_cyan_ilr_2     0.3470         NA         NA
+SD.f_JCZ38_qlogis   0.0644         NA         NA
+SD.log_k1           0.3994         NA         NA
+SD.log_k2           0.4373         NA         NA
+SD.log_tb           0.6419         NA         NA
+
+Correlation is not available
+
+Random effects:
+                    est. lower upper
+SD.log_k_JCZ38    1.4071    NA    NA
+SD.log_k_J9Z38    0.5774    NA    NA
+SD.log_k_JSE76    0.6214    NA    NA
+SD.f_cyan_ilr_1   0.3058    NA    NA
+SD.f_cyan_ilr_2   0.3470    NA    NA
+SD.f_JCZ38_qlogis 0.0644    NA    NA
+SD.log_k1         0.3994    NA    NA
+SD.log_k2         0.4373    NA    NA
+SD.log_tb         0.6419    NA    NA
+
+Variance model:
+     est. lower upper
+a.1 3.323    NA    NA
+
+Backtransformed parameters:
+                      est.     lower     upper
+cyan_0           1.020e+02 1.005e+02 1.035e+02
+k_JCZ38          3.112e-02 8.951e-03 1.082e-01
+k_J9Z38          6.129e-03 3.216e-03 1.168e-02
+k_JSE76          3.706e-03 1.798e-03 7.639e-03
+f_cyan_to_JCZ38  5.890e-01        NA        NA
+f_cyan_to_J9Z38  2.318e-01        NA        NA
+f_JCZ38_to_JSE76 1.000e+00 0.000e+00 1.000e+00
+k1               4.558e-02 3.164e-02 6.565e-02
+k2               1.243e-02 8.417e-03 1.835e-02
+tb               1.003e+01 5.557e+00 1.811e+01
+
+Resulting formation fractions:
+                   ff
+cyan_JCZ38  5.890e-01
+cyan_J9Z38  2.318e-01
+cyan_sink   1.793e-01
+JCZ38_JSE76 1.000e+00
+JCZ38_sink  5.861e-12
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   29.02 158.51    47.72   15.21   55.77
+JCZ38  22.27  73.98       NA      NA      NA
+J9Z38 113.09 375.69       NA      NA      NA
+JSE76 187.01 621.23       NA      NA      NA
+
+</code></pre>
+<p></p>
+</div>
+<div class="section level4">
+<h4 id="pathway-2">Pathway 2<a class="anchor" aria-label="anchor" href="#pathway-2"></a>
+</h4>
+<caption>
+Hierarchical FOMC path 2 fit with two-component error
+</caption>
+<pre><code>
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 07:54:36 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * (alpha/beta) * 1/((time/beta) + 1) *
+           cyan - k_JCZ38 * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76
+d_J9Z38/dt = + f_cyan_to_J9Z38 * (alpha/beta) * 1/((time/beta) + 1) *
+           cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 491.928 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+      102.4477        -1.8631        -5.1087        -2.5114         0.6826 
+  f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis      log_alpha       log_beta 
+        4.7944        15.9616        13.1566        -0.1564         2.9781 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          7.701       0.000       0.000       0.000       0.0000
+log_k_JCZ38     0.000       1.448       0.000       0.000       0.0000
+log_k_J9Z38     0.000       0.000       1.724       0.000       0.0000
+log_k_JSE76     0.000       0.000       0.000       3.659       0.0000
+f_cyan_ilr_1    0.000       0.000       0.000       0.000       0.6356
+f_cyan_ilr_2    0.000       0.000       0.000       0.000       0.0000
+f_JCZ38_qlogis  0.000       0.000       0.000       0.000       0.0000
+f_JSE76_qlogis  0.000       0.000       0.000       0.000       0.0000
+log_alpha       0.000       0.000       0.000       0.000       0.0000
+log_beta        0.000       0.000       0.000       0.000       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta
+cyan_0                 0.00           0.00           0.00    0.0000   0.0000
+log_k_JCZ38            0.00           0.00           0.00    0.0000   0.0000
+log_k_J9Z38            0.00           0.00           0.00    0.0000   0.0000
+log_k_JSE76            0.00           0.00           0.00    0.0000   0.0000
+f_cyan_ilr_1           0.00           0.00           0.00    0.0000   0.0000
+f_cyan_ilr_2          10.32           0.00           0.00    0.0000   0.0000
+f_JCZ38_qlogis         0.00          12.23           0.00    0.0000   0.0000
+f_JSE76_qlogis         0.00           0.00          14.99    0.0000   0.0000
+log_alpha              0.00           0.00           0.00    0.3924   0.0000
+log_beta               0.00           0.00           0.00    0.0000   0.5639
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2249 2241  -1104
+
+Optimised parameters:
+                       est.      lower     upper
+cyan_0            101.55265  9.920e+01  103.9059
+log_k_JCZ38        -2.32302 -2.832e+00   -1.8142
+log_k_J9Z38        -5.13082 -5.942e+00   -4.3199
+log_k_JSE76        -3.01756 -4.262e+00   -1.7736
+f_cyan_ilr_1        0.70850  3.657e-01    1.0513
+f_cyan_ilr_2        0.95775  2.612e-01    1.6543
+f_JCZ38_qlogis      3.86105  9.248e-01    6.7973
+f_JSE76_qlogis      7.51583 -1.120e+02  127.0392
+log_alpha          -0.15308 -4.508e-01    0.1446
+log_beta            2.99165  2.711e+00    3.2720
+a.1                 2.04034  1.843e+00    2.2382
+b.1                 0.06924  5.749e-02    0.0810
+SD.log_k_JCZ38      0.50818  1.390e-01    0.8774
+SD.log_k_J9Z38      0.86597  2.652e-01    1.4667
+SD.log_k_JSE76      1.38092  4.864e-01    2.2754
+SD.f_cyan_ilr_1     0.38204  1.354e-01    0.6286
+SD.f_cyan_ilr_2     0.55129  7.198e-02    1.0306
+SD.f_JCZ38_qlogis   1.88457  1.711e-02    3.7520
+SD.f_JSE76_qlogis   2.64018 -2.450e+03 2454.9447
+SD.log_alpha        0.31860  1.047e-01    0.5325
+SD.log_beta         0.24195  1.273e-02    0.4712
+
+Correlation: 
+               cyan_0  l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76
+log_k_JCZ38    -0.0235                                                        
+log_k_J9Z38    -0.0442  0.0047                                                
+log_k_JSE76    -0.0023  0.0966  0.0006                                        
+f_cyan_ilr_1   -0.0032  0.0070 -0.0536 -0.0001                                
+f_cyan_ilr_2   -0.5189  0.0452  0.1152  0.0013 -0.0304                        
+f_JCZ38_qlogis  0.1088 -0.0848 -0.0240  0.0040 -0.0384 -0.2303                
+f_JSE76_qlogis -0.0545  0.1315  0.0195  0.0020  0.0252  0.1737 -0.5939        
+log_alpha      -0.0445  0.0056  0.0261  0.0019 -0.0055  0.0586 -0.0239 -0.0284
+log_beta       -0.2388  0.0163  0.0566  0.0040 -0.0078  0.2183 -0.0714 -0.0332
+               log_lph
+log_k_JCZ38           
+log_k_J9Z38           
+log_k_JSE76           
+f_cyan_ilr_1          
+f_cyan_ilr_2          
+f_JCZ38_qlogis        
+f_JSE76_qlogis        
+log_alpha             
+log_beta        0.2135
+
+Random effects:
+                    est.      lower     upper
+SD.log_k_JCZ38    0.5082  1.390e-01    0.8774
+SD.log_k_J9Z38    0.8660  2.652e-01    1.4667
+SD.log_k_JSE76    1.3809  4.864e-01    2.2754
+SD.f_cyan_ilr_1   0.3820  1.354e-01    0.6286
+SD.f_cyan_ilr_2   0.5513  7.198e-02    1.0306
+SD.f_JCZ38_qlogis 1.8846  1.711e-02    3.7520
+SD.f_JSE76_qlogis 2.6402 -2.450e+03 2454.9447
+SD.log_alpha      0.3186  1.047e-01    0.5325
+SD.log_beta       0.2420  1.273e-02    0.4712
+
+Variance model:
+       est.   lower upper
+a.1 2.04034 1.84252 2.238
+b.1 0.06924 0.05749 0.081
+
+Backtransformed parameters:
+                      est.     lower    upper
+cyan_0           1.016e+02 9.920e+01 103.9059
+k_JCZ38          9.798e-02 5.890e-02   0.1630
+k_J9Z38          5.912e-03 2.627e-03   0.0133
+k_JSE76          4.892e-02 1.410e-02   0.1697
+f_cyan_to_JCZ38  6.432e-01        NA       NA
+f_cyan_to_J9Z38  2.362e-01        NA       NA
+f_JCZ38_to_JSE76 9.794e-01 7.160e-01   0.9989
+f_JSE76_to_JCZ38 9.995e-01 2.268e-49   1.0000
+alpha            8.581e-01 6.371e-01   1.1556
+beta             1.992e+01 1.505e+01  26.3646
+
+Resulting formation fractions:
+                   ff
+cyan_JCZ38  0.6432301
+cyan_J9Z38  0.2361657
+cyan_sink   0.1206042
+JCZ38_JSE76 0.9793879
+JCZ38_sink  0.0206121
+JSE76_JCZ38 0.9994559
+JSE76_sink  0.0005441
+
+Estimated disappearance times:
+         DT50   DT90 DT50back
+cyan   24.759 271.61    81.76
+JCZ38   7.075  23.50       NA
+J9Z38 117.249 389.49       NA
+JSE76  14.169  47.07       NA
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical DFOP path 2 fit with constant variance
+</caption>
+<pre><code>
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 07:55:32 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+           time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+           * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38 +
+           f_JSE76_to_JCZ38 * k_JSE76 * JSE76
+d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 548.554 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+      102.4380        -2.3107        -5.3123        -3.7120         0.6757 
+  f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis         log_k1         log_k2 
+        1.1439        13.1194        12.3492        -1.9317        -4.4557 
+      g_qlogis 
+       -0.5644 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          4.591      0.0000       0.000         0.0       0.0000
+log_k_JCZ38     0.000      0.7966       0.000         0.0       0.0000
+log_k_J9Z38     0.000      0.0000       1.561         0.0       0.0000
+log_k_JSE76     0.000      0.0000       0.000         0.8       0.0000
+f_cyan_ilr_1    0.000      0.0000       0.000         0.0       0.6349
+f_cyan_ilr_2    0.000      0.0000       0.000         0.0       0.0000
+f_JCZ38_qlogis  0.000      0.0000       0.000         0.0       0.0000
+f_JSE76_qlogis  0.000      0.0000       0.000         0.0       0.0000
+log_k1          0.000      0.0000       0.000         0.0       0.0000
+log_k2          0.000      0.0000       0.000         0.0       0.0000
+g_qlogis        0.000      0.0000       0.000         0.0       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2
+cyan_0                0.000           0.00           0.00  0.000 0.0000
+log_k_JCZ38           0.000           0.00           0.00  0.000 0.0000
+log_k_J9Z38           0.000           0.00           0.00  0.000 0.0000
+log_k_JSE76           0.000           0.00           0.00  0.000 0.0000
+f_cyan_ilr_1          0.000           0.00           0.00  0.000 0.0000
+f_cyan_ilr_2          1.797           0.00           0.00  0.000 0.0000
+f_JCZ38_qlogis        0.000          13.86           0.00  0.000 0.0000
+f_JSE76_qlogis        0.000           0.00          13.91  0.000 0.0000
+log_k1                0.000           0.00           0.00  1.106 0.0000
+log_k2                0.000           0.00           0.00  0.000 0.6141
+g_qlogis              0.000           0.00           0.00  0.000 0.0000
+               g_qlogis
+cyan_0            0.000
+log_k_JCZ38       0.000
+log_k_J9Z38       0.000
+log_k_JSE76       0.000
+f_cyan_ilr_1      0.000
+f_cyan_ilr_2      0.000
+f_JCZ38_qlogis    0.000
+f_JSE76_qlogis    0.000
+log_k1            0.000
+log_k2            0.000
+g_qlogis          1.595
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2288 2280  -1122
+
+Optimised parameters:
+                      est.      lower      upper
+cyan_0            102.7204  1.014e+02  1.040e+02
+log_k_JCZ38        -2.8925 -4.044e+00 -1.741e+00
+log_k_J9Z38        -5.1430 -5.828e+00 -4.457e+00
+log_k_JSE76        -3.5577 -4.174e+00 -2.941e+00
+f_cyan_ilr_1        0.6929  3.788e-01  1.007e+00
+f_cyan_ilr_2        0.6066  5.342e-02  1.160e+00
+f_JCZ38_qlogis      9.8071 -2.819e+03  2.838e+03
+f_JSE76_qlogis      2.2229  5.684e-01  3.877e+00
+log_k1             -1.9339 -2.609e+00 -1.258e+00
+log_k2             -4.4709 -4.935e+00 -4.007e+00
+g_qlogis           -0.4987 -1.373e+00  3.757e-01
+a.1                 2.7368  2.545e+00  2.928e+00
+SD.log_k_JCZ38      1.2747  4.577e-01  2.092e+00
+SD.log_k_J9Z38      0.6758  1.418e-01  1.210e+00
+SD.log_k_JSE76      0.5869  1.169e-01  1.057e+00
+SD.f_cyan_ilr_1     0.3392  1.161e-01  5.622e-01
+SD.f_cyan_ilr_2     0.4200  8.501e-02  7.550e-01
+SD.f_JCZ38_qlogis   0.8511 -1.137e+06  1.137e+06
+SD.f_JSE76_qlogis   0.3767 -5.238e-01  1.277e+00
+SD.log_k1           0.7475  2.601e-01  1.235e+00
+SD.log_k2           0.5179  1.837e-01  8.521e-01
+SD.g_qlogis         0.9817  3.553e-01  1.608e+00
+
+Correlation: 
+               cyan_0  l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76
+log_k_JCZ38    -0.0351                                                        
+log_k_J9Z38    -0.0541  0.0043                                                
+log_k_JSE76    -0.0078  0.0900 -0.0014                                        
+f_cyan_ilr_1   -0.0249  0.0268 -0.0962  0.0000                                
+f_cyan_ilr_2   -0.3560  0.0848  0.1545 -0.0022  0.0463                        
+f_JCZ38_qlogis  0.2005 -0.1226 -0.0347  0.0514 -0.1840 -0.5906                
+f_JSE76_qlogis -0.1638  0.1307  0.0266  0.0001  0.1645  0.5181 -0.9297        
+log_k1          0.0881 -0.0071  0.0005 -0.0070 -0.0064 -0.0346  0.0316 -0.0341
+log_k2          0.0238 -0.0003  0.0082 -0.0022 -0.0017 -0.0017 -0.0002 -0.0076
+g_qlogis        0.0198 -0.0002 -0.0109  0.0034  0.0017 -0.0176  0.0044  0.0051
+               log_k1  log_k2 
+log_k_JCZ38                   
+log_k_J9Z38                   
+log_k_JSE76                   
+f_cyan_ilr_1                  
+f_cyan_ilr_2                  
+f_JCZ38_qlogis                
+f_JSE76_qlogis                
+log_k1                        
+log_k2          0.0276        
+g_qlogis       -0.0283 -0.0309
+
+Random effects:
+                    est.      lower     upper
+SD.log_k_JCZ38    1.2747  4.577e-01 2.092e+00
+SD.log_k_J9Z38    0.6758  1.418e-01 1.210e+00
+SD.log_k_JSE76    0.5869  1.169e-01 1.057e+00
+SD.f_cyan_ilr_1   0.3392  1.161e-01 5.622e-01
+SD.f_cyan_ilr_2   0.4200  8.501e-02 7.550e-01
+SD.f_JCZ38_qlogis 0.8511 -1.137e+06 1.137e+06
+SD.f_JSE76_qlogis 0.3767 -5.238e-01 1.277e+00
+SD.log_k1         0.7475  2.601e-01 1.235e+00
+SD.log_k2         0.5179  1.837e-01 8.521e-01
+SD.g_qlogis       0.9817  3.553e-01 1.608e+00
+
+Variance model:
+     est. lower upper
+a.1 2.737 2.545 2.928
+
+Backtransformed parameters:
+                      est.     lower     upper
+cyan_0           102.72037 1.014e+02 104.00464
+k_JCZ38            0.05544 1.752e-02   0.17539
+k_J9Z38            0.00584 2.942e-03   0.01159
+k_JSE76            0.02850 1.539e-02   0.05279
+f_cyan_to_JCZ38    0.59995        NA        NA
+f_cyan_to_J9Z38    0.22519        NA        NA
+f_JCZ38_to_JSE76   0.99994 0.000e+00   1.00000
+f_JSE76_to_JCZ38   0.90229 6.384e-01   0.97971
+k1                 0.14459 7.357e-02   0.28414
+k2                 0.01144 7.192e-03   0.01819
+g                  0.37784 2.021e-01   0.59284
+
+Resulting formation fractions:
+                   ff
+cyan_JCZ38  5.999e-01
+cyan_J9Z38  2.252e-01
+cyan_sink   1.749e-01
+JCZ38_JSE76 9.999e-01
+JCZ38_sink  5.506e-05
+JSE76_JCZ38 9.023e-01
+JSE76_sink  9.771e-02
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   21.93 159.83    48.11   4.794    60.6
+JCZ38  12.50  41.53       NA      NA      NA
+J9Z38 118.69 394.27       NA      NA      NA
+JSE76  24.32  80.78       NA      NA      NA
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical DFOP path 2 fit with two-component error
+</caption>
+<pre><code>
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 07:57:56 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+           time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+           * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38 +
+           f_JSE76_to_JCZ38 * k_JSE76 * JSE76
+d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 691.67 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+      101.7393        -1.4493        -5.0118        -2.1269         0.6720 
+  f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis         log_k1         log_k2 
+        7.3362        13.4423        13.2659        -2.0061        -4.5527 
+      g_qlogis 
+       -0.5806 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          5.604        0.00       0.000       0.000       0.0000
+log_k_JCZ38     0.000        2.77       0.000       0.000       0.0000
+log_k_J9Z38     0.000        0.00       1.662       0.000       0.0000
+log_k_JSE76     0.000        0.00       0.000       5.021       0.0000
+f_cyan_ilr_1    0.000        0.00       0.000       0.000       0.6519
+f_cyan_ilr_2    0.000        0.00       0.000       0.000       0.0000
+f_JCZ38_qlogis  0.000        0.00       0.000       0.000       0.0000
+f_JSE76_qlogis  0.000        0.00       0.000       0.000       0.0000
+log_k1          0.000        0.00       0.000       0.000       0.0000
+log_k2          0.000        0.00       0.000       0.000       0.0000
+g_qlogis        0.000        0.00       0.000       0.000       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2
+cyan_0                 0.00           0.00           0.00 0.0000 0.0000
+log_k_JCZ38            0.00           0.00           0.00 0.0000 0.0000
+log_k_J9Z38            0.00           0.00           0.00 0.0000 0.0000
+log_k_JSE76            0.00           0.00           0.00 0.0000 0.0000
+f_cyan_ilr_1           0.00           0.00           0.00 0.0000 0.0000
+f_cyan_ilr_2          13.37           0.00           0.00 0.0000 0.0000
+f_JCZ38_qlogis         0.00          14.21           0.00 0.0000 0.0000
+f_JSE76_qlogis         0.00           0.00          14.58 0.0000 0.0000
+log_k1                 0.00           0.00           0.00 0.8453 0.0000
+log_k2                 0.00           0.00           0.00 0.0000 0.5969
+g_qlogis               0.00           0.00           0.00 0.0000 0.0000
+               g_qlogis
+cyan_0             0.00
+log_k_JCZ38        0.00
+log_k_J9Z38        0.00
+log_k_JSE76        0.00
+f_cyan_ilr_1       0.00
+f_cyan_ilr_2       0.00
+f_JCZ38_qlogis     0.00
+f_JSE76_qlogis     0.00
+log_k1             0.00
+log_k2             0.00
+g_qlogis           1.69
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2234 2226  -1095
+
+Optimised parameters:
+                       est.     lower     upper
+cyan_0            101.25496  99.14662 103.36331
+log_k_JCZ38        -2.55593  -3.32972  -1.78215
+log_k_J9Z38        -5.07103  -5.85423  -4.28783
+log_k_JSE76        -3.25468  -4.17577  -2.33360
+f_cyan_ilr_1        0.70139   0.35924   1.04355
+f_cyan_ilr_2        1.07712   0.17789   1.97636
+f_JCZ38_qlogis      3.57483   0.05990   7.08976
+f_JSE76_qlogis      4.54884  -7.25628  16.35395
+log_k1             -2.38201  -2.51639  -2.24763
+log_k2             -4.66741  -4.91865  -4.41617
+g_qlogis           -0.28446  -1.14192   0.57300
+a.1                 2.05925   1.86481   2.25369
+b.1                 0.06172   0.05062   0.07282
+SD.log_k_JCZ38      0.81137   0.25296   1.36977
+SD.log_k_J9Z38      0.83542   0.25395   1.41689
+SD.log_k_JSE76      0.97903   0.30100   1.65707
+SD.f_cyan_ilr_1     0.37878   0.13374   0.62382
+SD.f_cyan_ilr_2     0.67274   0.10102   1.24446
+SD.f_JCZ38_qlogis   1.35327  -0.42359   3.13012
+SD.f_JSE76_qlogis   1.43956 -19.14972  22.02884
+SD.log_k2           0.25329   0.07521   0.43138
+SD.g_qlogis         0.95167   0.35149   1.55184
+
+Correlation: 
+               cyan_0  l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76
+log_k_JCZ38    -0.0265                                                        
+log_k_J9Z38    -0.0392  0.0024                                                
+log_k_JSE76     0.0011  0.1220 -0.0016                                        
+f_cyan_ilr_1   -0.0161  0.0217 -0.0552  0.0034                                
+f_cyan_ilr_2   -0.4718  0.0829  0.1102  0.0042  0.0095                        
+f_JCZ38_qlogis  0.1609 -0.1318 -0.0277  0.0081 -0.1040 -0.4559                
+f_JSE76_qlogis -0.1289  0.1494  0.0219  0.0012  0.1004  0.4309 -0.8543        
+log_k1          0.2618 -0.0739 -0.0167 -0.0148 -0.0444 -0.2768  0.3518 -0.3818
+log_k2          0.0603 -0.0217  0.0174 -0.0058 -0.0197 -0.0533  0.0923 -0.1281
+g_qlogis        0.0362  0.0115 -0.0111  0.0040  0.0095 -0.0116 -0.0439  0.0651
+               log_k1  log_k2 
+log_k_JCZ38                   
+log_k_J9Z38                   
+log_k_JSE76                   
+f_cyan_ilr_1                  
+f_cyan_ilr_2                  
+f_JCZ38_qlogis                
+f_JSE76_qlogis                
+log_k1                        
+log_k2          0.3269        
+g_qlogis       -0.1656 -0.0928
+
+Random effects:
+                    est.     lower   upper
+SD.log_k_JCZ38    0.8114   0.25296  1.3698
+SD.log_k_J9Z38    0.8354   0.25395  1.4169
+SD.log_k_JSE76    0.9790   0.30100  1.6571
+SD.f_cyan_ilr_1   0.3788   0.13374  0.6238
+SD.f_cyan_ilr_2   0.6727   0.10102  1.2445
+SD.f_JCZ38_qlogis 1.3533  -0.42359  3.1301
+SD.f_JSE76_qlogis 1.4396 -19.14972 22.0288
+SD.log_k2         0.2533   0.07521  0.4314
+SD.g_qlogis       0.9517   0.35149  1.5518
+
+Variance model:
+       est.   lower   upper
+a.1 2.05925 1.86481 2.25369
+b.1 0.06172 0.05062 0.07282
+
+Backtransformed parameters:
+                      est.     lower     upper
+cyan_0           1.013e+02 9.915e+01 103.36331
+k_JCZ38          7.762e-02 3.580e-02   0.16828
+k_J9Z38          6.276e-03 2.868e-03   0.01373
+k_JSE76          3.859e-02 1.536e-02   0.09695
+f_cyan_to_JCZ38  6.520e-01        NA        NA
+f_cyan_to_J9Z38  2.418e-01        NA        NA
+f_JCZ38_to_JSE76 9.727e-01 5.150e-01   0.99917
+f_JSE76_to_JCZ38 9.895e-01 7.052e-04   1.00000
+k1               9.236e-02 8.075e-02   0.10565
+k2               9.397e-03 7.309e-03   0.01208
+g                4.294e-01 2.420e-01   0.63945
+
+Resulting formation fractions:
+                 ff
+cyan_JCZ38  0.65203
+cyan_J9Z38  0.24181
+cyan_sink   0.10616
+JCZ38_JSE76 0.97274
+JCZ38_sink  0.02726
+JSE76_JCZ38 0.98953
+JSE76_sink  0.01047
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   24.26 185.34    55.79   7.504   73.77
+JCZ38   8.93  29.66       NA      NA      NA
+J9Z38 110.45 366.89       NA      NA      NA
+JSE76  17.96  59.66       NA      NA      NA
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical SFORB path 2 fit with constant variance
+</caption>
+<pre><code>
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 07:55:26 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
+           cyan_free + k_cyan_bound_free * cyan_bound
+d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free *
+           cyan_bound
+d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38
+           * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76
+d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38
+           * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 542.162 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+          cyan_free_0       log_k_cyan_free log_k_cyan_free_bound 
+             102.4395               -2.7673               -2.8942 
+log_k_cyan_bound_free           log_k_JCZ38           log_k_J9Z38 
+              -3.6201               -2.3107               -5.3123 
+          log_k_JSE76          f_cyan_ilr_1          f_cyan_ilr_2 
+              -3.7120                0.6754                1.1448 
+       f_JCZ38_qlogis        f_JSE76_qlogis 
+              14.8408               15.4734 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+                      cyan_free_0 log_k_cyan_free log_k_cyan_free_bound
+cyan_free_0                 4.589          0.0000                  0.00
+log_k_cyan_free             0.000          0.4849                  0.00
+log_k_cyan_free_bound       0.000          0.0000                  1.62
+log_k_cyan_bound_free       0.000          0.0000                  0.00
+log_k_JCZ38                 0.000          0.0000                  0.00
+log_k_J9Z38                 0.000          0.0000                  0.00
+log_k_JSE76                 0.000          0.0000                  0.00
+f_cyan_ilr_1                0.000          0.0000                  0.00
+f_cyan_ilr_2                0.000          0.0000                  0.00
+f_JCZ38_qlogis              0.000          0.0000                  0.00
+f_JSE76_qlogis              0.000          0.0000                  0.00
+                      log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76
+cyan_free_0                           0.000      0.0000       0.000         0.0
+log_k_cyan_free                       0.000      0.0000       0.000         0.0
+log_k_cyan_free_bound                 0.000      0.0000       0.000         0.0
+log_k_cyan_bound_free                 1.197      0.0000       0.000         0.0
+log_k_JCZ38                           0.000      0.7966       0.000         0.0
+log_k_J9Z38                           0.000      0.0000       1.561         0.0
+log_k_JSE76                           0.000      0.0000       0.000         0.8
+f_cyan_ilr_1                          0.000      0.0000       0.000         0.0
+f_cyan_ilr_2                          0.000      0.0000       0.000         0.0
+f_JCZ38_qlogis                        0.000      0.0000       0.000         0.0
+f_JSE76_qlogis                        0.000      0.0000       0.000         0.0
+                      f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis
+cyan_free_0                 0.0000        0.000            0.0           0.00
+log_k_cyan_free             0.0000        0.000            0.0           0.00
+log_k_cyan_free_bound       0.0000        0.000            0.0           0.00
+log_k_cyan_bound_free       0.0000        0.000            0.0           0.00
+log_k_JCZ38                 0.0000        0.000            0.0           0.00
+log_k_J9Z38                 0.0000        0.000            0.0           0.00
+log_k_JSE76                 0.0000        0.000            0.0           0.00
+f_cyan_ilr_1                0.6349        0.000            0.0           0.00
+f_cyan_ilr_2                0.0000        1.797            0.0           0.00
+f_JCZ38_qlogis              0.0000        0.000           15.6           0.00
+f_JSE76_qlogis              0.0000        0.000            0.0          17.52
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2283 2275  -1120
+
+Optimised parameters:
+                             est.     lower    upper
+cyan_free_0              102.6517 101.40815 103.8952
+log_k_cyan_free           -2.8729  -3.18649  -2.5593
+log_k_cyan_free_bound     -2.7803  -3.60525  -1.9552
+log_k_cyan_bound_free     -3.5845  -4.16644  -3.0026
+log_k_JCZ38               -2.3411  -2.89698  -1.7852
+log_k_J9Z38               -5.2487  -6.01271  -4.4847
+log_k_JSE76               -3.0259  -4.28274  -1.7690
+f_cyan_ilr_1               0.7289   0.38214   1.0756
+f_cyan_ilr_2               0.6891   0.18277   1.1954
+f_JCZ38_qlogis             4.2162   0.47015   7.9622
+f_JSE76_qlogis             5.8911 -20.19088  31.9730
+a.1                        2.7159   2.52587   2.9060
+SD.log_k_cyan_free         0.3354   0.10979   0.5610
+SD.log_k_cyan_free_bound   0.9061   0.30969   1.5025
+SD.log_k_cyan_bound_free   0.6376   0.21229   1.0628
+SD.log_k_JCZ38             0.5499   0.14533   0.9545
+SD.log_k_J9Z38             0.7457   0.15106   1.3404
+SD.log_k_JSE76             1.3822   0.47329   2.2912
+SD.f_cyan_ilr_1            0.3820   0.13280   0.6313
+SD.f_cyan_ilr_2            0.4317   0.06803   0.7953
+SD.f_JCZ38_qlogis          1.8258  -0.25423   3.9059
+SD.f_JSE76_qlogis          2.2348 -83.33679  87.8065
+
+Correlation: 
+                      cyn_f_0 lg_k_c_ lg_k_cyn_f_ lg_k_cyn_b_ l__JCZ3 l__J9Z3
+log_k_cyan_free        0.1944                                                
+log_k_cyan_free_bound  0.0815  0.0814                                        
+log_k_cyan_bound_free  0.0106  0.0426  0.0585                                
+log_k_JCZ38           -0.0231 -0.0106 -0.0089     -0.0051                    
+log_k_J9Z38           -0.0457 -0.0108  0.0019      0.0129      0.0032        
+log_k_JSE76           -0.0054 -0.0024 -0.0017     -0.0005      0.1108  0.0009
+f_cyan_ilr_1           0.0051 -0.0005 -0.0035     -0.0056      0.0131 -0.0967
+f_cyan_ilr_2          -0.3182 -0.0771 -0.0309     -0.0038      0.0680  0.1643
+f_JCZ38_qlogis         0.0834  0.0369  0.0302      0.0172     -0.1145 -0.0204
+f_JSE76_qlogis        -0.0553 -0.0365 -0.0441     -0.0414      0.1579  0.0175
+                      l__JSE7 f_cy__1 f_cy__2 f_JCZ38
+log_k_cyan_free                                      
+log_k_cyan_free_bound                                
+log_k_cyan_bound_free                                
+log_k_JCZ38                                          
+log_k_J9Z38                                          
+log_k_JSE76                                          
+f_cyan_ilr_1          -0.0002                        
+f_cyan_ilr_2           0.0020 -0.0415                
+f_JCZ38_qlogis         0.0052 -0.0665 -0.3437        
+f_JSE76_qlogis         0.0066  0.0635  0.3491 -0.7487
+
+Random effects:
+                           est.     lower   upper
+SD.log_k_cyan_free       0.3354   0.10979  0.5610
+SD.log_k_cyan_free_bound 0.9061   0.30969  1.5025
+SD.log_k_cyan_bound_free 0.6376   0.21229  1.0628
+SD.log_k_JCZ38           0.5499   0.14533  0.9545
+SD.log_k_J9Z38           0.7457   0.15106  1.3404
+SD.log_k_JSE76           1.3822   0.47329  2.2912
+SD.f_cyan_ilr_1          0.3820   0.13280  0.6313
+SD.f_cyan_ilr_2          0.4317   0.06803  0.7953
+SD.f_JCZ38_qlogis        1.8258  -0.25423  3.9059
+SD.f_JSE76_qlogis        2.2348 -83.33679 87.8065
+
+Variance model:
+     est. lower upper
+a.1 2.716 2.526 2.906
+
+Backtransformed parameters:
+                          est.     lower     upper
+cyan_free_0          1.027e+02 1.014e+02 103.89517
+k_cyan_free          5.654e-02 4.132e-02   0.07736
+k_cyan_free_bound    6.202e-02 2.718e-02   0.14153
+k_cyan_bound_free    2.775e-02 1.551e-02   0.04966
+k_JCZ38              9.622e-02 5.519e-02   0.16777
+k_J9Z38              5.254e-03 2.447e-03   0.01128
+k_JSE76              4.852e-02 1.380e-02   0.17051
+f_cyan_free_to_JCZ38 6.197e-01 5.643e-01   0.84429
+f_cyan_free_to_J9Z38 2.211e-01 5.643e-01   0.84429
+f_JCZ38_to_JSE76     9.855e-01 6.154e-01   0.99965
+f_JSE76_to_JCZ38     9.972e-01 1.703e-09   1.00000
+
+Estimated Eigenvalues of SFORB model(s):
+cyan_b1 cyan_b2  cyan_g 
+0.13466 0.01165 0.36490 
+
+Resulting formation fractions:
+                      ff
+cyan_free_JCZ38 0.619745
+cyan_free_J9Z38 0.221083
+cyan_free_sink  0.159172
+cyan_free       1.000000
+JCZ38_JSE76     0.985460
+JCZ38_sink      0.014540
+JSE76_JCZ38     0.997244
+JSE76_sink      0.002756
+
+Estimated disappearance times:
+         DT50   DT90 DT50back DT50_cyan_b1 DT50_cyan_b2
+cyan   23.293 158.67    47.77        5.147         59.5
+JCZ38   7.203  23.93       NA           NA           NA
+J9Z38 131.918 438.22       NA           NA           NA
+JSE76  14.287  47.46       NA           NA           NA
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical SFORB path 2 fit with two-component error
+</caption>
+<pre><code>
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 07:58:06 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
+           cyan_free + k_cyan_bound_free * cyan_bound
+d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free *
+           cyan_bound
+d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38
+           * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76
+d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38
