Merge branch 'v1.2.3_pkgdown'

author: Johannes Ranke <jranke@uni-bremen.de> 2023-04-20 20:17:12 +0200
committer: Johannes Ranke <jranke@uni-bremen.de> 2023-04-20 20:17:12 +0200
commit: 7b7c4bf493ba15824ea43bed764661678b4aca03 (patch)
tree: 48de1e32327c36ee49fc476dc76ece8397ab55c6 /docs/articles/prebuilt
parent: 842998b688037c007d8876d7e1110c929fe2374c (diff)
parent: 9ae42bd20bc2543a94cf1581ba9820c2f9e3afbd (diff)
31 files changed, 9933 insertions, 0 deletions
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+      <a href="../../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a>
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+    <div class="page-header toc-ignore">
+      <h1 data-toc-skip>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 20 April 2023,
+last compiled on 20 April 2023</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="hidden 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 1.2.3 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">700.1</td>
+<td align="right">696.2</td>
+<td align="right">-340.1</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">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">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">C</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">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">OK</td>
+<td align="left">C</td>
+<td align="left">OK</td>
+<td align="left">OK</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">Fth, 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">Fth, FO</td>
+<td align="left">Fth, FO</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">NA</td>
+</tr>
+</tbody>
+</table>
+<p>The model comparison below suggests 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="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">2692.8</td>
+<td align="right">2686.6</td>
+<td align="right">-1330.4</td>
+</tr>
+<tr class="even">
+<td align="left">sfo_path_1 tc</td>
+<td align="right">17</td>
+<td align="right">2657.7</td>
+<td align="right">2651.1</td>
+<td align="right">-1311.9</td>
+</tr>
+<tr class="odd">
+<td align="left">fomc_path_1 const</td>
+<td align="right">18</td>
+<td align="right">2427.8</td>
+<td align="right">2420.8</td>
+<td align="right">-1195.9</td>
+</tr>
+<tr class="even">
+<td align="left">fomc_path_1 tc</td>
+<td align="right">19</td>
+<td align="right">2423.4</td>
+<td align="right">2416.0</td>
+<td align="right">-1192.7</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">2427.3</td>
+<td align="right">2419.5</td>
+<td align="right">-1193.7</td>
+</tr>
+<tr class="even">
+<td align="left">dfop_path_1 tc</td>
+<td align="right">20</td>
+<td align="right">2398.0</td>
+<td align="right">2390.2</td>
+<td align="right">-1179.0</td>
+</tr>
+<tr class="odd">
+<td align="left">sforb_path_1 tc</td>
+<td align="right">20</td>
+<td align="right">2399.8</td>
+<td align="right">2392.0</td>
+<td align="right">-1179.9</td>
+</tr>
+<tr class="even">
+<td align="left">hs_path_1 tc</td>
+<td align="right">21</td>
+<td align="right">2422.3</td>
+<td align="right">2414.1</td>
+<td align="right">-1190.2</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="cb16"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">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="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">"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="cb18"><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="cb19"><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">C</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="cb20"><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">C</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 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="cb21"><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="cb22"><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">OK</td>
+<td align="left">FO</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.</p>
+<div class="sourceCode" id="cb23"><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">sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)</td>
+<td align="left">NA</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 both fits, 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="cb24"><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="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 const</td>
+<td align="right">20</td>
+<td align="right">2308.3</td>
+<td align="right">2300.5</td>
+<td align="right">-1134.2</td>
+</tr>
+<tr class="even">
+<td align="left">fomc_path_2 tc</td>
+<td align="right">21</td>
+<td align="right">2248.3</td>
+<td align="right">2240.1</td>
+<td align="right">-1103.2</td>
+</tr>
+<tr class="odd">
+<td align="left">dfop_path_2 const</td>
+<td align="right">22</td>
+<td align="right">2289.6</td>
+<td align="right">2281.0</td>
+<td align="right">-1122.8</td>
+</tr>
+<tr class="even">
+<td align="left">sforb_path_2 const</td>
+<td align="right">22</td>
+<td align="right">2284.1</td>
+<td align="right">2275.5</td>
+<td align="right">-1120.0</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">2240.4</td>
+<td align="right">2231.8</td>
+<td align="right">-1098.2</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="cb25"><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="cb26"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">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="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">"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="cb28"><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="cb29"><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="cb30"><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="cb31"><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="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">2250.9</td>
+<td align="right">2243.5</td>
+<td align="right">-1106.5</td>
+</tr>
+<tr class="even">
+<td align="left">dfop_path_2 const</td>
+<td align="right">20</td>
+<td align="right">2281.7</td>
+<td align="right">2273.9</td>
+<td align="right">-1120.8</td>
+</tr>
+<tr class="odd">
+<td align="left">sforb_path_2 const</td>
+<td align="right">20</td>
+<td align="right">2279.5</td>
+<td align="right">2271.7</td>
+<td align="right">-1119.7</td>
+</tr>
+<tr class="even">
+<td align="left">dfop_path_2 tc</td>
+<td align="right">20</td>
+<td align="right">2231.5</td>
+<td align="right">2223.7</td>
+<td align="right">-1095.8</td>
+</tr>
+<tr class="odd">
+<td align="left">sforb_path_2 tc</td>
+<td align="right">20</td>
+<td align="right">2235.7</td>
+<td align="right">2227.9</td>
+<td align="right">-1097.9</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="cb32"><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="cb33"><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="cb34"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">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="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">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:      3.2 
+mkin version used for pre-fitting:  1.2.3 
+R version used for fitting:         4.2.3 
+Date of fit:     Thu Apr 20 07:44:55 2023 
+Date of summary: Thu Apr 20 20:01:30 2023 
+
+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 431.793 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        22.5404        10.4289 
+
+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        8.684           0.00
+f_JCZ38_qlogis       0.0000        0.000          13.48
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2693 2687  -1330
+
+Optimised parameters:
+                     est. lower upper
+cyan_0            95.0946    NA    NA
+log_k_cyan        -3.8544    NA    NA
+log_k_JCZ38       -3.0402    NA    NA
+log_k_J9Z38       -5.0109    NA    NA
+log_k_JSE76       -5.2857    NA    NA
+f_cyan_ilr_1       0.8069    NA    NA
+f_cyan_ilr_2      16.6623    NA    NA
+f_JCZ38_qlogis     1.3602    NA    NA
+a.1                4.8326    NA    NA
+SD.log_k_cyan      0.5842    NA    NA
+SD.log_k_JCZ38     1.2680    NA    NA
+SD.log_k_J9Z38     0.3626    NA    NA
+SD.log_k_JSE76     0.5244    NA    NA
+SD.f_cyan_ilr_1    0.2752    NA    NA
+SD.f_cyan_ilr_2    2.3556    NA    NA
+SD.f_JCZ38_qlogis  0.2400    NA    NA
+
+Correlation is not available
+
+Random effects:
+                    est. lower upper
+SD.log_k_cyan     0.5842    NA    NA
+SD.log_k_JCZ38    1.2680    NA    NA
+SD.log_k_J9Z38    0.3626    NA    NA
+SD.log_k_JSE76    0.5244    NA    NA
+SD.f_cyan_ilr_1   0.2752    NA    NA
+SD.f_cyan_ilr_2   2.3556    NA    NA
+SD.f_JCZ38_qlogis 0.2400    NA    NA
+
+Variance model:
+     est. lower upper
+a.1 4.833    NA    NA
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           95.094581    NA    NA
+k_cyan            0.021186    NA    NA
+k_JCZ38           0.047825    NA    NA
+k_J9Z38           0.006665    NA    NA
+k_JSE76           0.005063    NA    NA
+f_cyan_to_JCZ38   0.757885    NA    NA
+f_cyan_to_J9Z38   0.242115    NA    NA
+f_JCZ38_to_JSE76  0.795792    NA    NA
+
+Resulting formation fractions:
+                   ff
+cyan_JCZ38  7.579e-01
+cyan_J9Z38  2.421e-01
+cyan_sink   5.877e-10
+JCZ38_JSE76 7.958e-01
+JCZ38_sink  2.042e-01
+
+Estimated disappearance times:
+        DT50   DT90
+cyan   32.72 108.68
+JCZ38  14.49  48.15
+J9Z38 103.99 345.46
+JSE76 136.90 454.76
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical SFO path 1 fit with two-component error
+</caption>
+<pre><code>
+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.3 
+R version used for fitting:         4.2.3 
+Date of fit:     Thu Apr 20 07:44:53 2023 
+Date of summary: Thu Apr 20 20:01:30 2023 
+
+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 429.526 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        20.0030        15.1336 
+
+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        7.334           0.00
+f_JCZ38_qlogis       0.0000        0.000          11.78
+
+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            94.72923    NA    NA
+log_k_cyan        -3.91670    NA    NA
+log_k_JCZ38       -3.12917    NA    NA
+log_k_J9Z38       -5.06070    NA    NA
+log_k_JSE76       -5.09254    NA    NA
+f_cyan_ilr_1       0.81116    NA    NA
+f_cyan_ilr_2      39.97850    NA    NA
+f_JCZ38_qlogis     3.09728    NA    NA
+a.1                3.95044    NA    NA
+b.1                0.07998    NA    NA
+SD.log_k_cyan      0.58855    NA    NA
+SD.log_k_JCZ38     1.29753    NA    NA
+SD.log_k_J9Z38     0.62851    NA    NA
+SD.log_k_JSE76     0.37235    NA    NA
+SD.f_cyan_ilr_1    0.37346    NA    NA
+SD.f_cyan_ilr_2    1.41667    NA    NA
+SD.f_JCZ38_qlogis  1.81467    NA    NA
+
+Correlation is not available
+
+Random effects:
+                    est. lower upper
+SD.log_k_cyan     0.5886    NA    NA
+SD.log_k_JCZ38    1.2975    NA    NA
+SD.log_k_J9Z38    0.6285    NA    NA
+SD.log_k_JSE76    0.3724    NA    NA
+SD.f_cyan_ilr_1   0.3735    NA    NA
+SD.f_cyan_ilr_2   1.4167    NA    NA
+SD.f_JCZ38_qlogis 1.8147    NA    NA
+
+Variance model:
+       est. lower upper
+a.1 3.95044    NA    NA
+b.1 0.07998    NA    NA
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           94.729229    NA    NA
+k_cyan            0.019907    NA    NA
+k_JCZ38           0.043754    NA    NA
+k_J9Z38           0.006341    NA    NA
+k_JSE76           0.006142    NA    NA
+f_cyan_to_JCZ38   0.758991    NA    NA
+f_cyan_to_J9Z38   0.241009    NA    NA
+f_JCZ38_to_JSE76  0.956781    NA    NA
+
+Resulting formation fractions:
+                 ff
+cyan_JCZ38  0.75899
+cyan_J9Z38  0.24101
+cyan_sink   0.00000
+JCZ38_JSE76 0.95678
+JCZ38_sink  0.04322
+
+Estimated disappearance times:
+        DT50   DT90
+cyan   34.82 115.67
+JCZ38  15.84  52.63
+J9Z38 109.31 363.12
+JSE76 112.85 374.87
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical FOMC path 1 fit with constant variance
+</caption>
+<pre><code>
+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.3 
+R version used for fitting:         4.2.3 
+Date of fit:     Thu Apr 20 07:45:50 2023 
+Date of summary: Thu Apr 20 20:01:30 2023 
+
+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 477.996 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 
+        7.3870        15.7604        -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          12.33           0.00    0.0000   0.0000
+f_JCZ38_qlogis         0.00          20.42    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            101.0225 98.306270 103.7387
+log_k_JCZ38        -3.3786 -4.770657  -1.9866
+log_k_J9Z38        -5.2603 -5.902085  -4.6186
+log_k_JSE76        -6.1427 -7.318336  -4.9671
+f_cyan_ilr_1        0.7437  0.421215   1.0663
+f_cyan_ilr_2        0.9108  0.267977   1.5537
+f_JCZ38_qlogis      2.0487  0.524897   3.5724
+log_alpha          -0.2268 -0.618049   0.1644
+log_beta            2.8986  2.700701   3.0964
+a.1                 3.4058  3.169913   3.6416
+SD.cyan_0           2.5279  0.454190   4.6016
+SD.log_k_JCZ38      1.5636  0.572824   2.5543
+SD.log_k_J9Z38      0.5316 -0.004405   1.0677
+SD.log_k_JSE76      0.9903  0.106325   1.8742
+SD.f_cyan_ilr_1     0.3464  0.112066   0.5807
+SD.f_cyan_ilr_2     0.2804 -0.393900   0.9546
+SD.f_JCZ38_qlogis   0.9416 -0.152986   2.0362
+SD.log_alpha        0.4273  0.161044   0.6936
+
+Correlation: 
+               cyan_0  l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 log_lph
+log_k_JCZ38    -0.0156                                                        
+log_k_J9Z38    -0.0493  0.0073                                                
+log_k_JSE76    -0.0329  0.0018  0.0069                                        
+f_cyan_ilr_1   -0.0086  0.0180 -0.1406  0.0012                                
+f_cyan_ilr_2   -0.2629  0.0779  0.2826  0.0274  0.0099                        
+f_JCZ38_qlogis  0.0713 -0.0747 -0.0505  0.1169 -0.1022 -0.4893                
+log_alpha      -0.0556  0.0120  0.0336  0.0193  0.0036  0.0840 -0.0489        
+log_beta       -0.2898  0.0460  0.1305  0.0768  0.0190  0.4071 -0.1981  0.2772
+
+Random effects:
+                    est.     lower  upper
+SD.cyan_0         2.5279  0.454190 4.6016
+SD.log_k_JCZ38    1.5636  0.572824 2.5543
+SD.log_k_J9Z38    0.5316 -0.004405 1.0677
+SD.log_k_JSE76    0.9903  0.106325 1.8742
+SD.f_cyan_ilr_1   0.3464  0.112066 0.5807
+SD.f_cyan_ilr_2   0.2804 -0.393900 0.9546
+SD.f_JCZ38_qlogis 0.9416 -0.152986 2.0362
+SD.log_alpha      0.4273  0.161044 0.6936
+
+Variance model:
+     est. lower upper
+a.1 3.406  3.17 3.642
+
+Backtransformed parameters:
+                      est.     lower     upper
+cyan_0           1.010e+02 9.831e+01 1.037e+02
+k_JCZ38          3.409e-02 8.475e-03 1.372e-01
+k_J9Z38          5.194e-03 2.734e-03 9.867e-03
+k_JSE76          2.149e-03 6.633e-04 6.963e-03
+f_cyan_to_JCZ38  6.481e-01        NA        NA
+f_cyan_to_J9Z38  2.264e-01        NA        NA
+f_JCZ38_to_JSE76 8.858e-01 6.283e-01 9.727e-01
+alpha            7.971e-01 5.390e-01 1.179e+00
+beta             1.815e+01 1.489e+01 2.212e+01
+
+Resulting formation fractions:
+                ff
+cyan_JCZ38  0.6481
+cyan_J9Z38  0.2264
+cyan_sink   0.1255
+JCZ38_JSE76 0.8858
+JCZ38_sink  0.1142
+
+Estimated disappearance times:
+        DT50    DT90 DT50back
+cyan   25.15  308.01    92.72
+JCZ38  20.33   67.54       NA
+J9Z38 133.46  443.35       NA
+JSE76 322.53 1071.42       NA
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical FOMC path 1 fit with two-component error
+</caption>
+<pre><code>
+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.3 
+R version used for fitting:         4.2.3 
+Date of fit:     Thu Apr 20 07:45:45 2023 
+Date of summary: Thu Apr 20 20:01:30 2023 
+
+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 480.648 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 
+     101.13827       -3.32493       -5.08921       -5.93478        0.71330 
+  f_cyan_ilr_2 f_JCZ38_qlogis      log_alpha       log_beta 
+      10.05989       12.79248       -0.09621        3.10646 
+
+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          5.643       0.000       0.000        0.00       0.0000
+log_k_JCZ38     0.000       2.319       0.000        0.00       0.0000
+log_k_J9Z38     0.000       0.000       1.731        0.00       0.0000
+log_k_JSE76     0.000       0.000       0.000        1.86       0.0000
+f_cyan_ilr_1    0.000       0.000       0.000        0.00       0.7186
+f_cyan_ilr_2    0.000       0.000       0.000        0.00       0.0000
+f_JCZ38_qlogis  0.000       0.000       0.000        0.00       0.0000
+log_alpha       0.000       0.000       0.000        0.00       0.0000
+log_beta        0.000       0.000       0.000        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          12.49           0.00    0.0000   0.0000
+f_JCZ38_qlogis         0.00          20.19    0.0000   0.0000
+log_alpha              0.00           0.00    0.3142   0.0000
+log_beta               0.00           0.00    0.0000   0.7331
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2423 2416  -1193
+
+Optimised parameters:
+                       est. lower upper
+cyan_0            100.57649    NA    NA
+log_k_JCZ38        -3.46250    NA    NA
+log_k_J9Z38        -5.24442    NA    NA
+log_k_JSE76        -5.75229    NA    NA
+f_cyan_ilr_1        0.68480    NA    NA
+f_cyan_ilr_2        0.61670    NA    NA
+f_JCZ38_qlogis     87.97407    NA    NA
+log_alpha          -0.15699    NA    NA
+log_beta            3.01540    NA    NA
+a.1                 3.11518    NA    NA
+b.1                 0.04445    NA    NA
+SD.log_k_JCZ38      1.40732    NA    NA
+SD.log_k_J9Z38      0.56510    NA    NA
+SD.log_k_JSE76      0.72067    NA    NA
+SD.f_cyan_ilr_1     0.31199    NA    NA
+SD.f_cyan_ilr_2     0.36894    NA    NA
+SD.f_JCZ38_qlogis   6.92892    NA    NA
+SD.log_alpha        0.25662    NA    NA
+SD.log_beta         0.35845    NA    NA
+
+Correlation is not available
+
+Random effects:
+                    est. lower upper
+SD.log_k_JCZ38    1.4073    NA    NA
+SD.log_k_J9Z38    0.5651    NA    NA
+SD.log_k_JSE76    0.7207    NA    NA
+SD.f_cyan_ilr_1   0.3120    NA    NA
+SD.f_cyan_ilr_2   0.3689    NA    NA
+SD.f_JCZ38_qlogis 6.9289    NA    NA
+SD.log_alpha      0.2566    NA    NA
+SD.log_beta       0.3585    NA    NA
+
+Variance model:
+       est. lower upper
+a.1 3.11518    NA    NA
+b.1 0.04445    NA    NA
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.006e+02    NA    NA
+k_JCZ38          3.135e-02    NA    NA
+k_J9Z38          5.277e-03    NA    NA
+k_JSE76          3.175e-03    NA    NA
+f_cyan_to_JCZ38  5.991e-01    NA    NA
+f_cyan_to_J9Z38  2.275e-01    NA    NA
+f_JCZ38_to_JSE76 1.000e+00    NA    NA
+alpha            8.547e-01    NA    NA
+beta             2.040e+01    NA    NA
+
+Resulting formation fractions:
+                ff
+cyan_JCZ38  0.5991
+cyan_J9Z38  0.2275
+cyan_sink   0.1734
+JCZ38_JSE76 1.0000
+JCZ38_sink  0.0000
+
+Estimated disappearance times:
+        DT50   DT90 DT50back
+cyan   25.50 281.29    84.68
+JCZ38  22.11  73.44       NA
+J9Z38 131.36 436.35       NA
+JSE76 218.28 725.11       NA
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical DFOP path 1 fit with constant variance
+</caption>
+<pre><code>
+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.3 
+R version used for fitting:         4.2.3 
+Date of fit:     Thu Apr 20 07:46:41 2023 
+Date of summary: Thu Apr 20 20:01:30 2023 
+
+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 528.713 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 
+      102.0644        -3.4008        -5.0024        -5.8613         0.6855 
+  f_cyan_ilr_2 f_JCZ38_qlogis         log_k1         log_k2       g_qlogis 
+        1.2365        13.7245        -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          16.11 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            102.6079    NA    NA
+log_k_JCZ38        -3.4855    NA    NA
+log_k_J9Z38        -5.1686    NA    NA
+log_k_JSE76        -5.6697    NA    NA
+f_cyan_ilr_1        0.6714    NA    NA
+f_cyan_ilr_2        0.4986    NA    NA
+f_JCZ38_qlogis     55.4760    NA    NA
+log_k1             -1.8409    NA    NA
+log_k2             -4.4915    NA    NA
+g_qlogis           -0.6403    NA    NA
+a.1                 3.2387    NA    NA
+SD.log_k_JCZ38      1.4524    NA    NA
+SD.log_k_J9Z38      0.5151    NA    NA
+SD.log_k_JSE76      0.6514    NA    NA
+SD.f_cyan_ilr_1     0.3023    NA    NA
+SD.f_cyan_ilr_2     0.2959    NA    NA
+SD.f_JCZ38_qlogis   1.9984    NA    NA
+SD.log_k1           0.5188    NA    NA
+SD.log_k2           0.3894    NA    NA
+SD.g_qlogis         0.8579    NA    NA
+
+Correlation is not available
+
+Random effects:
+                    est. lower upper
+SD.log_k_JCZ38    1.4524    NA    NA
+SD.log_k_J9Z38    0.5151    NA    NA
+SD.log_k_JSE76    0.6514    NA    NA
+SD.f_cyan_ilr_1   0.3023    NA    NA
+SD.f_cyan_ilr_2   0.2959    NA    NA
+SD.f_JCZ38_qlogis 1.9984    NA    NA
+SD.log_k1         0.5188    NA    NA
+SD.log_k2         0.3894    NA    NA
+SD.g_qlogis       0.8579    NA    NA
+
+Variance model:
+     est. lower upper
+a.1 3.239    NA    NA
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.026e+02    NA    NA