+           * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 701.582 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+          cyan_free_0       log_k_cyan_free log_k_cyan_free_bound 
+             101.7511               -2.8370               -3.0162 
+log_k_cyan_bound_free           log_k_JCZ38           log_k_J9Z38 
+              -3.6600               -2.2988               -5.3129 
+          log_k_JSE76          f_cyan_ilr_1          f_cyan_ilr_2 
+              -3.6991                0.6722                4.8596 
+       f_JCZ38_qlogis        f_JSE76_qlogis 
+              13.4678               14.2149 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+                      cyan_free_0 log_k_cyan_free log_k_cyan_free_bound
+cyan_free_0                 5.629           0.000                 0.000
+log_k_cyan_free             0.000           0.446                 0.000
+log_k_cyan_free_bound       0.000           0.000                 1.449
+log_k_cyan_bound_free       0.000           0.000                 0.000
+log_k_JCZ38                 0.000           0.000                 0.000
+log_k_J9Z38                 0.000           0.000                 0.000
+log_k_JSE76                 0.000           0.000                 0.000
+f_cyan_ilr_1                0.000           0.000                 0.000
+f_cyan_ilr_2                0.000           0.000                 0.000
+f_JCZ38_qlogis              0.000           0.000                 0.000
+f_JSE76_qlogis              0.000           0.000                 0.000
+                      log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76
+cyan_free_0                           0.000      0.0000       0.000      0.0000
+log_k_cyan_free                       0.000      0.0000       0.000      0.0000
+log_k_cyan_free_bound                 0.000      0.0000       0.000      0.0000
+log_k_cyan_bound_free                 1.213      0.0000       0.000      0.0000
+log_k_JCZ38                           0.000      0.7801       0.000      0.0000
+log_k_J9Z38                           0.000      0.0000       1.575      0.0000
+log_k_JSE76                           0.000      0.0000       0.000      0.8078
+f_cyan_ilr_1                          0.000      0.0000       0.000      0.0000
+f_cyan_ilr_2                          0.000      0.0000       0.000      0.0000
+f_JCZ38_qlogis                        0.000      0.0000       0.000      0.0000
+f_JSE76_qlogis                        0.000      0.0000       0.000      0.0000
+                      f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis
+cyan_free_0                 0.0000        0.000           0.00           0.00
+log_k_cyan_free             0.0000        0.000           0.00           0.00
+log_k_cyan_free_bound       0.0000        0.000           0.00           0.00
+log_k_cyan_bound_free       0.0000        0.000           0.00           0.00
+log_k_JCZ38                 0.0000        0.000           0.00           0.00
+log_k_J9Z38                 0.0000        0.000           0.00           0.00
+log_k_JSE76                 0.0000        0.000           0.00           0.00
+f_cyan_ilr_1                0.6518        0.000           0.00           0.00
+f_cyan_ilr_2                0.0000        9.981           0.00           0.00
+f_JCZ38_qlogis              0.0000        0.000          14.26           0.00
+f_JSE76_qlogis              0.0000        0.000           0.00          16.17
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2240 2231  -1098
+
+Optimised parameters:
+                              est.      lower      upper
+cyan_free_0              100.73014  9.873e+01  1.027e+02
+log_k_cyan_free           -3.19634 -3.641e+00 -2.752e+00
+log_k_cyan_free_bound     -3.43533 -3.674e+00 -3.197e+00
+log_k_cyan_bound_free     -3.83282 -4.163e+00 -3.503e+00
+log_k_JCZ38               -2.51065 -3.225e+00 -1.796e+00
+log_k_J9Z38               -5.02539 -5.825e+00 -4.226e+00
+log_k_JSE76               -3.24777 -4.163e+00 -2.333e+00
+f_cyan_ilr_1               0.70640  3.562e-01  1.057e+00
+f_cyan_ilr_2               1.42704  3.170e-01  2.537e+00
+f_JCZ38_qlogis             2.84779  1.042e+00  4.654e+00
+f_JSE76_qlogis             8.63674 -6.407e+02  6.580e+02
+a.1                        2.07082  1.877e+00  2.265e+00
+b.1                        0.06227  5.098e-02  7.355e-02
+SD.log_k_cyan_free         0.49674  1.865e-01  8.069e-01
+SD.log_k_cyan_bound_free   0.28537  6.809e-02  5.027e-01
+SD.log_k_JCZ38             0.74846  2.305e-01  1.266e+00
+SD.log_k_J9Z38             0.86077  2.713e-01  1.450e+00
+SD.log_k_JSE76             0.97613  3.030e-01  1.649e+00
+SD.f_cyan_ilr_1            0.38994  1.382e-01  6.417e-01
+SD.f_cyan_ilr_2            0.82869  3.917e-02  1.618e+00
+SD.f_JCZ38_qlogis          1.05000 -2.808e-02  2.128e+00
+SD.f_JSE76_qlogis          0.44681 -3.985e+05  3.985e+05
+
+Correlation: 
+                      cyn_f_0 lg_k_c_ lg_k_cyn_f_ lg_k_cyn_b_ l__JCZ3 l__J9Z3
+log_k_cyan_free        0.0936                                                
+log_k_cyan_free_bound  0.1302  0.1627                                        
+log_k_cyan_bound_free  0.0029  0.0525  0.5181                                
+log_k_JCZ38           -0.0116 -0.0077 -0.0430     -0.0236                    
+log_k_J9Z38           -0.0192 -0.0077 -0.0048      0.0229     -0.0005        
+log_k_JSE76            0.0007 -0.0020 -0.0134     -0.0072      0.1225 -0.0016
+f_cyan_ilr_1          -0.0118 -0.0027 -0.0132     -0.0118      0.0127 -0.0505
+f_cyan_ilr_2          -0.4643 -0.0762 -0.1245      0.0137      0.0497  0.1003
+f_JCZ38_qlogis         0.0710  0.0371  0.1826      0.0925     -0.0869 -0.0130
+f_JSE76_qlogis        -0.0367 -0.0270 -0.2274     -0.1865      0.1244  0.0098
+                      l__JSE7 f_cy__1 f_cy__2 f_JCZ38
+log_k_cyan_free                                      
+log_k_cyan_free_bound                                
+log_k_cyan_bound_free                                
+log_k_JCZ38                                          
+log_k_J9Z38                                          
+log_k_JSE76                                          
+f_cyan_ilr_1           0.0036                        
+f_cyan_ilr_2           0.0050 -0.0201                
+f_JCZ38_qlogis         0.0142 -0.0529 -0.2698        
+f_JSE76_qlogis         0.0064  0.0345  0.2015 -0.7058
+
+Random effects:
+                           est.      lower     upper
+SD.log_k_cyan_free       0.4967  1.865e-01 8.069e-01
+SD.log_k_cyan_bound_free 0.2854  6.809e-02 5.027e-01
+SD.log_k_JCZ38           0.7485  2.305e-01 1.266e+00
+SD.log_k_J9Z38           0.8608  2.713e-01 1.450e+00
+SD.log_k_JSE76           0.9761  3.030e-01 1.649e+00
+SD.f_cyan_ilr_1          0.3899  1.382e-01 6.417e-01
+SD.f_cyan_ilr_2          0.8287  3.917e-02 1.618e+00
+SD.f_JCZ38_qlogis        1.0500 -2.808e-02 2.128e+00
+SD.f_JSE76_qlogis        0.4468 -3.985e+05 3.985e+05
+
+Variance model:
+       est.   lower   upper
+a.1 2.07082 1.87680 2.26483
+b.1 0.06227 0.05098 0.07355
+
+Backtransformed parameters:
+                          est.      lower     upper
+cyan_free_0          1.007e+02  9.873e+01 102.72898
+k_cyan_free          4.091e-02  2.623e-02   0.06382
+k_cyan_free_bound    3.221e-02  2.537e-02   0.04090
+k_cyan_bound_free    2.165e-02  1.557e-02   0.03011
+k_JCZ38              8.122e-02  3.975e-02   0.16594
+k_J9Z38              6.569e-03  2.954e-03   0.01461
+k_JSE76              3.886e-02  1.556e-02   0.09703
+f_cyan_free_to_JCZ38 6.785e-01  6.102e-01   0.97309
+f_cyan_free_to_J9Z38 2.498e-01  6.102e-01   0.97309
+f_JCZ38_to_JSE76     9.452e-01  7.392e-01   0.99056
+f_JSE76_to_JCZ38     9.998e-01 5.580e-279   1.00000
+
+Estimated Eigenvalues of SFORB model(s):
+cyan_b1 cyan_b2  cyan_g 
+0.08426 0.01051 0.41220 
+
+Resulting formation fractions:
+                       ff
+cyan_free_JCZ38 0.6784541
+cyan_free_J9Z38 0.2498405
+cyan_free_sink  0.0717054
+cyan_free       1.0000000
+JCZ38_JSE76     0.9452043
+JCZ38_sink      0.0547957
+JSE76_JCZ38     0.9998226
+JSE76_sink      0.0001774
+
+Estimated disappearance times:
+         DT50   DT90 DT50back DT50_cyan_b1 DT50_cyan_b2
+cyan   25.237 168.51    50.73        8.226        65.95
+JCZ38   8.535  28.35       NA           NA           NA
+J9Z38 105.517 350.52       NA           NA           NA
+JSE76  17.837  59.25       NA           NA           NA
+
+</code></pre>
+<p></p>
+</div>
+<div class="section level4">
+<h4 id="pathway-2-refined-fits">Pathway 2, refined fits<a class="anchor" aria-label="anchor" href="#pathway-2-refined-fits"></a>
+</h4>
+<caption>
+Hierarchical FOMC path 2 fit with reduced random effects, two-component
+error
+</caption>
+<pre><code>
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 08:11:01 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * (alpha/beta) * 1/((time/beta) + 1) *
+           cyan - k_JCZ38 * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76
+d_J9Z38/dt = + f_cyan_to_J9Z38 * (alpha/beta) * 1/((time/beta) + 1) *
+           cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 773.693 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+      102.4477        -1.8631        -5.1087        -2.5114         0.6826 
+  f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis      log_alpha       log_beta 
+        4.7944        15.9616        13.1566        -0.1564         2.9781 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          7.701       0.000       0.000       0.000       0.0000
+log_k_JCZ38     0.000       1.448       0.000       0.000       0.0000
+log_k_J9Z38     0.000       0.000       1.724       0.000       0.0000
+log_k_JSE76     0.000       0.000       0.000       3.659       0.0000
+f_cyan_ilr_1    0.000       0.000       0.000       0.000       0.6356
+f_cyan_ilr_2    0.000       0.000       0.000       0.000       0.0000
+f_JCZ38_qlogis  0.000       0.000       0.000       0.000       0.0000
+f_JSE76_qlogis  0.000       0.000       0.000       0.000       0.0000
+log_alpha       0.000       0.000       0.000       0.000       0.0000
+log_beta        0.000       0.000       0.000       0.000       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta
+cyan_0                 0.00           0.00           0.00    0.0000   0.0000
+log_k_JCZ38            0.00           0.00           0.00    0.0000   0.0000
+log_k_J9Z38            0.00           0.00           0.00    0.0000   0.0000
+log_k_JSE76            0.00           0.00           0.00    0.0000   0.0000
+f_cyan_ilr_1           0.00           0.00           0.00    0.0000   0.0000
+f_cyan_ilr_2          10.32           0.00           0.00    0.0000   0.0000
+f_JCZ38_qlogis         0.00          12.23           0.00    0.0000   0.0000
+f_JSE76_qlogis         0.00           0.00          14.99    0.0000   0.0000
+log_alpha              0.00           0.00           0.00    0.3924   0.0000
+log_beta               0.00           0.00           0.00    0.0000   0.5639
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2249 2242  -1106
+
+Optimised parameters:
+                     est.   lower  upper
+cyan_0          101.24524      NA     NA
+log_k_JCZ38      -2.85375      NA     NA
+log_k_J9Z38      -5.07729      NA     NA
+log_k_JSE76      -3.53511      NA     NA
+f_cyan_ilr_1      0.67478      NA     NA
+f_cyan_ilr_2      0.97152      NA     NA
+f_JCZ38_qlogis  213.48001      NA     NA
+f_JSE76_qlogis    2.02040      NA     NA
+log_alpha        -0.11041      NA     NA
+log_beta          3.06575      NA     NA
+a.1               2.05279 1.85495 2.2506
+b.1               0.07116 0.05912 0.0832
+SD.log_k_JCZ38    1.21713 0.44160 1.9927
+SD.log_k_J9Z38    0.88268 0.27541 1.4900
+SD.log_k_JSE76    0.59452 0.15005 1.0390
+SD.f_cyan_ilr_1   0.35370 0.12409 0.5833
+SD.f_cyan_ilr_2   0.78186 0.18547 1.3782
+SD.log_alpha      0.27781 0.08168 0.4739
+SD.log_beta       0.32608 0.06490 0.5873
+
+Correlation is not available
+
+Random effects:
+                  est.   lower  upper
+SD.log_k_JCZ38  1.2171 0.44160 1.9927
+SD.log_k_J9Z38  0.8827 0.27541 1.4900
+SD.log_k_JSE76  0.5945 0.15005 1.0390
+SD.f_cyan_ilr_1 0.3537 0.12409 0.5833
+SD.f_cyan_ilr_2 0.7819 0.18547 1.3782
+SD.log_alpha    0.2778 0.08168 0.4739
+SD.log_beta     0.3261 0.06490 0.5873
+
+Variance model:
+       est.   lower  upper
+a.1 2.05279 1.85495 2.2506
+b.1 0.07116 0.05912 0.0832
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.012e+02    NA    NA
+k_JCZ38          5.763e-02    NA    NA
+k_J9Z38          6.237e-03    NA    NA
+k_JSE76          2.916e-02    NA    NA
+f_cyan_to_JCZ38  6.354e-01    NA    NA
+f_cyan_to_J9Z38  2.447e-01    NA    NA
+f_JCZ38_to_JSE76 1.000e+00    NA    NA
+f_JSE76_to_JCZ38 8.829e-01    NA    NA
+alpha            8.955e-01    NA    NA
+beta             2.145e+01    NA    NA
+
+Resulting formation fractions:
+                ff
+cyan_JCZ38  0.6354
+cyan_J9Z38  0.2447
+cyan_sink   0.1200
+JCZ38_JSE76 1.0000
+JCZ38_sink  0.0000
+JSE76_JCZ38 0.8829
+JSE76_sink  0.1171
+
+Estimated disappearance times:
+        DT50   DT90 DT50back
+cyan   25.07 259.21    78.03
+JCZ38  12.03  39.96       NA
+J9Z38 111.14 369.19       NA
+JSE76  23.77  78.98       NA
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical DFOP path 2 fit with reduced random effects, constant
+variance
+</caption>
+<pre><code>
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 08:12:27 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+           time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+           * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38 +
+           f_JSE76_to_JCZ38 * k_JSE76 * JSE76
+d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 859.906 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+      102.4380        -2.3107        -5.3123        -3.7120         0.6757 
+  f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis         log_k1         log_k2 
+        1.1439        13.1194        12.3492        -1.9317        -4.4557 
+      g_qlogis 
+       -0.5644 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          4.591      0.0000       0.000         0.0       0.0000
+log_k_JCZ38     0.000      0.7966       0.000         0.0       0.0000
+log_k_J9Z38     0.000      0.0000       1.561         0.0       0.0000
+log_k_JSE76     0.000      0.0000       0.000         0.8       0.0000
+f_cyan_ilr_1    0.000      0.0000       0.000         0.0       0.6349
+f_cyan_ilr_2    0.000      0.0000       0.000         0.0       0.0000
+f_JCZ38_qlogis  0.000      0.0000       0.000         0.0       0.0000
+f_JSE76_qlogis  0.000      0.0000       0.000         0.0       0.0000
+log_k1          0.000      0.0000       0.000         0.0       0.0000
+log_k2          0.000      0.0000       0.000         0.0       0.0000
+g_qlogis        0.000      0.0000       0.000         0.0       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2
+cyan_0                0.000           0.00           0.00  0.000 0.0000
+log_k_JCZ38           0.000           0.00           0.00  0.000 0.0000
+log_k_J9Z38           0.000           0.00           0.00  0.000 0.0000
+log_k_JSE76           0.000           0.00           0.00  0.000 0.0000
+f_cyan_ilr_1          0.000           0.00           0.00  0.000 0.0000
+f_cyan_ilr_2          1.797           0.00           0.00  0.000 0.0000
+f_JCZ38_qlogis        0.000          13.86           0.00  0.000 0.0000
+f_JSE76_qlogis        0.000           0.00          13.91  0.000 0.0000
+log_k1                0.000           0.00           0.00  1.106 0.0000
+log_k2                0.000           0.00           0.00  0.000 0.6141
+g_qlogis              0.000           0.00           0.00  0.000 0.0000
+               g_qlogis
+cyan_0            0.000
+log_k_JCZ38       0.000
+log_k_J9Z38       0.000
+log_k_JSE76       0.000
+f_cyan_ilr_1      0.000
+f_cyan_ilr_2      0.000
+f_JCZ38_qlogis    0.000
+f_JSE76_qlogis    0.000
+log_k1            0.000
+log_k2            0.000
+g_qlogis          1.595
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2282 2274  -1121
+
+Optimised parameters:
+                     est.   lower  upper
+cyan_0           102.6036      NA     NA
+log_k_JCZ38       -2.9348      NA     NA
+log_k_J9Z38       -5.1617      NA     NA
+log_k_JSE76       -3.6396      NA     NA
+f_cyan_ilr_1       0.6991      NA     NA
+f_cyan_ilr_2       0.6341      NA     NA
+f_JCZ38_qlogis  4232.3011      NA     NA
+f_JSE76_qlogis     1.9658      NA     NA
+log_k1            -1.9503      NA     NA
+log_k2            -4.4745      NA     NA
+g_qlogis          -0.4967      NA     NA
+a.1                2.7461 2.59274 2.8994
+SD.log_k_JCZ38     1.3178 0.47602 2.1596
+SD.log_k_J9Z38     0.7022 0.15061 1.2538
+SD.log_k_JSE76     0.6566 0.15613 1.1570
+SD.f_cyan_ilr_1    0.3409 0.11666 0.5652
+SD.f_cyan_ilr_2    0.4385 0.09482 0.7821
+SD.log_k1          0.7381 0.25599 1.2202
+SD.log_k2          0.5133 0.18152 0.8450
+SD.g_qlogis        0.9866 0.35681 1.6164
+
+Correlation is not available
+
+Random effects:
+                  est.   lower  upper
+SD.log_k_JCZ38  1.3178 0.47602 2.1596
+SD.log_k_J9Z38  0.7022 0.15061 1.2538
+SD.log_k_JSE76  0.6566 0.15613 1.1570
+SD.f_cyan_ilr_1 0.3409 0.11666 0.5652
+SD.f_cyan_ilr_2 0.4385 0.09482 0.7821
+SD.log_k1       0.7381 0.25599 1.2202
+SD.log_k2       0.5133 0.18152 0.8450
+SD.g_qlogis     0.9866 0.35681 1.6164
+
+Variance model:
+     est. lower upper
+a.1 2.746 2.593 2.899
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.026e+02    NA    NA
+k_JCZ38          5.314e-02    NA    NA
+k_J9Z38          5.732e-03    NA    NA
+k_JSE76          2.626e-02    NA    NA
+f_cyan_to_JCZ38  6.051e-01    NA    NA
+f_cyan_to_J9Z38  2.251e-01    NA    NA
+f_JCZ38_to_JSE76 1.000e+00    NA    NA
+f_JSE76_to_JCZ38 8.772e-01    NA    NA
+k1               1.422e-01    NA    NA
+k2               1.140e-02    NA    NA
+g                3.783e-01    NA    NA
+
+Resulting formation fractions:
+                ff
+cyan_JCZ38  0.6051
+cyan_J9Z38  0.2251
+cyan_sink   0.1698
+JCZ38_JSE76 1.0000
+JCZ38_sink  0.0000
+JSE76_JCZ38 0.8772
+JSE76_sink  0.1228
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   22.05 160.35    48.27   4.873   60.83
+JCZ38  13.04  43.33       NA      NA      NA
+J9Z38 120.93 401.73       NA      NA      NA
+JSE76  26.39  87.68       NA      NA      NA
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical DFOP path 2 fit with reduced random effects, two-component
+error
+</caption>
+<pre><code>
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 08:12:54 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+           time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+           * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38 +
+           f_JSE76_to_JCZ38 * k_JSE76 * JSE76
+d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 886.298 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+      101.7393        -1.4493        -5.0118        -2.1269         0.6720 
+  f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis         log_k1         log_k2 
+        7.3362        13.4423        13.2659        -2.0061        -4.5527 
+      g_qlogis 
+       -0.5806 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          5.604        0.00       0.000       0.000       0.0000
+log_k_JCZ38     0.000        2.77       0.000       0.000       0.0000
+log_k_J9Z38     0.000        0.00       1.662       0.000       0.0000
+log_k_JSE76     0.000        0.00       0.000       5.021       0.0000
+f_cyan_ilr_1    0.000        0.00       0.000       0.000       0.6519
+f_cyan_ilr_2    0.000        0.00       0.000       0.000       0.0000
+f_JCZ38_qlogis  0.000        0.00       0.000       0.000       0.0000
+f_JSE76_qlogis  0.000        0.00       0.000       0.000       0.0000
+log_k1          0.000        0.00       0.000       0.000       0.0000
+log_k2          0.000        0.00       0.000       0.000       0.0000
+g_qlogis        0.000        0.00       0.000       0.000       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2
+cyan_0                 0.00           0.00           0.00 0.0000 0.0000
+log_k_JCZ38            0.00           0.00           0.00 0.0000 0.0000
+log_k_J9Z38            0.00           0.00           0.00 0.0000 0.0000
+log_k_JSE76            0.00           0.00           0.00 0.0000 0.0000
+f_cyan_ilr_1           0.00           0.00           0.00 0.0000 0.0000
+f_cyan_ilr_2          13.37           0.00           0.00 0.0000 0.0000
+f_JCZ38_qlogis         0.00          14.21           0.00 0.0000 0.0000
+f_JSE76_qlogis         0.00           0.00          14.58 0.0000 0.0000
+log_k1                 0.00           0.00           0.00 0.8453 0.0000
+log_k2                 0.00           0.00           0.00 0.0000 0.5969
+g_qlogis               0.00           0.00           0.00 0.0000 0.0000
+               g_qlogis
+cyan_0             0.00
+log_k_JCZ38        0.00
+log_k_J9Z38        0.00
+log_k_JSE76        0.00
+f_cyan_ilr_1       0.00
+f_cyan_ilr_2       0.00
+f_JCZ38_qlogis     0.00
+f_JSE76_qlogis     0.00
+log_k1             0.00
+log_k2             0.00
+g_qlogis           1.69
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2237 2229  -1099
+
+Optimised parameters:
+                     est.   lower   upper
+cyan_0          101.00243      NA      NA
+log_k_JCZ38      -2.80828      NA      NA
+log_k_J9Z38      -5.04449      NA      NA
+log_k_JSE76      -3.66981      NA      NA
+f_cyan_ilr_1      0.72564      NA      NA
+f_cyan_ilr_2      1.37978      NA      NA
+f_JCZ38_qlogis    1.98726      NA      NA
+f_JSE76_qlogis  414.80884      NA      NA
+log_k1           -2.38601      NA      NA
+log_k2           -4.63632      NA      NA
+g_qlogis         -0.33920      NA      NA
+a.1               2.10837 1.91261 2.30413
+b.1               0.06223 0.05085 0.07361
+SD.log_k_JCZ38    1.30902 0.48128 2.13675
+SD.log_k_J9Z38    0.83882 0.25790 1.41974
+SD.log_k_JSE76    0.58104 0.14201 1.02008
+SD.f_cyan_ilr_1   0.35421 0.12398 0.58443
+SD.f_cyan_ilr_2   0.79373 0.12007 1.46739
+SD.log_k2         0.27476 0.08557 0.46394
+SD.g_qlogis       0.96170 0.35463 1.56878
+
+Correlation is not available
+
+Random effects:
+                  est.   lower  upper
+SD.log_k_JCZ38  1.3090 0.48128 2.1367
+SD.log_k_J9Z38  0.8388 0.25790 1.4197
+SD.log_k_JSE76  0.5810 0.14201 1.0201
+SD.f_cyan_ilr_1 0.3542 0.12398 0.5844
+SD.f_cyan_ilr_2 0.7937 0.12007 1.4674
+SD.log_k2       0.2748 0.08557 0.4639
+SD.g_qlogis     0.9617 0.35463 1.5688
+
+Variance model:
+       est.   lower   upper
+a.1 2.10837 1.91261 2.30413
+b.1 0.06223 0.05085 0.07361
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.010e+02    NA    NA
+k_JCZ38          6.031e-02    NA    NA
+k_J9Z38          6.445e-03    NA    NA
+k_JSE76          2.548e-02    NA    NA
+f_cyan_to_JCZ38  6.808e-01    NA    NA
+f_cyan_to_J9Z38  2.440e-01    NA    NA
+f_JCZ38_to_JSE76 8.795e-01    NA    NA
+f_JSE76_to_JCZ38 1.000e+00    NA    NA
+k1               9.200e-02    NA    NA
+k2               9.693e-03    NA    NA
+g                4.160e-01    NA    NA
+
+Resulting formation fractions:
+                 ff
+cyan_JCZ38  0.68081
+cyan_J9Z38  0.24398
+cyan_sink   0.07521
+JCZ38_JSE76 0.87945
+JCZ38_sink  0.12055
+JSE76_JCZ38 1.00000
+JSE76_sink  0.00000
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   25.00 182.05     54.8   7.535   71.51
+JCZ38  11.49  38.18       NA      NA      NA
+J9Z38 107.55 357.28       NA      NA      NA
+JSE76  27.20  90.36       NA      NA      NA
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical SFORB path 2 fit with reduced random effects, constant
+variance
+</caption>
+<pre><code>
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 08:12:32 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
+           cyan_free + k_cyan_bound_free * cyan_bound
+d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free *
+           cyan_bound
+d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38
+           * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76
+d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38
+           * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 865.121 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+          cyan_free_0       log_k_cyan_free log_k_cyan_free_bound 
+             102.4395               -2.7673               -2.8942 
+log_k_cyan_bound_free           log_k_JCZ38           log_k_J9Z38 
+              -3.6201               -2.3107               -5.3123 
+          log_k_JSE76          f_cyan_ilr_1          f_cyan_ilr_2 
+              -3.7120                0.6754                1.1448 
+       f_JCZ38_qlogis        f_JSE76_qlogis 
+              14.8408               15.4734 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+                      cyan_free_0 log_k_cyan_free log_k_cyan_free_bound
+cyan_free_0                 4.589          0.0000                  0.00
+log_k_cyan_free             0.000          0.4849                  0.00
+log_k_cyan_free_bound       0.000          0.0000                  1.62
+log_k_cyan_bound_free       0.000          0.0000                  0.00
+log_k_JCZ38                 0.000          0.0000                  0.00
+log_k_J9Z38                 0.000          0.0000                  0.00
+log_k_JSE76                 0.000          0.0000                  0.00
+f_cyan_ilr_1                0.000          0.0000                  0.00
+f_cyan_ilr_2                0.000          0.0000                  0.00
+f_JCZ38_qlogis              0.000          0.0000                  0.00
+f_JSE76_qlogis              0.000          0.0000                  0.00
+                      log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76
+cyan_free_0                           0.000      0.0000       0.000         0.0
+log_k_cyan_free                       0.000      0.0000       0.000         0.0
+log_k_cyan_free_bound                 0.000      0.0000       0.000         0.0
+log_k_cyan_bound_free                 1.197      0.0000       0.000         0.0
+log_k_JCZ38                           0.000      0.7966       0.000         0.0
+log_k_J9Z38                           0.000      0.0000       1.561         0.0
+log_k_JSE76                           0.000      0.0000       0.000         0.8
+f_cyan_ilr_1                          0.000      0.0000       0.000         0.0
+f_cyan_ilr_2                          0.000      0.0000       0.000         0.0
+f_JCZ38_qlogis                        0.000      0.0000       0.000         0.0
+f_JSE76_qlogis                        0.000      0.0000       0.000         0.0
+                      f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis
+cyan_free_0                 0.0000        0.000            0.0           0.00
+log_k_cyan_free             0.0000        0.000            0.0           0.00
+log_k_cyan_free_bound       0.0000        0.000            0.0           0.00
+log_k_cyan_bound_free       0.0000        0.000            0.0           0.00
+log_k_JCZ38                 0.0000        0.000            0.0           0.00
+log_k_J9Z38                 0.0000        0.000            0.0           0.00
+log_k_JSE76                 0.0000        0.000            0.0           0.00
+f_cyan_ilr_1                0.6349        0.000            0.0           0.00
+f_cyan_ilr_2                0.0000        1.797            0.0           0.00
+f_JCZ38_qlogis              0.0000        0.000           15.6           0.00
+f_JSE76_qlogis              0.0000        0.000            0.0          17.52
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2280 2272  -1120
+
+Optimised parameters:
+                              est.   lower  upper
+cyan_free_0               102.6532      NA     NA
+log_k_cyan_free            -2.8547      NA     NA
+log_k_cyan_free_bound      -2.7004      NA     NA
+log_k_cyan_bound_free      -3.5078      NA     NA
+log_k_JCZ38                -2.9255      NA     NA
+log_k_J9Z38                -5.1089      NA     NA
+log_k_JSE76                -3.6263      NA     NA
+f_cyan_ilr_1                0.6873      NA     NA
+f_cyan_ilr_2                0.6498      NA     NA
+f_JCZ38_qlogis           3624.2149      NA     NA
+f_JSE76_qlogis              1.9991      NA     NA
+a.1                         2.7472 2.55559 2.9388
+SD.log_k_cyan_free          0.3227 0.10296 0.5423
+SD.log_k_cyan_free_bound    0.8757 0.29525 1.4562
+SD.log_k_cyan_bound_free    0.6128 0.20220 1.0233
+SD.log_k_JCZ38              1.3431 0.48474 2.2014
+SD.log_k_J9Z38              0.6881 0.14714 1.2291
+SD.log_k_JSE76              0.6461 0.15321 1.1390
+SD.f_cyan_ilr_1             0.3361 0.11376 0.5585
+SD.f_cyan_ilr_2             0.4286 0.08419 0.7730
+
+Correlation is not available
+
+Random effects:
+                           est.   lower  upper
+SD.log_k_cyan_free       0.3227 0.10296 0.5423
+SD.log_k_cyan_free_bound 0.8757 0.29525 1.4562
+SD.log_k_cyan_bound_free 0.6128 0.20220 1.0233
+SD.log_k_JCZ38           1.3431 0.48474 2.2014
+SD.log_k_J9Z38           0.6881 0.14714 1.2291
+SD.log_k_JSE76           0.6461 0.15321 1.1390
+SD.f_cyan_ilr_1          0.3361 0.11376 0.5585
+SD.f_cyan_ilr_2          0.4286 0.08419 0.7730
+
+Variance model:
+     est. lower upper
+a.1 2.747 2.556 2.939
+
+Backtransformed parameters:
+                          est. lower upper
+cyan_free_0          1.027e+02    NA    NA
+k_cyan_free          5.758e-02    NA    NA
+k_cyan_free_bound    6.718e-02    NA    NA
+k_cyan_bound_free    2.996e-02    NA    NA
+k_JCZ38              5.364e-02    NA    NA
+k_J9Z38              6.042e-03    NA    NA
+k_JSE76              2.662e-02    NA    NA
+f_cyan_free_to_JCZ38 6.039e-01    NA    NA
+f_cyan_free_to_J9Z38 2.285e-01    NA    NA
+f_JCZ38_to_JSE76     1.000e+00    NA    NA
+f_JSE76_to_JCZ38     8.807e-01    NA    NA
+
+Estimated Eigenvalues of SFORB model(s):
+cyan_b1 cyan_b2  cyan_g 
+ 0.1426  0.0121  0.3484 
+
+Resulting formation fractions:
+                    ff
+cyan_free_JCZ38 0.6039
+cyan_free_J9Z38 0.2285
+cyan_free_sink  0.1676
+cyan_free       1.0000
+JCZ38_JSE76     1.0000
+JCZ38_sink      0.0000
+JSE76_JCZ38     0.8807
+JSE76_sink      0.1193
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_cyan_b1 DT50_cyan_b2
+cyan   23.84 154.95    46.65         4.86        57.31
+JCZ38  12.92  42.93       NA           NA           NA
+J9Z38 114.71 381.07       NA           NA           NA
+JSE76  26.04  86.51       NA           NA           NA
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical SFORB path 2 fit with reduced random effects, two-component
+error
+</caption>
+<pre><code>
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 08:12:36 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
+           cyan_free + k_cyan_bound_free * cyan_bound
+d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free *
+           cyan_bound
+d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38
+           * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76
+d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38
+           * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 868.952 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+          cyan_free_0       log_k_cyan_free log_k_cyan_free_bound 