+k_JCZ38          3.064e-02    NA    NA
+k_J9Z38          5.692e-03    NA    NA
+k_JSE76          3.449e-03    NA    NA
+f_cyan_to_JCZ38  5.798e-01    NA    NA
+f_cyan_to_J9Z38  2.243e-01    NA    NA
+f_JCZ38_to_JSE76 1.000e+00    NA    NA
+k1               1.587e-01    NA    NA
+k2               1.120e-02    NA    NA
+g                3.452e-01    NA    NA
+
+Resulting formation fractions:
+                ff
+cyan_JCZ38  0.5798
+cyan_J9Z38  0.2243
+cyan_sink   0.1958
+JCZ38_JSE76 1.0000
+JCZ38_sink  0.0000
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   25.21 167.73    50.49   4.368   61.87
+JCZ38  22.62  75.15       NA      NA      NA
+J9Z38 121.77 404.50       NA      NA      NA
+JSE76 200.98 667.64       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:      3.2 
+mkin version used for pre-fitting:  1.2.3 
+R version used for fitting:         4.2.3 
+Date of fit:     Thu Apr 20 07:49:05 2023 
+Date of summary: Thu Apr 20 20:01:30 2023 
+
+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 673.139 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 
+        6.7799        13.7245        -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       0.6838
+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          11.77           0.00 0.0000 0.0000    0.000
+f_JCZ38_qlogis         0.00          16.11 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            100.8076    NA    NA
+log_k_JCZ38        -3.4684    NA    NA
+log_k_J9Z38        -5.0844    NA    NA
+log_k_JSE76        -5.5743    NA    NA
+f_cyan_ilr_1        0.6669    NA    NA
+f_cyan_ilr_2        0.7912    NA    NA
+f_JCZ38_qlogis     84.1825    NA    NA
+log_k1             -2.1671    NA    NA
+log_k2             -4.5447    NA    NA
+g_qlogis           -0.5631    NA    NA
+a.1                 2.9627    NA    NA
+b.1                 0.0444    NA    NA
+SD.log_k_JCZ38      1.4044    NA    NA
+SD.log_k_J9Z38      0.6410    NA    NA
+SD.log_k_JSE76      0.5391    NA    NA
+SD.f_cyan_ilr_1     0.3203    NA    NA
+SD.f_cyan_ilr_2     0.5038    NA    NA
+SD.f_JCZ38_qlogis   3.5865    NA    NA
+SD.log_k2           0.3119    NA    NA
+SD.g_qlogis         0.8276    NA    NA
+
+Correlation is not available
+
+Random effects:
+                    est. lower upper
+SD.log_k_JCZ38    1.4044    NA    NA
+SD.log_k_J9Z38    0.6410    NA    NA
+SD.log_k_JSE76    0.5391    NA    NA
+SD.f_cyan_ilr_1   0.3203    NA    NA
+SD.f_cyan_ilr_2   0.5038    NA    NA
+SD.f_JCZ38_qlogis 3.5865    NA    NA
+SD.log_k2         0.3119    NA    NA
+SD.g_qlogis       0.8276    NA    NA
+
+Variance model:
+      est. lower upper
+a.1 2.9627    NA    NA
+b.1 0.0444    NA    NA
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.008e+02    NA    NA
+k_JCZ38          3.117e-02    NA    NA
+k_J9Z38          6.193e-03    NA    NA
+k_JSE76          3.794e-03    NA    NA
+f_cyan_to_JCZ38  6.149e-01    NA    NA
+f_cyan_to_J9Z38  2.395e-01    NA    NA
+f_JCZ38_to_JSE76 1.000e+00    NA    NA
+k1               1.145e-01    NA    NA
+k2               1.062e-02    NA    NA
+g                3.628e-01    NA    NA
+
+Resulting formation fractions:
+                ff
+cyan_JCZ38  0.6149
+cyan_J9Z38  0.2395
+cyan_sink   0.1456
+JCZ38_JSE76 1.0000
+JCZ38_sink  0.0000
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   26.26 174.32    52.47   6.053   65.25
+JCZ38  22.24  73.88       NA      NA      NA
+J9Z38 111.93 371.82       NA      NA      NA
+JSE76 182.69 606.88       NA      NA      NA
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical SFORB path 1 fit with constant variance
+</caption>
+<pre><code>
+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.3 
+R version used for fitting:         4.2.3 
+Date of fit:     Thu Apr 20 07:46:35 2023 
+Date of summary: Thu Apr 20 20:01:30 2023 
+
+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 531.17 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 
+              13.7418 
+
+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          16.14
+
+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              102.7803    NA    NA
+log_k_cyan_free           -2.8068    NA    NA
+log_k_cyan_free_bound     -2.5714    NA    NA
+log_k_cyan_bound_free     -3.4426    NA    NA
+log_k_JCZ38               -3.4994    NA    NA
+log_k_J9Z38               -5.1148    NA    NA
+log_k_JSE76               -5.6335    NA    NA
+f_cyan_ilr_1               0.6597    NA    NA
+f_cyan_ilr_2               0.5132    NA    NA
+f_JCZ38_qlogis            37.2090    NA    NA
+a.1                        3.2367    NA    NA
+SD.log_k_cyan_free         0.3161    NA    NA
+SD.log_k_cyan_free_bound   0.8103    NA    NA
+SD.log_k_cyan_bound_free   0.5554    NA    NA
+SD.log_k_JCZ38             1.4858    NA    NA
+SD.log_k_J9Z38             0.5859    NA    NA
+SD.log_k_JSE76             0.6195    NA    NA
+SD.f_cyan_ilr_1            0.3118    NA    NA
+SD.f_cyan_ilr_2            0.3344    NA    NA
+SD.f_JCZ38_qlogis          0.5518    NA    NA
+
+Correlation is not available
+
+Random effects:
+                           est. lower upper
+SD.log_k_cyan_free       0.3161    NA    NA
+SD.log_k_cyan_free_bound 0.8103    NA    NA
+SD.log_k_cyan_bound_free 0.5554    NA    NA
+SD.log_k_JCZ38           1.4858    NA    NA
+SD.log_k_J9Z38           0.5859    NA    NA
+SD.log_k_JSE76           0.6195    NA    NA
+SD.f_cyan_ilr_1          0.3118    NA    NA
+SD.f_cyan_ilr_2          0.3344    NA    NA
+SD.f_JCZ38_qlogis        0.5518    NA    NA
+
+Variance model:
+     est. lower upper
+a.1 3.237    NA    NA
+
+Backtransformed parameters:
+                          est. lower upper
+cyan_free_0          1.028e+02    NA    NA
+k_cyan_free          6.040e-02    NA    NA
+k_cyan_free_bound    7.643e-02    NA    NA
+k_cyan_bound_free    3.198e-02    NA    NA
+k_JCZ38              3.022e-02    NA    NA
+k_J9Z38              6.007e-03    NA    NA
+k_JSE76              3.576e-03    NA    NA
+f_cyan_free_to_JCZ38 5.787e-01    NA    NA
+f_cyan_free_to_J9Z38 2.277e-01    NA    NA
+f_JCZ38_to_JSE76     1.000e+00    NA    NA
+
+Estimated Eigenvalues of SFORB model(s):
+cyan_b1 cyan_b2  cyan_g 
+0.15646 0.01235 0.33341 
+
+Resulting formation fractions:
+                    ff
+cyan_free_JCZ38 0.5787
+cyan_free_J9Z38 0.2277
+cyan_free_sink  0.1936
+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   24.48 153.7    46.26         4.43        56.15
+JCZ38  22.94  76.2       NA           NA           NA
+J9Z38 115.39 383.3       NA           NA           NA
+JSE76 193.84 643.9       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:      3.2 
+mkin version used for pre-fitting:  1.2.3 
+R version used for fitting:         4.2.3 
+Date of fit:     Thu Apr 20 07:49:08 2023 
+Date of summary: Thu Apr 20 20:01:30 2023 
+
+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 675.659 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                6.8139 
+       f_JCZ38_qlogis 
+              13.7419 
+
+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        11.84           0.00
+f_JCZ38_qlogis              0.0000         0.00          16.14
+
+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              100.69983    NA    NA
+log_k_cyan_free           -3.11584    NA    NA
+log_k_cyan_free_bound     -3.15216    NA    NA
+log_k_cyan_bound_free     -3.65986    NA    NA
+log_k_JCZ38               -3.47811    NA    NA
+log_k_J9Z38               -5.08835    NA    NA
+log_k_JSE76               -5.55514    NA    NA
+f_cyan_ilr_1               0.66764    NA    NA
+f_cyan_ilr_2               0.78329    NA    NA
+f_JCZ38_qlogis            25.35245    NA    NA
+a.1                        2.99088    NA    NA
+b.1                        0.04346    NA    NA
+SD.log_k_cyan_free         0.48797    NA    NA
+SD.log_k_cyan_bound_free   0.27243    NA    NA
+SD.log_k_JCZ38             1.42450    NA    NA
+SD.log_k_J9Z38             0.63496    NA    NA
+SD.log_k_JSE76             0.55951    NA    NA
+SD.f_cyan_ilr_1            0.32687    NA    NA
+SD.f_cyan_ilr_2            0.48056    NA    NA
+SD.f_JCZ38_qlogis          0.43818    NA    NA
+
+Correlation is not available
+
+Random effects:
+                           est. lower upper
+SD.log_k_cyan_free       0.4880    NA    NA
+SD.log_k_cyan_bound_free 0.2724    NA    NA
+SD.log_k_JCZ38           1.4245    NA    NA
+SD.log_k_J9Z38           0.6350    NA    NA
+SD.log_k_JSE76           0.5595    NA    NA
+SD.f_cyan_ilr_1          0.3269    NA    NA
+SD.f_cyan_ilr_2          0.4806    NA    NA
+SD.f_JCZ38_qlogis        0.4382    NA    NA
+
+Variance model:
+       est. lower upper
+a.1 2.99088    NA    NA
+b.1 0.04346    NA    NA
+
+Backtransformed parameters:
+                          est. lower upper
+cyan_free_0          1.007e+02    NA    NA
+k_cyan_free          4.434e-02    NA    NA
+k_cyan_free_bound    4.276e-02    NA    NA
+k_cyan_bound_free    2.574e-02    NA    NA
+k_JCZ38              3.087e-02    NA    NA
+k_J9Z38              6.168e-03    NA    NA
+k_JSE76              3.868e-03    NA    NA
+f_cyan_free_to_JCZ38 6.143e-01    NA    NA
+f_cyan_free_to_J9Z38 2.389e-01    NA    NA
+f_JCZ38_to_JSE76     1.000e+00    NA    NA
+
+Estimated Eigenvalues of SFORB model(s):
+cyan_b1 cyan_b2  cyan_g 
+0.10161 0.01123 0.36636 
+
+Resulting formation fractions:
+                       ff
+cyan_free_JCZ38 6.143e-01
+cyan_free_J9Z38 2.389e-01
+cyan_free_sink  1.468e-01
+cyan_free       1.000e+00
+JCZ38_JSE76     1.000e+00
+JCZ38_sink      9.763e-12
+
+Estimated disappearance times:
+        DT50  DT90 DT50back DT50_cyan_b1 DT50_cyan_b2
+cyan   25.91 164.4    49.49        6.822        61.72
+JCZ38  22.46  74.6       NA           NA           NA
+J9Z38 112.37 373.3       NA           NA           NA
+JSE76 179.22 595.4       NA           NA           NA
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical HS path 1 fit with constant variance
+</caption>
+<pre><code>
+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.3 
+R version used for fitting:         4.2.3 
+Date of fit:     Thu Apr 20 07:46:30 2023 
+Date of summary: Thu Apr 20 20:01:30 2023 
+
+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 525.846 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 
+      102.8738        -3.4490        -4.9348        -5.5989         0.6469 
+  f_cyan_ilr_2 f_JCZ38_qlogis         log_k1         log_k2         log_tb 
+        1.2854         9.7193        -2.9084        -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          5.409        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       1.006       0.0000