+             101.7511               -2.8370               -3.0162 
+log_k_cyan_bound_free           log_k_JCZ38           log_k_J9Z38 
+              -3.6600               -2.2988               -5.3129 
+          log_k_JSE76          f_cyan_ilr_1          f_cyan_ilr_2 
+              -3.6991                0.6722                4.8596 
+       f_JCZ38_qlogis        f_JSE76_qlogis 
+              13.4678               14.2149 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+                      cyan_free_0 log_k_cyan_free log_k_cyan_free_bound
+cyan_free_0                 5.629           0.000                 0.000
+log_k_cyan_free             0.000           0.446                 0.000
+log_k_cyan_free_bound       0.000           0.000                 1.449
+log_k_cyan_bound_free       0.000           0.000                 0.000
+log_k_JCZ38                 0.000           0.000                 0.000
+log_k_J9Z38                 0.000           0.000                 0.000
+log_k_JSE76                 0.000           0.000                 0.000
+f_cyan_ilr_1                0.000           0.000                 0.000
+f_cyan_ilr_2                0.000           0.000                 0.000
+f_JCZ38_qlogis              0.000           0.000                 0.000
+f_JSE76_qlogis              0.000           0.000                 0.000
+                      log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76
+cyan_free_0                           0.000      0.0000       0.000      0.0000
+log_k_cyan_free                       0.000      0.0000       0.000      0.0000
+log_k_cyan_free_bound                 0.000      0.0000       0.000      0.0000
+log_k_cyan_bound_free                 1.213      0.0000       0.000      0.0000
+log_k_JCZ38                           0.000      0.7801       0.000      0.0000
+log_k_J9Z38                           0.000      0.0000       1.575      0.0000
+log_k_JSE76                           0.000      0.0000       0.000      0.8078
+f_cyan_ilr_1                          0.000      0.0000       0.000      0.0000
+f_cyan_ilr_2                          0.000      0.0000       0.000      0.0000
+f_JCZ38_qlogis                        0.000      0.0000       0.000      0.0000
+f_JSE76_qlogis                        0.000      0.0000       0.000      0.0000
+                      f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis
+cyan_free_0                 0.0000        0.000           0.00           0.00
+log_k_cyan_free             0.0000        0.000           0.00           0.00
+log_k_cyan_free_bound       0.0000        0.000           0.00           0.00
+log_k_cyan_bound_free       0.0000        0.000           0.00           0.00
+log_k_JCZ38                 0.0000        0.000           0.00           0.00
+log_k_J9Z38                 0.0000        0.000           0.00           0.00
+log_k_JSE76                 0.0000        0.000           0.00           0.00
+f_cyan_ilr_1                0.6518        0.000           0.00           0.00
+f_cyan_ilr_2                0.0000        9.981           0.00           0.00
+f_JCZ38_qlogis              0.0000        0.000          14.26           0.00
+f_JSE76_qlogis              0.0000        0.000           0.00          16.17
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2241 2233  -1101
+
+Optimised parameters:
+                              est.   lower   upper
+cyan_free_0              100.95469      NA      NA
+log_k_cyan_free           -3.18706      NA      NA
+log_k_cyan_free_bound     -3.38455      NA      NA
+log_k_cyan_bound_free     -3.75788      NA      NA
+log_k_JCZ38               -2.77024      NA      NA
+log_k_J9Z38               -5.03665      NA      NA
+log_k_JSE76               -3.60289      NA      NA
+f_cyan_ilr_1               0.72263      NA      NA
+f_cyan_ilr_2               1.45352      NA      NA
+f_JCZ38_qlogis             2.00778      NA      NA
+f_JSE76_qlogis           941.58570      NA      NA
+a.1                        2.11130 1.91479 2.30780
+b.1                        0.06299 0.05152 0.07445
+SD.log_k_cyan_free         0.50098 0.18805 0.81390
+SD.log_k_cyan_bound_free   0.31671 0.08467 0.54875
+SD.log_k_JCZ38             1.25865 0.45932 2.05798
+SD.log_k_J9Z38             0.86833 0.27222 1.46444
+SD.log_k_JSE76             0.59325 0.14711 1.03940
+SD.f_cyan_ilr_1            0.35705 0.12521 0.58890
+SD.f_cyan_ilr_2            0.88541 0.13797 1.63286
+
+Correlation is not available
+
+Random effects:
+                           est.   lower  upper
+SD.log_k_cyan_free       0.5010 0.18805 0.8139
+SD.log_k_cyan_bound_free 0.3167 0.08467 0.5487
+SD.log_k_JCZ38           1.2587 0.45932 2.0580
+SD.log_k_J9Z38           0.8683 0.27222 1.4644
+SD.log_k_JSE76           0.5933 0.14711 1.0394
+SD.f_cyan_ilr_1          0.3571 0.12521 0.5889
+SD.f_cyan_ilr_2          0.8854 0.13797 1.6329
+
+Variance model:
+       est.   lower   upper
+a.1 2.11130 1.91479 2.30780
+b.1 0.06299 0.05152 0.07445
+
+Backtransformed parameters:
+                          est. lower upper
+cyan_free_0          1.010e+02    NA    NA
+k_cyan_free          4.129e-02    NA    NA
+k_cyan_free_bound    3.389e-02    NA    NA
+k_cyan_bound_free    2.333e-02    NA    NA
+k_JCZ38              6.265e-02    NA    NA
+k_J9Z38              6.495e-03    NA    NA
+k_JSE76              2.724e-02    NA    NA
+f_cyan_free_to_JCZ38 6.844e-01    NA    NA
+f_cyan_free_to_J9Z38 2.463e-01    NA    NA
+f_JCZ38_to_JSE76     8.816e-01    NA    NA
+f_JSE76_to_JCZ38     1.000e+00    NA    NA
+
+Estimated Eigenvalues of SFORB model(s):
+cyan_b1 cyan_b2  cyan_g 
+0.08751 0.01101 0.39586 
+
+Resulting formation fractions:
+                     ff
+cyan_free_JCZ38 0.68444
+cyan_free_J9Z38 0.24633
+cyan_free_sink  0.06923
+cyan_free       1.00000
+JCZ38_JSE76     0.88161
+JCZ38_sink      0.11839
+JSE76_JCZ38     1.00000
+JSE76_sink      0.00000
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_cyan_b1 DT50_cyan_b2
+cyan   25.36 163.36    49.18        7.921        62.95
+JCZ38  11.06  36.75       NA           NA           NA
+J9Z38 106.71 354.49       NA           NA           NA
+JSE76  25.44  84.51       NA           NA           NA
+
+</code></pre>
+<p></p>
+</div>
+</div>
+<div class="section level3">
+<h3 id="session-info">Session info<a class="anchor" aria-label="anchor" href="#session-info"></a>
+</h3>
+<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=de_DE.UTF-8        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] parallel  stats     graphics  grDevices utils     datasets  methods  
+[8] base     
+
+other attached packages:
+[1] rmarkdown_2.29  nvimcom_0.9-167 saemix_3.3      npde_3.5       
+[5] knitr_1.49      mkin_1.2.10    
+
+loaded via a namespace (and not attached):
+ [1] sass_0.4.9        utf8_1.2.4        generics_0.1.3    lattice_0.22-6   
+ [5] digest_0.6.37     magrittr_2.0.3    evaluate_1.0.1    grid_4.4.2       
+ [9] fastmap_1.2.0     cellranger_1.1.0  jsonlite_1.8.9    processx_3.8.4   
+[13] pkgbuild_1.4.5    deSolve_1.40      mclust_6.1.1      ps_1.8.1         
+[17] gridExtra_2.3     fansi_1.0.6       scales_1.3.0      codetools_0.2-20 
+[21] textshaping_0.4.1 jquerylib_0.1.4   cli_3.6.3         rlang_1.1.4      
+[25] munsell_0.5.1     cachem_1.1.0      yaml_2.3.10       inline_0.3.20    
+[29] tools_4.4.2       dplyr_1.1.4       colorspace_2.1-1  ggplot2_3.5.1    
+[33] vctrs_0.6.5       R6_2.5.1          zoo_1.8-12        lifecycle_1.0.4  
+[37] fs_1.6.5          htmlwidgets_1.6.4 MASS_7.3-61       ragg_1.3.3       
+[41] callr_3.7.6       pkgconfig_2.0.3   desc_1.4.3        pkgdown_2.1.1    
+[45] pillar_1.9.0      bslib_0.8.0       gtable_0.3.6      glue_1.8.0       
+[49] systemfonts_1.1.0 xfun_0.49         tibble_3.2.1      lmtest_0.9-40    
+[53] tidyselect_1.2.1  htmltools_0.5.8.1 nlme_3.1-166      compiler_4.4.2   
+[57] readxl_1.4.3     </code></pre>
+</div>
+<div class="section level3">
+<h3 id="hardware-info">Hardware info<a class="anchor" aria-label="anchor" href="#hardware-info"></a>
+</h3>
+<pre><code>CPU model: AMD Ryzen 9 7950X 16-Core Processor</code></pre>
+<pre><code>MemTotal:       64927788 kB</code></pre>
+</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>
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+    <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_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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+  <main id="main" class="col-md-9"><div class="page-header">
+
+      <h1>Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</h1>
+                        <h4 data-toc-skip class="author">Johannes
+Ranke</h4>
+            
+            <h4 data-toc-skip class="date">Last change on 5 January
+2023, last compiled on 14 Februar 2025</h4>
+      
+      <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/prebuilt/2022_dmta_parent.rmd" class="external-link"><code>vignettes/prebuilt/2022_dmta_parent.rmd</code></a></small>
+      <div class="d-none name"><code>2022_dmta_parent.rmd</code></div>
+    </div>
+
+    
+    
+<div class="section level2">
+<h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#introduction"></a>
+</h2>
+<p>The purpose of this document is to demonstrate how nonlinear
+hierarchical models (NLHM) based on the parent degradation models SFO,
+FOMC, DFOP and HS can be fitted with the mkin package.</p>
+<p>It was assembled in the course of work package 1.1 of Project Number
+173340 (Application of nonlinear hierarchical models to the kinetic
+evaluation of chemical degradation data) of the German Environment
+Agency carried out in 2022 and 2023.</p>
+<p>The mkin package is used in version 1.2.10. It contains the test data
+and the functions used in the evaluations. The <code>saemix</code>
+package is used as a backend for fitting the NLHM, but is also loaded to
+make the convergence plot function available.</p>
+<p>This document is processed with the <code>knitr</code> package, which
+also provides the <code>kable</code> function that is used to improve
+the display of tabular data in R markdown documents. For parallel
+processing, the <code>parallel</code> package is used.</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="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://yihui.org/knitr/" class="external-link">knitr</a></span><span class="op">)</span></span>
+<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="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">parallel</span><span class="op">)</span></span>
+<span><span class="va">n_cores</span> <span class="op">&lt;-</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>
+<span><span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/Sys.info.html" class="external-link">Sys.info</a></span><span class="op">(</span><span class="op">)</span><span class="op">[</span><span class="st">"sysname"</span><span class="op">]</span> <span class="op">==</span> <span class="st">"Windows"</span><span class="op">)</span> <span class="op">{</span></span>
+<span>  <span class="va">cl</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makePSOCKcluster</a></span><span class="op">(</span><span class="va">n_cores</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">cl</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makeForkCluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span>
+<span><span class="op">}</span></span></code></pre></div>
+</div>
+<div class="section level2">
+<h2 id="data">Data<a class="anchor" aria-label="anchor" href="#data"></a>
+</h2>
+<p>The test data are available in the mkin package as an object of class
+<code>mkindsg</code> (mkin dataset group) under the identifier
+<code>dimethenamid_2018</code>. The following preprocessing steps are
+still necessary:</p>
+<ul>
+<li>The data available for the enantiomer dimethenamid-P (DMTAP) are
+renamed to have the same substance name as the data for the racemic
+mixture dimethenamid (DMTA). The reason for this is that no difference
+between their degradation behaviour was identified in the EU risk
+assessment.</li>
+<li>The data for transformation products and unnecessary columns are
+discarded</li>
+<li>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 that are independent of temperature</li>
+<li>Finally, datasets observed in the same soil (<code>Elliot 1</code>
+and <code>Elliot 2</code>) are combined, resulting in dimethenamid
+(DMTA) data from six soils.</li>
+</ul>
+<p>The following commented R code performs this preprocessing.</p>
+<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="co"># Apply a function to each of the seven datasets in the mkindsg object to create a list</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 class="co"># Get a dataset</span></span>
+<span>  <span class="va">ds_i</span><span class="op">[</span><span class="va">ds_i</span><span class="op">$</span><span class="va">name</span> <span class="op">==</span> <span class="st">"DMTAP"</span>, <span class="st">"name"</span><span class="op">]</span> <span class="op">&lt;-</span>  <span class="st">"DMTA"</span>              <span class="co"># Rename DMTAP to DMTA</span></span>
+<span>  <span class="va">ds_i</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/subset.html" class="external-link">subset</a></span><span class="op">(</span><span class="va">ds_i</span>, <span class="va">name</span> <span class="op">==</span> <span class="st">"DMTA"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"name"</span>, <span class="st">"time"</span>, <span class="st">"value"</span><span class="op">)</span><span class="op">)</span> <span class="co"># Select data</span></span>
+<span>  <span class="va">ds_i</span><span class="op">$</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 class="co"># Normalise time</span></span>
+<span>  <span class="va">ds_i</span>                                                       <span class="co"># Return the dataset</span></span>
+<span><span class="op">}</span><span class="op">)</span></span>
+<span></span>
+<span><span class="co"># Use dataset titles as names for the list elements</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>
+<span><span class="co"># Combine data for Elliot soil to obtain a named list with six elements</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 class="co">#</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>
+<p>The following tables show the 6 datasets.</p>
+<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="kw">for</span> <span class="op">(</span><span class="va">ds_name</span> <span class="kw">in</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">)</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="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="fu"><a href="../../reference/mkin_long_to_wide.html">mkin_long_to_wide</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">[[</span><span class="va">ds_name</span><span class="op">]</span><span class="op">]</span><span class="op">)</span>,</span>
+<span>      caption <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">"Dataset"</span>, <span class="va">ds_name</span><span class="op">)</span>,</span>
+<span>      label <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste0</a></span><span class="op">(</span><span class="st">"tab:"</span>, <span class="va">ds_name</span><span class="op">)</span>, booktabs <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span><span class="op">)</span></span>
+<span>    <span class="fu"><a href="https://rdrr.io/r/base/cat.html" class="external-link">cat</a></span><span class="op">(</span><span class="st">"\n\\clearpage\n"</span><span class="op">)</span></span>
+<span><span class="op">}</span></span></code></pre></div>
+<table class="table">
+<caption>Dataset Calke</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">DMTA</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0</td>
+<td align="right">95.8</td>
+</tr>
+<tr class="even">
+<td align="right">0</td>
+<td align="right">98.7</td>
+</tr>
+<tr class="odd">
+<td align="right">14</td>
+<td align="right">60.5</td>
+</tr>
+<tr class="even">
+<td align="right">30</td>
+<td align="right">39.1</td>
+</tr>
+<tr class="odd">
+<td align="right">59</td>
+<td align="right">15.2</td>
+</tr>
+<tr class="even">
+<td align="right">120</td>
+<td align="right">4.8</td>
+</tr>
+<tr class="odd">
+<td align="right">120</td>
+<td align="right">4.6</td>
+</tr>
+</tbody>
+</table>
+<table class="table">
+<caption>Dataset Borstel</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">DMTA</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.000000</td>
+<td align="right">100.5</td>
+</tr>
+<tr class="even">
+<td align="right">0.000000</td>
+<td align="right">99.6</td>
+</tr>
+<tr class="odd">
+<td align="right">1.941295</td>
+<td align="right">91.9</td>
+</tr>
+<tr class="even">
+<td align="right">1.941295</td>
+<td align="right">91.3</td>
+</tr>
+<tr class="odd">
+<td align="right">6.794534</td>
+<td align="right">81.8</td>
+</tr>
+<tr class="even">
+<td align="right">6.794534</td>
+<td align="right">82.1</td>
+</tr>
+<tr class="odd">
+<td align="right">13.589067</td>
+<td align="right">69.1</td>
+</tr>
+<tr class="even">
+<td align="right">13.589067</td>
+<td align="right">68.0</td>
+</tr>
+<tr class="odd">
+<td align="right">27.178135</td>
+<td align="right">51.4</td>
+</tr>
+<tr class="even">
+<td align="right">27.178135</td>
+<td align="right">51.4</td>
+</tr>
+<tr class="odd">
+<td align="right">56.297565</td>
+<td align="right">27.6</td>
+</tr>
+<tr class="even">
+<td align="right">56.297565</td>
+<td align="right">26.8</td>
+</tr>
+<tr class="odd">
+<td align="right">86.387643</td>
+<td align="right">15.7</td>
+</tr>
+<tr class="even">
+<td align="right">86.387643</td>
+<td align="right">15.3</td>
+</tr>
+<tr class="odd">
+<td align="right">115.507073</td>
+<td align="right">7.9</td>
+</tr>
+<tr class="even">
+<td align="right">115.507073</td>
+<td align="right">8.1</td>
+</tr>
+</tbody>
+</table>
+<table class="table">
+<caption>Dataset Flaach</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">DMTA</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.0000000</td>
+<td align="right">96.5</td>
+</tr>
+<tr class="even">
+<td align="right">0.0000000</td>
+<td align="right">96.8</td>
+</tr>
+<tr class="odd">
+<td align="right">0.0000000</td>
+<td align="right">97.0</td>
+</tr>
+<tr class="even">
+<td align="right">0.6233856</td>
+<td align="right">82.9</td>
+</tr>
+<tr class="odd">
+<td align="right">0.6233856</td>
+<td align="right">86.7</td>
+</tr>
+<tr class="even">
+<td align="right">0.6233856</td>
+<td align="right">87.4</td>
+</tr>
+<tr class="odd">
+<td align="right">1.8701567</td>
+<td align="right">72.8</td>
+</tr>
+<tr class="even">
+<td align="right">1.8701567</td>
+<td align="right">69.9</td>
+</tr>
+<tr class="odd">
+<td align="right">1.8701567</td>
+<td align="right">71.9</td>
+</tr>
+<tr class="even">
+<td align="right">4.3636989</td>
+<td align="right">51.4</td>
+</tr>
+<tr class="odd">
+<td align="right">4.3636989</td>
+<td align="right">52.9</td>
+</tr>
+<tr class="even">
+<td align="right">4.3636989</td>
+<td align="right">48.6</td>
+</tr>
+<tr class="odd">
+<td align="right">8.7273979</td>
+<td align="right">28.5</td>
+</tr>
+<tr class="even">
+<td align="right">8.7273979</td>
+<td align="right">27.3</td>
+</tr>
+<tr class="odd">
+<td align="right">8.7273979</td>
+<td align="right">27.5</td>
+</tr>
+<tr class="even">
+<td align="right">13.0910968</td>
+<td align="right">14.8</td>
+</tr>
+<tr class="odd">
+<td align="right">13.0910968</td>
+<td align="right">13.4</td>
+</tr>
+<tr class="even">
+<td align="right">13.0910968</td>
+<td align="right">14.4</td>
+</tr>
+<tr class="odd">
+<td align="right">17.4547957</td>
+<td align="right">7.7</td>
+</tr>
+<tr class="even">
+<td align="right">17.4547957</td>
+<td align="right">7.3</td>
+</tr>
+<tr class="odd">
+<td align="right">17.4547957</td>
+<td align="right">8.1</td>
+</tr>
+<tr class="even">
+<td align="right">26.1821936</td>
+<td align="right">2.0</td>
+</tr>
+<tr class="odd">
+<td align="right">26.1821936</td>
+<td align="right">1.5</td>
+</tr>
+<tr class="even">
+<td align="right">26.1821936</td>
+<td align="right">1.9</td>
+</tr>
+<tr class="odd">
+<td align="right">34.9095915</td>
+<td align="right">1.3</td>
+</tr>
+<tr class="even">
+<td align="right">34.9095915</td>
+<td align="right">1.0</td>
+</tr>
+<tr class="odd">
+<td align="right">34.9095915</td>
+<td align="right">1.1</td>
+</tr>
+<tr class="even">
+<td align="right">43.6369893</td>
+<td align="right">0.9</td>
+</tr>
+<tr class="odd">
+<td align="right">43.6369893</td>
+<td align="right">0.7</td>
+</tr>
+<tr class="even">
+<td align="right">43.6369893</td>
+<td align="right">0.7</td>
+</tr>
+<tr class="odd">
+<td align="right">52.3643872</td>
+<td align="right">0.6</td>
+</tr>
+<tr class="even">
+<td align="right">52.3643872</td>
+<td align="right">0.4</td>
+</tr>
+<tr class="odd">
+<td align="right">52.3643872</td>
+<td align="right">0.5</td>
+</tr>
+<tr class="even">
+<td align="right">74.8062674</td>
+<td align="right">0.4</td>
+</tr>
+<tr class="odd">
+<td align="right">74.8062674</td>
+<td align="right">0.3</td>
+</tr>
+<tr class="even">
+<td align="right">74.8062674</td>
+<td align="right">0.3</td>
+</tr>
+</tbody>
+</table>
+<table class="table">
+<caption>Dataset BBA 2.2</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">DMTA</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.0000000</td>
+<td align="right">98.09</td>
+</tr>
+<tr class="even">
+<td align="right">0.0000000</td>
+<td align="right">98.77</td>
+</tr>
+<tr class="odd">
+<td align="right">0.7678922</td>
+<td align="right">93.52</td>
+</tr>
+<tr class="even">
+<td align="right">0.7678922</td>
+<td align="right">92.03</td>
+</tr>
+<tr class="odd">
+<td align="right">2.3036765</td>
+<td align="right">88.39</td>
+</tr>
+<tr class="even">
+<td align="right">2.3036765</td>
+<td align="right">87.18</td>
+</tr>
+<tr class="odd">
+<td align="right">5.3752452</td>
+<td align="right">69.38</td>
+</tr>
+<tr class="even">
+<td align="right">5.3752452</td>
+<td align="right">71.06</td>
+</tr>
+<tr class="odd">
+<td align="right">10.7504904</td>
+<td align="right">45.21</td>
+</tr>
+<tr class="even">
+<td align="right">10.7504904</td>
+<td align="right">46.81</td>
+</tr>
+<tr class="odd">
+<td align="right">16.1257355</td>
+<td align="right">30.54</td>
+</tr>
+<tr class="even">
+<td align="right">16.1257355</td>
+<td align="right">30.07</td>
+</tr>
+<tr class="odd">
+<td align="right">21.5009807</td>
+<td align="right">21.60</td>
+</tr>
+<tr class="even">
+<td align="right">21.5009807</td>
+<td align="right">20.41</td>
+</tr>
+<tr class="odd">
+<td align="right">32.2514711</td>
+<td align="right">9.10</td>
+</tr>
+<tr class="even">
+<td align="right">32.2514711</td>
+<td align="right">9.70</td>
+</tr>
+<tr class="odd">
+<td align="right">43.0019614</td>
+<td align="right">6.58</td>
+</tr>
+<tr class="even">
+<td align="right">43.0019614</td>
+<td align="right">6.31</td>
+</tr>
+<tr class="odd">
+<td align="right">53.7524518</td>
+<td align="right">3.47</td>
+</tr>
+<tr class="even">
+<td align="right">53.7524518</td>
+<td align="right">3.52</td>
+</tr>
+<tr class="odd">
+<td align="right">64.5029421</td>
+<td align="right">3.40</td>
+</tr>
+<tr class="even">
+<td align="right">64.5029421</td>
+<td align="right">3.67</td>
+</tr>
+<tr class="odd">
+<td align="right">91.3791680</td>
+<td align="right">1.62</td>
+</tr>
+<tr class="even">
+<td align="right">91.3791680</td>
+<td align="right">1.62</td>
+</tr>
+</tbody>
+</table>
+<table class="table">
+<caption>Dataset BBA 2.3</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">DMTA</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.0000000</td>
+<td align="right">99.33</td>
+</tr>
+<tr class="even">
+<td align="right">0.0000000</td>
+<td align="right">97.44</td>
+</tr>
+<tr class="odd">
+<td align="right">0.6733938</td>
+<td align="right">93.73</td>
+</tr>
+<tr class="even">
+<td align="right">0.6733938</td>
+<td align="right">93.77</td>
+</tr>
+<tr class="odd">
+<td align="right">2.0201814</td>
+<td align="right">87.84</td>
+</tr>
+<tr class="even">
+<td align="right">2.0201814</td>
+<td align="right">89.82</td>
+</tr>
+<tr class="odd">
+<td align="right">4.7137565</td>
+<td align="right">71.61</td>
+</tr>
+<tr class="even">
+<td align="right">4.7137565</td>
+<td align="right">71.42</td>
+</tr>
+<tr class="odd">
+<td align="right">9.4275131</td>
+<td align="right">45.60</td>
+</tr>
+<tr class="even">
+<td align="right">9.4275131</td>
+<td align="right">45.42</td>
+</tr>
+<tr class="odd">
+<td align="right">14.1412696</td>
+<td align="right">31.12</td>
+</tr>
+<tr class="even">
+<td align="right">14.1412696</td>
+<td align="right">31.68</td>
+</tr>
+<tr class="odd">
+<td align="right">18.8550262</td>
+<td align="right">23.20</td>
+</tr>
+<tr class="even">
+<td align="right">18.8550262</td>
+<td align="right">24.13</td>
+</tr>
+<tr class="odd">
+<td align="right">28.2825393</td>
+<td align="right">9.43</td>
+</tr>
+<tr class="even">
+<td align="right">28.2825393</td>
+<td align="right">9.82</td>
+</tr>
+<tr class="odd">
+<td align="right">37.7100523</td>
+<td align="right">7.08</td>
+</tr>
+<tr class="even">
+<td align="right">37.7100523</td>
+<td align="right">8.64</td>
+</tr>
+<tr class="odd">
+<td align="right">47.1375654</td>
+<td align="right">4.41</td>
+</tr>
+<tr class="even">
+<td align="right">47.1375654</td>
+<td align="right">4.78</td>
+</tr>
+<tr class="odd">
+<td align="right">56.5650785</td>
+<td align="right">4.92</td>
+</tr>
+<tr class="even">
+<td align="right">56.5650785</td>
+<td align="right">5.08</td>
+</tr>
+<tr class="odd">
+<td align="right">80.1338612</td>
+<td align="right">2.13</td>
+</tr>
+<tr class="even">
+<td align="right">80.1338612</td>
+<td align="right">2.23</td>
+</tr>
+</tbody>
+</table>
+<table class="table">
+<caption>Dataset Elliot</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">DMTA</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.000000</td>
+<td align="right">97.5</td>
+</tr>
+<tr class="even">
+<td align="right">0.000000</td>
+<td align="right">100.7</td>
+</tr>
+<tr class="odd">
+<td align="right">1.228478</td>
+<td align="right">86.4</td>
+</tr>
+<tr class="even">
+<td align="right">1.228478</td>
+<td align="right">88.5</td>
+</tr>
+<tr class="odd">
+<td align="right">3.685435</td>
+<td align="right">69.8</td>
+</tr>
+<tr class="even">
+<td align="right">3.685435</td>
+<td align="right">77.1</td>
+</tr>
+<tr class="odd">
+<td align="right">8.599349</td>
+<td align="right">59.0</td>
+</tr>
+<tr class="even">
+<td align="right">8.599349</td>
+<td align="right">54.2</td>
+</tr>
+<tr class="odd">
+<td align="right">17.198697</td>
+<td align="right">31.3</td>
+</tr>
+<tr class="even">
+<td align="right">17.198697</td>
+<td align="right">33.5</td>
+</tr>
+<tr class="odd">
+<td align="right">25.798046</td>
+<td align="right">19.6</td>
+</tr>
+<tr class="even">
+<td align="right">25.798046</td>
+<td align="right">20.9</td>
+</tr>
+<tr class="odd">
+<td align="right">34.397395</td>
+<td align="right">13.3</td>
+</tr>
+<tr class="even">
+<td align="right">34.397395</td>
+<td align="right">15.8</td>
+</tr>
+<tr class="odd">
+<td align="right">51.596092</td>
+<td align="right">6.7</td>
+</tr>
+<tr class="even">
+<td align="right">51.596092</td>
+<td align="right">8.7</td>
+</tr>
+<tr class="odd">
+<td align="right">68.794789</td>
+<td align="right">8.8</td>
+</tr>
+<tr class="even">
+<td align="right">68.794789</td>
+<td align="right">8.7</td>
+</tr>
+<tr class="odd">
+<td align="right">103.192184</td>
+<td align="right">6.0</td>
+</tr>
+<tr class="even">
+<td align="right">103.192184</td>
+<td align="right">4.4</td>
+</tr>
+<tr class="odd">
+<td align="right">146.188928</td>
+<td align="right">3.3</td>
+</tr>
+<tr class="even">
+<td align="right">146.188928</td>
+<td align="right">2.8</td>
+</tr>
+<tr class="odd">
+<td align="right">223.583066</td>
+<td align="right">1.4</td>
+</tr>
+<tr class="even">
+<td align="right">223.583066</td>
+<td align="right">1.8</td>
+</tr>
+<tr class="odd">
+<td align="right">0.000000</td>
+<td align="right">93.4</td>
+</tr>
+<tr class="even">
+<td align="right">0.000000</td>
+<td align="right">103.2</td>
+</tr>
+<tr class="odd">
+<td align="right">1.228478</td>
+<td align="right">89.2</td>
+</tr>
+<tr class="even">
+<td align="right">1.228478</td>
+<td align="right">86.6</td>
+</tr>
+<tr class="odd">
+<td align="right">3.685435</td>
+<td align="right">78.2</td>
+</tr>
+<tr class="even">
+<td align="right">3.685435</td>
+<td align="right">78.1</td>
+</tr>
+<tr class="odd">
+<td align="right">8.599349</td>
+<td align="right">55.6</td>
+</tr>
+<tr class="even">
+<td align="right">8.599349</td>
+<td align="right">53.0</td>
+</tr>
+<tr class="odd">
+<td align="right">17.198697</td>
+<td align="right">33.7</td>
+</tr>
+<tr class="even">
+<td align="right">17.198697</td>
+<td align="right">33.2</td>
+</tr>
+<tr class="odd">
+<td align="right">25.798046</td>
+<td align="right">20.9</td>
+</tr>
+<tr class="even">
+<td align="right">25.798046</td>
+<td align="right">19.9</td>
+</tr>
+<tr class="odd">
+<td align="right">34.397395</td>
+<td align="right">18.2</td>
+</tr>
+<tr class="even">
+<td align="right">34.397395</td>
+<td align="right">12.7</td>
+</tr>
+<tr class="odd">
+<td align="right">51.596092</td>
+<td align="right">7.8</td>
+</tr>
+<tr class="even">
+<td align="right">51.596092</td>
+<td align="right">9.0</td>
+</tr>
+<tr class="odd">
+<td align="right">68.794789</td>
+<td align="right">11.4</td>
+</tr>
+<tr class="even">
+<td align="right">68.794789</td>
+<td align="right">9.0</td>
+</tr>
+<tr class="odd">
+<td align="right">103.192184</td>
+<td align="right">3.9</td>
+</tr>
+<tr class="even">
+<td align="right">103.192184</td>
+<td align="right">4.4</td>
+</tr>
+<tr class="odd">
+<td align="right">146.188928</td>
+<td align="right">2.6</td>
+</tr>
+<tr class="even">
+<td align="right">146.188928</td>
+<td align="right">3.4</td>
+</tr>
+<tr class="odd">
+<td align="right">223.583066</td>
+<td align="right">2.0</td>
+</tr>
+<tr class="even">
+<td align="right">223.583066</td>
+<td align="right">1.7</td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="section level2">
+<h2 id="separate-evaluations">Separate evaluations<a class="anchor" aria-label="anchor" href="#separate-evaluations"></a>
+</h2>
+<p>In order to obtain suitable starting parameters for the NLHM fits,
+separate fits of the four models to the data for each soil are generated
+using the <code>mmkin</code> function from the <code>mkin</code>
+package. In a first step, constant variance is assumed. Convergence is
+checked with the <code>status</code> function.</p>
+<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">deg_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">"FOMC"</span>, <span class="st">"DFOP"</span>, <span class="st">"HS"</span><span class="op">)</span></span>
+<span><span class="va">f_sep_const</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span></span>
+<span>  <span class="va">deg_mods</span>,</span>
+<span>  <span class="va">dmta_ds</span>,</span>
+<span>  error_model <span class="op">=</span> <span class="st">"const"</span>,</span>