+f_cyan_ilr_1    0.000        0.00        0.00       0.000       0.6371
+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          2.167           0.00 0.0000 0.0000 0.0000
+f_JCZ38_qlogis        0.000          10.22 0.0000 0.0000 0.0000
+log_k1                0.000           0.00 0.7003 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 0.6774
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2427 2420  -1194
+
+Optimised parameters:
+                       est. lower upper
+cyan_0            101.84849    NA    NA
+log_k_JCZ38        -3.47365    NA    NA
+log_k_J9Z38        -5.10562    NA    NA
+log_k_JSE76        -5.60318    NA    NA
+f_cyan_ilr_1        0.66127    NA    NA
+f_cyan_ilr_2        0.60283    NA    NA
+f_JCZ38_qlogis     45.06408    NA    NA
+log_k1             -3.10124    NA    NA
+log_k2             -4.39028    NA    NA
+log_tb              2.32256    NA    NA
+a.1                 3.32683    NA    NA
+SD.log_k_JCZ38      1.41427    NA    NA
+SD.log_k_J9Z38      0.54767    NA    NA
+SD.log_k_JSE76      0.62147    NA    NA
+SD.f_cyan_ilr_1     0.30189    NA    NA
+SD.f_cyan_ilr_2     0.34960    NA    NA
+SD.f_JCZ38_qlogis   0.04644    NA    NA
+SD.log_k1           0.39534    NA    NA
+SD.log_k2           0.43468    NA    NA
+SD.log_tb           0.60781    NA    NA
+
+Correlation is not available
+
+Random effects:
+                     est. lower upper
+SD.log_k_JCZ38    1.41427    NA    NA
+SD.log_k_J9Z38    0.54767    NA    NA
+SD.log_k_JSE76    0.62147    NA    NA
+SD.f_cyan_ilr_1   0.30189    NA    NA
+SD.f_cyan_ilr_2   0.34960    NA    NA
+SD.f_JCZ38_qlogis 0.04644    NA    NA
+SD.log_k1         0.39534    NA    NA
+SD.log_k2         0.43468    NA    NA
+SD.log_tb         0.60781    NA    NA
+
+Variance model:
+     est. lower upper
+a.1 3.327    NA    NA
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.018e+02    NA    NA
+k_JCZ38          3.100e-02    NA    NA
+k_J9Z38          6.063e-03    NA    NA
+k_JSE76          3.686e-03    NA    NA
+f_cyan_to_JCZ38  5.910e-01    NA    NA
+f_cyan_to_J9Z38  2.320e-01    NA    NA
+f_JCZ38_to_JSE76 1.000e+00    NA    NA
+k1               4.499e-02    NA    NA
+k2               1.240e-02    NA    NA
+tb               1.020e+01    NA    NA
+
+Resulting formation fractions:
+               ff
+cyan_JCZ38  0.591
+cyan_J9Z38  0.232
+cyan_sink   0.177
+JCZ38_JSE76 1.000
+JCZ38_sink  0.000
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   29.09 158.91    47.84   15.41   55.91
+JCZ38  22.36  74.27       NA      NA      NA
+J9Z38 114.33 379.80       NA      NA      NA
+JSE76 188.04 624.66       NA      NA      NA
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical HS path 1 fit with two-component error
+</caption>
+<pre><code>
+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.3 
+R version used for fitting:         4.2.3 
+Date of fit:     Thu Apr 20 07:46:19 2023 
+Date of summary: Thu Apr 20 20:01:30 2023 
+
+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 514.968 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 
+       101.168         -3.358         -4.941         -5.794          0.676 
+  f_cyan_ilr_2 f_JCZ38_qlogis         log_k1         log_k2         log_tb 
+         5.740         13.863         -3.147         -4.262          2.173 
+
+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           5.79       0.000       0.000       0.000       0.0000
+log_k_JCZ38      0.00       2.271       0.000       0.000       0.0000
+log_k_J9Z38      0.00       0.000       1.614       0.000       0.0000
+log_k_JSE76      0.00       0.000       0.000       1.264       0.0000
+f_cyan_ilr_1     0.00       0.000       0.000       0.000       0.6761
+f_cyan_ilr_2     0.00       0.000       0.000       0.000       0.0000
+f_JCZ38_qlogis   0.00       0.000       0.000       0.000       0.0000
+log_k1           0.00       0.000       0.000       0.000       0.0000
+log_k2           0.00       0.000       0.000       0.000       0.0000
+log_tb           0.00       0.000       0.000       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  0.000
+log_k_JCZ38           0.000           0.00 0.0000 0.0000  0.000
+log_k_J9Z38           0.000           0.00 0.0000 0.0000  0.000
+log_k_JSE76           0.000           0.00 0.0000 0.0000  0.000
+f_cyan_ilr_1          0.000           0.00 0.0000 0.0000  0.000
+f_cyan_ilr_2          9.572           0.00 0.0000 0.0000  0.000
+f_JCZ38_qlogis        0.000          19.19 0.0000 0.0000  0.000
+log_k1                0.000           0.00 0.8705 0.0000  0.000
+log_k2                0.000           0.00 0.0000 0.9288  0.000
+log_tb                0.000           0.00 0.0000 0.0000  1.065
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2422 2414  -1190
+
+Optimised parameters:
+                      est. lower upper
+cyan_0            100.9521    NA    NA
+log_k_JCZ38        -3.4629    NA    NA
+log_k_J9Z38        -5.0346    NA    NA
+log_k_JSE76        -5.5722    NA    NA
+f_cyan_ilr_1        0.6560    NA    NA
+f_cyan_ilr_2        0.7983    NA    NA
+f_JCZ38_qlogis     42.7949    NA    NA
+log_k1             -3.1721    NA    NA
+log_k2             -4.4039    NA    NA
+log_tb              2.3994    NA    NA
+a.1                 3.0586    NA    NA
+b.1                 0.0380    NA    NA
+SD.log_k_JCZ38      1.3754    NA    NA
+SD.log_k_J9Z38      0.6703    NA    NA
+SD.log_k_JSE76      0.5876    NA    NA
+SD.f_cyan_ilr_1     0.3272    NA    NA
+SD.f_cyan_ilr_2     0.5300    NA    NA
+SD.f_JCZ38_qlogis   6.4465    NA    NA
+SD.log_k1           0.4135    NA    NA
+SD.log_k2           0.4182    NA    NA
+SD.log_tb           0.6035    NA    NA
+
+Correlation is not available
+
+Random effects:
+                    est. lower upper
+SD.log_k_JCZ38    1.3754    NA    NA
+SD.log_k_J9Z38    0.6703    NA    NA
+SD.log_k_JSE76    0.5876    NA    NA
+SD.f_cyan_ilr_1   0.3272    NA    NA
+SD.f_cyan_ilr_2   0.5300    NA    NA
+SD.f_JCZ38_qlogis 6.4465    NA    NA
+SD.log_k1         0.4135    NA    NA
+SD.log_k2         0.4182    NA    NA
+SD.log_tb         0.6035    NA    NA
+
+Variance model:
+     est. lower upper
+a.1 3.059    NA    NA
+b.1 0.038    NA    NA
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.010e+02    NA    NA
+k_JCZ38          3.134e-02    NA    NA
+k_J9Z38          6.509e-03    NA    NA
+k_JSE76          3.802e-03    NA    NA
+f_cyan_to_JCZ38  6.127e-01    NA    NA
+f_cyan_to_J9Z38  2.423e-01    NA    NA
+f_JCZ38_to_JSE76 1.000e+00    NA    NA
+k1               4.191e-02    NA    NA
+k2               1.223e-02    NA    NA
+tb               1.102e+01    NA    NA
+
+Resulting formation fractions:
+                ff
+cyan_JCZ38  0.6127
+cyan_J9Z38  0.2423
+cyan_sink   0.1449
+JCZ38_JSE76 1.0000
+JCZ38_sink  0.0000
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   29.94 161.54    48.63   16.54   56.68
+JCZ38  22.12  73.47       NA      NA      NA
+J9Z38 106.50 353.77       NA      NA      NA
+JSE76 182.30 605.60       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 constant variance
+</caption>
+<pre><code>
+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.3 
+R version used for fitting:         4.2.3 
+Date of fit:     Thu Apr 20 07:58:00 2023 
+Date of summary: Thu Apr 20 20:01:30 2023 
+
+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 522.351 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 
+      101.8173        -1.8998        -5.1449        -2.5415         0.6705 
+  f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis      log_alpha       log_beta 
+        4.4669        16.1281        13.3327        -0.2314         2.8738 
+
+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          5.742       0.000       0.000        0.00       0.0000
+log_k_JCZ38     0.000       1.402       0.000        0.00       0.0000
+log_k_J9Z38     0.000       0.000       1.718        0.00       0.0000
+log_k_JSE76     0.000       0.000       0.000        3.57       0.0000
+f_cyan_ilr_1    0.000       0.000       0.000        0.00       0.5926
+f_cyan_ilr_2    0.000       0.000       0.000        0.00       0.0000
+f_JCZ38_qlogis  0.000       0.000       0.000        0.00       0.0000
+f_JSE76_qlogis  0.000       0.000       0.000        0.00       0.0000
+log_alpha       0.000       0.000       0.000        0.00       0.0000
+log_beta        0.000       0.000       0.000        0.00       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          10.56           0.00           0.00    0.0000   0.0000
+f_JCZ38_qlogis         0.00          12.04           0.00    0.0000   0.0000
+f_JSE76_qlogis         0.00           0.00          15.26    0.0000   0.0000
+log_alpha              0.00           0.00           0.00    0.4708   0.0000
+log_beta               0.00           0.00           0.00    0.0000   0.4432
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2308 2301  -1134
+
+Optimised parameters:
+                      est.    lower     upper
+cyan_0            101.9586 99.22024 104.69700
+log_k_JCZ38        -2.4861 -3.17661  -1.79560
+log_k_J9Z38        -5.3926 -6.08842  -4.69684
+log_k_JSE76        -3.1193 -4.12904  -2.10962
+f_cyan_ilr_1        0.7368  0.42085   1.05276
+f_cyan_ilr_2        0.6196  0.06052   1.17861
+f_JCZ38_qlogis      4.8970 -4.68003  14.47398
+f_JSE76_qlogis      4.4066 -1.02087   9.83398
+log_alpha          -0.3021 -0.68264   0.07838
+log_beta            2.7438  2.57970   2.90786
+a.1                 2.9008  2.69920   3.10245
+SD.cyan_0           2.7081  0.64216   4.77401
+SD.log_k_JCZ38      0.7043  0.19951   1.20907
+SD.log_k_J9Z38      0.6248  0.05790   1.19180
+SD.log_k_JSE76      1.0750  0.33157   1.81839
+SD.f_cyan_ilr_1     0.3429  0.11688   0.56892
+SD.f_cyan_ilr_2     0.4774  0.09381   0.86097
+SD.f_JCZ38_qlogis   1.5565 -7.83970  10.95279
+SD.f_JSE76_qlogis   1.6871 -1.25577   4.63000
+SD.log_alpha        0.4216  0.15913   0.68405
+
+Correlation: 
+               cyan_0  l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76
+log_k_JCZ38    -0.0167                                                        
+log_k_J9Z38    -0.0307  0.0057                                                
+log_k_JSE76    -0.0032  0.1358  0.0009                                        
+f_cyan_ilr_1   -0.0087  0.0206 -0.1158 -0.0009                                
+f_cyan_ilr_2   -0.1598  0.0690  0.1770  0.0002 -0.0007                        
+f_JCZ38_qlogis  0.0966 -0.1132 -0.0440  0.0182 -0.1385 -0.4583                
+f_JSE76_qlogis -0.0647  0.1157  0.0333 -0.0026  0.1110  0.3620 -0.8586        
+log_alpha      -0.0389  0.0113  0.0209  0.0021  0.0041  0.0451 -0.0605  0.0412
+log_beta       -0.2508  0.0533  0.0977  0.0098  0.0220  0.2741 -0.2934  0.1999
+               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        0.2281
+
+Random effects:
+                    est.    lower   upper
+SD.cyan_0         2.7081  0.64216  4.7740
+SD.log_k_JCZ38    0.7043  0.19951  1.2091
+SD.log_k_J9Z38    0.6248  0.05790  1.1918
+SD.log_k_JSE76    1.0750  0.33157  1.8184
+SD.f_cyan_ilr_1   0.3429  0.11688  0.5689
+SD.f_cyan_ilr_2   0.4774  0.09381  0.8610
+SD.f_JCZ38_qlogis 1.5565 -7.83970 10.9528
+SD.f_JSE76_qlogis 1.6871 -1.25577  4.6300
+SD.log_alpha      0.4216  0.15913  0.6840
+
+Variance model:
+     est. lower upper
+a.1 2.901 2.699 3.102
+
+Backtransformed parameters:
+                      est.     lower     upper
+cyan_0           101.95862 99.220240 1.047e+02
+k_JCZ38            0.08323  0.041727 1.660e-01
+k_J9Z38            0.00455  0.002269 9.124e-03
+k_JSE76            0.04419  0.016098 1.213e-01
+f_cyan_to_JCZ38    0.61318        NA        NA
+f_cyan_to_J9Z38    0.21630        NA        NA
+f_JCZ38_to_JSE76   0.99259  0.009193 1.000e+00
+f_JSE76_to_JCZ38   0.98795  0.264857 9.999e-01
+alpha              0.73924  0.505281 1.082e+00
+beta              15.54568 13.193194 1.832e+01
+
+Resulting formation fractions:
+                  ff
+cyan_JCZ38  0.613182
+cyan_J9Z38  0.216298
+cyan_sink   0.170519
+JCZ38_JSE76 0.992586
+JCZ38_sink  0.007414
+JSE76_JCZ38 0.987950
+JSE76_sink  0.012050
+
+Estimated disappearance times:
+         DT50   DT90 DT50back
+cyan   24.157 334.68    100.7
+JCZ38   8.328  27.66       NA
+J9Z38 152.341 506.06       NA
+JSE76  15.687  52.11       NA
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical FOMC path 2 fit with two-component error
+</caption>
+<pre><code>
+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.3 
+R version used for fitting:         4.2.3 
+Date of fit:     Thu Apr 20 07:57:52 2023 
+Date of summary: Thu Apr 20 20:01:30 2023 
+
+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 514.301 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 
+      101.9028        -1.9055        -5.0249        -2.5646         0.6807 
+  f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis      log_alpha       log_beta 
+        4.8883        16.0676         9.3923        -0.1346         3.0364 
+
+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          6.321       0.000       0.000       0.000       0.0000
+log_k_JCZ38     0.000       1.392       0.000       0.000       0.0000
+log_k_J9Z38     0.000       0.000       1.561       0.000       0.0000
+log_k_JSE76     0.000       0.000       0.000       3.614       0.0000
+f_cyan_ilr_1    0.000       0.000       0.000       0.000       0.6339
+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          10.41           0.00           0.00    0.0000   0.0000
+f_JCZ38_qlogis         0.00          12.24           0.00    0.0000   0.0000
+f_JSE76_qlogis         0.00           0.00          15.13    0.0000   0.0000
+log_alpha              0.00           0.00           0.00    0.3701   0.0000
+log_beta               0.00           0.00           0.00    0.0000   0.5662
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2248 2240  -1103
+
+Optimised parameters:
+                       est.      lower      upper
+cyan_0            101.55545  9.920e+01  1.039e+02
+log_k_JCZ38        -2.37354 -2.928e+00 -1.819e+00
+log_k_J9Z38        -5.14736 -5.960e+00 -4.335e+00
+log_k_JSE76        -3.07802 -4.243e+00 -1.913e+00
+f_cyan_ilr_1        0.71263  3.655e-01  1.060e+00
+f_cyan_ilr_2        0.95202  2.701e-01  1.634e+00
+f_JCZ38_qlogis      3.58473  1.251e+00  5.919e+00
+f_JSE76_qlogis     19.03623 -1.037e+07  1.037e+07
+log_alpha          -0.15297 -4.490e-01  1.431e-01
+log_beta            2.99230  2.706e+00  3.278e+00
+a.1                 2.04816         NA         NA
+b.1                 0.06886         NA         NA
+SD.log_k_JCZ38      0.56174         NA         NA
+SD.log_k_J9Z38      0.86509         NA         NA
+SD.log_k_JSE76      1.28450         NA         NA
+SD.f_cyan_ilr_1     0.38705         NA         NA
+SD.f_cyan_ilr_2     0.54153         NA         NA
+SD.f_JCZ38_qlogis   1.65311         NA         NA
+SD.f_JSE76_qlogis   7.51468         NA         NA
+SD.log_alpha        0.31586         NA         NA
+SD.log_beta         0.24696         NA         NA
+
+Correlation is not available
+
+Random effects:
+                    est. lower upper
+SD.log_k_JCZ38    0.5617    NA    NA
+SD.log_k_J9Z38    0.8651    NA    NA
+SD.log_k_JSE76    1.2845    NA    NA
+SD.f_cyan_ilr_1   0.3870    NA    NA
+SD.f_cyan_ilr_2   0.5415    NA    NA
+SD.f_JCZ38_qlogis 1.6531    NA    NA
+SD.f_JSE76_qlogis 7.5147    NA    NA
+SD.log_alpha      0.3159    NA    NA
+SD.log_beta       0.2470    NA    NA
+
+Variance model:
+       est. lower upper
+a.1 2.04816    NA    NA
+b.1 0.06886    NA    NA
+
+Backtransformed parameters:
+                      est.    lower    upper
+cyan_0           1.016e+02 99.20301 103.9079
+k_JCZ38          9.315e-02  0.05349   0.1622
+k_J9Z38          5.815e-03  0.00258   0.0131
+k_JSE76          4.605e-02  0.01436   0.1477
+f_cyan_to_JCZ38  6.438e-01       NA       NA
+f_cyan_to_J9Z38  2.350e-01       NA       NA
+f_JCZ38_to_JSE76 9.730e-01  0.77745   0.9973
+f_JSE76_to_JCZ38 1.000e+00  0.00000   1.0000
+alpha            8.582e-01  0.63824   1.1538
+beta             1.993e+01 14.97621  26.5262
+
+Resulting formation fractions:
+                   ff
+cyan_JCZ38  6.438e-01
+cyan_J9Z38  2.350e-01
+cyan_sink   1.212e-01
+JCZ38_JSE76 9.730e-01
+JCZ38_sink  2.700e-02
+JSE76_JCZ38 1.000e+00
+JSE76_sink  5.403e-09
+
+Estimated disappearance times:
+         DT50   DT90 DT50back
+cyan   24.771 271.70    81.79
+JCZ38   7.441  24.72       NA
+J9Z38 119.205 395.99       NA
+JSE76  15.052  50.00       NA
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical DFOP path 2 fit with constant variance
+</caption>
+<pre><code>
+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.3 
+R version used for fitting:         4.2.3 
+Date of fit:     Thu Apr 20 07:58:43 2023 
+Date of summary: Thu Apr 20 20:01:30 2023 
+
+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 565.562 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 
+      102.4358        -2.3107        -5.3123        -3.7120         0.6753 
+  f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis         log_k1         log_k2 
+        1.1462        12.4095        12.3630        -1.9317        -4.4557 
+      g_qlogis 
+       -0.5648 
+
+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          4.594      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            0.0  0.000 0.0000
+log_k_JCZ38           0.000           0.00            0.0  0.000 0.0000
+log_k_J9Z38           0.000           0.00            0.0  0.000 0.0000
+log_k_JSE76           0.000           0.00            0.0  0.000 0.0000
+f_cyan_ilr_1          0.000           0.00            0.0  0.000 0.0000
+f_cyan_ilr_2          1.797           0.00            0.0  0.000 0.0000
+f_JCZ38_qlogis        0.000          13.85            0.0  0.000 0.0000
+f_JSE76_qlogis        0.000           0.00           14.1  0.000 0.0000
+log_k1                0.000           0.00            0.0  1.106 0.0000
+log_k2                0.000           0.00            0.0  0.000 0.6141
+g_qlogis              0.000           0.00            0.0  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
+  2290 2281  -1123
+
+Optimised parameters:
+                      est.     lower    upper
+cyan_0            102.6903 101.44420 103.9365
+log_k_JCZ38        -2.4018  -2.98058  -1.8230
+log_k_J9Z38        -5.1865  -5.92931  -4.4437
+log_k_JSE76        -3.0784  -4.25226  -1.9045
+f_cyan_ilr_1        0.7157   0.37625   1.0551
+f_cyan_ilr_2        0.7073   0.20136   1.2132
+f_JCZ38_qlogis      4.6797   0.43240   8.9269
+f_JSE76_qlogis      5.0080  -1.01380  11.0299
+log_k1             -1.9620  -2.62909  -1.2949
+log_k2             -4.4894  -4.94958  -4.0292
+g_qlogis           -0.4658  -1.34443   0.4129
+a.1                 2.7158   2.52576   2.9059
+SD.log_k_JCZ38      0.5818   0.15679   1.0067
+SD.log_k_J9Z38      0.7421   0.16751   1.3167
+SD.log_k_JSE76      1.2841   0.43247   2.1356
+SD.f_cyan_ilr_1     0.3748   0.13040   0.6192
+SD.f_cyan_ilr_2     0.4550   0.08396   0.8261
+SD.f_JCZ38_qlogis   2.0862  -0.73390   4.9062
+SD.f_JSE76_qlogis   1.9585  -3.14773   7.0647
+SD.log_k1           0.7389   0.25761   1.2201
+SD.log_k2           0.5132   0.18143   0.8450
+SD.g_qlogis         0.9870   0.35773   1.6164
+
+Correlation: 
+               cyan_0  l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76
+log_k_JCZ38    -0.0170                                                        
+log_k_J9Z38    -0.0457  0.0016                                                
+log_k_JSE76    -0.0046  0.1183  0.0005                                        
+f_cyan_ilr_1    0.0079  0.0072 -0.0909  0.0003                                
+f_cyan_ilr_2   -0.3114  0.0343  0.1542  0.0023 -0.0519                        
+f_JCZ38_qlogis  0.0777 -0.0601 -0.0152  0.0080 -0.0520 -0.2524                
+f_JSE76_qlogis -0.0356  0.0817  0.0073  0.0051  0.0388  0.1959 -0.6236        
+log_k1          0.0848 -0.0028  0.0010 -0.0010 -0.0014 -0.0245  0.0121 -0.0177
+log_k2          0.0274 -0.0001  0.0075  0.0000 -0.0023 -0.0060  0.0000 -0.0130
+g_qlogis        0.0159  0.0002 -0.0095  0.0002  0.0029 -0.0140 -0.0001  0.0149
+               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          0.0280        
+g_qlogis       -0.0278 -0.0310
+
+Random effects:
+                    est.    lower  upper
+SD.log_k_JCZ38    0.5818  0.15679 1.0067
+SD.log_k_J9Z38    0.7421  0.16751 1.3167
+SD.log_k_JSE76    1.2841  0.43247 2.1356
+SD.f_cyan_ilr_1   0.3748  0.13040 0.6192
+SD.f_cyan_ilr_2   0.4550  0.08396 0.8261
+SD.f_JCZ38_qlogis 2.0862 -0.73390 4.9062
+SD.f_JSE76_qlogis 1.9585 -3.14773 7.0647
+SD.log_k1         0.7389  0.25761 1.2201
+SD.log_k2         0.5132  0.18143 0.8450
+SD.g_qlogis       0.9870  0.35773 1.6164
+
+Variance model:
+     est. lower upper
+a.1 2.716 2.526 2.906
+
+Backtransformed parameters:
+                      est.     lower     upper
+cyan_0           1.027e+02 1.014e+02 103.93649
+k_JCZ38          9.056e-02 5.076e-02   0.16154
+k_J9Z38          5.591e-03 2.660e-03   0.01175
+k_JSE76          4.603e-02 1.423e-02   0.14890
+f_cyan_to_JCZ38  6.184e-01        NA        NA
+f_cyan_to_J9Z38  2.248e-01        NA        NA
+f_JCZ38_to_JSE76 9.908e-01 6.064e-01   0.99987