+<span>  quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
+<span></span>
+<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_const</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><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="left">Calke</th>
+<th align="left">Borstel</th>
+<th align="left">Flaach</th>
+<th align="left">BBA 2.2</th>
+<th align="left">BBA 2.3</th>
+<th align="left">Elliot</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">SFO</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">FOMC</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="odd">
+<td align="left">DFOP</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">HS</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+</tbody>
+</table>
+<p>In the table above, OK indicates convergence, and C indicates failure
+to converge. All separate fits with constant variance converged, with
+the sole exception of the HS fit to the BBA 2.2 data. To prepare for
+fitting NLHM using the two-component error model, the separate fits are
+updated assuming two-component error.</p>
+<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">f_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">f_sep_const</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span>
+<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_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><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="left">Calke</th>
+<th align="left">Borstel</th>
+<th align="left">Flaach</th>
+<th align="left">BBA 2.2</th>
+<th align="left">BBA 2.3</th>
+<th align="left">Elliot</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">SFO</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">FOMC</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+</tr>
+<tr class="odd">
+<td align="left">DFOP</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">HS</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+</tbody>
+</table>
+<p>Using the two-component error model, the one fit that did not
+converge with constant variance did converge, but other non-SFO fits
+failed to converge.</p>
+</div>
+<div class="section level2">
+<h2 id="hierarchichal-model-fits">Hierarchichal model fits<a class="anchor" aria-label="anchor" href="#hierarchichal-model-fits"></a>
+</h2>
+<p>The following code fits eight versions of hierarchical models to the
+data, using SFO, FOMC, DFOP and HS for the parent compound, and using
+either constant variance or two-component error for the error model. The
+default parameter distribution model in mkin allows for variation of all
+degradation parameters across the assumed population of soils. In other
+words, each degradation parameter is associated with a random effect as
+a first step. The <code>mhmkin</code> function makes it possible to fit
+all eight versions in parallel (given a sufficient number of computing
+cores being available) to save execution time.</p>
+<p>Convergence plots and summaries for these fits are shown in the
+appendix.</p>
+<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">f_saem</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mhmkin.html">mhmkin</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_sep_const</span>, <span class="va">f_sep_tc</span><span class="op">)</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span></span></code></pre></div>
+<p>The output of the <code>status</code> function shows that all fits
+terminated successfully.</p>
+<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_saem</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><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="left">const</th>
+<th align="left">tc</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">SFO</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">FOMC</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="odd">
+<td align="left">DFOP</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">HS</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+</tbody>
+</table>
+<p>The AIC and BIC values show that the biphasic models DFOP and HS give
+the best fits.</p>
+<div class="sourceCode" id="cb8"><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</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">FOMC const</td>
+<td align="right">7</td>
+<td align="right">734.2</td>
+<td align="right">732.7</td>
+<td align="right">-360.1</td>
+</tr>
+<tr class="even">
+<td align="left">FOMC tc</td>
+<td align="right">8</td>
+<td align="right">720.7</td>
+<td align="right">719.1</td>
+<td align="right">-352.4</td>
+</tr>
+<tr class="odd">
+<td align="left">DFOP const</td>
+<td align="right">9</td>
+<td align="right">711.8</td>
+<td align="right">710.0</td>
+<td align="right">-346.9</td>
+</tr>
+<tr class="even">
+<td align="left">HS const</td>
+<td align="right">9</td>
+<td align="right">714.0</td>
+<td align="right">712.1</td>
+<td align="right">-348.0</td>
+</tr>
+<tr class="odd">
+<td align="left">DFOP tc</td>
+<td align="right">10</td>
+<td align="right">665.7</td>
+<td align="right">663.6</td>
+<td align="right">-322.9</td>
+</tr>
+<tr class="even">
+<td align="left">HS tc</td>
+<td align="right">10</td>
+<td align="right">667.1</td>
+<td align="right">665.0</td>
+<td align="right">-323.6</td>
+</tr>
+</tbody>
+</table>
+<p>The DFOP model is preferred here, as it has a better mechanistic
+basis for batch experiments with constant incubation conditions. Also,
+it shows the lowest AIC and BIC values in the first set of fits when
+combined with the two-component error model. Therefore, the DFOP model
+was selected for further refinements of the fits with the aim to make
+the model fully identifiable.</p>
+<div class="section level3">
+<h3 id="parameter-identifiability-based-on-the-fisher-information-matrix">Parameter identifiability based on the Fisher Information
+Matrix<a class="anchor" aria-label="anchor" href="#parameter-identifiability-based-on-the-fisher-information-matrix"></a>
+</h3>
+<p>Using the <code>illparms</code> function, ill-defined statistical
+model parameters such as standard deviations of the degradation
+parameters in the population and error model parameters can be
+found.</p>
+<div class="sourceCode" id="cb9"><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">f_saem</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><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="left">const</th>
+<th align="left">tc</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">SFO</td>
+<td align="left"></td>
+<td align="left">b.1</td>
+</tr>
+<tr class="even">
+<td align="left">FOMC</td>
+<td align="left"></td>
+<td align="left">sd(DMTA_0)</td>
+</tr>
+<tr class="odd">
+<td align="left">DFOP</td>
+<td align="left">sd(k2)</td>
+<td align="left">sd(k2)</td>
+</tr>
+<tr class="even">
+<td align="left">HS</td>
+<td align="left"></td>
+<td align="left">sd(tb)</td>
+</tr>
+</tbody>
+</table>
+<p>According to the <code>illparms</code> function, the fitted standard
+deviation of the second kinetic rate constant <code>k2</code> is
+ill-defined in both DFOP fits. This suggests that different values would
+be obtained for this standard deviation when using different starting
+values.</p>
+<p>The thus identified overparameterisation is addressed by removing the
+random effect for <code>k2</code> from the parameter model.</p>
+<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">f_saem_dfop_tc_no_ranef_k2</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">f_saem</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span>,</span>
+<span>  no_random_effect <span class="op">=</span> <span class="st">"k2"</span><span class="op">)</span></span></code></pre></div>
+<p>For the resulting fit, it is checked whether there are still
+ill-defined parameters,</p>
+<div class="sourceCode" id="cb11"><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">f_saem_dfop_tc_no_ranef_k2</span><span class="op">)</span></span></code></pre></div>
+<p>which is not the case. Below, the refined model is compared with the
+previous best model. The model without random effect for <code>k2</code>
+is a reduced version of the previous model. Therefore, the models are
+nested and can be compared using the likelihood ratio test. This is
+achieved with the argument <code>test = TRUE</code> to the
+<code>anova</code> function.</p>
+<div class="sourceCode" id="cb12"><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</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span>, <span class="va">f_saem_dfop_tc_no_ranef_k2</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</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>format.args <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>digits <span class="op">=</span> <span class="fl">4</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<colgroup>
+<col width="38%">
+<col width="7%">
+<col width="8%">
+<col width="8%">
+<col width="9%">
+<col width="8%">
+<col width="4%">
+<col width="15%">
+</colgroup>
+<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>
+<th align="right">Chisq</th>
+<th align="right">Df</th>
+<th align="right">Pr(&gt;Chisq)</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">f_saem_dfop_tc_no_ranef_k2</td>
+<td align="right">9</td>
+<td align="right">663.7</td>
+<td align="right">661.8</td>
+<td align="right">-322.9</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+</tr>
+<tr class="even">
+<td align="left">f_saem[[“DFOP”, “tc”]]</td>
+<td align="right">10</td>
+<td align="right">665.7</td>
+<td align="right">663.6</td>
+<td align="right">-322.9</td>
+<td align="right">0</td>
+<td align="right">1</td>
+<td align="right">1</td>
+</tr>
+</tbody>
+</table>
+<p>The AIC and BIC criteria are lower after removal of the ill-defined
+random effect for <code>k2</code>. The p value of the likelihood ratio
+test is much greater than 0.05, indicating that the model with the
+higher likelihood (here the model with random effects for all
+degradation parameters <code>f_saem[["DFOP", "tc"]]</code>) does not fit
+significantly better than the model with the lower likelihood (the
+reduced model <code>f_saem_dfop_tc_no_ranef_k2</code>).</p>
+<p>Therefore, AIC, BIC and likelihood ratio test suggest the use of the
+reduced model.</p>
+<p>The convergence of the fit is checked visually.</p>
+<div class="figure" style="text-align: center">
+<img src="2022_dmta_parent_files/figure-html/convergence-saem-dfop-tc-no-ranef-k2-1.png" alt="Convergence plot for the NLHM DFOP fit with two-component error and without a random effect on 'k2'" width="864"><p class="caption">
+Convergence plot for the NLHM DFOP fit with two-component error and
+without a random effect on ‘k2’
+</p>
+</div>
+<p>All parameters appear to have converged to a satisfactory degree. The
+final fit is plotted using the plot method from the mkin package.</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_saem_dfop_tc_no_ranef_k2</span><span class="op">)</span></span></code></pre></div>
+<div class="figure" style="text-align: center">
+<img src="2022_dmta_parent_files/figure-html/plot-saem-dfop-tc-no-ranef-k2-1.png" alt="Plot of the final NLHM DFOP fit" width="864"><p class="caption">
+Plot of the final NLHM DFOP fit
+</p>
+</div>
+<p>Finally, a summary report of the fit is produced.</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">f_saem_dfop_tc_no_ranef_k2</span><span class="op">)</span></span></code></pre></div>
+<pre><code>saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 08:13:19 2025 
+Date of summary: Fri Feb 14 08:13:19 2025 
+
+Equations:
+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
+
+Model predictions using solution type analytical 
+
+Fitted in 4.154 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+  DMTA_0       k1       k2        g 
+98.71186  0.08675  0.01374  0.93491 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 k1 k2 g
+DMTA_0  98.71  0  0 0
+k1       0.00  1  0 0
+k2       0.00  0  1 0
+g        0.00  0  0 1
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+    AIC   BIC logLik
+  663.7 661.8 -322.9
+
+Optimised parameters:
+               est.     lower     upper
+DMTA_0    98.256267 96.286112 100.22642
+k1         0.064037  0.033281   0.09479
+k2         0.008469  0.006002   0.01094
+g          0.954167  0.914460   0.99387
+a.1        1.061795  0.878608   1.24498
+b.1        0.029550  0.022593   0.03651
+SD.DMTA_0  2.068581  0.427178   3.70998
+SD.k1      0.598285  0.258235   0.93833
+SD.g       1.016689  0.360061   1.67332
+
+Correlation: 
+   DMTA_0  k1      k2     
+k1  0.0213                
+k2  0.0541  0.0344        
+g  -0.0521 -0.0286 -0.2744
+
+Random effects:
+            est.  lower  upper
+SD.DMTA_0 2.0686 0.4272 3.7100
+SD.k1     0.5983 0.2582 0.9383
+SD.g      1.0167 0.3601 1.6733
+
+Variance model:
+       est.   lower   upper
+a.1 1.06180 0.87861 1.24498
+b.1 0.02955 0.02259 0.03651
+
+Estimated disappearance times:
+      DT50  DT90 DT50back DT50_k1 DT50_k2
+DMTA 11.45 41.32    12.44   10.82   81.85</code></pre>
+</div>
+<div class="section level3">
+<h3 id="alternative-check-of-parameter-identifiability">Alternative check of parameter identifiability<a class="anchor" aria-label="anchor" href="#alternative-check-of-parameter-identifiability"></a>
+</h3>
+<p>The parameter check used in the <code>illparms</code> function is
+based on a quadratic approximation of the likelihood surface near its
+optimum, which is calculated using the Fisher Information Matrix (FIM).
+An alternative way to check parameter identifiability <span class="citation">(Duchesne et al. 2021)</span> based on a multistart
+approach has recently been implemented in mkin.</p>
+<p>The graph below shows boxplots of the parameters obtained in 50 runs
+of the saem algorithm with different parameter combinations, sampled
+from the range of the parameters obtained for the individual datasets
+fitted separately using nonlinear regression.</p>
+<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">f_saem_dfop_tc_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</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span>, n <span class="op">=</span> <span class="fl">50</span>, cores <span class="op">=</span> <span class="fl">15</span><span class="op">)</span></span></code></pre></div>
+<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/par.html" class="external-link">par</a></span><span class="op">(</span>mar <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">6.1</span>, <span class="fl">4.1</span>, <span class="fl">2.1</span>, <span class="fl">2.1</span><span class="op">)</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_dfop_tc_multi</span>, lpos <span class="op">=</span> <span class="st">"bottomright"</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">0.3</span>, <span class="fl">10</span><span class="op">)</span>, las <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div>
+<div class="figure" style="text-align: center">
+<img src="2022_dmta_parent_files/figure-html/multistart-full-par-1.png" alt="Scaled parameters from the multistart runs, full model" width="960"><p class="caption">
+Scaled parameters from the multistart runs, full model
+</p>
+</div>
+<p>The graph clearly confirms the lack of identifiability of the
+variance of <code>k2</code> in the full model. The overparameterisation
+of the model also indicates a lack of identifiability of the variance of
+parameter <code>g</code>.</p>
+<p>The parameter boxplots of the multistart runs with the reduced model
+shown below indicate that all runs give similar results, regardless of
+the starting parameters.</p>
+<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">f_saem_dfop_tc_no_ranef_k2_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_dfop_tc_no_ranef_k2</span>,</span>
+<span>  n <span class="op">=</span> <span class="fl">50</span>, cores <span class="op">=</span> <span class="fl">15</span><span class="op">)</span></span></code></pre></div>
+<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/par.html" class="external-link">par</a></span><span class="op">(</span>mar <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">6.1</span>, <span class="fl">4.1</span>, <span class="fl">2.1</span>, <span class="fl">2.1</span><span class="op">)</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_dfop_tc_no_ranef_k2_multi</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>, las <span class="op">=</span> <span class="fl">2</span>,</span>
+<span>  lpos <span class="op">=</span> <span class="st">"bottomright"</span><span class="op">)</span></span></code></pre></div>
+<div class="figure" style="text-align: center">
+<img src="2022_dmta_parent_files/figure-html/multistart-reduced-par-1.png" alt="Scaled parameters from the multistart runs, reduced model" width="960"><p class="caption">
+Scaled parameters from the multistart runs, reduced model
+</p>
+</div>
+<p>When only the parameters of the top 25% of the fits are shown (based
+on a feature introduced in mkin 1.2.2 currently under development), the
+scatter is even less as shown below.</p>
+<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/par.html" class="external-link">par</a></span><span class="op">(</span>mar <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">6.1</span>, <span class="fl">4.1</span>, <span class="fl">2.1</span>, <span class="fl">2.1</span><span class="op">)</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_dfop_tc_no_ranef_k2_multi</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>, las <span class="op">=</span> <span class="fl">2</span>, llquant <span class="op">=</span> <span class="fl">0.25</span>,</span>
+<span>  lpos <span class="op">=</span> <span class="st">"bottomright"</span><span class="op">)</span></span></code></pre></div>
+<div class="figure" style="text-align: center">
+<img src="2022_dmta_parent_files/figure-html/multistart-reduced-par-llquant-1.png" alt="Scaled parameters from the multistart runs, reduced model, fits with the top 25\% likelihood values" width="960"><p class="caption">
+Scaled parameters from the multistart runs, reduced model, fits with the
+top 25% likelihood values
+</p>
+</div>
+</div>
+</div>
+<div class="section level2">
+<h2 id="conclusions">Conclusions<a class="anchor" aria-label="anchor" href="#conclusions"></a>
+</h2>
+<p>Fitting the four parent degradation models SFO, FOMC, DFOP and HS as
+part of hierarchical model fits with two different error models and
+normal distributions of the transformed degradation parameters works
+without technical problems. The biphasic models DFOP and HS gave the
+best fit to the data, but the default parameter distribution model was
+not fully identifiable. Removing the random effect for the second
+kinetic rate constant of the DFOP model resulted in a reduced model that
+was fully identifiable and showed the lowest values for the model
+selection criteria AIC and BIC. The reliability of the identification of
+all model parameters was confirmed using multiple starting values.</p>
+</div>
+<div class="section level2">
+<h2 id="acknowledgements">Acknowledgements<a class="anchor" aria-label="anchor" href="#acknowledgements"></a>
+</h2>
+<p>The helpful comments by Janina Wöltjen of the German Environment
+Agency are gratefully acknowledged.</p>
+</div>
+<div class="section level2">
+<h2 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-duchesne_2021" class="csl-entry">
+Duchesne, Ronan, Anissa Guillemin, Olivier Gandrillon, and Fabien
+Crauste. 2021. <span>“Practical Identifiability in the Frame of
+Nonlinear Mixed Effects Models: The Example of the in Vitro
+Erythropoiesis.”</span> <em>BMC Bioinformatics</em> 22 (478). <a href="https://doi.org/10.1186/s12859-021-04373-4" class="external-link">https://doi.org/10.1186/s12859-021-04373-4</a>.
+</div>
+</div>
+</div>
+<div class="section level2">
+<h2 id="appendix">Appendix<a class="anchor" aria-label="anchor" href="#appendix"></a>
+</h2>
+<div class="section level3">
+<h3 id="hierarchical-model-fit-listings">Hierarchical model fit listings<a class="anchor" aria-label="anchor" href="#hierarchical-model-fit-listings"></a>
+</h3>
+<caption>
+Hierarchical mkin fit of the SFO model with error model const
+</caption>
+<pre><code>
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 08:13:11 2025 
+Date of summary: Fri Feb 14 08:14:22 2025 
+
+Equations:
+d_DMTA/dt = - k_DMTA * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical 
+
+Fitted in 0.869 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+ DMTA_0  k_DMTA 
+97.2953  0.0566 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 k_DMTA
+DMTA_0   97.3      0
+k_DMTA    0.0      1
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+    AIC   BIC logLik
+  796.3 795.3 -393.2
+
+Optimised parameters:
+              est.    lower   upper
+DMTA_0    97.28130 95.71113 98.8515
+k_DMTA     0.05665  0.02909  0.0842
+a.1        2.66442  2.35579  2.9731
+SD.DMTA_0  1.54776  0.15447  2.9411
+SD.k_DMTA  0.60690  0.26248  0.9513
+
+Correlation: 
+       DMTA_0
+k_DMTA 0.0168
+
+Random effects:
+            est.  lower  upper
+SD.DMTA_0 1.5478 0.1545 2.9411
+SD.k_DMTA 0.6069 0.2625 0.9513
+
+Variance model:
+     est. lower upper
+a.1 2.664 2.356 2.973
+
+Estimated disappearance times:
+      DT50  DT90
+DMTA 12.24 40.65
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical mkin fit of the SFO model with error model tc
+</caption>
+<pre><code>
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 08:13:13 2025 
+Date of summary: Fri Feb 14 08:14:22 2025 
+
+Equations:
+d_DMTA/dt = - k_DMTA * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical 
+
+Fitted in 2.423 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+  DMTA_0   k_DMTA 
+96.99175  0.05603 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 k_DMTA
+DMTA_0  96.99      0
+k_DMTA   0.00      1
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+    AIC   BIC logLik
+  798.3 797.1 -393.2
+
+Optimised parameters:
+               est.    lower    upper
+DMTA_0    97.271822 95.70316 98.84049
+k_DMTA     0.056638  0.02911  0.08417
+a.1        2.660081  2.27492  3.04525
+b.1        0.001665 -0.14451  0.14784
+SD.DMTA_0  1.545520  0.14301  2.94803
+SD.k_DMTA  0.606422  0.26227  0.95057
+
+Correlation: 
+       DMTA_0
+k_DMTA 0.0169
+
+Random effects:
+            est.  lower  upper
+SD.DMTA_0 1.5455 0.1430 2.9480
+SD.k_DMTA 0.6064 0.2623 0.9506
+
+Variance model:
+        est.   lower  upper
+a.1 2.660081  2.2749 3.0452
+b.1 0.001665 -0.1445 0.1478
+
+Estimated disappearance times:
+      DT50  DT90
+DMTA 12.24 40.65
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical mkin fit of the FOMC model with error model const
+</caption>
+<pre><code>
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 08:13:11 2025 
+Date of summary: Fri Feb 14 08:14:22 2025 
+
+Equations:
+d_DMTA/dt = - (alpha/beta) * 1/((time/beta) + 1) * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical 
+
+Fitted in 1.228 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+ DMTA_0   alpha    beta 
+ 98.292   9.909 156.341 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 alpha beta
+DMTA_0  98.29     0    0
+alpha    0.00     1    0
+beta     0.00     0    1
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+    AIC   BIC logLik
+  734.2 732.7 -360.1
+
+Optimised parameters:
+              est.   lower   upper
+DMTA_0     98.3435 96.9033  99.784
+alpha       7.2007  2.5889  11.812
+beta      112.8745 34.8816 190.867
+a.1         2.0459  1.8054   2.286
+SD.DMTA_0   1.4795  0.2717   2.687
+SD.alpha    0.6396  0.1509   1.128
+SD.beta     0.6874  0.1587   1.216
+
+Correlation: 
+      DMTA_0  alpha  
+alpha -0.1125        
+beta  -0.1227  0.3632
+
+Random effects:
+            est.  lower upper
+SD.DMTA_0 1.4795 0.2717 2.687
+SD.alpha  0.6396 0.1509 1.128
+SD.beta   0.6874 0.1587 1.216
+
+Variance model:
+     est. lower upper
+a.1 2.046 1.805 2.286
+
+Estimated disappearance times:
+      DT50  DT90 DT50back
+DMTA 11.41 42.53     12.8
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical mkin fit of the FOMC model with error model tc
+</caption>
+<pre><code>
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 08:13:13 2025 
+Date of summary: Fri Feb 14 08:14:22 2025 
+
+Equations:
+d_DMTA/dt = - (alpha/beta) * 1/((time/beta) + 1) * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical 
+
+Fitted in 2.87 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+DMTA_0  alpha   beta 
+98.772  4.663 92.597 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 alpha beta
+DMTA_0  98.77     0    0
+alpha    0.00     1    0
+beta     0.00     0    1
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+    AIC   BIC logLik
+  720.7 719.1 -352.4
+
+Optimised parameters:
+              est.    lower     upper
+DMTA_0    99.10577 97.33296 100.87859
+alpha      5.46260  2.52199   8.40321
+beta      81.66080 30.46664 132.85497
+a.1        1.50219  1.25801   1.74636
+b.1        0.02893  0.02048   0.03739
+SD.DMTA_0  1.61887 -0.03843   3.27618
+SD.alpha   0.58145  0.17364   0.98925
+SD.beta    0.68205  0.21108   1.15302
+
+Correlation: 
+      DMTA_0  alpha  
+alpha -0.1321        
+beta  -0.1430  0.2467
+
+Random effects:
+            est.    lower  upper
+SD.DMTA_0 1.6189 -0.03843 3.2762
+SD.alpha  0.5814  0.17364 0.9892
+SD.beta   0.6821  0.21108 1.1530
+
+Variance model:
+       est.   lower   upper
+a.1 1.50219 1.25801 1.74636
+b.1 0.02893 0.02048 0.03739
+
+Estimated disappearance times:
+      DT50  DT90 DT50back
+DMTA 11.05 42.81    12.89
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical mkin fit of the DFOP model with error model const
+</caption>
+<pre><code>
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 08:13:12 2025 
+Date of summary: Fri Feb 14 08:14:22 2025 
+
+Equations:
+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
+
+Model predictions using solution type analytical 
+
+Fitted in 1.843 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+  DMTA_0       k1       k2        g 
+98.64383  0.09211  0.02999  0.76814 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 k1 k2 g
+DMTA_0  98.64  0  0 0
+k1       0.00  1  0 0
+k2       0.00  0  1 0
+g        0.00  0  0 1
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+    AIC BIC logLik
+  711.8 710 -346.9
+
+Optimised parameters:
+               est.     lower    upper
+DMTA_0    98.092481 96.573899 99.61106
+k1         0.062499  0.030336  0.09466
+k2         0.009065 -0.005133  0.02326
+g          0.948967  0.862080  1.03586
+a.1        1.821671  1.604774  2.03857
+SD.DMTA_0  1.677785  0.472066  2.88350
+SD.k1      0.634962  0.270788  0.99914
+SD.k2      1.033498 -0.205994  2.27299
+SD.g       1.710046  0.428642  2.99145
+
+Correlation: 
+   DMTA_0  k1      k2     
+k1  0.0246                
+k2  0.0491  0.0953        
+g  -0.0552 -0.0889 -0.4795
+
+Random effects:
+           est.   lower  upper
+SD.DMTA_0 1.678  0.4721 2.8835
+SD.k1     0.635  0.2708 0.9991
+SD.k2     1.033 -0.2060 2.2730
+SD.g      1.710  0.4286 2.9914
+
+Variance model:
+     est. lower upper
+a.1 1.822 1.605 2.039
+
+Estimated disappearance times:
+      DT50 DT90 DT50back DT50_k1 DT50_k2
+DMTA 11.79 42.8    12.88   11.09   76.46
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical mkin fit of the DFOP model with error model tc
+</caption>
+<pre><code>
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 08:13:14 2025 
+Date of summary: Fri Feb 14 08:14:22 2025 
+
+Equations:
+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
+
+Model predictions using solution type analytical 
+
+Fitted in 3.469 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+  DMTA_0       k1       k2        g 
+98.71186  0.08675  0.01374  0.93491 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 k1 k2 g
+DMTA_0  98.71  0  0 0
+k1       0.00  1  0 0
+k2       0.00  0  1 0
+g        0.00  0  0 1
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+    AIC   BIC logLik
+  665.7 663.6 -322.9
+
+Optimised parameters:
+               est.     lower     upper
+DMTA_0    98.347470 96.380815 100.31413
+k1         0.064524  0.034279   0.09477
+k2         0.008304  0.005843   0.01076
+g          0.952128  0.909578   0.99468
+a.1        1.068907  0.883665   1.25415
+b.1        0.029265  0.022318   0.03621
+SD.DMTA_0  2.065796  0.427951   3.70364
+SD.k1      0.583703  0.251796   0.91561
+SD.k2      0.004167 -7.831228   7.83956
+SD.g       1.064450  0.397479   1.73142
+
+Correlation: 
+   DMTA_0  k1      k2     
+k1  0.0223                
+k2  0.0568  0.0394        
+g  -0.0464 -0.0269 -0.2713
+
+Random effects:
+              est.   lower  upper
+SD.DMTA_0 2.065796  0.4280 3.7036
+SD.k1     0.583703  0.2518 0.9156
+SD.k2     0.004167 -7.8312 7.8396
+SD.g      1.064450  0.3975 1.7314
+
+Variance model:
+       est.   lower   upper
+a.1 1.06891 0.88367 1.25415
+b.1 0.02927 0.02232 0.03621
+
+Estimated disappearance times:
+      DT50  DT90 DT50back DT50_k1 DT50_k2
+DMTA 11.39 41.36    12.45   10.74   83.48
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical mkin fit of the HS model with error model const
+</caption>
+<pre><code>
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 08:13:12 2025 
+Date of summary: Fri Feb 14 08:14:22 2025 
+
+Equations:
+d_DMTA/dt = - ifelse(time &lt;= tb, k1, k2) * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical 
+
+Fitted in 1.698 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+  DMTA_0       k1       k2       tb 
+97.82176  0.06931  0.02997 11.13945 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 k1 k2 tb
+DMTA_0  97.82  0  0  0
+k1       0.00  1  0  0
+k2       0.00  0  1  0
+tb       0.00  0  0  1
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+  AIC   BIC logLik
+  714 712.1   -348
+
+Optimised parameters:
+              est.    lower    upper
+DMTA_0    98.16102 96.47747 99.84456
+k1         0.07876  0.05261  0.10491
+k2         0.02227  0.01706  0.02747
+tb        13.99089 -7.40049 35.38228
+a.1        1.82305  1.60700  2.03910
+SD.DMTA_0  1.88413  0.56204  3.20622
+SD.k1      0.34292  0.10482  0.58102
+SD.k2      0.19851  0.01718  0.37985
+SD.tb      1.68168  0.58064  2.78272
+
+Correlation: 
+   DMTA_0  k1      k2     
+k1  0.0142                
+k2  0.0001 -0.0025        
+tb  0.0165 -0.1256 -0.0301
+
+Random effects:
+            est.   lower  upper
+SD.DMTA_0 1.8841 0.56204 3.2062
+SD.k1     0.3429 0.10482 0.5810
+SD.k2     0.1985 0.01718 0.3798
+SD.tb     1.6817 0.58064 2.7827
+
+Variance model:
+     est. lower upper
+a.1 1.823 1.607 2.039
+
+Estimated disappearance times:
+      DT50  DT90 DT50back DT50_k1 DT50_k2
+DMTA 8.801 67.91    20.44   8.801   31.13
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical mkin fit of the HS model with error model tc
+</caption>
+<pre><code>
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 08:13:13 2025 
+Date of summary: Fri Feb 14 08:14:22 2025 
+
+Equations:
+d_DMTA/dt = - ifelse(time &lt;= tb, k1, k2) * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical 
+
+Fitted in 3.307 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+  DMTA_0       k1       k2       tb 
+98.45190  0.07525  0.02576 19.19375 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 k1 k2 tb
+DMTA_0  98.45  0  0  0
+k1       0.00  1  0  0
+k2       0.00  0  1  0
+tb       0.00  0  0  1