+f_JSE76_to_JCZ38 9.934e-01 2.662e-01   0.99998
+k1               1.406e-01 7.214e-02   0.27393
+k2               1.123e-02 7.086e-03   0.01779
+g                3.856e-01 2.068e-01   0.60177
+
+Resulting formation fractions:
+                  ff
+cyan_JCZ38  0.618443
+cyan_J9Z38  0.224770
+cyan_sink   0.156787
+JCZ38_JSE76 0.990803
+JCZ38_sink  0.009197
+JSE76_JCZ38 0.993360
+JSE76_sink  0.006640
+
+Estimated disappearance times:
+         DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   21.674 161.70    48.68   4.931   61.74
+JCZ38   7.654  25.43       NA      NA      NA
+J9Z38 123.966 411.81       NA      NA      NA
+JSE76  15.057  50.02       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:      3.2 
+mkin version used for pre-fitting:  1.2.3 
+R version used for fitting:         4.2.3 
+Date of fit:     Thu Apr 20 08:01:24 2023 
+Date of summary: Thu Apr 20 20:01:30 2023 
+
+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 726.501 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 
+      101.7523        -1.5948        -5.0119        -2.2723         0.6719 
+  f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis         log_k1         log_k2 
+        5.1681        12.8238        12.4130        -2.0057        -4.5526 
+      g_qlogis 
+       -0.5805 
+
+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          5.627       0.000       0.000       0.000       0.0000
+log_k_JCZ38     0.000       2.327       0.000       0.000       0.0000
+log_k_J9Z38     0.000       0.000       1.664       0.000       0.0000
+log_k_JSE76     0.000       0.000       0.000       4.566       0.0000
+f_cyan_ilr_1    0.000       0.000       0.000       0.000       0.6519
+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_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 f_JSE76_qlogis log_k1 log_k2
+cyan_0                  0.0           0.00           0.00 0.0000 0.0000
+log_k_JCZ38             0.0           0.00           0.00 0.0000 0.0000
+log_k_J9Z38             0.0           0.00           0.00 0.0000 0.0000
+log_k_JSE76             0.0           0.00           0.00 0.0000 0.0000
+f_cyan_ilr_1            0.0           0.00           0.00 0.0000 0.0000
+f_cyan_ilr_2           10.1           0.00           0.00 0.0000 0.0000
+f_JCZ38_qlogis          0.0          13.99           0.00 0.0000 0.0000
+f_JSE76_qlogis          0.0           0.00          14.15 0.0000 0.0000
+log_k1                  0.0           0.00           0.00 0.8452 0.0000
+log_k2                  0.0           0.00           0.00 0.0000 0.5968
+g_qlogis                0.0           0.00           0.00 0.0000 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          1.691
+
+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            101.10667  9.903e+01  103.18265
+log_k_JCZ38        -2.49437 -3.297e+00   -1.69221
+log_k_J9Z38        -5.08171 -5.875e+00   -4.28846
+log_k_JSE76        -3.20072 -4.180e+00   -2.22163
+f_cyan_ilr_1        0.71059  3.639e-01    1.05727
+f_cyan_ilr_2        1.15398  2.981e-01    2.00984
+f_JCZ38_qlogis      3.18027  1.056e+00    5.30452
+f_JSE76_qlogis      5.61578 -2.505e+01   36.28077
+log_k1             -2.38875 -2.517e+00   -2.26045
+log_k2             -4.67246 -4.928e+00   -4.41715
+g_qlogis           -0.28231 -1.135e+00    0.57058
+a.1                 2.08190  1.856e+00    2.30785
+b.1                 0.06114  5.015e-02    0.07214
+SD.log_k_JCZ38      0.84622  2.637e-01    1.42873
+SD.log_k_J9Z38      0.84564  2.566e-01    1.43464
+SD.log_k_JSE76      1.04385  3.242e-01    1.76351
+SD.f_cyan_ilr_1     0.38568  1.362e-01    0.63514
+SD.f_cyan_ilr_2     0.68046  7.166e-02    1.28925
+SD.f_JCZ38_qlogis   1.25244 -4.213e-02    2.54700
+SD.f_JSE76_qlogis   0.28202 -1.515e+03 1515.87968
+SD.log_k2           0.25749  7.655e-02    0.43843
+SD.g_qlogis         0.94535  3.490e-01    1.54174
+
+Correlation: 
+               cyan_0  l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76
+log_k_JCZ38    -0.0086                                                        
+log_k_J9Z38    -0.0363 -0.0007                                                
+log_k_JSE76     0.0015  0.1210 -0.0017                                        
+f_cyan_ilr_1   -0.0048  0.0095 -0.0572  0.0030                                
+f_cyan_ilr_2   -0.4788  0.0328  0.1143  0.0027 -0.0316                        
+f_JCZ38_qlogis  0.0736 -0.0664 -0.0137  0.0145 -0.0444 -0.2175                
+f_JSE76_qlogis -0.0137  0.0971  0.0035  0.0009  0.0293  0.1333 -0.6767        
+log_k1          0.2345 -0.0350 -0.0099 -0.0113 -0.0126 -0.1652  0.1756 -0.2161
+log_k2          0.0440 -0.0133  0.0199 -0.0040 -0.0097 -0.0119  0.0604 -0.1306
+g_qlogis        0.0438  0.0078 -0.0123  0.0029  0.0046 -0.0363 -0.0318  0.0736
+               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          0.3198        
+g_qlogis       -0.1666 -0.0954
+
+Random effects:
+                    est.      lower     upper
+SD.log_k_JCZ38    0.8462  2.637e-01    1.4287
+SD.log_k_J9Z38    0.8456  2.566e-01    1.4346
+SD.log_k_JSE76    1.0439  3.242e-01    1.7635
+SD.f_cyan_ilr_1   0.3857  1.362e-01    0.6351
+SD.f_cyan_ilr_2   0.6805  7.166e-02    1.2893
+SD.f_JCZ38_qlogis 1.2524 -4.213e-02    2.5470
+SD.f_JSE76_qlogis 0.2820 -1.515e+03 1515.8797
+SD.log_k2         0.2575  7.655e-02    0.4384
+SD.g_qlogis       0.9453  3.490e-01    1.5417
+
+Variance model:
+       est.   lower   upper
+a.1 2.08190 1.85595 2.30785
+b.1 0.06114 0.05015 0.07214
+
+Backtransformed parameters:
+                      est.     lower     upper
+cyan_0           1.011e+02 9.903e+01 103.18265
+k_JCZ38          8.255e-02 3.701e-02   0.18411
+k_J9Z38          6.209e-03 2.809e-03   0.01373
+k_JSE76          4.073e-02 1.530e-02   0.10843
+f_cyan_to_JCZ38  6.608e-01        NA        NA
+f_cyan_to_J9Z38  2.419e-01        NA        NA
+f_JCZ38_to_JSE76 9.601e-01 7.419e-01   0.99506
+f_JSE76_to_JCZ38 9.964e-01 1.322e-11   1.00000
+k1               9.174e-02 8.070e-02   0.10430
+k2               9.349e-03 7.243e-03   0.01207
+g                4.299e-01 2.432e-01   0.63890
+
+Resulting formation fractions:
+                  ff
+cyan_JCZ38  0.660808
+cyan_J9Z38  0.241904
+cyan_sink   0.097288
+JCZ38_JSE76 0.960085
+JCZ38_sink  0.039915
+JSE76_JCZ38 0.996373
+JSE76_sink  0.003627
+
+Estimated disappearance times:
+         DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   24.359 186.18    56.05   7.555   74.14
+JCZ38   8.397  27.89       NA      NA      NA
+J9Z38 111.631 370.83       NA      NA      NA
+JSE76  17.017  56.53       NA      NA      NA
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical SFORB path 2 fit with constant variance
+</caption>
+<pre><code>
+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.3 
+R version used for fitting:         4.2.3 
+Date of fit:     Thu Apr 20 07:58:46 2023 
+Date of summary: Thu Apr 20 20:01:30 2023 
+
+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 568.562 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 
+             102.4394               -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 
+              13.2672               13.3538 
+
+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           0.00           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                0.6349        0.000           0.00           0.00
+f_cyan_ilr_2                0.0000        1.797           0.00           0.00
+f_JCZ38_qlogis              0.0000        0.000          13.84           0.00
+f_JSE76_qlogis              0.0000        0.000           0.00          14.66
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2284 2275  -1120
+
+Optimised parameters:
+                             est.      lower      upper
+cyan_free_0              102.7730  1.015e+02  1.041e+02
+log_k_cyan_free           -2.8530 -3.167e+00 -2.539e+00
+log_k_cyan_free_bound     -2.7326 -3.543e+00 -1.922e+00
+log_k_cyan_bound_free     -3.5582 -4.126e+00 -2.990e+00
+log_k_JCZ38               -2.3810 -2.921e+00 -1.841e+00
+log_k_J9Z38               -5.2301 -5.963e+00 -4.497e+00
+log_k_JSE76               -3.0286 -4.286e+00 -1.771e+00
+f_cyan_ilr_1               0.7081  3.733e-01  1.043e+00
+f_cyan_ilr_2               0.5847  7.846e-03  1.162e+00
+f_JCZ38_qlogis             9.5676 -1.323e+03  1.342e+03
+f_JSE76_qlogis             3.7042  7.254e-02  7.336e+00
+a.1                        2.7222  2.532e+00  2.913e+00
+SD.log_k_cyan_free         0.3338  1.086e-01  5.589e-01
+SD.log_k_cyan_free_bound   0.8888  3.023e-01  1.475e+00
+SD.log_k_cyan_bound_free   0.6220  2.063e-01  1.038e+00
+SD.log_k_JCZ38             0.5221  1.334e-01  9.108e-01
+SD.log_k_J9Z38             0.7104  1.371e-01  1.284e+00
+SD.log_k_JSE76             1.3837  4.753e-01  2.292e+00
+SD.f_cyan_ilr_1            0.3620  1.248e-01  5.992e-01
+SD.f_cyan_ilr_2            0.4259  8.145e-02  7.704e-01
+SD.f_JCZ38_qlogis          3.5332 -1.037e+05  1.037e+05
+SD.f_JSE76_qlogis          1.6990 -2.771e-01  3.675e+00
+
+Correlation: 
+                      cyn_f_0 lg_k_c_ lg_k_cyn_f_ lg_k_cyn_b_ l__JCZ3 l__J9Z3
+log_k_cyan_free        0.2126                                                
+log_k_cyan_free_bound  0.0894  0.0871                                        
+log_k_cyan_bound_free  0.0033  0.0410  0.0583                                
+log_k_JCZ38           -0.0708 -0.0280 -0.0147      0.0019                    
+log_k_J9Z38           -0.0535 -0.0138  0.0012      0.0148      0.0085        
+log_k_JSE76           -0.0066 -0.0030 -0.0021     -0.0005      0.1090  0.0010
+f_cyan_ilr_1          -0.0364 -0.0157 -0.0095     -0.0015      0.0458 -0.0960
+f_cyan_ilr_2          -0.3814 -0.1104 -0.0423      0.0146      0.1540  0.1526
+f_JCZ38_qlogis         0.2507  0.0969  0.0482     -0.0097     -0.2282 -0.0363
+f_JSE76_qlogis        -0.1648 -0.0710 -0.0443     -0.0087      0.2002  0.0226
+                      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           0.0001                        
+f_cyan_ilr_2           0.0031  0.0586                
+f_JCZ38_qlogis         0.0023 -0.1867 -0.6255        
+f_JSE76_qlogis         0.0082  0.1356  0.4519 -0.7951
+
+Random effects:
+                           est.      lower     upper
+SD.log_k_cyan_free       0.3338  1.086e-01 5.589e-01
+SD.log_k_cyan_free_bound 0.8888  3.023e-01 1.475e+00
+SD.log_k_cyan_bound_free 0.6220  2.063e-01 1.038e+00
+SD.log_k_JCZ38           0.5221  1.334e-01 9.108e-01
+SD.log_k_J9Z38           0.7104  1.371e-01 1.284e+00
+SD.log_k_JSE76           1.3837  4.753e-01 2.292e+00
+SD.f_cyan_ilr_1          0.3620  1.248e-01 5.992e-01
+SD.f_cyan_ilr_2          0.4259  8.145e-02 7.704e-01
+SD.f_JCZ38_qlogis        3.5332 -1.037e+05 1.037e+05
+SD.f_JSE76_qlogis        1.6990 -2.771e-01 3.675e+00
+
+Variance model:
+     est. lower upper
+a.1 2.722 2.532 2.913
+
+Backtransformed parameters:
+                          est.     lower     upper
+cyan_free_0          1.028e+02 1.015e+02 104.06475
+k_cyan_free          5.767e-02 4.213e-02   0.07894
+k_cyan_free_bound    6.505e-02 2.892e-02   0.14633
+k_cyan_bound_free    2.849e-02 1.614e-02   0.05028
+k_JCZ38              9.246e-02 5.390e-02   0.15859
+k_J9Z38              5.353e-03 2.572e-03   0.01114
+k_JSE76              4.838e-02 1.376e-02   0.17009
+f_cyan_free_to_JCZ38 6.011e-01 5.028e-01   0.83792
+f_cyan_free_to_J9Z38 2.208e-01 5.028e-01   0.83792
+f_JCZ38_to_JSE76     9.999e-01 0.000e+00   1.00000
+f_JSE76_to_JCZ38     9.760e-01 5.181e-01   0.99935
+
+Estimated Eigenvalues of SFORB model(s):
+cyan_b1 cyan_b2  cyan_g 
+0.13942 0.01178 0.35948 
+
+Resulting formation fractions:
+                       ff
+cyan_free_JCZ38 6.011e-01
+cyan_free_J9Z38 2.208e-01
+cyan_free_sink  1.780e-01
+cyan_free       1.000e+00
+JCZ38_JSE76     9.999e-01
+JCZ38_sink      6.996e-05
+JSE76_JCZ38     9.760e-01
+JSE76_sink      2.403e-02
+
+Estimated disappearance times:
+         DT50   DT90 DT50back DT50_cyan_b1 DT50_cyan_b2
+cyan   23.390 157.60    47.44        4.971        58.82
+JCZ38   7.497  24.90       NA           NA           NA
+J9Z38 129.482 430.13       NA           NA           NA
+JSE76  14.326  47.59       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:      3.2 
+mkin version used for pre-fitting:  1.2.3 
+R version used for fitting:         4.2.3 
+Date of fit:     Thu Apr 20 08:01:30 2023 
+Date of summary: Thu Apr 20 20:01:30 2023 
+
+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 732.212 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 
+              101.751                -2.837                -3.016 
+log_k_cyan_bound_free           log_k_JCZ38           log_k_J9Z38 
+               -3.660                -2.299                -5.313 
+          log_k_JSE76          f_cyan_ilr_1          f_cyan_ilr_2 
+               -3.699                 0.672                 5.873 
+       f_JCZ38_qlogis        f_JSE76_qlogis 
+               13.216                13.338 
+
+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         0.00           0.00           0.00
+log_k_cyan_free             0.0000         0.00           0.00           0.00
+log_k_cyan_free_bound       0.0000         0.00           0.00           0.00
+log_k_cyan_bound_free       0.0000         0.00           0.00           0.00
+log_k_JCZ38                 0.0000         0.00           0.00           0.00
+log_k_J9Z38                 0.0000         0.00           0.00           0.00
+log_k_JSE76                 0.0000         0.00           0.00           0.00
+f_cyan_ilr_1                0.6519         0.00           0.00           0.00
+f_cyan_ilr_2                0.0000        10.78           0.00           0.00
+f_JCZ38_qlogis              0.0000         0.00          13.96           0.00
+f_JSE76_qlogis              0.0000         0.00           0.00          14.69
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2240 2232  -1098
+
+Optimised parameters:
+                              est.     lower    upper
+cyan_free_0              101.10205  98.99221 103.2119
+log_k_cyan_free           -3.16929  -3.61395  -2.7246
+log_k_cyan_free_bound     -3.38259  -3.63022  -3.1350
+log_k_cyan_bound_free     -3.81075  -4.13888  -3.4826
+log_k_JCZ38               -2.42057  -3.00756  -1.8336
+log_k_J9Z38               -5.07501  -5.85138  -4.2986
+log_k_JSE76               -3.12442  -4.21277  -2.0361
+f_cyan_ilr_1               0.70577   0.35788   1.0537
+f_cyan_ilr_2               1.14824   0.15810   2.1384
+f_JCZ38_qlogis             3.52245   0.43257   6.6123
+f_JSE76_qlogis             5.65140 -21.22295  32.5257
+a.1                        2.07062   1.84329   2.2980
+b.1                        0.06227   0.05124   0.0733
+SD.log_k_cyan_free         0.49468   0.18566   0.8037
+SD.log_k_cyan_bound_free   0.28972   0.07188   0.5076
+SD.log_k_JCZ38             0.58852   0.16800   1.0090
+SD.log_k_J9Z38             0.82500   0.24730   1.4027
+SD.log_k_JSE76             1.19201   0.40313   1.9809
+SD.f_cyan_ilr_1            0.38534   0.13640   0.6343
+SD.f_cyan_ilr_2            0.72463   0.10076   1.3485
+SD.f_JCZ38_qlogis          1.38223  -0.20997   2.9744
+SD.f_JSE76_qlogis          2.07989 -72.53027  76.6901
+
+Correlation: 
+                      cyn_f_0 lg_k_c_ lg_k_cyn_f_ lg_k_cyn_b_ l__JCZ3 l__J9Z3
+log_k_cyan_free        0.1117                                                
+log_k_cyan_free_bound  0.1763  0.1828                                        
+log_k_cyan_bound_free  0.0120  0.0593  0.5030                                
+log_k_JCZ38           -0.0459 -0.0230 -0.0931     -0.0337                    
+log_k_J9Z38           -0.0381 -0.0123 -0.0139      0.0237      0.0063        
+log_k_JSE76           -0.0044 -0.0038 -0.0175     -0.0072      0.1120  0.0003
+f_cyan_ilr_1          -0.0199 -0.0087 -0.0407     -0.0233      0.0268 -0.0552
+f_cyan_ilr_2          -0.4806 -0.1015 -0.2291     -0.0269      0.1156  0.1113
+f_JCZ38_qlogis         0.1805  0.0825  0.3085      0.0963     -0.1674 -0.0314
+f_JSE76_qlogis        -0.1586 -0.0810 -0.3560     -0.1563      0.2025  0.0278
+                      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           0.0024                        
+f_cyan_ilr_2           0.0087  0.0172                
+f_JCZ38_qlogis        -0.0016 -0.1047 -0.4656        
+f_JSE76_qlogis         0.0119  0.1034  0.4584 -0.8137
+
+Random effects:
+                           est.     lower   upper
+SD.log_k_cyan_free       0.4947   0.18566  0.8037
+SD.log_k_cyan_bound_free 0.2897   0.07188  0.5076
+SD.log_k_JCZ38           0.5885   0.16800  1.0090
+SD.log_k_J9Z38           0.8250   0.24730  1.4027
+SD.log_k_JSE76           1.1920   0.40313  1.9809
+SD.f_cyan_ilr_1          0.3853   0.13640  0.6343
+SD.f_cyan_ilr_2          0.7246   0.10076  1.3485
+SD.f_JCZ38_qlogis        1.3822  -0.20997  2.9744
+SD.f_JSE76_qlogis        2.0799 -72.53027 76.6901
+
+Variance model:
+       est.   lower  upper
+a.1 2.07062 1.84329 2.2980
+b.1 0.06227 0.05124 0.0733
+
+Backtransformed parameters:
+                          est.     lower     upper
+cyan_free_0          1.011e+02 9.899e+01 103.21190
+k_cyan_free          4.203e-02 2.695e-02   0.06557
+k_cyan_free_bound    3.396e-02 2.651e-02   0.04350
+k_cyan_bound_free    2.213e-02 1.594e-02   0.03073
+k_JCZ38              8.887e-02 4.941e-02   0.15984
+k_J9Z38              6.251e-03 2.876e-03   0.01359
+k_JSE76              4.396e-02 1.481e-02   0.13054
+f_cyan_free_to_JCZ38 6.590e-01 5.557e-01   0.95365
+f_cyan_free_to_J9Z38 2.429e-01 5.557e-01   0.95365
+f_JCZ38_to_JSE76     9.713e-01 6.065e-01   0.99866
+f_JSE76_to_JCZ38     9.965e-01 6.067e-10   1.00000
+
+Estimated Eigenvalues of SFORB model(s):
+cyan_b1 cyan_b2  cyan_g 
+0.08749 0.01063 0.40855 
+
+Resulting formation fractions:
+                     ff
+cyan_free_JCZ38 0.65905
+cyan_free_J9Z38 0.24291
+cyan_free_sink  0.09805
+cyan_free       1.00000
+JCZ38_JSE76     0.97132
+JCZ38_sink      0.02868
+JSE76_JCZ38     0.99650
+JSE76_sink      0.00350
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_cyan_b1 DT50_cyan_b2
+cyan   24.91 167.16    50.32        7.922        65.19
+JCZ38   7.80  25.91       NA           NA           NA
+J9Z38 110.89 368.36       NA           NA           NA
+JSE76  15.77  52.38       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:      3.2 
+mkin version used for pre-fitting:  1.2.3 
+R version used for fitting:         4.2.3 
+Date of fit:     Thu Apr 20 08:15:01 2023 
+Date of summary: Thu Apr 20 20:01:31 2023 
+
+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 808.728 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 
+      101.9028        -1.9055        -5.0249        -2.5646         0.6807 
+  f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis      log_alpha       log_beta 
+        4.8883        16.0676         9.3923        -0.1346         3.0364 
+
+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          6.321       0.000       0.000       0.000       0.0000
+log_k_JCZ38     0.000       1.392       0.000       0.000       0.0000
+log_k_J9Z38     0.000       0.000       1.561       0.000       0.0000
+log_k_JSE76     0.000       0.000       0.000       3.614       0.0000
+f_cyan_ilr_1    0.000       0.000       0.000       0.000       0.6339
+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          10.41           0.00           0.00    0.0000   0.0000
+f_JCZ38_qlogis         0.00          12.24           0.00    0.0000   0.0000
+f_JSE76_qlogis         0.00           0.00          15.13    0.0000   0.0000
+log_alpha              0.00           0.00           0.00    0.3701   0.0000
+log_beta               0.00           0.00           0.00    0.0000   0.5662
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2251 2244  -1106
+
+Optimised parameters:
+                      est.   lower   upper
+cyan_0           101.05768      NA      NA
+log_k_JCZ38       -2.73252      NA      NA
+log_k_J9Z38       -5.07399      NA      NA
+log_k_JSE76       -3.52863      NA      NA
+f_cyan_ilr_1       0.72176      NA      NA
+f_cyan_ilr_2       1.34610      NA      NA
+f_JCZ38_qlogis     2.08337      NA      NA
+f_JSE76_qlogis  1590.31880      NA      NA
+log_alpha         -0.09336      NA      NA
+log_beta           3.10191      NA      NA
+a.1                2.08557 1.85439 2.31675
+b.1                0.06998 0.05800 0.08197
+SD.log_k_JCZ38     1.20053 0.43329 1.96777
+SD.log_k_J9Z38     0.85854 0.26708 1.45000
+SD.log_k_JSE76     0.62528 0.16061 1.08995
+SD.f_cyan_ilr_1    0.35190 0.12340 0.58039
+SD.f_cyan_ilr_2    0.85385 0.15391 1.55378
+SD.log_alpha       0.28971 0.08718 0.49225
+SD.log_beta        0.31614 0.05938 0.57290
+
+Correlation is not available
+
+Random effects:
+                  est.   lower  upper
+SD.log_k_JCZ38  1.2005 0.43329 1.9678
+SD.log_k_J9Z38  0.8585 0.26708 1.4500
+SD.log_k_JSE76  0.6253 0.16061 1.0900
+SD.f_cyan_ilr_1 0.3519 0.12340 0.5804
+SD.f_cyan_ilr_2 0.8538 0.15391 1.5538
+SD.log_alpha    0.2897 0.08718 0.4923
+SD.log_beta     0.3161 0.05938 0.5729
+
+Variance model:
+       est. lower   upper
+a.1 2.08557 1.854 2.31675
+b.1 0.06998 0.058 0.08197
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.011e+02    NA    NA