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+    AIC BIC logLik
+  667.1 665 -323.6
+
+Optimised parameters:
+              est.    lower    upper
+DMTA_0    97.76571 95.81350 99.71791
+k1         0.05855  0.03080  0.08630
+k2         0.02337  0.01664  0.03010
+tb        31.09638 29.38289 32.80987
+a.1        1.08835  0.90059  1.27611
+b.1        0.02964  0.02261  0.03667
+SD.DMTA_0  2.04877  0.42553  3.67200
+SD.k1      0.59166  0.25621  0.92711
+SD.k2      0.30698  0.09561  0.51835
+SD.tb      0.01274 -0.10915  0.13464
+
+Correlation: 
+   DMTA_0  k1      k2     
+k1  0.0160                
+k2 -0.0070 -0.0024        
+tb -0.0668 -0.0103 -0.2013
+
+Random effects:
+             est.    lower  upper
+SD.DMTA_0 2.04877  0.42553 3.6720
+SD.k1     0.59166  0.25621 0.9271
+SD.k2     0.30698  0.09561 0.5183
+SD.tb     0.01274 -0.10915 0.1346
+
+Variance model:
+       est.   lower   upper
+a.1 1.08835 0.90059 1.27611
+b.1 0.02964 0.02261 0.03667
+
+Estimated disappearance times:
+      DT50  DT90 DT50back DT50_k1 DT50_k2
+DMTA 11.84 51.71    15.57   11.84   29.66
+
+</code></pre>
+<p></p>
+</div>
+<div class="section level3">
+<h3 id="hierarchical-model-convergence-plots">Hierarchical model convergence plots<a class="anchor" aria-label="anchor" href="#hierarchical-model-convergence-plots"></a>
+</h3>
+<div class="figure" style="text-align: center">
+<img src="2022_dmta_parent_files/figure-html/convergence-saem-sfo-const-1.png" alt="Convergence plot for the NLHM SFO fit with constant variance" width="864"><p class="caption">
+Convergence plot for the NLHM SFO fit with constant variance
+</p>
+</div>
+<div class="figure" style="text-align: center">
+<img src="2022_dmta_parent_files/figure-html/convergence-saem-sfo-tc-1.png" alt="Convergence plot for the NLHM SFO fit with two-component error" width="864"><p class="caption">
+Convergence plot for the NLHM SFO fit with two-component error
+</p>
+</div>
+<div class="figure" style="text-align: center">
+<img src="2022_dmta_parent_files/figure-html/convergence-saem-fomc-const-1.png" alt="Convergence plot for the NLHM FOMC fit with constant variance" width="864"><p class="caption">
+Convergence plot for the NLHM FOMC fit with constant variance
+</p>
+</div>
+<div class="figure" style="text-align: center">
+<img src="2022_dmta_parent_files/figure-html/convergence-saem-fomc-tc-1.png" alt="Convergence plot for the NLHM FOMC fit with two-component error" width="864"><p class="caption">
+Convergence plot for the NLHM FOMC fit with two-component error
+</p>
+</div>
+<div class="figure" style="text-align: center">
+<img src="2022_dmta_parent_files/figure-html/convergence-saem-dfop-const-1.png" alt="Convergence plot for the NLHM DFOP fit with constant variance" width="864"><p class="caption">
+Convergence plot for the NLHM DFOP fit with constant variance
+</p>
+</div>
+<div class="figure" style="text-align: center">
+<img src="2022_dmta_parent_files/figure-html/convergence-saem-dfop-tc-1.png" alt="Convergence plot for the NLHM DFOP fit with two-component error" width="864"><p class="caption">
+Convergence plot for the NLHM DFOP fit with two-component error
+</p>
+</div>
+<div class="figure" style="text-align: center">
+<img src="2022_dmta_parent_files/figure-html/convergence-saem-hs-const-1.png" alt="Convergence plot for the NLHM HS fit with constant variance" width="864"><p class="caption">
+Convergence plot for the NLHM HS fit with constant variance
+</p>
+</div>
+<div class="figure" style="text-align: center">
+<img src="2022_dmta_parent_files/figure-html/convergence-saem-hs-tc-1.png" alt="Convergence plot for the NLHM HS fit with two-component error" width="864"><p class="caption">
+Convergence plot for the NLHM HS fit with two-component error
+</p>
+</div>
+</div>
+<div class="section level3">
+<h3 id="session-info">Session info<a class="anchor" aria-label="anchor" href="#session-info"></a>
+</h3>
+<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=de_DE.UTF-8        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] parallel  stats     graphics  grDevices utils     datasets  methods  
+[8] base     
+
+other attached packages:
+[1] rmarkdown_2.29  nvimcom_0.9-167 saemix_3.3      npde_3.5       
+[5] knitr_1.49      mkin_1.2.10    
+
+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  gridExtra_2.3     jquerylib_0.1.4   systemfonts_1.1.0
+ [9] scales_1.3.0      textshaping_0.4.1 yaml_2.3.10       fastmap_1.2.0    
+[13] lattice_0.22-6    ggplot2_3.5.1     R6_2.5.1          generics_0.1.3   
+[17] lmtest_0.9-40     MASS_7.3-61       htmlwidgets_1.6.4 tibble_3.2.1     
+[21] desc_1.4.3        munsell_0.5.1     bslib_0.8.0       pillar_1.9.0     
+[25] rlang_1.1.4       utf8_1.2.4        cachem_1.1.0      xfun_0.49        
+[29] fs_1.6.5          sass_0.4.9        cli_3.6.3         pkgdown_2.1.1    
+[33] magrittr_2.0.3    digest_0.6.37     grid_4.4.2        mclust_6.1.1     
+[37] lifecycle_1.0.4   nlme_3.1-166      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  pkgconfig_2.0.3   tools_4.4.2      
+[49] htmltools_0.5.8.1</code></pre>
+</div>
+<div class="section level3">
+<h3 id="hardware-info">Hardware info<a class="anchor" aria-label="anchor" href="#hardware-info"></a>
+</h3>
+<pre><code>CPU model: AMD Ryzen 9 7950X 16-Core Processor</code></pre>
+<pre><code>MemTotal:       64927788 kB</code></pre>
+</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>
+</div>
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+
+      <h1>Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</h1>
+                        <h4 data-toc-skip class="author">Johannes
+Ranke</h4>
+            
+            <h4 data-toc-skip class="date">Last change on 20 April 2023,
+last compiled on 14 Februar 2025</h4>
+      
+      <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/prebuilt/2022_dmta_pathway.rmd" class="external-link"><code>vignettes/prebuilt/2022_dmta_pathway.rmd</code></a></small>
+      <div class="d-none name"><code>2022_dmta_pathway.rmd</code></div>
+    </div>
+
+    
+    
+<div class="section level2">
+<h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#introduction"></a>
+</h2>
+<p>The purpose of this document is to test demonstrate how nonlinear
+hierarchical models (NLHM) based on the parent degradation models SFO,
+FOMC, DFOP and HS, with parallel formation of two or more metabolites
+can be fitted with the mkin package.</p>
+<p>It was assembled in the course of work package 1.2 of Project Number
+173340 (Application of nonlinear hierarchical models to the kinetic
+evaluation of chemical degradation data) of the German Environment
+Agency carried out in 2022 and 2023.</p>
+<p>The mkin package is used in version 1.2.10, which is currently under
+development. It contains the test data, and the functions used in the
+evaluations. The <code>saemix</code> package is used as a backend for
+fitting the NLHM, but is also loaded to make the convergence plot
+function available.</p>
+<p>This document is processed with the <code>knitr</code> package, which
+also provides the <code>kable</code> function that is used to improve
+the display of tabular data in R markdown documents. For parallel
+processing, the <code>parallel</code> package is used.</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="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://yihui.org/knitr/" class="external-link">knitr</a></span><span class="op">)</span></span>
+<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="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">parallel</span><span class="op">)</span></span>
+<span><span class="va">n_cores</span> <span class="op">&lt;-</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>
+<span></span>
+<span><span class="co"># We need to start a new cluster after defining a compiled model that is</span></span>
+<span><span class="co"># saved as a DLL to the user directory, therefore we define a function</span></span>
+<span><span class="co"># This is used again after defining the pathway model</span></span>
+<span><span class="va">start_cluster</span> <span class="op">&lt;-</span> <span class="kw">function</span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span> <span class="op">{</span></span>
+<span>  <span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/Sys.info.html" class="external-link">Sys.info</a></span><span class="op">(</span><span class="op">)</span><span class="op">[</span><span class="st">"sysname"</span><span class="op">]</span> <span class="op">==</span> <span class="st">"Windows"</span><span class="op">)</span> <span class="op">{</span></span>
+<span>    <span class="va">ret</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makePSOCKcluster</a></span><span class="op">(</span><span class="va">n_cores</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">ret</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makeForkCluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span>
+<span>  <span class="op">}</span></span>
+<span>  <span class="kw"><a href="https://rdrr.io/r/base/function.html" class="external-link">return</a></span><span class="op">(</span><span class="va">ret</span><span class="op">)</span></span>
+<span><span class="op">}</span></span></code></pre></div>
+</div>
+<div class="section level2">
+<h2 id="data">Data<a class="anchor" aria-label="anchor" href="#data"></a>
+</h2>
+<p>The test data are available in the mkin package as an object of class
+<code>mkindsg</code> (mkin dataset group) under the identifier
+<code>dimethenamid_2018</code>. The following preprocessing steps are
+done in this document.</p>
+<ul>
+<li>The data available for the enantiomer dimethenamid-P (DMTAP) are
+renamed to have the same substance name as the data for the racemic
+mixture dimethenamid (DMTA). The reason for this is that no difference
+between their degradation behaviour was identified in the EU risk
+assessment.</li>
+<li>Unnecessary columns are discarded</li>
+<li>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 that are independent of temperature</li>
+<li>Finally, datasets observed in the same soil (<code>Elliot 1</code>
+and <code>Elliot 2</code>) are combined, resulting in dimethenamid
+(DMTA) data from six soils.</li>
+</ul>
+<p>The following commented R code performs this preprocessing.</p>
+<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="co"># Apply a function to each of the seven datasets in the mkindsg object to create a list</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 class="co"># Get a dataset</span></span>
+<span>  <span class="va">ds_i</span><span class="op">[</span><span class="va">ds_i</span><span class="op">$</span><span class="va">name</span> <span class="op">==</span> <span class="st">"DMTAP"</span>, <span class="st">"name"</span><span class="op">]</span> <span class="op">&lt;-</span>  <span class="st">"DMTA"</span>              <span class="co"># Rename DMTAP to DMTA</span></span>
+<span>  <span class="va">ds_i</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/subset.html" class="external-link">subset</a></span><span class="op">(</span><span class="va">ds_i</span>, select <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"name"</span>, <span class="st">"time"</span>, <span class="st">"value"</span><span class="op">)</span><span class="op">)</span> <span class="co"># Select data</span></span>
+<span>  <span class="va">ds_i</span><span class="op">$</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 class="co"># Normalise time</span></span>
+<span>  <span class="va">ds_i</span>                                                       <span class="co"># Return the dataset</span></span>
+<span><span class="op">}</span><span class="op">)</span></span>
+<span></span>
+<span><span class="co"># Use dataset titles as names for the list elements</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>
+<span><span class="co"># Combine data for Elliot soil to obtain a named list with six elements</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 class="co">#</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>
+<p>The following tables show the 6 datasets.</p>
+<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="kw">for</span> <span class="op">(</span><span class="va">ds_name</span> <span class="kw">in</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">)</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>
+<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="fu"><a href="../../reference/mkin_long_to_wide.html">mkin_long_to_wide</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">[[</span><span class="va">ds_name</span><span class="op">]</span><span class="op">]</span><span class="op">)</span>,</span>
+<span>      caption <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">"Dataset"</span>, <span class="va">ds_name</span><span class="op">)</span>,</span>
+<span>      booktabs <span class="op">=</span> <span class="cn">TRUE</span>, row.names <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">)</span></span>
+<span>    <span class="fu"><a href="https://rdrr.io/r/base/cat.html" class="external-link">cat</a></span><span class="op">(</span><span class="st">"\n\\clearpage\n"</span><span class="op">)</span></span>
+<span><span class="op">}</span></span></code></pre></div>
+<table class="table">
+<caption>Dataset Calke</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">DMTA</th>
+<th align="right">M23</th>
+<th align="right">M27</th>
+<th align="right">M31</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0</td>
+<td align="right">95.8</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+</tr>
+<tr class="even">
+<td align="right">0</td>
+<td align="right">98.7</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+</tr>
+<tr class="odd">
+<td align="right">14</td>
+<td align="right">60.5</td>
+<td align="right">4.1</td>
+<td align="right">1.5</td>
+<td align="right">2.0</td>
+</tr>
+<tr class="even">
+<td align="right">30</td>
+<td align="right">39.1</td>
+<td align="right">5.3</td>
+<td align="right">2.4</td>
+<td align="right">2.1</td>
+</tr>
+<tr class="odd">
+<td align="right">59</td>
+<td align="right">15.2</td>
+<td align="right">6.0</td>
+<td align="right">3.2</td>
+<td align="right">2.2</td>
+</tr>
+<tr class="even">
+<td align="right">120</td>
+<td align="right">4.8</td>
+<td align="right">4.3</td>
+<td align="right">3.8</td>
+<td align="right">1.8</td>
+</tr>
+<tr class="odd">
+<td align="right">120</td>
+<td align="right">4.6</td>
+<td align="right">4.1</td>
+<td align="right">3.7</td>
+<td align="right">2.1</td>
+</tr>
+</tbody>
+</table>
+<table class="table">
+<caption>Dataset Borstel</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">DMTA</th>
+<th align="right">M23</th>
+<th align="right">M27</th>
+<th align="right">M31</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.000000</td>
+<td align="right">100.5</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+</tr>
+<tr class="even">
+<td align="right">0.000000</td>
+<td align="right">99.6</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+</tr>
+<tr class="odd">
+<td align="right">1.941295</td>
+<td align="right">91.9</td>
+<td align="right">0.4</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+</tr>
+<tr class="even">
+<td align="right">1.941295</td>
+<td align="right">91.3</td>
+<td align="right">0.5</td>
+<td align="right">0.3</td>
+<td align="right">0.1</td>
+</tr>
+<tr class="odd">
+<td align="right">6.794534</td>
+<td align="right">81.8</td>
+<td align="right">1.2</td>
+<td align="right">0.8</td>
+<td align="right">1.0</td>
+</tr>
+<tr class="even">
+<td align="right">6.794534</td>
+<td align="right">82.1</td>
+<td align="right">1.3</td>
+<td align="right">0.9</td>
+<td align="right">0.9</td>
+</tr>
+<tr class="odd">
+<td align="right">13.589067</td>
+<td align="right">69.1</td>
+<td align="right">2.8</td>
+<td align="right">1.4</td>
+<td align="right">2.0</td>
+</tr>
+<tr class="even">
+<td align="right">13.589067</td>
+<td align="right">68.0</td>
+<td align="right">2.0</td>
+<td align="right">1.4</td>
+<td align="right">2.5</td>
+</tr>
+<tr class="odd">
+<td align="right">27.178135</td>
+<td align="right">51.4</td>
+<td align="right">2.9</td>
+<td align="right">2.7</td>
+<td align="right">4.3</td>
+</tr>
+<tr class="even">
+<td align="right">27.178135</td>
+<td align="right">51.4</td>
+<td align="right">4.9</td>
+<td align="right">2.6</td>
+<td align="right">3.2</td>
+</tr>
+<tr class="odd">
+<td align="right">56.297565</td>
+<td align="right">27.6</td>
+<td align="right">12.2</td>
+<td align="right">4.4</td>
+<td align="right">4.3</td>
+</tr>
+<tr class="even">
+<td align="right">56.297565</td>
+<td align="right">26.8</td>
+<td align="right">12.2</td>
+<td align="right">4.7</td>
+<td align="right">4.8</td>
+</tr>
+<tr class="odd">
+<td align="right">86.387643</td>
+<td align="right">15.7</td>
+<td align="right">12.2</td>
+<td align="right">5.4</td>
+<td align="right">5.0</td>
+</tr>
+<tr class="even">
+<td align="right">86.387643</td>
+<td align="right">15.3</td>
+<td align="right">12.0</td>
+<td align="right">5.2</td>
+<td align="right">5.1</td>
+</tr>
+<tr class="odd">
+<td align="right">115.507073</td>
+<td align="right">7.9</td>
+<td align="right">10.4</td>
+<td align="right">5.4</td>
+<td align="right">4.3</td>
+</tr>
+<tr class="even">
+<td align="right">115.507073</td>
+<td align="right">8.1</td>
+<td align="right">11.6</td>
+<td align="right">5.4</td>
+<td align="right">4.4</td>
+</tr>
+</tbody>
+</table>
+<table class="table">
+<caption>Dataset Flaach</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">DMTA</th>
+<th align="right">M23</th>
+<th align="right">M27</th>
+<th align="right">M31</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.0000000</td>
+<td align="right">96.5</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+</tr>
+<tr class="even">
+<td align="right">0.0000000</td>
+<td align="right">96.8</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+</tr>
+<tr class="odd">
+<td align="right">0.0000000</td>
+<td align="right">97.0</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+</tr>
+<tr class="even">
+<td align="right">0.6233856</td>
+<td align="right">82.9</td>
+<td align="right">0.7</td>
+<td align="right">1.1</td>
+<td align="right">0.3</td>
+</tr>
+<tr class="odd">
+<td align="right">0.6233856</td>
+<td align="right">86.7</td>
+<td align="right">0.7</td>
+<td align="right">1.1</td>
+<td align="right">0.3</td>
+</tr>
+<tr class="even">
+<td align="right">0.6233856</td>
+<td align="right">87.4</td>
+<td align="right">0.2</td>
+<td align="right">0.3</td>
+<td align="right">0.1</td>
+</tr>
+<tr class="odd">
+<td align="right">1.8701567</td>
+<td align="right">72.8</td>
+<td align="right">2.2</td>
+<td align="right">2.6</td>
+<td align="right">0.7</td>
+</tr>
+<tr class="even">
+<td align="right">1.8701567</td>
+<td align="right">69.9</td>
+<td align="right">1.8</td>
+<td align="right">2.4</td>
+<td align="right">0.6</td>
+</tr>
+<tr class="odd">
+<td align="right">1.8701567</td>
+<td align="right">71.9</td>
+<td align="right">1.6</td>
+<td align="right">2.3</td>
+<td align="right">0.7</td>
+</tr>
+<tr class="even">
+<td align="right">4.3636989</td>
+<td align="right">51.4</td>
+<td align="right">4.1</td>
+<td align="right">5.0</td>
+<td align="right">1.3</td>
+</tr>
+<tr class="odd">
+<td align="right">4.3636989</td>
+<td align="right">52.9</td>
+<td align="right">4.2</td>
+<td align="right">5.9</td>
+<td align="right">1.2</td>
+</tr>
+<tr class="even">
+<td align="right">4.3636989</td>
+<td align="right">48.6</td>
+<td align="right">4.2</td>
+<td align="right">4.8</td>
+<td align="right">1.4</td>
+</tr>
+<tr class="odd">
+<td align="right">8.7273979</td>
+<td align="right">28.5</td>
+<td align="right">7.5</td>
+<td align="right">8.5</td>
+<td align="right">2.4</td>
+</tr>
+<tr class="even">
+<td align="right">8.7273979</td>
+<td align="right">27.3</td>
+<td align="right">7.1</td>
+<td align="right">8.5</td>
+<td align="right">2.1</td>
+</tr>
+<tr class="odd">
+<td align="right">8.7273979</td>
+<td align="right">27.5</td>
+<td align="right">7.5</td>
+<td align="right">8.3</td>
+<td align="right">2.3</td>
+</tr>
+<tr class="even">
+<td align="right">13.0910968</td>
+<td align="right">14.8</td>
+<td align="right">8.4</td>
+<td align="right">9.3</td>
+<td align="right">3.3</td>
+</tr>
+<tr class="odd">
+<td align="right">13.0910968</td>
+<td align="right">13.4</td>
+<td align="right">6.8</td>
+<td align="right">8.7</td>
+<td align="right">2.4</td>
+</tr>
+<tr class="even">
+<td align="right">13.0910968</td>
+<td align="right">14.4</td>
+<td align="right">8.0</td>
+<td align="right">9.1</td>
+<td align="right">2.6</td>
+</tr>
+<tr class="odd">
+<td align="right">17.4547957</td>
+<td align="right">7.7</td>
+<td align="right">7.2</td>
+<td align="right">8.6</td>
+<td align="right">4.0</td>
+</tr>
+<tr class="even">
+<td align="right">17.4547957</td>
+<td align="right">7.3</td>
+<td align="right">7.2</td>
+<td align="right">8.5</td>
+<td align="right">3.6</td>
+</tr>
+<tr class="odd">
+<td align="right">17.4547957</td>
+<td align="right">8.1</td>
+<td align="right">6.9</td>
+<td align="right">8.9</td>
+<td align="right">3.3</td>
+</tr>
+<tr class="even">
+<td align="right">26.1821936</td>
+<td align="right">2.0</td>
+<td align="right">4.9</td>
+<td align="right">8.1</td>
+<td align="right">2.1</td>
+</tr>
+<tr class="odd">
+<td align="right">26.1821936</td>
+<td align="right">1.5</td>
+<td align="right">4.3</td>
+<td align="right">7.7</td>
+<td align="right">1.7</td>
+</tr>
+<tr class="even">
+<td align="right">26.1821936</td>
+<td align="right">1.9</td>
+<td align="right">4.5</td>
+<td align="right">7.4</td>
+<td align="right">1.8</td>
+</tr>
+<tr class="odd">
+<td align="right">34.9095915</td>
+<td align="right">1.3</td>
+<td align="right">3.8</td>
+<td align="right">5.9</td>
+<td align="right">1.6</td>
+</tr>
+<tr class="even">
+<td align="right">34.9095915</td>
+<td align="right">1.0</td>
+<td align="right">3.1</td>
+<td align="right">6.0</td>
+<td align="right">1.6</td>
+</tr>
+<tr class="odd">
+<td align="right">34.9095915</td>
+<td align="right">1.1</td>
+<td align="right">3.1</td>
+<td align="right">5.9</td>
+<td align="right">1.4</td>
+</tr>
+<tr class="even">
+<td align="right">43.6369893</td>
+<td align="right">0.9</td>
+<td align="right">2.7</td>
+<td align="right">5.6</td>
+<td align="right">1.8</td>
+</tr>
+<tr class="odd">
+<td align="right">43.6369893</td>
+<td align="right">0.7</td>
+<td align="right">2.3</td>
+<td align="right">5.2</td>
+<td align="right">1.5</td>
+</tr>
+<tr class="even">
+<td align="right">43.6369893</td>
+<td align="right">0.7</td>
+<td align="right">2.1</td>
+<td align="right">5.6</td>
+<td align="right">1.3</td>
+</tr>
+<tr class="odd">
+<td align="right">52.3643872</td>
+<td align="right">0.6</td>
+<td align="right">1.6</td>
+<td align="right">4.3</td>
+<td align="right">1.2</td>
+</tr>
+<tr class="even">
+<td align="right">52.3643872</td>
+<td align="right">0.4</td>
+<td align="right">1.1</td>
+<td align="right">3.7</td>
+<td align="right">0.9</td>
+</tr>
+<tr class="odd">
+<td align="right">52.3643872</td>
+<td align="right">0.5</td>
+<td align="right">1.3</td>
+<td align="right">3.9</td>
+<td align="right">1.1</td>
+</tr>
+<tr class="even">
+<td align="right">74.8062674</td>
+<td align="right">0.4</td>
+<td align="right">0.4</td>
+<td align="right">2.5</td>
+<td align="right">0.5</td>
+</tr>
+<tr class="odd">
+<td align="right">74.8062674</td>
+<td align="right">0.3</td>
+<td align="right">0.4</td>
+<td align="right">2.4</td>
+<td align="right">0.5</td>
+</tr>
+<tr class="even">
+<td align="right">74.8062674</td>
+<td align="right">0.3</td>
+<td align="right">0.3</td>
+<td align="right">2.2</td>
+<td align="right">0.3</td>
+</tr>
+</tbody>
+</table>
+<table class="table">
+<caption>Dataset BBA 2.2</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">DMTA</th>
+<th align="right">M23</th>
+<th align="right">M27</th>
+<th align="right">M31</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.0000000</td>
+<td align="right">98.09</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+</tr>
+<tr class="even">
+<td align="right">0.0000000</td>
+<td align="right">98.77</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+</tr>
+<tr class="odd">
+<td align="right">0.7678922</td>
+<td align="right">93.52</td>
+<td align="right">0.36</td>
+<td align="right">0.42</td>
+<td align="right">0.36</td>
+</tr>
+<tr class="even">
+<td align="right">0.7678922</td>
+<td align="right">92.03</td>
+<td align="right">0.40</td>
+<td align="right">0.47</td>
+<td align="right">0.33</td>
+</tr>
+<tr class="odd">
+<td align="right">2.3036765</td>
+<td align="right">88.39</td>
+<td align="right">1.03</td>
+<td align="right">0.71</td>
+<td align="right">0.55</td>
+</tr>
+<tr class="even">
+<td align="right">2.3036765</td>
+<td align="right">87.18</td>
+<td align="right">1.07</td>
+<td align="right">0.82</td>
+<td align="right">0.64</td>
+</tr>
+<tr class="odd">
+<td align="right">5.3752452</td>
+<td align="right">69.38</td>
+<td align="right">3.60</td>
+<td align="right">2.19</td>
+<td align="right">1.94</td>
+</tr>
+<tr class="even">
+<td align="right">5.3752452</td>
+<td align="right">71.06</td>
+<td align="right">3.66</td>
+<td align="right">2.28</td>
+<td align="right">1.62</td>
+</tr>
+<tr class="odd">
+<td align="right">10.7504904</td>
+<td align="right">45.21</td>
+<td align="right">6.97</td>
+<td align="right">5.45</td>
+<td align="right">4.22</td>
+</tr>
+<tr class="even">
+<td align="right">10.7504904</td>
+<td align="right">46.81</td>
+<td align="right">7.22</td>
+<td align="right">5.19</td>
+<td align="right">4.37</td>
+</tr>
+<tr class="odd">
+<td align="right">16.1257355</td>
+<td align="right">30.54</td>
+<td align="right">8.65</td>
+<td align="right">8.81</td>
+<td align="right">6.31</td>
+</tr>
+<tr class="even">
+<td align="right">16.1257355</td>
+<td align="right">30.07</td>
+<td align="right">8.38</td>
+<td align="right">7.93</td>
+<td align="right">6.85</td>
+</tr>
+<tr class="odd">
+<td align="right">21.5009807</td>
+<td align="right">21.60</td>
+<td align="right">9.10</td>
+<td align="right">10.25</td>
+<td align="right">7.05</td>
+</tr>
+<tr class="even">
+<td align="right">21.5009807</td>
+<td align="right">20.41</td>
+<td align="right">8.63</td>
+<td align="right">10.77</td>
+<td align="right">6.84</td>
+</tr>
+<tr class="odd">
+<td align="right">32.2514711</td>
+<td align="right">9.10</td>
+<td align="right">7.63</td>
+<td align="right">10.89</td>
+<td align="right">6.53</td>
+</tr>
+<tr class="even">
+<td align="right">32.2514711</td>
+<td align="right">9.70</td>
+<td align="right">8.01</td>
+<td align="right">10.85</td>
+<td align="right">7.11</td>
+</tr>
+<tr class="odd">
+<td align="right">43.0019614</td>
+<td align="right">6.58</td>
+<td align="right">6.40</td>
+<td align="right">10.41</td>
+<td align="right">6.06</td>
+</tr>
+<tr class="even">
+<td align="right">43.0019614</td>
+<td align="right">6.31</td>
+<td align="right">6.35</td>
+<td align="right">10.35</td>
+<td align="right">6.05</td>
+</tr>
+<tr class="odd">
+<td align="right">53.7524518</td>
+<td align="right">3.47</td>
+<td align="right">5.35</td>
+<td align="right">9.92</td>
+<td align="right">5.50</td>
+</tr>
+<tr class="even">
+<td align="right">53.7524518</td>
+<td align="right">3.52</td>
+<td align="right">5.06</td>
+<td align="right">9.42</td>
+<td align="right">5.07</td>
+</tr>
+<tr class="odd">
+<td align="right">64.5029421</td>
+<td align="right">3.40</td>
+<td align="right">5.14</td>
+<td align="right">9.15</td>
+<td align="right">4.94</td>
+</tr>
+<tr class="even">
+<td align="right">64.5029421</td>
+<td align="right">3.67</td>
+<td align="right">5.91</td>
+<td align="right">9.25</td>
+<td align="right">4.39</td>
+</tr>
+<tr class="odd">
+<td align="right">91.3791680</td>
+<td align="right">1.62</td>
+<td align="right">3.35</td>
+<td align="right">7.14</td>
+<td align="right">3.64</td>
+</tr>
+<tr class="even">
+<td align="right">91.3791680</td>
+<td align="right">1.62</td>
+<td align="right">2.87</td>
+<td align="right">7.13</td>
+<td align="right">3.55</td>
+</tr>
+</tbody>
+</table>
+<table class="table">
+<caption>Dataset BBA 2.3</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">DMTA</th>
+<th align="right">M23</th>
+<th align="right">M27</th>
+<th align="right">M31</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.0000000</td>
+<td align="right">99.33</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+</tr>
+<tr class="even">
+<td align="right">0.0000000</td>
+<td align="right">97.44</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+</tr>
+<tr class="odd">
+<td align="right">0.6733938</td>
+<td align="right">93.73</td>
+<td align="right">0.18</td>
+<td align="right">0.50</td>
+<td align="right">0.47</td>
+</tr>
+<tr class="even">
+<td align="right">0.6733938</td>
+<td align="right">93.77</td>
+<td align="right">0.18</td>
+<td align="right">0.83</td>
+<td align="right">0.34</td>
+</tr>
+<tr class="odd">
+<td align="right">2.0201814</td>
+<td align="right">87.84</td>
+<td align="right">0.52</td>
+<td align="right">1.25</td>
+<td align="right">1.00</td>
+</tr>
+<tr class="even">
+<td align="right">2.0201814</td>
+<td align="right">89.82</td>
+<td align="right">0.43</td>
+<td align="right">1.09</td>
+<td align="right">0.89</td>
+</tr>
+<tr class="odd">
+<td align="right">4.7137565</td>
+<td align="right">71.61</td>
+<td align="right">1.19</td>
+<td align="right">3.28</td>
+<td align="right">3.58</td>
+</tr>
+<tr class="even">
+<td align="right">4.7137565</td>
+<td align="right">71.42</td>
+<td align="right">1.11</td>
+<td align="right">3.24</td>
+<td align="right">3.41</td>
+</tr>
+<tr class="odd">
+<td align="right">9.4275131</td>
+<td align="right">45.60</td>
+<td align="right">2.26</td>
+<td align="right">7.17</td>
+<td align="right">8.74</td>
+</tr>
+<tr class="even">
+<td align="right">9.4275131</td>
+<td align="right">45.42</td>
+<td align="right">1.99</td>
+<td align="right">7.91</td>
+<td align="right">8.28</td>
+</tr>
+<tr class="odd">
+<td align="right">14.1412696</td>
+<td align="right">31.12</td>
+<td align="right">2.81</td>
+<td align="right">10.15</td>
+<td align="right">9.67</td>
+</tr>
+<tr class="even">
+<td align="right">14.1412696</td>
+<td align="right">31.68</td>
+<td align="right">2.83</td>
+<td align="right">9.55</td>
+<td align="right">8.95</td>
+</tr>
+<tr class="odd">
+<td align="right">18.8550262</td>
+<td align="right">23.20</td>
+<td align="right">3.39</td>
+<td align="right">12.09</td>
+<td align="right">10.34</td>
+</tr>
+<tr class="even">
+<td align="right">18.8550262</td>
+<td align="right">24.13</td>
+<td align="right">3.56</td>
+<td align="right">11.89</td>
+<td align="right">10.00</td>
+</tr>
+<tr class="odd">
+<td align="right">28.2825393</td>
+<td align="right">9.43</td>
+<td align="right">3.49</td>
+<td align="right">13.32</td>
+<td align="right">7.89</td>
+</tr>
+<tr class="even">
+<td align="right">28.2825393</td>
+<td align="right">9.82</td>
+<td align="right">3.28</td>
+<td align="right">12.05</td>
+<td align="right">8.13</td>
+</tr>
+<tr class="odd">
+<td align="right">37.7100523</td>
+<td align="right">7.08</td>
+<td align="right">2.80</td>
+<td align="right">10.04</td>
+<td align="right">5.06</td>
+</tr>
+<tr class="even">
+<td align="right">37.7100523</td>
+<td align="right">8.64</td>
+<td align="right">2.97</td>
+<td align="right">10.78</td>
+<td align="right">5.54</td>
+</tr>
+<tr class="odd">
+<td align="right">47.1375654</td>
+<td align="right">4.41</td>
+<td align="right">2.42</td>
+<td align="right">9.32</td>
+<td align="right">3.79</td>
+</tr>
+<tr class="even">
+<td align="right">47.1375654</td>
+<td align="right">4.78</td>
+<td align="right">2.51</td>
+<td align="right">9.62</td>
+<td align="right">4.11</td>
+</tr>
+<tr class="odd">
+<td align="right">56.5650785</td>
+<td align="right">4.92</td>
+<td align="right">2.22</td>
+<td align="right">8.00</td>
+<td align="right">3.11</td>
+</tr>
+<tr class="even">
+<td align="right">56.5650785</td>
+<td align="right">5.08</td>
+<td align="right">1.95</td>
+<td align="right">8.45</td>
+<td align="right">2.98</td>
+</tr>
+<tr class="odd">
+<td align="right">80.1338612</td>
+<td align="right">2.13</td>
+<td align="right">1.28</td>
+<td align="right">5.71</td>
+<td align="right">1.78</td>
+</tr>
+<tr class="even">
+<td align="right">80.1338612</td>
+<td align="right">2.23</td>
+<td align="right">0.99</td>
+<td align="right">3.33</td>
+<td align="right">1.55</td>
+</tr>
+</tbody>
+</table>
+<table class="table">
+<caption>Dataset Elliot</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">DMTA</th>
+<th align="right">M23</th>
+<th align="right">M27</th>
+<th align="right">M31</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.000000</td>
+<td align="right">97.5</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+</tr>
+<tr class="even">
+<td align="right">0.000000</td>
+<td align="right">100.7</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+</tr>
+<tr class="odd">
+<td align="right">1.228478</td>
+<td align="right">86.4</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+</tr>
+<tr class="even">
+<td align="right">1.228478</td>
+<td align="right">88.5</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">1.5</td>
+</tr>
+<tr class="odd">
+<td align="right">3.685435</td>
+<td align="right">69.8</td>
+<td align="right">2.8</td>
+<td align="right">2.3</td>
+<td align="right">5.0</td>
+</tr>
+<tr class="even">
+<td align="right">3.685435</td>
+<td align="right">77.1</td>
+<td align="right">1.7</td>
+<td align="right">2.1</td>
+<td align="right">2.4</td>
+</tr>
+<tr class="odd">
+<td align="right">8.599349</td>
+<td align="right">59.0</td>
+<td align="right">4.3</td>
+<td align="right">4.0</td>
+<td align="right">4.3</td>
+</tr>
+<tr class="even">
+<td align="right">8.599349</td>
+<td align="right">54.2</td>
+<td align="right">5.8</td>
+<td align="right">3.4</td>
+<td align="right">5.0</td>
+</tr>
+<tr class="odd">
+<td align="right">17.198697</td>
+<td align="right">31.3</td>
+<td align="right">8.2</td>
+<td align="right">6.6</td>
+<td align="right">8.0</td>
+</tr>
+<tr class="even">
+<td align="right">17.198697</td>
+<td align="right">33.5</td>
+<td align="right">5.2</td>
+<td align="right">6.9</td>
+<td align="right">7.7</td>
+</tr>
+<tr class="odd">
+<td align="right">25.798046</td>
+<td align="right">19.6</td>
+<td align="right">5.1</td>
+<td align="right">8.2</td>
+<td align="right">7.8</td>
+</tr>
+<tr class="even">
+<td align="right">25.798046</td>
+<td align="right">20.9</td>
+<td align="right">6.1</td>
+<td align="right">8.8</td>
+<td align="right">6.5</td>
+</tr>
+<tr class="odd">
+<td align="right">34.397395</td>
+<td align="right">13.3</td>
+<td align="right">6.0</td>
+<td align="right">9.7</td>
+<td align="right">8.0</td>
+</tr>
+<tr class="even">
+<td align="right">34.397395</td>
+<td align="right">15.8</td>
+<td align="right">6.0</td>
+<td align="right">8.8</td>
+<td align="right">7.4</td>
+</tr>
+<tr class="odd">
+<td align="right">51.596092</td>
+<td align="right">6.7</td>
+<td align="right">5.0</td>
+<td align="right">8.3</td>
+<td align="right">6.9</td>
+</tr>
+<tr class="even">
+<td align="right">51.596092</td>
+<td align="right">8.7</td>
+<td align="right">4.2</td>
+<td align="right">9.2</td>
+<td align="right">9.0</td>
+</tr>
+<tr class="odd">
+<td align="right">68.794789</td>
+<td align="right">8.8</td>
+<td align="right">3.9</td>
+<td align="right">9.3</td>
+<td align="right">5.5</td>
+</tr>
+<tr class="even">
+<td align="right">68.794789</td>
+<td align="right">8.7</td>
+<td align="right">2.9</td>
+<td align="right">8.5</td>
+<td align="right">6.1</td>
+</tr>
+<tr class="odd">
+<td align="right">103.192184</td>
+<td align="right">6.0</td>
+<td align="right">1.9</td>
+<td align="right">8.6</td>
+<td align="right">6.1</td>
+</tr>
+<tr class="even">
+<td align="right">103.192184</td>
+<td align="right">4.4</td>
+<td align="right">1.5</td>
+<td align="right">6.0</td>
+<td align="right">4.0</td>
+</tr>
+<tr class="odd">
+<td align="right">146.188928</td>
+<td align="right">3.3</td>
+<td align="right">2.0</td>
+<td align="right">5.6</td>
+<td align="right">3.1</td>
+</tr>
+<tr class="even">
+<td align="right">146.188928</td>
+<td align="right">2.8</td>
+<td align="right">2.3</td>
+<td align="right">4.5</td>
+<td align="right">2.9</td>
+</tr>
+<tr class="odd">
+<td align="right">223.583066</td>
+<td align="right">1.4</td>
+<td align="right">1.2</td>
+<td align="right">4.1</td>
+<td align="right">1.8</td>
+</tr>
+<tr class="even">
+<td align="right">223.583066</td>
+<td align="right">1.8</td>
+<td align="right">1.9</td>
+<td align="right">3.9</td>
+<td align="right">2.6</td>
+</tr>
+<tr class="odd">
+<td align="right">0.000000</td>
+<td align="right">93.4</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+</tr>
+<tr class="even">
+<td align="right">0.000000</td>
+<td align="right">103.2</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+</tr>
+<tr class="odd">
+<td align="right">1.228478</td>
+<td align="right">89.2</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">1.3</td>
+</tr>
+<tr class="even">
+<td align="right">1.228478</td>
+<td align="right">86.6</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+<td align="right">NA</td>
+</tr>
+<tr class="odd">
+<td align="right">3.685435</td>
+<td align="right">78.2</td>
+<td align="right">2.6</td>
+<td align="right">1.0</td>
+<td align="right">3.1</td>
+</tr>
+<tr class="even">
+<td align="right">3.685435</td>
+<td align="right">78.1</td>
+<td align="right">2.4</td>
+<td align="right">2.6</td>
+<td align="right">2.3</td>
+</tr>
+<tr class="odd">
+<td align="right">8.599349</td>
+<td align="right">55.6</td>
+<td align="right">5.5</td>
+<td align="right">4.5</td>
+<td align="right">3.4</td>
+</tr>
+<tr class="even">
+<td align="right">8.599349</td>
+<td align="right">53.0</td>
+<td align="right">5.6</td>
+<td align="right">4.6</td>
+<td align="right">4.3</td>
+</tr>
+<tr class="odd">
+<td align="right">17.198697</td>
+<td align="right">33.7</td>
+<td align="right">7.3</td>
+<td align="right">7.6</td>
+<td align="right">7.8</td>
+</tr>
+<tr class="even">
+<td align="right">17.198697</td>
+<td align="right">33.2</td>
+<td align="right">6.5</td>
+<td align="right">6.7</td>
+<td align="right">8.7</td>
+</tr>
+<tr class="odd">
+<td align="right">25.798046</td>
+<td align="right">20.9</td>
+<td align="right">5.8</td>
+<td align="right">8.7</td>
+<td align="right">7.7</td>
+</tr>
+<tr class="even">
+<td align="right">25.798046</td>
+<td align="right">19.9</td>
+<td align="right">7.7</td>
+<td align="right">7.6</td>
+<td align="right">6.5</td>
+</tr>
+<tr class="odd">
+<td align="right">34.397395</td>
+<td align="right">18.2</td>
+<td align="right">7.8</td>
+<td align="right">8.0</td>
+<td align="right">6.3</td>
+</tr>
+<tr class="even">
+<td align="right">34.397395</td>
+<td align="right">12.7</td>
+<td align="right">7.3</td>
+<td align="right">8.6</td>
+<td align="right">8.7</td>
+</tr>
+<tr class="odd">
+<td align="right">51.596092</td>
+<td align="right">7.8</td>
+<td align="right">7.0</td>
+<td align="right">7.4</td>
+<td align="right">5.7</td>
+</tr>
+<tr class="even">
+<td align="right">51.596092</td>
+<td align="right">9.0</td>
+<td align="right">6.3</td>
+<td align="right">7.2</td>
+<td align="right">4.2</td>
+</tr>
+<tr class="odd">
+<td align="right">68.794789</td>
+<td align="right">11.4</td>
+<td align="right">4.3</td>
+<td align="right">10.3</td>
+<td align="right">3.2</td>
+</tr>
+<tr class="even">
+<td align="right">68.794789</td>
+<td align="right">9.0</td>
+<td align="right">3.8</td>
+<td align="right">9.4</td>
+<td align="right">4.2</td>
+</tr>
+<tr class="odd">
+<td align="right">103.192184</td>
+<td align="right">3.9</td>
+<td align="right">2.6</td>
+<td align="right">6.5</td>
+<td align="right">3.8</td>
+</tr>
+<tr class="even">
+<td align="right">103.192184</td>
+<td align="right">4.4</td>
+<td align="right">2.8</td>
+<td align="right">6.9</td>
+<td align="right">4.0</td>
+</tr>
+<tr class="odd">
+<td align="right">146.188928</td>
+<td align="right">2.6</td>
+<td align="right">1.6</td>
+<td align="right">4.6</td>
+<td align="right">4.5</td>
+</tr>
+<tr class="even">
+<td align="right">146.188928</td>
+<td align="right">3.4</td>
+<td align="right">1.1</td>
+<td align="right">4.5</td>
+<td align="right">4.5</td>
+</tr>
+<tr class="odd">
+<td align="right">223.583066</td>
+<td align="right">2.0</td>
+<td align="right">1.4</td>
+<td align="right">4.3</td>
+<td align="right">3.8</td>
+</tr>
+<tr class="even">
+<td align="right">223.583066</td>
+<td align="right">1.7</td>
+<td align="right">1.3</td>
+<td align="right">4.2</td>
+<td align="right">2.3</td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="section level2">
+<h2 id="separate-evaluations">Separate evaluations<a class="anchor" aria-label="anchor" href="#separate-evaluations"></a>
+</h2>
+<p>As a first step to obtain suitable starting parameters for the NLHM
+fits, we do separate fits of several variants of the pathway model used
+previously <span class="citation">(Ranke et al. 2021)</span>, varying
+the kinetic model for the parent compound. Because the SFORB model often
+provides faster convergence than the DFOP model, and can sometimes be
+fitted where the DFOP model results in errors, it is included in the set
+of parent models tested here.</p>
+<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="kw">if</span> <span class="op">(</span><span class="op">!</span><span class="fu"><a href="https://rdrr.io/r/base/files2.html" class="external-link">dir.exists</a></span><span class="op">(</span><span class="st">"dmta_dlls"</span><span class="op">)</span><span class="op">)</span> <span class="fu"><a href="https://rdrr.io/r/base/files2.html" class="external-link">dir.create</a></span><span class="op">(</span><span class="st">"dmta_dlls"</span><span class="op">)</span></span>
+<span><span class="va">m_sfo_path_1</span> <span class="op">&lt;-</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">"SFO"</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>
+<span>  name <span class="op">=</span> <span class="st">"m_sfo_path"</span>, dll_dir <span class="op">=</span> <span class="st">"dmta_dlls"</span>,</span>
+<span>  unload <span class="op">=</span> <span class="cn">TRUE</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span>,</span>
+<span>  quiet <span class="op">=</span> <span class="cn">TRUE</span></span>
+<span><span class="op">)</span></span>
+<span><span class="va">m_fomc_path_1</span> <span class="op">&lt;-</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">"FOMC"</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>
+<span>  name <span class="op">=</span> <span class="st">"m_fomc_path"</span>, dll_dir <span class="op">=</span> <span class="st">"dmta_dlls"</span>,</span>
+<span>  unload <span class="op">=</span> <span class="cn">TRUE</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span>,</span>
+<span>  quiet <span class="op">=</span> <span class="cn">TRUE</span></span>
+<span><span class="op">)</span></span>
+<span><span class="va">m_dfop_path_1</span> <span class="op">&lt;-</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="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>
+<span>  name <span class="op">=</span> <span class="st">"m_dfop_path"</span>, dll_dir <span class="op">=</span> <span class="st">"dmta_dlls"</span>,</span>
+<span>  unload <span class="op">=</span> <span class="cn">TRUE</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span>,</span>
+<span>  quiet <span class="op">=</span> <span class="cn">TRUE</span></span>
+<span><span class="op">)</span></span>
+<span><span class="va">m_sforb_path_1</span> <span class="op">&lt;-</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>
+<span>  name <span class="op">=</span> <span class="st">"m_sforb_path"</span>, dll_dir <span class="op">=</span> <span class="st">"dmta_dlls"</span>,</span>
+<span>  unload <span class="op">=</span> <span class="cn">TRUE</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span>,</span>
+<span>  quiet <span class="op">=</span> <span class="cn">TRUE</span></span>
+<span><span class="op">)</span></span>
+<span><span class="va">m_hs_path_1</span> <span class="op">&lt;-</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">"HS"</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>
+<span>  name <span class="op">=</span> <span class="st">"m_hs_path"</span>, dll_dir <span class="op">=</span> <span class="st">"dmta_dlls"</span>,</span>
+<span>  unload <span class="op">=</span> <span class="cn">TRUE</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span>,</span>
+<span>  quiet <span class="op">=</span> <span class="cn">TRUE</span></span>
+<span><span class="op">)</span></span>
+<span><span class="va">cl</span> <span class="op">&lt;-</span> <span class="fu">start_cluster</span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span>
+<span></span>
+<span><span class="va">deg_mods_1</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>  sfo_path_1 <span class="op">=</span> <span class="va">m_sfo_path_1</span>,</span>
+<span>  fomc_path_1 <span class="op">=</span> <span class="va">m_fomc_path_1</span>,</span>
+<span>  dfop_path_1 <span class="op">=</span> <span class="va">m_dfop_path_1</span>,</span>
+<span>  sforb_path_1 <span class="op">=</span> <span class="va">m_sforb_path_1</span>,</span>
+<span>  hs_path_1 <span class="op">=</span> <span class="va">m_hs_path_1</span><span class="op">)</span></span>
+<span></span>
+<span><span class="va">sep_1_const</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span></span>
+<span>  <span class="va">deg_mods_1</span>,</span>
+<span>  <span class="va">dmta_ds</span>,</span>
+<span>  error_model <span class="op">=</span> <span class="st">"const"</span>,</span>
+<span>  quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
+<span></span>
+<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">sep_1_const</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><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="left">Calke</th>
+<th align="left">Borstel</th>
+<th align="left">Flaach</th>
+<th align="left">BBA 2.2</th>
+<th align="left">BBA 2.3</th>
+<th align="left">Elliot</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">sfo_path_1</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">fomc_path_1</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="odd">
+<td align="left">dfop_path_1</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">sforb_path_1</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="odd">
+<td align="left">hs_path_1</td>
+<td align="left">C</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+<td align="left">C</td>
+<td align="left">C</td>
+</tr>
+</tbody>
+</table>
+<p>All separate pathway fits with SFO or FOMC for the parent and
+constant variance converged (status OK). Most fits with DFOP or SFORB
+for the parent converged as well. The fits with HS for the parent did
+not converge with default settings.</p>
+<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">sep_1_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">sep_1_const</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span>
+<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">sep_1_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><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="left">Calke</th>
+<th align="left">Borstel</th>
+<th align="left">Flaach</th>
+<th align="left">BBA 2.2</th>
+<th align="left">BBA 2.3</th>
+<th align="left">Elliot</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">sfo_path_1</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">fomc_path_1</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="odd">
+<td align="left">dfop_path_1</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">sforb_path_1</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="odd">
+<td align="left">hs_path_1</td>
+<td align="left">C</td>
+<td align="left">C</td>
+<td align="left">C</td>
+<td align="left">C</td>
+<td align="left">C</td>
+<td align="left">C</td>
+</tr>
+</tbody>
+</table>
+<p>With the two-component error model, the set of fits with convergence
+problems is slightly different, with convergence problems appearing for
+different data sets when applying the DFOP and SFORB model and some
+additional convergence problems when using the FOMC model for the
+parent.</p>
+</div>
+<div class="section level2">
+<h2 id="hierarchichal-model-fits">Hierarchichal model fits<a class="anchor" aria-label="anchor" href="#hierarchichal-model-fits"></a>
+</h2>
+<p>The following code fits two sets of the corresponding hierarchical
+models to the data, one assuming constant variance, and one assuming
+two-component error.</p>
+<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">saem_1</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mhmkin.html">mhmkin</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">sep_1_const</span>, <span class="va">sep_1_tc</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<p>The run time for these fits was around two hours on five year old
+hardware. After a recent hardware upgrade these fits complete in less
+than twenty minutes.</p>
+<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">saem_1</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><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="left">const</th>
+<th align="left">tc</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">sfo_path_1</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">fomc_path_1</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="odd">
+<td align="left">dfop_path_1</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">sforb_path_1</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="odd">
+<td align="left">hs_path_1</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+</tbody>
+</table>
+<p>According to the <code>status</code> function, all fits terminated
+successfully.</p>
+<div class="sourceCode" id="cb8"><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">saem_1</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_path_1 const</td>
+<td align="right">17</td>
+<td align="right">2291.8</td>
+<td align="right">2288.3</td>
+<td align="right">-1128.9</td>
+</tr>
+<tr class="even">
+<td align="left">sfo_path_1 tc</td>
+<td align="right">18</td>
+<td align="right">2276.4</td>
+<td align="right">2272.7</td>
+<td align="right">-1120.2</td>
+</tr>
+<tr class="odd">
+<td align="left">fomc_path_1 const</td>
+<td align="right">19</td>
+<td align="right">2095.9</td>
+<td align="right">2091.9</td>
+<td align="right">-1028.9</td>
+</tr>
+<tr class="even">
+<td align="left">fomc_path_1 tc</td>
+<td align="right">20</td>
+<td align="right">1939.0</td>
+<td align="right">1934.8</td>
+<td align="right">-949.5</td>
+</tr>
+<tr class="odd">
+<td align="left">dfop_path_1 const</td>
+<td align="right">21</td>
+<td align="right">2039.7</td>
+<td align="right">2035.3</td>
+<td align="right">-998.8</td>
+</tr>
+<tr class="even">
+<td align="left">sforb_path_1 const</td>
+<td align="right">21</td>
+<td align="right">2017.7</td>
+<td align="right">2013.4</td>
+<td align="right">-987.9</td>
+</tr>
+<tr class="odd">
+<td align="left">hs_path_1 const</td>
+<td align="right">21</td>
+<td align="right">2023.7</td>
+<td align="right">2019.3</td>
+<td align="right">-990.9</td>
+</tr>
+<tr class="even">
+<td align="left">dfop_path_1 tc</td>
+<td align="right">22</td>
+<td align="right">1881.7</td>
+<td align="right">1877.1</td>
+<td align="right">-918.9</td>
+</tr>
+<tr class="odd">
+<td align="left">sforb_path_1 tc</td>
+<td align="right">22</td>
+<td align="right">1832.7</td>
+<td align="right">1828.1</td>
+<td align="right">-894.3</td>
+</tr>
+<tr class="even">
+<td align="left">hs_path_1 tc</td>
+<td align="right">22</td>
+<td align="right">1831.6</td>
+<td align="right">1827.0</td>
+<td align="right">-893.8</td>
+</tr>
+</tbody>
+</table>
+<p>When the goodness-of-fit of the models is compared, a warning is
+obtained, indicating that the likelihood of the pathway fit with SFORB
+for the parent compound and constant variance could not be calculated
+with importance sampling (method ‘is’). As this is the default method on
+which all AIC and BIC comparisons are based, this variant is not
+included in the model comparison table. Comparing the goodness-of-fit of
+the remaining models, HS model model with two-component error provides
+the best fit. However, for batch experiments performed with constant
+conditions such as the experiments evaluated here, there is no reason to
+assume a discontinuity, so the SFORB model is preferable from a
+mechanistic viewpoint. In addition, the information criteria AIC and BIC
+are very similar for HS and SFORB. Therefore, the SFORB model is
+selected here for further refinements.</p>
+<div class="section level3">
+<h3 id="parameter-identifiability-based-on-the-fisher-information-matrix">Parameter identifiability based on the Fisher Information
+Matrix<a class="anchor" aria-label="anchor" href="#parameter-identifiability-based-on-the-fisher-information-matrix"></a>
+</h3>
+<p>Using the <code>illparms</code> function, ill-defined statistical
+model parameters such as standard deviations of the degradation
+parameters in the population and error model parameters can be
+found.</p>
+<div class="sourceCode" id="cb9"><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">saem_1</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><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="left">const</th>
+<th align="left">tc</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">sfo_path_1</td>
+<td align="left"></td>
+<td align="left">sd(DMTA_0)</td>
+</tr>
+<tr class="even">
+<td align="left">fomc_path_1</td>
+<td align="left"></td>
+<td align="left">sd(DMTA_0)</td>
+</tr>
+<tr class="odd">
+<td align="left">dfop_path_1</td>
+<td align="left"></td>
+<td align="left"></td>
+</tr>
+<tr class="even">
+<td align="left">sforb_path_1</td>
+<td align="left">sd(log_k_DMTA_bound_free)</td>
+<td align="left">sd(log_k_DMTA_bound_free)</td>
+</tr>
+<tr class="odd">
+<td align="left">hs_path_1</td>
+<td align="left"></td>
+<td align="left">sd(log_tb)</td>
+</tr>
+</tbody>
+</table>
+<p>When using constant variance, no ill-defined variance parameters are
+identified with the <code>illparms</code> function in any of the
+degradation models. When using the two-component error model, there is
+one ill-defined variance parameter in all variants except for the
+variant using DFOP for the parent compound.</p>
+<p>For the selected combination of the SFORB pathway model with
+two-component error, the random effect for the rate constant from
+reversibly bound DMTA to the free DMTA (<code>k_DMTA_bound_free</code>)
+is not well-defined. Therefore, the fit is updated without assuming a
+random effect for this parameter.</p>
+<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">saem_sforb_path_1_tc_reduced</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">saem_1</span><span class="op">[[</span><span class="st">"sforb_path_1"</span>, <span class="st">"tc"</span><span class="op">]</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>
+<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">saem_sforb_path_1_tc_reduced</span><span class="op">)</span></span></code></pre></div>
+<p>As expected, no ill-defined parameters remain. The model comparison
+below shows that the reduced model is preferable.</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/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">[[</span><span class="st">"sforb_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span>, <span class="va">saem_sforb_path_1_tc_reduced</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">saem_sforb_path_1_tc_reduced</td>
+<td align="right">21</td>
+<td align="right">1830.4</td>
+<td align="right">1826.0</td>
+<td align="right">-894.2</td>
+</tr>
+<tr class="even">
+<td align="left">saem_1[[“sforb_path_1”, “tc”]]</td>
+<td align="right">22</td>
+<td align="right">1832.7</td>
+<td align="right">1828.1</td>
+<td align="right">-894.3</td>
+</tr>
+</tbody>
+</table>
+<p>The convergence plot of the refined fit is shown below.</p>
+<div class="sourceCode" id="cb12"><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">saem_sforb_path_1_tc_reduced</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="2022_dmta_pathway_files/figure-html/saem-sforb-path-1-tc-reduced-convergence-1.png" width="700" style="display: block; margin: auto;"></p>
+<p>For some parameters, for example for <code>f_DMTA_ilr_1</code> and
+<code>f_DMTA_ilr_2</code>, i.e. for two of the parameters determining
+the formation fractions of the parallel formation of the three
+metabolites, some movement of the parameters is still visible in the
+second phase of the algorithm. However, the amplitude of this movement
+is in the range of the amplitude towards the end of the first phase.
+Therefore, it is likely that an increase in iterations would not improve
+the parameter estimates very much, and it is proposed that the fit is
+acceptable. No numeric convergence criterion is implemented in
+saemix.</p>
+</div>
+<div class="section level3">
+<h3 id="alternative-check-of-parameter-identifiability">Alternative check of parameter identifiability<a class="anchor" aria-label="anchor" href="#alternative-check-of-parameter-identifiability"></a>
+</h3>
+<p>As an alternative check of parameter identifiability <span class="citation">(Duchesne et al. 2021)</span>, multistart runs were
+performed on the basis of the refined fit shown above.</p>
+<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">saem_sforb_path_1_tc_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">saem_sforb_path_1_tc_reduced</span>,</span>
+<span>  n <span class="op">=</span> <span class="fl">32</span>, cores <span class="op">=</span> <span class="fl">10</span><span class="op">)</span></span></code></pre></div>
+<pre><code> 
+  (subscript) logical subscript too long</code></pre>
+<div class="sourceCode" id="cb15"><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">saem_sforb_path_1_tc_reduced_multi</span><span class="op">)</span></span></code></pre></div>
+<pre><code>&lt;multistart&gt; object with 32 fits:
+ E OK 
+ 7 25 
+OK: Fit terminated successfully
+E: Error</code></pre>
+<p>Out of the 32 fits that were initiated, only 17 terminated without an
+error. The reason for this is that the wide variation of starting
+parameters in combination with the parameter variation that is used in
+the SAEM algorithm leads to parameter combinations for the degradation
+model that the numerical integration routine cannot cope with. Because
+of this variation of initial parameters, some of the model fits take up
+to two times more time than the original fit.</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/graphics/par.html" class="external-link">par</a></span><span class="op">(</span>mar <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">12.1</span>, <span class="fl">4.1</span>, <span class="fl">2.1</span>, <span class="fl">2.1</span><span class="op">)</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">saem_sforb_path_1_tc_reduced_multi</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>, las <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div>
+<div class="figure" style="text-align: center">
+<img src="2022_dmta_pathway_files/figure-html/unnamed-chunk-2-1.png" alt="Parameter boxplots for the multistart runs that succeeded" width="960"><p class="caption">
+Parameter boxplots for the multistart runs that succeeded
+</p>
+</div>
+<p>However, visual analysis of the boxplot of the parameters obtained in
+the successful fits confirms that the results are sufficiently
+independent of the starting parameters, and there are no remaining
+ill-defined parameters.</p>
+</div>
+</div>
+<div class="section level2">
+<h2 id="plots-of-selected-fits">Plots of selected fits<a class="anchor" aria-label="anchor" href="#plots-of-selected-fits"></a>
+</h2>
+<p>The SFORB pathway fits with full and reduced parameter distribution
+model are shown below.</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/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">[[</span><span class="st">"sforb_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
+<div class="figure" style="text-align: center">
+<img src="2022_dmta_pathway_files/figure-html/unnamed-chunk-3-1.png" alt="SFORB pathway fit with two-component error" width="700"><p class="caption">
+SFORB pathway fit with two-component error
+</p>
+</div>
+<div class="sourceCode" id="cb19"><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">saem_sforb_path_1_tc_reduced</span><span class="op">)</span></span></code></pre></div>
+<div class="figure" style="text-align: center">
+<img src="2022_dmta_pathway_files/figure-html/unnamed-chunk-4-1.png" alt="SFORB pathway fit with two-component error, reduced parameter model" width="700"><p class="caption">
+SFORB pathway fit with two-component error, reduced parameter model
+</p>
+</div>
+<p>Plots of the remaining fits and listings for all successful fits are
+shown in the Appendix.</p>
+<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">stopCluster</a></span><span class="op">(</span><span class="va">cl</span><span class="op">)</span></span></code></pre></div>
+</div>
+<div class="section level2">
+<h2 id="conclusions">Conclusions<a class="anchor" aria-label="anchor" href="#conclusions"></a>
+</h2>
+<p>Pathway fits with SFO, FOMC, DFOP, SFORB and HS models for the parent
+compound could be successfully performed.</p>
+</div>
+<div class="section level2">
+<h2 id="acknowledgements">Acknowledgements<a class="anchor" aria-label="anchor" href="#acknowledgements"></a>
+</h2>
+<p>The helpful comments by Janina Wöltjen of the German Environment
+Agency on earlier versions of this document are gratefully
+acknowledged.</p>
+</div>
+<div class="section level2">
+<h2 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-duchesne_2021" class="csl-entry">
+Duchesne, Ronan, Anissa Guillemin, Olivier Gandrillon, and Fabien
+Crauste. 2021. <span>“Practical Identifiability in the Frame of
+Nonlinear Mixed Effects Models: The Example of the in Vitro
+Erythropoiesis.”</span> <em>BMC Bioinformatics</em> 22 (478). <a href="https://doi.org/10.1186/s12859-021-04373-4" class="external-link">https://doi.org/10.1186/s12859-021-04373-4</a>.
+</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>
+</div>
+<div class="section level2">
+<h2 id="appendix">Appendix<a class="anchor" aria-label="anchor" href="#appendix"></a>
+</h2>
+<div class="section level3">
+<h3 id="plots-of-hierarchical-fits-not-selected-for-refinement">Plots of hierarchical fits not selected for refinement<a class="anchor" aria-label="anchor" href="#plots-of-hierarchical-fits-not-selected-for-refinement"></a>
+</h3>
+<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/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">[[</span><span class="st">"sfo_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
+<div class="figure" style="text-align: center">
+<img src="2022_dmta_pathway_files/figure-html/unnamed-chunk-6-1.png" alt="SFO pathway fit with two-component error" width="700"><p class="caption">
+SFO pathway fit with two-component error
+</p>
+</div>
+<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">saem_1</span><span class="op">[[</span><span class="st">"fomc_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
+<div class="figure" style="text-align: center">
+<img src="2022_dmta_pathway_files/figure-html/unnamed-chunk-7-1.png" alt="FOMC pathway fit with two-component error" width="700"><p class="caption">
+FOMC pathway fit with two-component error
+</p>
+</div>
+<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/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">[[</span><span class="st">"sforb_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
+<div class="figure" style="text-align: center">
+<img src="2022_dmta_pathway_files/figure-html/unnamed-chunk-8-1.png" alt="HS pathway fit with two-component error" width="700"><p class="caption">
+HS pathway fit with two-component error
+</p>
+</div>
+</div>
+<div class="section level3">
+<h3 id="hierarchical-model-fit-listings">Hierarchical model fit listings<a class="anchor" aria-label="anchor" href="#hierarchical-model-fit-listings"></a>
+</h3>
+<div class="section level4">
+<h4 id="fits-with-random-effects-for-all-degradation-parameters">Fits with random effects for all degradation parameters<a class="anchor" aria-label="anchor" href="#fits-with-random-effects-for-all-degradation-parameters"></a>
+</h4>
+
+</div>
+<div class="section level4">
+<h4 id="improved-fit-of-the-sforb-pathway-model-with-two-component-error">Improved fit of the SFORB pathway model with two-component
+error<a class="anchor" aria-label="anchor" href="#improved-fit-of-the-sforb-pathway-model-with-two-component-error"></a>
+</h4>
+
+</div>
+</div>
+<div class="section level3">
+<h3 id="session-info">Session info<a class="anchor" aria-label="anchor" href="#session-info"></a>
+</h3>
+<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=de_DE.UTF-8        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] parallel  stats     graphics  grDevices utils     datasets  methods  
+[8] base     
+
+other attached packages:
+[1] rmarkdown_2.29  nvimcom_0.9-167 saemix_3.3      npde_3.5       
+[5] knitr_1.49      mkin_1.2.10    
+
+loaded via a namespace (and not attached):
+ [1] sass_0.4.9        utf8_1.2.4        generics_0.1.3    lattice_0.22-6   
+ [5] digest_0.6.37     magrittr_2.0.3    evaluate_1.0.1    grid_4.4.2       
+ [9] fastmap_1.2.0     jsonlite_1.8.9    processx_3.8.4    pkgbuild_1.4.5   
+[13] deSolve_1.40      mclust_6.1.1      ps_1.8.1          gridExtra_2.3    
+[17] fansi_1.0.6       scales_1.3.0      codetools_0.2-20  textshaping_0.4.1
+[21] jquerylib_0.1.4   cli_3.6.3         rlang_1.1.4       munsell_0.5.1    
+[25] cachem_1.1.0      yaml_2.3.10       inline_0.3.20     tools_4.4.2      
+[29] dplyr_1.1.4       colorspace_2.1-1  ggplot2_3.5.1     vctrs_0.6.5      
+[33] R6_2.5.1          zoo_1.8-12        lifecycle_1.0.4   fs_1.6.5         
+[37] htmlwidgets_1.6.4 MASS_7.3-61       ragg_1.3.3        pkgconfig_2.0.3  
+[41] desc_1.4.3        callr_3.7.6       pkgdown_2.1.1     pillar_1.9.0     
+[45] bslib_0.8.0       gtable_0.3.6      glue_1.8.0        systemfonts_1.1.0
+[49] xfun_0.49         tibble_3.2.1      lmtest_0.9-40     tidyselect_1.2.1 
+[53] htmltools_0.5.8.1 nlme_3.1-166      compiler_4.4.2   </code></pre>
+</div>
+<div class="section level3">
+<h3 id="hardware-info">Hardware info<a class="anchor" aria-label="anchor" href="#hardware-info"></a>
+</h3>
+<pre><code>CPU model: AMD Ryzen 9 7950X 16-Core Processor</code></pre>
+<pre><code>MemTotal:       64927788 kB</code></pre>
+</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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+
+      <h1>Testing covariate modelling in hierarchical parent degradation kinetics with residue data on mesotrione</h1>
+                        <h4 data-toc-skip class="author">Johannes
+Ranke</h4>
+            
+            <h4 data-toc-skip class="date">Last change on 4 August 2023,
+last compiled on 14 Februar 2025</h4>
+      
+      <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/prebuilt/2023_mesotrione_parent.rmd" class="external-link"><code>vignettes/prebuilt/2023_mesotrione_parent.rmd</code></a></small>
+      <div class="d-none name"><code>2023_mesotrione_parent.rmd</code></div>
+    </div>
+
+    
+    
+<div class="section level2">
+<h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#introduction"></a>
+</h2>
+<p>The purpose of this document is to test demonstrate how nonlinear
+hierarchical models (NLHM) based on the parent degradation models SFO,
+FOMC, DFOP and HS can be fitted with the mkin package, also considering
+the influence of covariates like soil pH on different degradation
+parameters. Because in some other case studies, the SFORB
+parameterisation of biexponential decline has shown some advantages over
+the DFOP parameterisation, SFORB was included in the list of tested
+models as well.</p>
+<p>The mkin package is used in version 1.2.10, which is contains the
+functions that were used for the evaluations. The <code>saemix</code>
+package is used as a backend for fitting the NLHM, but is also loaded to
+make the convergence plot function available.</p>
+<p>This document is processed with the <code>knitr</code> package, which
+also provides the <code>kable</code> function that is used to improve
+the display of tabular data in R markdown documents. For parallel
+processing, the <code>parallel</code> package is used.</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="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://yihui.org/knitr/" class="external-link">knitr</a></span><span class="op">)</span></span>
+<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="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">parallel</span><span class="op">)</span></span>
+<span><span class="va">n_cores</span> <span class="op">&lt;-</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>
+<span><span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/Sys.info.html" class="external-link">Sys.info</a></span><span class="op">(</span><span class="op">)</span><span class="op">[</span><span class="st">"sysname"</span><span class="op">]</span> <span class="op">==</span> <span class="st">"Windows"</span><span class="op">)</span> <span class="op">{</span></span>
+<span>  <span class="va">cl</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makePSOCKcluster</a></span><span class="op">(</span><span class="va">n_cores</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">cl</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makeForkCluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span>
+<span><span class="op">}</span></span></code></pre></div>
+<div class="section level3">
+<h3 id="test-data">Test data<a class="anchor" aria-label="anchor" href="#test-data"></a>
+</h3>
+<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">data_file</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.file.html" class="external-link">system.file</a></span><span class="op">(</span></span>
+<span>  <span class="st">"testdata"</span>, <span class="st">"mesotrione_soil_efsa_2016.xlsx"</span>, package <span class="op">=</span> <span class="st">"mkin"</span><span class="op">)</span></span>
+<span><span class="va">meso_ds</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/read_spreadsheet.html">read_spreadsheet</a></span><span class="op">(</span><span class="va">data_file</span>, parent_only <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
+<p>The following tables show the covariate data and the 18 datasets that
+were read in from the spreadsheet file.</p>
+<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">pH</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/attr.html" class="external-link">attr</a></span><span class="op">(</span><span class="va">meso_ds</span>, <span class="st">"covariates"</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">pH</span>, caption <span class="op">=</span> <span class="st">"Covariate data"</span><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<caption>Covariate data</caption>
+<thead><tr class="header">
+<th align="left"></th>
+<th align="right">pH</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">Richmond</td>
+<td align="right">6.2</td>
+</tr>
+<tr class="even">
+<td align="left">Richmond 2</td>
+<td align="right">6.2</td>
+</tr>
+<tr class="odd">
+<td align="left">ERTC</td>
+<td align="right">6.4</td>
+</tr>
+<tr class="even">
+<td align="left">Toulouse</td>
+<td align="right">7.7</td>
+</tr>
+<tr class="odd">
+<td align="left">Picket Piece</td>
+<td align="right">7.1</td>
+</tr>
+<tr class="even">
+<td align="left">721</td>
+<td align="right">5.6</td>
+</tr>
+<tr class="odd">
+<td align="left">722</td>
+<td align="right">5.7</td>
+</tr>
+<tr class="even">
+<td align="left">723</td>
+<td align="right">5.4</td>
+</tr>
+<tr class="odd">
+<td align="left">724</td>
+<td align="right">4.8</td>
+</tr>
+<tr class="even">
+<td align="left">725</td>
+<td align="right">5.8</td>
+</tr>
+<tr class="odd">
+<td align="left">727</td>
+<td align="right">5.1</td>
+</tr>
+<tr class="even">
+<td align="left">728</td>
+<td align="right">5.9</td>
+</tr>
+<tr class="odd">
+<td align="left">729</td>
+<td align="right">5.6</td>
+</tr>
+<tr class="even">
+<td align="left">730</td>
+<td align="right">5.3</td>
+</tr>
+<tr class="odd">
+<td align="left">731</td>
+<td align="right">6.1</td>
+</tr>
+<tr class="even">
+<td align="left">732</td>
+<td align="right">5.0</td>
+</tr>
+<tr class="odd">
+<td align="left">741</td>
+<td align="right">5.7</td>
+</tr>
+<tr class="even">
+<td align="left">742</td>
+<td align="right">7.2</td>
+</tr>
+</tbody>
+</table>
+<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="kw">for</span> <span class="op">(</span><span class="va">ds_name</span> <span class="kw">in</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">meso_ds</span><span class="op">)</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>
+<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="fu"><a href="../../reference/mkin_long_to_wide.html">mkin_long_to_wide</a></span><span class="op">(</span><span class="va">meso_ds</span><span class="op">[[</span><span class="va">ds_name</span><span class="op">]</span><span class="op">]</span><span class="op">)</span>,</span>
+<span>      caption <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">"Dataset"</span>, <span class="va">ds_name</span><span class="op">)</span>,</span>
+<span>      booktabs <span class="op">=</span> <span class="cn">TRUE</span>, row.names <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">)</span></span>
+<span><span class="op">}</span></span></code></pre></div>
+<table class="table">
+<caption>Dataset Richmond</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">meso</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.000000</td>
+<td align="right">91.00</td>
+</tr>
+<tr class="even">
+<td align="right">1.179050</td>
+<td align="right">86.70</td>
+</tr>
+<tr class="odd">
+<td align="right">3.537149</td>
+<td align="right">73.60</td>
+</tr>
+<tr class="even">
+<td align="right">7.074299</td>
+<td align="right">61.50</td>
+</tr>
+<tr class="odd">
+<td align="right">10.611448</td>
+<td align="right">55.70</td>
+</tr>
+<tr class="even">
+<td align="right">15.327647</td>
+<td align="right">47.70</td>
+</tr>
+<tr class="odd">
+<td align="right">17.685747</td>
+<td align="right">39.50</td>
+</tr>
+<tr class="even">
+<td align="right">24.760046</td>
+<td align="right">29.80</td>
+</tr>
+<tr class="odd">
+<td align="right">35.371494</td>
+<td align="right">19.60</td>
+</tr>
+<tr class="even">
+<td align="right">68.384889</td>
+<td align="right">5.67</td>
+</tr>
+<tr class="odd">
+<td align="right">0.000000</td>
+<td align="right">97.90</td>
+</tr>
+<tr class="even">
+<td align="right">1.179050</td>
+<td align="right">96.40</td>
+</tr>
+<tr class="odd">
+<td align="right">3.537149</td>
+<td align="right">89.10</td>
+</tr>
+<tr class="even">
+<td align="right">7.074299</td>
+<td align="right">74.40</td>
+</tr>
+<tr class="odd">
+<td align="right">10.611448</td>
+<td align="right">57.40</td>
+</tr>
+<tr class="even">
+<td align="right">15.327647</td>
+<td align="right">46.30</td>
+</tr>
+<tr class="odd">
+<td align="right">18.864797</td>
+<td align="right">35.50</td>
+</tr>
+<tr class="even">
+<td align="right">27.118146</td>
+<td align="right">27.20</td>
+</tr>
+<tr class="odd">
+<td align="right">35.371494</td>
+<td align="right">19.10</td>
+</tr>
+<tr class="even">
+<td align="right">74.280138</td>
+<td align="right">6.50</td>
+</tr>
+<tr class="odd">
+<td align="right">108.472582</td>
+<td align="right">3.40</td>
+</tr>
+<tr class="even">
+<td align="right">142.665027</td>
+<td align="right">2.20</td>
+</tr>
+</tbody>
+</table>
+<table class="table">
+<caption>Dataset Richmond 2</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">meso</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.000000</td>
+<td align="right">96.0</td>
+</tr>
+<tr class="even">
+<td align="right">2.422004</td>
+<td align="right">82.4</td>
+</tr>
+<tr class="odd">
+<td align="right">5.651343</td>
+<td align="right">71.2</td>
+</tr>
+<tr class="even">
+<td align="right">8.073348</td>
+<td align="right">53.1</td>
+</tr>
+<tr class="odd">
+<td align="right">11.302687</td>
+<td align="right">48.5</td>
+</tr>
+<tr class="even">
+<td align="right">16.954030</td>
+<td align="right">33.4</td>
+</tr>
+<tr class="odd">
+<td align="right">22.605373</td>
+<td align="right">24.2</td>
+</tr>
+<tr class="even">
+<td align="right">45.210746</td>
+<td align="right">11.9</td>
+</tr>
+</tbody>
+</table>
+<table class="table">
+<caption>Dataset ERTC</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">meso</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.000000</td>
+<td align="right">99.9</td>
+</tr>
+<tr class="even">
+<td align="right">2.755193</td>
+<td align="right">80.0</td>
+</tr>
+<tr class="odd">
+<td align="right">6.428782</td>
+<td align="right">42.1</td>
+</tr>
+<tr class="even">
+<td align="right">9.183975</td>
+<td align="right">50.1</td>
+</tr>
+<tr class="odd">
+<td align="right">12.857565</td>
+<td align="right">28.4</td>
+</tr>
+<tr class="even">
+<td align="right">19.286347</td>
+<td align="right">39.8</td>
+</tr>
+<tr class="odd">
+<td align="right">25.715130</td>
+<td align="right">29.9</td>
+</tr>
+<tr class="even">
+<td align="right">51.430259</td>
+<td align="right">2.5</td>
+</tr>
+</tbody>
+</table>
+<table class="table">
+<caption>Dataset Toulouse</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">meso</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.000000</td>
+<td align="right">96.8</td>
+</tr>
+<tr class="even">
+<td align="right">2.897983</td>
+<td align="right">63.3</td>
+</tr>
+<tr class="odd">
+<td align="right">6.761960</td>
+<td align="right">22.3</td>
+</tr>
+<tr class="even">
+<td align="right">9.659942</td>
+<td align="right">16.6</td>
+</tr>
+<tr class="odd">
+<td align="right">13.523919</td>
+<td align="right">16.1</td>
+</tr>
+<tr class="even">
+<td align="right">20.285879</td>
+<td align="right">17.2</td>
+</tr>
+<tr class="odd">
+<td align="right">27.047838</td>
+<td align="right">1.8</td>
+</tr>
+</tbody>
+</table>
+<table class="table">
+<caption>Dataset Picket Piece</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">meso</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.000000</td>
+<td align="right">102.0</td>
+</tr>
+<tr class="even">
+<td align="right">2.841195</td>
+<td align="right">73.7</td>
+</tr>
+<tr class="odd">
+<td align="right">6.629454</td>
+<td align="right">35.5</td>
+</tr>
+<tr class="even">
+<td align="right">9.470649</td>
+<td align="right">31.8</td>
+</tr>
+<tr class="odd">
+<td align="right">13.258909</td>
+<td align="right">18.0</td>
+</tr>
+<tr class="even">
+<td align="right">19.888364</td>
+<td align="right">3.7</td>
+</tr>
+</tbody>
+</table>
+<table class="table">
+<caption>Dataset 721</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">meso</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.00000</td>
+<td align="right">86.4</td>
+</tr>
+<tr class="even">
+<td align="right">11.24366</td>
+<td align="right">61.4</td>
+</tr>
+<tr class="odd">
+<td align="right">22.48733</td>
+<td align="right">49.8</td>
+</tr>
+<tr class="even">
+<td align="right">33.73099</td>
+<td align="right">41.0</td>
+</tr>
+<tr class="odd">
+<td align="right">44.97466</td>
+<td align="right">35.1</td>
+</tr>
+</tbody>
+</table>
+<table class="table">
+<caption>Dataset 722</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">meso</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.00000</td>
+<td align="right">90.3</td>
+</tr>
+<tr class="even">
+<td align="right">11.24366</td>
+<td align="right">52.1</td>
+</tr>
+<tr class="odd">
+<td align="right">22.48733</td>
+<td align="right">37.4</td>
+</tr>
+<tr class="even">
+<td align="right">33.73099</td>
+<td align="right">21.2</td>
+</tr>
+<tr class="odd">
+<td align="right">44.97466</td>
+<td align="right">14.3</td>
+</tr>
+</tbody>
+</table>
+<table class="table">
+<caption>Dataset 723</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">meso</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.00000</td>
+<td align="right">89.3</td>
+</tr>
+<tr class="even">
+<td align="right">11.24366</td>
+<td align="right">70.8</td>
+</tr>
+<tr class="odd">
+<td align="right">22.48733</td>
+<td align="right">51.1</td>
+</tr>
+<tr class="even">
+<td align="right">33.73099</td>
+<td align="right">42.7</td>
+</tr>
+<tr class="odd">
+<td align="right">44.97466</td>
+<td align="right">26.7</td>
+</tr>
+</tbody>
+</table>
+<table class="table">
+<caption>Dataset 724</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">meso</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.000000</td>
+<td align="right">89.4</td>
+</tr>
+<tr class="even">
+<td align="right">9.008208</td>
+<td align="right">65.2</td>
+</tr>
+<tr class="odd">
+<td align="right">18.016415</td>
+<td align="right">55.8</td>
+</tr>
+<tr class="even">
+<td align="right">27.024623</td>
+<td align="right">46.0</td>
+</tr>
+<tr class="odd">
+<td align="right">36.032831</td>
+<td align="right">41.7</td>
+</tr>
+</tbody>
+</table>
+<table class="table">
+<caption>Dataset 725</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">meso</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.00000</td>
+<td align="right">89.0</td>
+</tr>
+<tr class="even">
+<td align="right">10.99058</td>
+<td align="right">35.4</td>
+</tr>
+<tr class="odd">
+<td align="right">21.98116</td>
+<td align="right">18.6</td>
+</tr>
+<tr class="even">
+<td align="right">32.97174</td>
+<td align="right">11.6</td>
+</tr>
+<tr class="odd">
+<td align="right">43.96232</td>
+<td align="right">7.6</td>
+</tr>
+</tbody>
+</table>
+<table class="table">
+<caption>Dataset 727</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">meso</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.00000</td>
+<td align="right">91.3</td>
+</tr>
+<tr class="even">
+<td align="right">10.96104</td>
+<td align="right">63.2</td>
+</tr>
+<tr class="odd">
+<td align="right">21.92209</td>
+<td align="right">51.1</td>
+</tr>
+<tr class="even">
+<td align="right">32.88313</td>
+<td align="right">42.0</td>
+</tr>
+<tr class="odd">
+<td align="right">43.84417</td>
+<td align="right">40.8</td>
+</tr>
+</tbody>
+</table>
+<table class="table">
+<caption>Dataset 728</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">meso</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.00000</td>
+<td align="right">91.8</td>
+</tr>
+<tr class="even">
+<td align="right">11.24366</td>
+<td align="right">43.6</td>
+</tr>
+<tr class="odd">
+<td align="right">22.48733</td>
+<td align="right">22.0</td>
+</tr>
+<tr class="even">
+<td align="right">33.73099</td>
+<td align="right">15.9</td>
+</tr>
+<tr class="odd">
+<td align="right">44.97466</td>
+<td align="right">8.8</td>
+</tr>
+</tbody>
+</table>
+<table class="table">
+<caption>Dataset 729</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">meso</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.00000</td>
+<td align="right">91.6</td>
+</tr>
+<tr class="even">
+<td align="right">11.24366</td>
+<td align="right">60.5</td>
+</tr>
+<tr class="odd">
+<td align="right">22.48733</td>
+<td align="right">43.5</td>
+</tr>
+<tr class="even">
+<td align="right">33.73099</td>
+<td align="right">28.4</td>
+</tr>
+<tr class="odd">
+<td align="right">44.97466</td>
+<td align="right">20.5</td>
+</tr>
+</tbody>
+</table>
+<table class="table">
+<caption>Dataset 730</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">meso</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.00000</td>
+<td align="right">92.7</td>
+</tr>
+<tr class="even">
+<td align="right">11.07446</td>
+<td align="right">58.9</td>
+</tr>
+<tr class="odd">
+<td align="right">22.14893</td>
+<td align="right">44.0</td>
+</tr>
+<tr class="even">
+<td align="right">33.22339</td>
+<td align="right">46.0</td>
+</tr>
+<tr class="odd">
+<td align="right">44.29785</td>
+<td align="right">29.3</td>
+</tr>
+</tbody>
+</table>
+<table class="table">
+<caption>Dataset 731</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">meso</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.00000</td>
+<td align="right">92.1</td>
+</tr>
+<tr class="even">
+<td align="right">11.24366</td>
+<td align="right">64.4</td>
+</tr>
+<tr class="odd">
+<td align="right">22.48733</td>
+<td align="right">45.3</td>
+</tr>
+<tr class="even">
+<td align="right">33.73099</td>
+<td align="right">33.6</td>
+</tr>
+<tr class="odd">
+<td align="right">44.97466</td>
+<td align="right">23.5</td>
+</tr>
+</tbody>
+</table>
+<table class="table">
+<caption>Dataset 732</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">meso</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.00000</td>
+<td align="right">90.3</td>
+</tr>
+<tr class="even">
+<td align="right">11.24366</td>
+<td align="right">58.2</td>
+</tr>
+<tr class="odd">
+<td align="right">22.48733</td>
+<td align="right">40.1</td>
+</tr>
+<tr class="even">
+<td align="right">33.73099</td>
+<td align="right">33.1</td>
+</tr>
+<tr class="odd">
+<td align="right">44.97466</td>
+<td align="right">25.8</td>
+</tr>
+</tbody>
+</table>
+<table class="table">
+<caption>Dataset 741</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">meso</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.00000</td>
+<td align="right">90.3</td>
+</tr>
+<tr class="even">
+<td align="right">10.84712</td>
+<td align="right">68.7</td>
+</tr>
+<tr class="odd">
+<td align="right">21.69424</td>
+<td align="right">58.0</td>
+</tr>
+<tr class="even">
+<td align="right">32.54136</td>
+<td align="right">52.2</td>
+</tr>
+<tr class="odd">
+<td align="right">43.38848</td>
+<td align="right">48.0</td>
+</tr>
+</tbody>
+</table>
+<table class="table">
+<caption>Dataset 742</caption>
+<thead><tr class="header">
+<th align="right">time</th>
+<th align="right">meso</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="right">0.00000</td>
+<td align="right">92.0</td>
+</tr>
+<tr class="even">
+<td align="right">11.24366</td>
+<td align="right">60.9</td>
+</tr>
+<tr class="odd">
+<td align="right">22.48733</td>
+<td align="right">36.2</td>
+</tr>
+<tr class="even">
+<td align="right">33.73099</td>
+<td align="right">18.3</td>
+</tr>
+<tr class="odd">
+<td align="right">44.97466</td>
+<td align="right">8.7</td>
+</tr>
+</tbody>
+</table>
+</div>
+</div>
+<div class="section level2">
+<h2 id="separate-evaluations">Separate evaluations<a class="anchor" aria-label="anchor" href="#separate-evaluations"></a>
+</h2>
+<p>In order to obtain suitable starting parameters for the NLHM fits,
+separate fits of the five models to the data for each soil are generated
+using the <code>mmkin</code> function from the mkin package. In a first
+step, constant variance is assumed. Convergence is checked with the
+<code>status</code> function.</p>
+<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">deg_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">"FOMC"</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">f_sep_const</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span></span>
+<span>  <span class="va">deg_mods</span>,</span>
+<span>  <span class="va">meso_ds</span>,</span>
+<span>  error_model <span class="op">=</span> <span class="st">"const"</span>,</span>
+<span>  cluster <span class="op">=</span> <span class="va">cl</span>,</span>
+<span>  quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
+<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span>, <span class="fl">1</span><span class="op">:</span><span class="fl">5</span><span class="op">]</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><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="left">Richmond</th>
+<th align="left">Richmond 2</th>
+<th align="left">ERTC</th>
+<th align="left">Toulouse</th>
+<th align="left">Picket Piece</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">SFO</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">FOMC</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+</tr>
+<tr class="odd">
+<td align="left">DFOP</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">SFORB</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="odd">
+<td align="left">HS</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+</tbody>
+</table>
+<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span>, <span class="fl">6</span><span class="op">:</span><span class="fl">18</span><span class="op">]</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><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<colgroup>
+<col width="10%">
+<col width="6%">
+<col width="6%">
+<col width="6%">
+<col width="6%">
+<col width="6%">
+<col width="6%">
+<col width="6%">
+<col width="6%">
+<col width="6%">
+<col width="6%">
+<col width="6%">
+<col width="6%">
+<col width="6%">
+</colgroup>
+<thead><tr class="header">
+<th align="left"></th>
+<th align="left">721</th>
+<th align="left">722</th>
+<th align="left">723</th>
+<th align="left">724</th>
+<th align="left">725</th>
+<th align="left">727</th>
+<th align="left">728</th>
+<th align="left">729</th>
+<th align="left">730</th>
+<th align="left">731</th>
+<th align="left">732</th>
+<th align="left">741</th>
+<th align="left">742</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">SFO</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">FOMC</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="odd">
+<td align="left">DFOP</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">SFORB</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="odd">
+<td align="left">HS</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+</tbody>
+</table>
+<p>In the tables above, OK indicates convergence and C indicates failure
+to converge. Most separate fits with constant variance converged, with
+the exception of two FOMC fits, one SFORB fit and one HS fit.</p>
+<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">f_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">f_sep_const</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span></code></pre></div>
+<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_tc</span><span class="op">[</span>, <span class="fl">1</span><span class="op">:</span><span class="fl">5</span><span class="op">]</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><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="left">Richmond</th>
+<th align="left">Richmond 2</th>
+<th align="left">ERTC</th>
+<th align="left">Toulouse</th>
+<th align="left">Picket Piece</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">SFO</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">FOMC</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="odd">
+<td align="left">DFOP</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">SFORB</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="odd">
+<td align="left">HS</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+</tbody>
+</table>
+<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_tc</span><span class="op">[</span>, <span class="fl">6</span><span class="op">:</span><span class="fl">18</span><span class="op">]</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><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<colgroup>
+<col width="10%">
+<col width="6%">
+<col width="6%">
+<col width="6%">
+<col width="6%">
+<col width="6%">
+<col width="6%">
+<col width="6%">
+<col width="6%">
+<col width="6%">
+<col width="6%">
+<col width="6%">
+<col width="6%">
+<col width="6%">
+</colgroup>
+<thead><tr class="header">
+<th align="left"></th>
+<th align="left">721</th>
+<th align="left">722</th>
+<th align="left">723</th>
+<th align="left">724</th>
+<th align="left">725</th>
+<th align="left">727</th>
+<th align="left">728</th>
+<th align="left">729</th>
+<th align="left">730</th>
+<th align="left">731</th>
+<th align="left">732</th>
+<th align="left">741</th>
+<th align="left">742</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">SFO</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">FOMC</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+</tr>
+<tr class="odd">
+<td align="left">DFOP</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">SFORB</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+</tr>
+<tr class="odd">
+<td align="left">HS</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+</tbody>
+</table>
+<p>With the two-component error model, the set of fits that did not
+converge is larger, with convergence problems appearing for a number of
+non-SFO fits.</p>
+</div>
+<div class="section level2">
+<h2 id="hierarchical-model-fits-without-covariate-effect">Hierarchical model fits without covariate effect<a class="anchor" aria-label="anchor" href="#hierarchical-model-fits-without-covariate-effect"></a>
+</h2>
+<p>The following code fits hierarchical kinetic models for the ten
+combinations of the five different degradation models with the two
+different error models in parallel.</p>
+<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">f_saem_1</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mhmkin.html">mhmkin</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_sep_const</span>, <span class="va">f_sep_tc</span><span class="op">)</span>, cluster <span class="op">=</span> <span class="va">cl</span><span class="op">)</span></span>
+<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_saem_1</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><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="left">const</th>
+<th align="left">tc</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">SFO</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">FOMC</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="odd">
+<td align="left">DFOP</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">SFORB</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="odd">
+<td align="left">HS</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+</tbody>
+</table>
+<p>All fits terminate without errors (status OK).</p>
+<div class="sourceCode" id="cb12"><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_1</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">800.0</td>
+<td align="right">804.5</td>
+<td align="right">-395.0</td>
+</tr>
+<tr class="even">
+<td align="left">SFO tc</td>
+<td align="right">6</td>
+<td align="right">801.9</td>
+<td align="right">807.2</td>
+<td align="right">-394.9</td>
+</tr>
+<tr class="odd">
+<td align="left">FOMC const</td>
+<td align="right">7</td>
+<td align="right">787.4</td>
+<td align="right">793.6</td>
+<td align="right">-386.7</td>
+</tr>
+<tr class="even">
+<td align="left">FOMC tc</td>
+<td align="right">8</td>
+<td align="right">788.9</td>
+<td align="right">796.1</td>
+<td align="right">-386.5</td>
+</tr>
+<tr class="odd">
+<td align="left">DFOP const</td>
+<td align="right">9</td>
+<td align="right">787.6</td>
+<td align="right">795.6</td>
+<td align="right">-384.8</td>
+</tr>
+<tr class="even">
+<td align="left">SFORB const</td>
+<td align="right">9</td>
+<td align="right">787.4</td>
+<td align="right">795.4</td>
+<td align="right">-384.7</td>
+</tr>
+<tr class="odd">
+<td align="left">HS const</td>
+<td align="right">9</td>
+<td align="right">781.9</td>
+<td align="right">789.9</td>
+<td align="right">-382.0</td>
+</tr>
+<tr class="even">
+<td align="left">DFOP tc</td>
+<td align="right">10</td>
+<td align="right">787.4</td>
+<td align="right">796.3</td>
+<td align="right">-383.7</td>
+</tr>
+<tr class="odd">
+<td align="left">SFORB tc</td>
+<td align="right">10</td>
+<td align="right">795.8</td>
+<td align="right">804.7</td>
+<td align="right">-387.9</td>
+</tr>
+<tr class="even">
+<td align="left">HS tc</td>
+<td align="right">10</td>
+<td align="right">783.7</td>
+<td align="right">792.7</td>
+<td align="right">-381.9</td>
+</tr>
+</tbody>
+</table>
+<p>The model comparisons show that the fits with constant variance are
+consistently preferable to the corresponding fits with two-component
+error for these data. This is confirmed by the fact that the parameter
+<code>b.1</code> (the relative standard deviation in the fits obtained
+with the saemix package), is ill-defined in all fits.</p>
+<div class="sourceCode" id="cb13"><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">f_saem_1</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><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<colgroup>
+<col width="6%">
+<col width="44%">
+<col width="49%">
+</colgroup>
+<thead><tr class="header">
+<th align="left"></th>
+<th align="left">const</th>
+<th align="left">tc</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">SFO</td>
+<td align="left">sd(meso_0)</td>
+<td align="left">sd(meso_0), b.1</td>
+</tr>
+<tr class="even">
+<td align="left">FOMC</td>
+<td align="left">sd(meso_0), sd(log_beta)</td>
+<td align="left">sd(meso_0), sd(log_beta), b.1</td>
+</tr>
+<tr class="odd">
+<td align="left">DFOP</td>
+<td align="left">sd(meso_0), sd(log_k1)</td>
+<td align="left">sd(meso_0), sd(g_qlogis), b.1</td>
+</tr>
+<tr class="even">
+<td align="left">SFORB</td>
+<td align="left">sd(meso_free_0), sd(log_k_meso_free_bound)</td>
+<td align="left">sd(meso_free_0), sd(log_k_meso_free_bound), b.1</td>
+</tr>
+<tr class="odd">
+<td align="left">HS</td>
+<td align="left">sd(meso_0)</td>
+<td align="left">sd(meso_0), b.1</td>
+</tr>
+</tbody>
+</table>
+<p>For obtaining fits with only well-defined random effects, we update
+the set of fits, excluding random effects that were ill-defined
+according to the <code>illparms</code> function.</p>
+<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">f_saem_2</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">f_saem_1</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span><span class="op">)</span></span>
+<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_saem_2</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><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="left">const</th>
+<th align="left">tc</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">SFO</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">FOMC</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="odd">
+<td align="left">DFOP</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="even">
+<td align="left">SFORB</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+<tr class="odd">
+<td align="left">HS</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+</tr>
+</tbody>
+</table>
+<p>The updated fits terminate without errors.</p>
+<div class="sourceCode" id="cb15"><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">f_saem_2</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><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="left">const</th>
+<th align="left">tc</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">SFO</td>
+<td align="left"></td>
+<td align="left">b.1</td>
+</tr>
+<tr class="even">
+<td align="left">FOMC</td>
+<td align="left"></td>
+<td align="left">b.1</td>
+</tr>
+<tr class="odd">
+<td align="left">DFOP</td>
+<td align="left"></td>
+<td align="left">b.1</td>
+</tr>
+<tr class="even">
+<td align="left">SFORB</td>
+<td align="left"></td>
+<td align="left">b.1</td>
+</tr>
+<tr class="odd">
+<td align="left">HS</td>
+<td align="left"></td>
+<td align="left">b.1</td>
+</tr>
+</tbody>
+</table>
+<p>No ill-defined errors remain in the fits with constant variance.</p>
+</div>
+<div class="section level2">
+<h2 id="hierarchical-model-fits-with-covariate-effect">Hierarchical model fits with covariate effect<a class="anchor" aria-label="anchor" href="#hierarchical-model-fits-with-covariate-effect"></a>
+</h2>
+<p>In the following sections, hierarchical fits including a model for
+the influence of pH on selected degradation parameters are shown for all
+parent models. Constant variance is selected as the error model based on
+the fits without covariate effects. Random effects that were ill-defined
+in the fits without pH influence are excluded. A potential influence of
+the soil pH is only included for parameters with a well-defined random
+effect, because experience has shown that only for such parameters a
+significant pH effect could be found.</p>
+<div class="section level3">
+<h3 id="sfo">SFO<a class="anchor" aria-label="anchor" href="#sfo"></a>
+</h3>
+<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">sfo_pH</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_sep_const</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="st">"meso_0"</span>, covariates <span class="op">=</span> <span class="va">pH</span>,</span>
+<span>  covariate_models <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">log_k_meso</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">sfo_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</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">2</span><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="right">est.</th>
+<th align="right">lower</th>
+<th align="right">upper</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">meso_0</td>
+<td align="right">91.35</td>
+<td align="right">89.27</td>
+<td align="right">93.43</td>
+</tr>
+<tr class="even">
+<td align="left">log_k_meso</td>
+<td align="right">-6.66</td>
+<td align="right">-7.97</td>
+<td align="right">-5.35</td>
+</tr>
+<tr class="odd">
+<td align="left">beta_pH(log_k_meso)</td>
+<td align="right">0.59</td>
+<td align="right">0.37</td>
+<td align="right">0.81</td>
+</tr>
+<tr class="even">
+<td align="left">a.1</td>
+<td align="right">5.48</td>
+<td align="right">4.71</td>
+<td align="right">6.24</td>
+</tr>
+<tr class="odd">
+<td align="left">SD.log_k_meso</td>
+<td align="right">0.35</td>
+<td align="right">0.23</td>
+<td align="right">0.47</td>
+</tr>
+</tbody>
+</table>
+<p>The parameter showing the pH influence in the above table is
+<code>beta_pH(log_k_meso)</code>. Its confidence interval does not
+include zero, indicating that the influence of soil pH on the log of the
+degradation rate constant is significantly greater than zero.</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/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"SFO"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span>, <span class="va">sfo_pH</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
+<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets
+
+                           npar    AIC    BIC     Lik  Chisq Df Pr(&gt;Chisq)    
+f_saem_2[["SFO", "const"]]    4 797.56 801.12 -394.78                         
+sfo_pH                        5 783.09 787.54 -386.54 16.473  1  4.934e-05 ***
+---
+Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre>
+<p>The comparison with the SFO fit without covariate effect confirms
+that considering the soil pH improves the model, both by comparison of
+AIC and BIC and by the likelihood ratio test.</p>
+<div class="sourceCode" id="cb20"><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">sfo_pH</span><span class="op">)</span></span></code></pre></div>
+<p><img src="2023_mesotrione_parent_files/figure-html/unnamed-chunk-8-1.png" width="700" style="display: block; margin: auto;"></p>
+<p>Endpoints for a model with covariates are by default calculated for
+the median of the covariate values. This quantile can be adapted, or a
+specific covariate value can be given as shown below.</p>
+<div class="sourceCode" id="cb21"><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">sfo_pH</span><span class="op">)</span></span></code></pre></div>
+<pre><code>$covariates
+      pH
+50% 5.75
+
+$distimes
+         DT50     DT90
+meso 18.52069 61.52441</code></pre>
+<div class="sourceCode" id="cb23"><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">sfo_pH</span>, covariate_quantile <span class="op">=</span> <span class="fl">0.9</span><span class="op">)</span></span></code></pre></div>
+<pre><code>$covariates
+      pH
+90% 7.13
+
+$distimes
+         DT50     DT90
+meso 8.237019 27.36278</code></pre>
+<div class="sourceCode" id="cb25"><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">sfo_pH</span>, covariates <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>pH <span class="op">=</span> <span class="fl">7.0</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<pre><code>$covariates
+     pH
+User  7
+
+$distimes
+        DT50    DT90
+meso 8.89035 29.5331</code></pre>
+</div>
+<div class="section level3">
+<h3 id="fomc">FOMC<a class="anchor" aria-label="anchor" href="#fomc"></a>
+</h3>
+<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">fomc_pH</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_sep_const</span><span class="op">[</span><span class="st">"FOMC"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="st">"meso_0"</span>, covariates <span class="op">=</span> <span class="va">pH</span>,</span>
+<span>  covariate_models <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">log_alpha</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<div class="sourceCode" id="cb28"><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">fomc_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</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">2</span><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="right">est.</th>
+<th align="right">lower</th>
+<th align="right">upper</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">meso_0</td>
+<td align="right">92.84</td>
+<td align="right">90.75</td>
+<td align="right">94.93</td>
+</tr>
+<tr class="even">
+<td align="left">log_alpha</td>
+<td align="right">-2.21</td>
+<td align="right">-3.49</td>
+<td align="right">-0.92</td>
+</tr>
+<tr class="odd">
+<td align="left">beta_pH(log_alpha)</td>
+<td align="right">0.58</td>
+<td align="right">0.37</td>
+<td align="right">0.79</td>
+</tr>
+<tr class="even">
+<td align="left">log_beta</td>
+<td align="right">4.21</td>
+<td align="right">3.44</td>
+<td align="right">4.99</td>
+</tr>
+<tr class="odd">
+<td align="left">a.1</td>
+<td align="right">5.03</td>
+<td align="right">4.32</td>
+<td align="right">5.73</td>
+</tr>
+<tr class="even">
+<td align="left">SD.log_alpha</td>
+<td align="right">0.00</td>
+<td align="right">-23.77</td>
+<td align="right">23.78</td>
+</tr>
+<tr class="odd">
+<td align="left">SD.log_beta</td>
+<td align="right">0.37</td>
+<td align="right">0.01</td>
+<td align="right">0.74</td>
+</tr>
+</tbody>
+</table>
+<p>As in the case of SFO, the confidence interval of the slope parameter
+(here <code>beta_pH(log_alpha)</code>) quantifying the influence of soil
+pH does not include zero, and the model comparison clearly indicates
+that the model with covariate influence is preferable. However, the
+random effect for <code>alpha</code> is not well-defined any more after
+inclusion of the covariate effect (the confidence interval of
+<code>SD.log_alpha</code> includes zero).</p>
+<div class="sourceCode" id="cb29"><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">fomc_pH</span><span class="op">)</span></span></code></pre></div>
+<pre><code>[1] "sd(log_alpha)"</code></pre>
+<p>Therefore, the model is updated without this random effect, and no
+ill-defined parameters remain.</p>
+<div class="sourceCode" id="cb31"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">fomc_pH_2</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">fomc_pH</span>, no_random_effect <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">"meso_0"</span>, <span class="st">"log_alpha"</span><span class="op">)</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">fomc_pH_2</span><span class="op">)</span></span></code></pre></div>
+<div class="sourceCode" id="cb32"><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_2</span><span class="op">[[</span><span class="st">"FOMC"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span>, <span class="va">fomc_pH</span>, <span class="va">fomc_pH_2</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
+<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets
+
+                            npar    AIC    BIC     Lik  Chisq Df Pr(&gt;Chisq)    
+f_saem_2[["FOMC", "const"]]    5 783.25 787.71 -386.63                         
+fomc_pH_2                      6 767.49 772.83 -377.75 17.762  1  2.503e-05 ***
+fomc_pH                        7 770.07 776.30 -378.04  0.000  1          1    
+---
+Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre>
+<p>Model comparison indicates that including pH dependence significantly
+improves the fit, and that the reduced model with covariate influence
+results in the most preferable FOMC fit.</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">fomc_pH_2</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</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">2</span><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="right">est.</th>
+<th align="right">lower</th>
+<th align="right">upper</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">meso_0</td>
+<td align="right">93.05</td>
+<td align="right">90.98</td>
+<td align="right">95.13</td>
+</tr>
+<tr class="even">
+<td align="left">log_alpha</td>
+<td align="right">-2.91</td>
+<td align="right">-4.18</td>
+<td align="right">-1.63</td>
+</tr>
+<tr class="odd">
+<td align="left">beta_pH(log_alpha)</td>
+<td align="right">0.66</td>
+<td align="right">0.44</td>
+<td align="right">0.87</td>
+</tr>
+<tr class="even">
+<td align="left">log_beta</td>
+<td align="right">3.95</td>
+<td align="right">3.29</td>
+<td align="right">4.62</td>
+</tr>
+<tr class="odd">
+<td align="left">a.1</td>
+<td align="right">4.98</td>
+<td align="right">4.28</td>
+<td align="right">5.68</td>
+</tr>
+<tr class="even">
+<td align="left">SD.log_beta</td>
+<td align="right">0.40</td>
+<td align="right">0.26</td>
+<td align="right">0.54</td>
+</tr>
+</tbody>
+</table>
+<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/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">fomc_pH_2</span><span class="op">)</span></span></code></pre></div>
+<p><img src="2023_mesotrione_parent_files/figure-html/unnamed-chunk-14-1.png" width="700" style="display: block; margin: auto;"></p>
+<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">fomc_pH_2</span><span class="op">)</span></span></code></pre></div>
+<pre><code>$covariates
+      pH
+50% 5.75
+
+$distimes
+         DT50     DT90 DT50back
+meso 17.30248 82.91343 24.95943</code></pre>
+<div class="sourceCode" id="cb38"><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">fomc_pH_2</span>, covariates <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>pH <span class="op">=</span> <span class="fl">7</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<pre><code>$covariates
+     pH
+User  7
+
+$distimes
+         DT50     DT90 DT50back
+meso 6.986239 27.02927 8.136621</code></pre>
+</div>
+<div class="section level3">
+<h3 id="dfop">DFOP<a class="anchor" aria-label="anchor" href="#dfop"></a>
+</h3>
+<p>In the DFOP fits without covariate effects, random effects for two
+degradation parameters (<code>k2</code> and <code>g</code>) were
+identifiable.</p>
+<div class="sourceCode" id="cb40"><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">f_saem_2</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</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">2</span><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="right">est.</th>
+<th align="right">lower</th>
+<th align="right">upper</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">meso_0</td>
+<td align="right">93.61</td>
+<td align="right">91.58</td>
+<td align="right">95.63</td>
+</tr>
+<tr class="even">
+<td align="left">log_k1</td>
+<td align="right">-1.53</td>
+<td align="right">-2.27</td>
+<td align="right">-0.79</td>
+</tr>
+<tr class="odd">
+<td align="left">log_k2</td>
+<td align="right">-3.42</td>
+<td align="right">-3.73</td>
+<td align="right">-3.11</td>
+</tr>
+<tr class="even">
+<td align="left">g_qlogis</td>
+<td align="right">-1.67</td>
+<td align="right">-2.57</td>
+<td align="right">-0.77</td>
+</tr>
+<tr class="odd">
+<td align="left">a.1</td>
+<td align="right">4.74</td>
+<td align="right">4.02</td>
+<td align="right">5.45</td>
+</tr>
+<tr class="even">
+<td align="left">SD.log_k2</td>
+<td align="right">0.60</td>
+<td align="right">0.38</td>
+<td align="right">0.81</td>
+</tr>
+<tr class="odd">
+<td align="left">SD.g_qlogis</td>
+<td align="right">0.94</td>
+<td align="right">0.33</td>
+<td align="right">1.54</td>
+</tr>
+</tbody>
+</table>
+<p>A fit with pH dependent degradation parameters was obtained by
+excluding the same random effects as in the refined DFOP fit without
+covariate influence, and including covariate models for the two
+identifiable parameters <code>k2</code> and <code>g</code>.</p>
+<div class="sourceCode" id="cb41"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">dfop_pH</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_sep_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, no_random_effect <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">"meso_0"</span>, <span class="st">"log_k1"</span><span class="op">)</span>,</span>
+<span>  covariates <span class="op">=</span> <span class="va">pH</span>,</span>
+<span>  covariate_models <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">log_k2</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">g_qlogis</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<p>The corresponding parameters for the influence of soil pH are
+<code>beta_pH(log_k2)</code> for the influence of soil pH on
+<code>k2</code>, and <code>beta_pH(g_qlogis)</code> for its influence on
+<code>g</code>.</p>
+<div class="sourceCode" id="cb42"><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">dfop_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</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">2</span><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="right">est.</th>
+<th align="right">lower</th>
+<th align="right">upper</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">meso_0</td>
+<td align="right">92.84</td>
+<td align="right">90.85</td>
+<td align="right">94.84</td>
+</tr>
+<tr class="even">
+<td align="left">log_k1</td>
+<td align="right">-2.82</td>
+<td align="right">-3.09</td>
+<td align="right">-2.54</td>
+</tr>
+<tr class="odd">
+<td align="left">log_k2</td>
+<td align="right">-11.48</td>
+<td align="right">-15.32</td>
+<td align="right">-7.64</td>
+</tr>
+<tr class="even">
+<td align="left">beta_pH(log_k2)</td>
+<td align="right">1.31</td>
+<td align="right">0.69</td>
+<td align="right">1.92</td>
+</tr>
+<tr class="odd">
+<td align="left">g_qlogis</td>
+<td align="right">3.13</td>
+<td align="right">0.47</td>
+<td align="right">5.80</td>
+</tr>
+<tr class="even">
+<td align="left">beta_pH(g_qlogis)</td>
+<td align="right">-0.57</td>
+<td align="right">-1.04</td>
+<td align="right">-0.09</td>
+</tr>
+<tr class="odd">
+<td align="left">a.1</td>
+<td align="right">4.96</td>
+<td align="right">4.26</td>
+<td align="right">5.65</td>
+</tr>
+<tr class="even">
+<td align="left">SD.log_k2</td>
+<td align="right">0.76</td>
+<td align="right">0.47</td>
+<td align="right">1.05</td>
+</tr>
+<tr class="odd">
+<td align="left">SD.g_qlogis</td>
+<td align="right">0.01</td>
+<td align="right">-9.96</td>
+<td align="right">9.97</td>
+</tr>
+</tbody>
+</table>
+<div class="sourceCode" id="cb43"><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_pH</span><span class="op">)</span></span></code></pre></div>
+<pre><code>[1] "sd(g_qlogis)"</code></pre>
+<p>Confidence intervals for neither of them include zero, indicating a
+significant difference from zero. However, the random effect for
+<code>g</code> is now ill-defined. The fit is updated without this
+ill-defined random effect.</p>
+<div class="sourceCode" id="cb45"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">dfop_pH_2</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">dfop_pH</span>,</span>
+<span>  no_random_effect <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">"meso_0"</span>, <span class="st">"log_k1"</span>, <span class="st">"g_qlogis"</span><span class="op">)</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">dfop_pH_2</span><span class="op">)</span></span></code></pre></div>
+<pre><code>[1] "beta_pH(g_qlogis)"</code></pre>
+<p>Now, the slope parameter for the pH effect on <code>g</code> is
+ill-defined. Therefore, another attempt is made without the
+corresponding covariate model.</p>
+<div class="sourceCode" id="cb47"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">dfop_pH_3</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_sep_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, no_random_effect <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">"meso_0"</span>, <span class="st">"log_k1"</span><span class="op">)</span>,</span>
+<span>  covariates <span class="op">=</span> <span class="va">pH</span>,</span>
+<span>  covariate_models <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">log_k2</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</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">dfop_pH_3</span><span class="op">)</span></span></code></pre></div>
+<pre><code>[1] "sd(g_qlogis)"</code></pre>
+<p>As the random effect for <code>g</code> is again ill-defined, the fit
+is repeated without it.</p>
+<div class="sourceCode" id="cb49"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">dfop_pH_4</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">dfop_pH_3</span>, no_random_effect <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">"meso_0"</span>, <span class="st">"log_k1"</span>, <span class="st">"g_qlogis"</span><span class="op">)</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">dfop_pH_4</span><span class="op">)</span></span></code></pre></div>
+<p>While no ill-defined parameters remain, model comparison suggests
+that the previous model <code>dfop_pH_2</code> with two pH dependent
+parameters is preferable, based on information criteria as well as based
+on the likelihood ratio test.</p>
+<div class="sourceCode" id="cb50"><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_2</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span>, <span class="va">dfop_pH</span>, <span class="va">dfop_pH_2</span>, <span class="va">dfop_pH_3</span>, <span class="va">dfop_pH_4</span><span class="op">)</span></span></code></pre></div>
+<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets
+
+                            npar    AIC    BIC     Lik
+f_saem_2[["DFOP", "const"]]    7 782.94 789.18 -384.47
+dfop_pH_4                      7 767.35 773.58 -376.68
+dfop_pH_2                      8 765.14 772.26 -374.57
+dfop_pH_3                      8 769.00 776.12 -376.50
+dfop_pH                        9 769.10 777.11 -375.55</code></pre>
+<div class="sourceCode" id="cb52"><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">dfop_pH_2</span>, <span class="va">dfop_pH_4</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
+<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets
+
+          npar    AIC    BIC     Lik  Chisq Df Pr(&gt;Chisq)  
+dfop_pH_4    7 767.35 773.58 -376.68                       
+dfop_pH_2    8 765.14 772.26 -374.57 4.2153  1    0.04006 *
+---
+Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre>
+<p>When focussing on parameter identifiability using the test if the
+confidence interval includes zero, <code>dfop_pH_4</code> would still be
+the preferred model. However, it should be kept in mind that parameter
+confidence intervals are constructed using a simple linearisation of the
+likelihood. As the confidence interval of the random effect for
+<code>g</code> only marginally includes zero, it is suggested that this
+is acceptable, and that <code>dfop_pH_2</code> can be considered the
+most preferable model.</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/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">dfop_pH_2</span><span class="op">)</span></span></code></pre></div>
+<p><img src="2023_mesotrione_parent_files/figure-html/unnamed-chunk-19-1.png" width="700" style="display: block; margin: auto;"></p>
+<div class="sourceCode" id="cb55"><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">dfop_pH_2</span><span class="op">)</span></span></code></pre></div>
+<pre><code>$covariates
+      pH
+50% 5.75
+
+$distimes
+         DT50     DT90 DT50back  DT50_k1  DT50_k2
+meso 18.36876 73.51841 22.13125 4.191901 23.98672</code></pre>
+<div class="sourceCode" id="cb57"><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">dfop_pH_2</span>, covariates <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>pH <span class="op">=</span> <span class="fl">7</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<pre><code>$covariates
+     pH
+User  7
+
+$distimes
+         DT50     DT90 DT50back  DT50_k1  DT50_k2
+meso 8.346428 28.34437 8.532507 4.191901 8.753618</code></pre>
+</div>
+<div class="section level3">
+<h3 id="sforb">SFORB<a class="anchor" aria-label="anchor" href="#sforb"></a>
+</h3>
+<div class="sourceCode" id="cb59"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">sforb_pH</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_sep_const</span><span class="op">[</span><span class="st">"SFORB"</span>, <span class="op">]</span>, no_random_effect <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">"meso_free_0"</span>, <span class="st">"log_k_meso_free_bound"</span><span class="op">)</span>,</span>
+<span>  covariates <span class="op">=</span> <span class="va">pH</span>,</span>
+<span>  covariate_models <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">log_k_meso_free</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">log_k_meso_bound_free</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<div class="sourceCode" id="cb60"><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">sforb_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</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">2</span><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="right">est.</th>
+<th align="right">lower</th>
+<th align="right">upper</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">meso_free_0</td>
+<td align="right">93.42</td>
+<td align="right">91.32</td>
+<td align="right">95.52</td>
+</tr>
+<tr class="even">
+<td align="left">log_k_meso_free</td>
+<td align="right">-5.37</td>
+<td align="right">-6.94</td>
+<td align="right">-3.81</td>
+</tr>
+<tr class="odd">
+<td align="left">beta_pH(log_k_meso_free)</td>
+<td align="right">0.42</td>
+<td align="right">0.18</td>
+<td align="right">0.67</td>
+</tr>
+<tr class="even">
+<td align="left">log_k_meso_free_bound</td>
+<td align="right">-3.49</td>
+<td align="right">-4.92</td>
+<td align="right">-2.05</td>
+</tr>
+<tr class="odd">
+<td align="left">log_k_meso_bound_free</td>
+<td align="right">-9.98</td>
+<td align="right">-19.22</td>
+<td align="right">-0.74</td>
+</tr>
+<tr class="even">
+<td align="left">beta_pH(log_k_meso_bound_free)</td>
+<td align="right">1.23</td>
+<td align="right">-0.21</td>
+<td align="right">2.67</td>
+</tr>
+<tr class="odd">
+<td align="left">a.1</td>
+<td align="right">4.90</td>
+<td align="right">4.18</td>
+<td align="right">5.63</td>
+</tr>
+<tr class="even">
+<td align="left">SD.log_k_meso_free</td>
+<td align="right">0.35</td>
+<td align="right">0.23</td>
+<td align="right">0.47</td>
+</tr>
+<tr class="odd">
+<td align="left">SD.log_k_meso_bound_free</td>
+<td align="right">0.13</td>
+<td align="right">-1.95</td>
+<td align="right">2.20</td>
+</tr>
+</tbody>
+</table>
+<p>The confidence interval of
+<code>beta_pH(log_k_meso_bound_free)</code> includes zero, indicating
+that the influence of soil pH on <code>k_meso_bound_free</code> cannot
+reliably be quantified. Also, the confidence interval for the random
+effect on this parameter (<code>SD.log_k_meso_bound_free</code>)
+includes zero.</p>
+<p>Using the <code>illparms</code> function, these ill-defined
+parameters can be found more conveniently.</p>
+<div class="sourceCode" id="cb61"><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_pH</span><span class="op">)</span></span></code></pre></div>
+<pre><code>[1] "sd(log_k_meso_bound_free)"      "beta_pH(log_k_meso_bound_free)"</code></pre>
+<p>To remove the ill-defined parameters, a second variant of the SFORB
+model with pH influence is fitted. No ill-defined parameters remain.</p>
+<div class="sourceCode" id="cb63"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">sforb_pH_2</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">sforb_pH</span>,</span>
+<span>  no_random_effect <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">"meso_free_0"</span>, <span class="st">"log_k_meso_free_bound"</span>, <span class="st">"log_k_meso_bound_free"</span><span class="op">)</span>,</span>
+<span>  covariate_models <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">log_k_meso_free</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</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">sforb_pH_2</span><span class="op">)</span></span></code></pre></div>
+<p>The model comparison of the SFORB fits includes the refined model
+without covariate effect, and both versions of the SFORB fit with
+covariate effect.</p>
+<div class="sourceCode" id="cb64"><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_2</span><span class="op">[[</span><span class="st">"SFORB"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span>, <span class="va">sforb_pH</span>, <span class="va">sforb_pH_2</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
+<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets
+
+                             npar    AIC    BIC     Lik   Chisq Df Pr(&gt;Chisq)  
+f_saem_2[["SFORB", "const"]]    7 783.40 789.63 -384.70                        
+sforb_pH_2                      7 770.94 777.17 -378.47 12.4616  0             
+sforb_pH                        9 768.81 776.83 -375.41  6.1258  2    0.04675 *
+---
+Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre>
+<p>The first model including pH influence is preferable based on
+information criteria and the likelihood ratio test. However, as it is
+not fully identifiable, the second model is selected.</p>
+<div class="sourceCode" id="cb66"><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">sforb_pH_2</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</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">2</span><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="right">est.</th>
+<th align="right">lower</th>
+<th align="right">upper</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">meso_free_0</td>
+<td align="right">93.32</td>
+<td align="right">91.16</td>
+<td align="right">95.48</td>
+</tr>
+<tr class="even">
+<td align="left">log_k_meso_free</td>
+<td align="right">-6.15</td>
+<td align="right">-7.43</td>
+<td align="right">-4.86</td>
+</tr>
+<tr class="odd">
+<td align="left">beta_pH(log_k_meso_free)</td>
+<td align="right">0.54</td>
+<td align="right">0.33</td>
+<td align="right">0.75</td>
+</tr>
+<tr class="even">
+<td align="left">log_k_meso_free_bound</td>
+<td align="right">-3.80</td>
+<td align="right">-5.20</td>
+<td align="right">-2.40</td>
+</tr>
+<tr class="odd">
+<td align="left">log_k_meso_bound_free</td>
+<td align="right">-2.95</td>
+<td align="right">-4.26</td>
+<td align="right">-1.64</td>
+</tr>
+<tr class="even">
+<td align="left">a.1</td>
+<td align="right">5.08</td>
+<td align="right">4.38</td>
+<td align="right">5.79</td>
+</tr>
+<tr class="odd">
+<td align="left">SD.log_k_meso_free</td>
+<td align="right">0.33</td>
+<td align="right">0.22</td>
+<td align="right">0.45</td>
+</tr>
+</tbody>
+</table>
+<div class="sourceCode" id="cb67"><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">sforb_pH_2</span><span class="op">)</span></span></code></pre></div>
+<p><img src="2023_mesotrione_parent_files/figure-html/unnamed-chunk-25-1.png" width="700" style="display: block; margin: auto;"></p>
+<div class="sourceCode" id="cb68"><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">sforb_pH_2</span><span class="op">)</span></span></code></pre></div>
+<pre><code>$covariates
+      pH
+50% 5.75
+
+$ff
+meso_free 
+        1 
+
+$SFORB
+   meso_b1    meso_b2     meso_g 
+0.09735824 0.02631699 0.31602120 
+
+$distimes
+         DT50     DT90 DT50back DT50_meso_b1 DT50_meso_b2
+meso 16.86549 73.15824 22.02282     7.119554     26.33839</code></pre>
+<div class="sourceCode" id="cb70"><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">sforb_pH_2</span>, covariates <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>pH <span class="op">=</span> <span class="fl">7</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<pre><code>$covariates
+     pH
+User  7
+
+$ff
+meso_free 
+        1 
+
+$SFORB
+   meso_b1    meso_b2     meso_g 
+0.13315233 0.03795988 0.61186191 
+
+$distimes
+         DT50     DT90 DT50back DT50_meso_b1 DT50_meso_b2
+meso 7.932495 36.93311 11.11797     5.205671        18.26</code></pre>
+</div>
+<div class="section level3">
+<h3 id="hs">HS<a class="anchor" aria-label="anchor" href="#hs"></a>
+</h3>
+<div class="sourceCode" id="cb72"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">hs_pH</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_sep_const</span><span class="op">[</span><span class="st">"HS"</span>, <span class="op">]</span>, no_random_effect <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">"meso_0"</span><span class="op">)</span>,</span>
+<span>  covariates <span class="op">=</span> <span class="va">pH</span>,</span>
+<span>  covariate_models <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">log_k1</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">log_k2</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">log_tb</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<div class="sourceCode" id="cb73"><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">hs_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</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">2</span><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="right">est.</th>
+<th align="right">lower</th>
+<th align="right">upper</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">meso_0</td>
+<td align="right">93.33</td>
+<td align="right">91.47</td>
+<td align="right">95.19</td>
+</tr>
+<tr class="even">
+<td align="left">log_k1</td>
+<td align="right">-5.81</td>
+<td align="right">-7.27</td>
+<td align="right">-4.36</td>
+</tr>
+<tr class="odd">
+<td align="left">beta_pH(log_k1)</td>
+<td align="right">0.47</td>
+<td align="right">0.23</td>
+<td align="right">0.72</td>
+</tr>
+<tr class="even">
+<td align="left">log_k2</td>
+<td align="right">-6.80</td>
+<td align="right">-8.76</td>
+<td align="right">-4.83</td>
+</tr>
+<tr class="odd">
+<td align="left">beta_pH(log_k2)</td>
+<td align="right">0.54</td>
+<td align="right">0.21</td>
+<td align="right">0.87</td>
+</tr>
+<tr class="even">
+<td align="left">log_tb</td>
+<td align="right">3.25</td>
+<td align="right">1.25</td>
+<td align="right">5.25</td>
+</tr>
+<tr class="odd">
+<td align="left">beta_pH(log_tb)</td>
+<td align="right">-0.10</td>
+<td align="right">-0.43</td>
+<td align="right">0.23</td>
+</tr>
+<tr class="even">
+<td align="left">a.1</td>
+<td align="right">4.49</td>
+<td align="right">3.78</td>
+<td align="right">5.21</td>
+</tr>
+<tr class="odd">
+<td align="left">SD.log_k1</td>
+<td align="right">0.37</td>
+<td align="right">0.24</td>
+<td align="right">0.51</td>
+</tr>
+<tr class="even">
+<td align="left">SD.log_k2</td>
+<td align="right">0.29</td>
+<td align="right">0.10</td>
+<td align="right">0.48</td>
+</tr>
+<tr class="odd">
+<td align="left">SD.log_tb</td>
+<td align="right">0.25</td>
+<td align="right">-0.07</td>
+<td align="right">0.57</td>
+</tr>
+</tbody>
+</table>
+<div class="sourceCode" id="cb74"><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">hs_pH</span><span class="op">)</span></span></code></pre></div>
+<pre><code>[1] "sd(log_tb)"      "beta_pH(log_tb)"</code></pre>
+<p>According to the output of the <code>illparms</code> function, the
+random effect on the break time <code>tb</code> cannot reliably be
+quantified, neither can the influence of soil pH on <code>tb</code>. The
+fit is repeated without the corresponding covariate model, and no
+ill-defined parameters remain.</p>
+<div class="sourceCode" id="cb76"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">hs_pH_2</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">hs_pH</span>, covariate_models <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">log_k1</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">log_k2</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</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">hs_pH_2</span><span class="op">)</span></span></code></pre></div>
+<p>Model comparison confirms that this model is preferable to the fit
+without covariate influence, and also to the first version with
+covariate influence.</p>
+<div class="sourceCode" id="cb77"><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_2</span><span class="op">[[</span><span class="st">"HS"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span>, <span class="va">hs_pH</span>, <span class="va">hs_pH_2</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
+<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets
+
+                          npar    AIC    BIC     Lik  Chisq Df Pr(&gt;Chisq)    
+f_saem_2[["HS", "const"]]    8 780.08 787.20 -382.04                         
+hs_pH_2                     10 766.47 775.37 -373.23 17.606  2  0.0001503 ***
+hs_pH                       11 769.80 779.59 -373.90  0.000  1  1.0000000    
+---
+Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre>
+<div class="sourceCode" id="cb79"><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">hs_pH_2</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</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">2</span><span class="op">)</span></span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left"></th>
+<th align="right">est.</th>
+<th align="right">lower</th>
+<th align="right">upper</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">meso_0</td>
+<td align="right">93.33</td>
+<td align="right">91.50</td>
+<td align="right">95.15</td>
+</tr>
+<tr class="even">
+<td align="left">log_k1</td>
+<td align="right">-5.68</td>
+<td align="right">-7.09</td>
+<td align="right">-4.27</td>
+</tr>
+<tr class="odd">
+<td align="left">beta_pH(log_k1)</td>
+<td align="right">0.46</td>
+<td align="right">0.22</td>
+<td align="right">0.69</td>
+</tr>
+<tr class="even">
+<td align="left">log_k2</td>
+<td align="right">-6.61</td>
+<td align="right">-8.34</td>
+<td align="right">-4.88</td>
+</tr>
+<tr class="odd">
+<td align="left">beta_pH(log_k2)</td>
+<td align="right">0.50</td>
+<td align="right">0.21</td>
+<td align="right">0.79</td>
+</tr>
+<tr class="even">
+<td align="left">log_tb</td>
+<td align="right">2.70</td>
+<td align="right">2.33</td>
+<td align="right">3.08</td>
+</tr>
+<tr class="odd">
+<td align="left">a.1</td>
+<td align="right">4.45</td>
+<td align="right">3.74</td>
+<td align="right">5.16</td>
+</tr>
+<tr class="even">
+<td align="left">SD.log_k1</td>
+<td align="right">0.36</td>
+<td align="right">0.22</td>
+<td align="right">0.49</td>
+</tr>
+<tr class="odd">
+<td align="left">SD.log_k2</td>
+<td align="right">0.23</td>
+<td align="right">0.02</td>
+<td align="right">0.43</td>
+</tr>
+<tr class="even">
+<td align="left">SD.log_tb</td>
+<td align="right">0.55</td>
+<td align="right">0.25</td>
+<td align="right">0.85</td>
+</tr>
+</tbody>
+</table>
+<div class="sourceCode" id="cb80"><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">hs_pH_2</span><span class="op">)</span></span></code></pre></div>
+<p><img src="2023_mesotrione_parent_files/figure-html/unnamed-chunk-30-1.png" width="700" style="display: block; margin: auto;"></p>
+<div class="sourceCode" id="cb81"><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">hs_pH_2</span><span class="op">)</span></span></code></pre></div>
+<pre><code>$covariates
+      pH
+50% 5.75
+
+$distimes
+         DT50     DT90 DT50back  DT50_k1  DT50_k2
+meso 14.68725 82.45287 24.82079 14.68725 29.29299</code></pre>
+<div class="sourceCode" id="cb83"><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">hs_pH_2</span>, covariates <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>pH <span class="op">=</span> <span class="fl">7</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<pre><code>$covariates
+     pH
+User  7
+
+$distimes
+         DT50     DT90 DT50back  DT50_k1  DT50_k2
+meso 8.298536 38.85371 11.69613 8.298536 15.71561</code></pre>
+</div>
+<div class="section level3">
+<h3 id="comparison-across-parent-models">Comparison across parent models<a class="anchor" aria-label="anchor" href="#comparison-across-parent-models"></a>
+</h3>
+<p>After model reduction for all models with pH influence, they are
+compared with each other.</p>
+<div class="sourceCode" id="cb85"><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">sfo_pH</span>, <span class="va">fomc_pH_2</span>, <span class="va">dfop_pH_2</span>, <span class="va">dfop_pH_4</span>, <span class="va">sforb_pH_2</span>, <span class="va">hs_pH_2</span><span class="op">)</span></span></code></pre></div>
+<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets
+
+           npar    AIC    BIC     Lik
+sfo_pH        5 783.09 787.54 -386.54
+fomc_pH_2     6 767.49 772.83 -377.75
+dfop_pH_4     7 767.35 773.58 -376.68
+sforb_pH_2    7 770.94 777.17 -378.47
+dfop_pH_2     8 765.14 772.26 -374.57
+hs_pH_2      10 766.47 775.37 -373.23</code></pre>
+<p>The DFOP model with pH influence on <code>k2</code> and
+<code>g</code> and a random effect only on <code>k2</code> is finally
+selected as the best fit.</p>
+<p>The endpoints resulting from this model are listed below. Please
+refer to the Appendix for a detailed listing.</p>
+<div class="sourceCode" id="cb87"><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">dfop_pH_2</span><span class="op">)</span></span></code></pre></div>
+<pre><code>$covariates
+      pH
+50% 5.75
+
+$distimes
+         DT50     DT90 DT50back  DT50_k1  DT50_k2
+meso 18.36876 73.51841 22.13125 4.191901 23.98672</code></pre>
+<div class="sourceCode" id="cb89"><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">dfop_pH_2</span>, covariates <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>pH <span class="op">=</span> <span class="fl">7</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<pre><code>$covariates
+     pH
+User  7
+
+$distimes
+         DT50     DT90 DT50back  DT50_k1  DT50_k2
+meso 8.346428 28.34437 8.532507 4.191901 8.753618</code></pre>
+</div>
+</div>
+<div class="section level2">
+<h2 id="conclusions">Conclusions<a class="anchor" aria-label="anchor" href="#conclusions"></a>
+</h2>
+<p>These evaluations demonstrate that covariate effects can be included
+for all types of parent degradation models. These models can then be
+further refined to make them fully identifiable.</p>
+</div>
+<div class="section level2">
+<h2 id="appendix">Appendix<a class="anchor" aria-label="anchor" href="#appendix"></a>
+</h2>
+<div class="section level3">
+<h3 id="hierarchical-fit-listings">Hierarchical fit listings<a class="anchor" aria-label="anchor" href="#hierarchical-fit-listings"></a>
+</h3>
+<div class="section level4">
+<h4 id="fits-without-covariate-effects">Fits without covariate effects<a class="anchor" aria-label="anchor" href="#fits-without-covariate-effects"></a>
+</h4>
+
+</div>
+<div class="section level4">
+<h4 id="fits-with-covariate-effects">Fits with covariate effects<a class="anchor" aria-label="anchor" href="#fits-with-covariate-effects"></a>
+</h4>
+
+</div>
+</div>
+<div class="section level3">
+<h3 id="session-info">Session info<a class="anchor" aria-label="anchor" href="#session-info"></a>
+</h3>
+<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=de_DE.UTF-8        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] parallel  stats     graphics  grDevices utils     datasets  methods  
+[8] base     
+
+other attached packages:
+[1] rmarkdown_2.29  nvimcom_0.9-167 saemix_3.3      npde_3.5       
+[5] knitr_1.49      mkin_1.2.10    
+
+loaded via a namespace (and not attached):
+ [1] sass_0.4.9        utf8_1.2.4        generics_0.1.3    lattice_0.22-6   
+ [5] digest_0.6.37     magrittr_2.0.3    evaluate_1.0.1    grid_4.4.2       
+ [9] fastmap_1.2.0     cellranger_1.1.0  jsonlite_1.8.9    mclust_6.1.1     
+[13] gridExtra_2.3     fansi_1.0.6       scales_1.3.0      codetools_0.2-20 
+[17] textshaping_0.4.1 jquerylib_0.1.4   cli_3.6.3         rlang_1.1.4      
+[21] munsell_0.5.1     cachem_1.1.0      yaml_2.3.10       tools_4.4.2      
+[25] dplyr_1.1.4       colorspace_2.1-1  ggplot2_3.5.1     vctrs_0.6.5      
+[29] R6_2.5.1          zoo_1.8-12        lifecycle_1.0.4   fs_1.6.5         
+[33] htmlwidgets_1.6.4 MASS_7.3-61       ragg_1.3.3        pkgconfig_2.0.3  
+[37] desc_1.4.3        pkgdown_2.1.1     pillar_1.9.0      bslib_0.8.0      
+[41] gtable_0.3.6      glue_1.8.0        systemfonts_1.1.0 xfun_0.49        
+[45] tibble_3.2.1      lmtest_0.9-40     tidyselect_1.2.1  htmltools_0.5.8.1
+[49] nlme_3.1-166      compiler_4.4.2    readxl_1.4.3     </code></pre>
+</div>
+<div class="section level3">
+<h3 id="hardware-info">Hardware info<a class="anchor" aria-label="anchor" href="#hardware-info"></a>
+</h3>
+<pre><code>CPU model: AMD Ryzen 9 7950X 16-Core Processor</code></pre>
+<pre><code>MemTotal:       64927788 kB</code></pre>
+</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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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/prebuilt
parent	b0f08271d1dae8ffaf57f557c27eba1314ece1d5 (diff)