+k_JCZ38          6.506e-02    NA    NA
+k_J9Z38          6.257e-03    NA    NA
+k_JSE76          2.935e-02    NA    NA
+f_cyan_to_JCZ38  6.776e-01    NA    NA
+f_cyan_to_J9Z38  2.442e-01    NA    NA
+f_JCZ38_to_JSE76 8.893e-01    NA    NA
+f_JSE76_to_JCZ38 1.000e+00    NA    NA
+alpha            9.109e-01    NA    NA
+beta             2.224e+01    NA    NA
+
+Resulting formation fractions:
+                 ff
+cyan_JCZ38  0.67761
+cyan_J9Z38  0.24417
+cyan_sink   0.07822
+JCZ38_JSE76 0.88928
+JCZ38_sink  0.11072
+JSE76_JCZ38 1.00000
+JSE76_sink  0.00000
+
+Estimated disappearance times:
+        DT50   DT90 DT50back
+cyan   25.36 256.37    77.18
+JCZ38  10.65  35.39       NA
+J9Z38 110.77 367.98       NA
+JSE76  23.62  78.47       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:      3.2 
+mkin version used for pre-fitting:  1.2.3 
+R version used for fitting:         4.2.3 
+Date of fit:     Thu Apr 20 08:16:32 2023 
+Date of summary: Thu Apr 20 20:01:31 2023 
+
+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 900.061 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 
+      102.4358        -2.3107        -5.3123        -3.7120         0.6753 
+  f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis         log_k1         log_k2 
+        1.1462        12.4095        12.3630        -1.9317        -4.4557 
+      g_qlogis 
+       -0.5648 
+
+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          4.594      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            0.0  0.000 0.0000
+log_k_JCZ38           0.000           0.00            0.0  0.000 0.0000
+log_k_J9Z38           0.000           0.00            0.0  0.000 0.0000
+log_k_JSE76           0.000           0.00            0.0  0.000 0.0000
+f_cyan_ilr_1          0.000           0.00            0.0  0.000 0.0000
+f_cyan_ilr_2          1.797           0.00            0.0  0.000 0.0000
+f_JCZ38_qlogis        0.000          13.85            0.0  0.000 0.0000
+f_JSE76_qlogis        0.000           0.00           14.1  0.000 0.0000
+log_k1                0.000           0.00            0.0  1.106 0.0000
+log_k2                0.000           0.00            0.0  0.000 0.6141
+g_qlogis              0.000           0.00            0.0  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           102.5254      NA     NA
+log_k_JCZ38       -2.9358      NA     NA
+log_k_J9Z38       -5.1424      NA     NA
+log_k_JSE76       -3.6458      NA     NA
+f_cyan_ilr_1       0.6957      NA     NA
+f_cyan_ilr_2       0.6635      NA     NA
+f_JCZ38_qlogis  4984.8163      NA     NA
+f_JSE76_qlogis     1.9415      NA     NA
+log_k1            -1.9456      NA     NA
+log_k2            -4.4705      NA     NA
+g_qlogis          -0.5117      NA     NA
+a.1                2.7455 2.55392 2.9370
+SD.log_k_JCZ38     1.3163 0.47635 2.1563
+SD.log_k_J9Z38     0.7162 0.16133 1.2711
+SD.log_k_JSE76     0.6457 0.15249 1.1390
+SD.f_cyan_ilr_1    0.3424 0.11714 0.5677
+SD.f_cyan_ilr_2    0.4524 0.09709 0.8077
+SD.log_k1          0.7353 0.25445 1.2161
+SD.log_k2          0.5137 0.18206 0.8453
+SD.g_qlogis        0.9857 0.35651 1.6148
+
+Correlation is not available
+
+Random effects:
+                  est.   lower  upper
+SD.log_k_JCZ38  1.3163 0.47635 2.1563
+SD.log_k_J9Z38  0.7162 0.16133 1.2711
+SD.log_k_JSE76  0.6457 0.15249 1.1390
+SD.f_cyan_ilr_1 0.3424 0.11714 0.5677
+SD.f_cyan_ilr_2 0.4524 0.09709 0.8077
+SD.log_k1       0.7353 0.25445 1.2161
+SD.log_k2       0.5137 0.18206 0.8453
+SD.g_qlogis     0.9857 0.35651 1.6148
+
+Variance model:
+     est. lower upper
+a.1 2.745 2.554 2.937
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.025e+02    NA    NA
+k_JCZ38          5.309e-02    NA    NA
+k_J9Z38          5.844e-03    NA    NA
+k_JSE76          2.610e-02    NA    NA
+f_cyan_to_JCZ38  6.079e-01    NA    NA
+f_cyan_to_J9Z38  2.272e-01    NA    NA
+f_JCZ38_to_JSE76 1.000e+00    NA    NA
+f_JSE76_to_JCZ38 8.745e-01    NA    NA
+k1               1.429e-01    NA    NA
+k2               1.144e-02    NA    NA
+g                3.748e-01    NA    NA
+
+Resulting formation fractions:
+                ff
+cyan_JCZ38  0.6079
+cyan_J9Z38  0.2272
+cyan_sink   0.1649
+JCZ38_JSE76 1.0000
+JCZ38_sink  0.0000
+JSE76_JCZ38 0.8745
+JSE76_sink  0.1255
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   22.29 160.20    48.22    4.85   60.58
+JCZ38  13.06  43.37       NA      NA      NA
+J9Z38 118.61 394.02       NA      NA      NA
+JSE76  26.56  88.22       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:      3.2 
+mkin version used for pre-fitting:  1.2.3 
+R version used for fitting:         4.2.3 
+Date of fit:     Thu Apr 20 08:16:47 2023 
+Date of summary: Thu Apr 20 20:01:31 2023 
+
+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 914.763 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 
+      101.7523        -1.5948        -5.0119        -2.2723         0.6719 
+  f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis         log_k1         log_k2 
+        5.1681        12.8238        12.4130        -2.0057        -4.5526 
+      g_qlogis 
+       -0.5805 
+
+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          5.627       0.000       0.000       0.000       0.0000
+log_k_JCZ38     0.000       2.327       0.000       0.000       0.0000
+log_k_J9Z38     0.000       0.000       1.664       0.000       0.0000
+log_k_JSE76     0.000       0.000       0.000       4.566       0.0000
+f_cyan_ilr_1    0.000       0.000       0.000       0.000       0.6519
+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_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 f_JSE76_qlogis log_k1 log_k2
+cyan_0                  0.0           0.00           0.00 0.0000 0.0000
+log_k_JCZ38             0.0           0.00           0.00 0.0000 0.0000
+log_k_J9Z38             0.0           0.00           0.00 0.0000 0.0000
+log_k_JSE76             0.0           0.00           0.00 0.0000 0.0000
+f_cyan_ilr_1            0.0           0.00           0.00 0.0000 0.0000
+f_cyan_ilr_2           10.1           0.00           0.00 0.0000 0.0000
+f_JCZ38_qlogis          0.0          13.99           0.00 0.0000 0.0000
+f_JSE76_qlogis          0.0           0.00          14.15 0.0000 0.0000
+log_k1                  0.0           0.00           0.00 0.8452 0.0000
+log_k2                  0.0           0.00           0.00 0.0000 0.5968
+g_qlogis                0.0           0.00           0.00 0.0000 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          1.691
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2232 2224  -1096
+
+Optimised parameters:
+                     est.   lower   upper
+cyan_0          101.20051      NA      NA
+log_k_JCZ38      -2.93542      NA      NA
+log_k_J9Z38      -5.03151      NA      NA
+log_k_JSE76      -3.67679      NA      NA
+f_cyan_ilr_1      0.67290      NA      NA
+f_cyan_ilr_2      0.99787      NA      NA
+f_JCZ38_qlogis  348.32484      NA      NA
+f_JSE76_qlogis    1.87846      NA      NA
+log_k1           -2.32738      NA      NA
+log_k2           -4.61295      NA      NA
+g_qlogis         -0.38342      NA      NA
+a.1               2.06184 1.83746 2.28622
+b.1               0.06329 0.05211 0.07447
+SD.log_k_JCZ38    1.29042 0.47468 2.10617
+SD.log_k_J9Z38    0.84235 0.25903 1.42566
+SD.log_k_JSE76    0.56930 0.13934 0.99926
+SD.f_cyan_ilr_1   0.35183 0.12298 0.58068
+SD.f_cyan_ilr_2   0.77269 0.17908 1.36631
+SD.log_k2         0.28549 0.09210 0.47888
+SD.g_qlogis       0.93830 0.34568 1.53093
+
+Correlation is not available
+
+Random effects:
+                  est.  lower  upper
+SD.log_k_JCZ38  1.2904 0.4747 2.1062
+SD.log_k_J9Z38  0.8423 0.2590 1.4257
+SD.log_k_JSE76  0.5693 0.1393 0.9993
+SD.f_cyan_ilr_1 0.3518 0.1230 0.5807
+SD.f_cyan_ilr_2 0.7727 0.1791 1.3663
+SD.log_k2       0.2855 0.0921 0.4789
+SD.g_qlogis     0.9383 0.3457 1.5309
+
+Variance model:
+       est.   lower   upper
+a.1 2.06184 1.83746 2.28622
+b.1 0.06329 0.05211 0.07447
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.012e+02    NA    NA
+k_JCZ38          5.311e-02    NA    NA
+k_J9Z38          6.529e-03    NA    NA
+k_JSE76          2.530e-02    NA    NA
+f_cyan_to_JCZ38  6.373e-01    NA    NA
+f_cyan_to_J9Z38  2.461e-01    NA    NA
+f_JCZ38_to_JSE76 1.000e+00    NA    NA
+f_JSE76_to_JCZ38 8.674e-01    NA    NA
+k1               9.755e-02    NA    NA
+k2               9.922e-03    NA    NA
+g                4.053e-01    NA    NA
+
+Resulting formation fractions:
+                ff
+cyan_JCZ38  0.6373
+cyan_J9Z38  0.2461
+cyan_sink   0.1167
+JCZ38_JSE76 1.0000
+JCZ38_sink  0.0000
+JSE76_JCZ38 0.8674
+JSE76_sink  0.1326
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   24.93 179.68    54.09   7.105   69.86
+JCZ38  13.05  43.36       NA      NA      NA
+J9Z38 106.16 352.67       NA      NA      NA
+JSE76  27.39  91.00       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:      3.2 
+mkin version used for pre-fitting:  1.2.3 
+R version used for fitting:         4.2.3 
+Date of fit:     Thu Apr 20 08:16:33 2023 
+Date of summary: Thu Apr 20 20:01:31 2023 
+
+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 901.179 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 
+             102.4394               -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 
+              13.2672               13.3538 
+
+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           0.00           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                0.6349        0.000           0.00           0.00
+f_cyan_ilr_2                0.0000        1.797           0.00           0.00
+f_JCZ38_qlogis              0.0000        0.000          13.84           0.00
+f_JSE76_qlogis              0.0000        0.000           0.00          14.66
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2279 2272  -1120
+
+Optimised parameters:
+                              est.   lower  upper
+cyan_free_0               102.5621      NA     NA
+log_k_cyan_free            -2.8531      NA     NA
+log_k_cyan_free_bound      -2.6916      NA     NA
+log_k_cyan_bound_free      -3.5032      NA     NA
+log_k_JCZ38                -2.9436      NA     NA
+log_k_J9Z38                -5.1140      NA     NA
+log_k_JSE76                -3.6472      NA     NA
+f_cyan_ilr_1                0.6887      NA     NA
+f_cyan_ilr_2                0.6874      NA     NA
+f_JCZ38_qlogis           4063.6389      NA     NA
+f_JSE76_qlogis              1.9556      NA     NA
+a.1                         2.7460 2.55451 2.9376
+SD.log_k_cyan_free          0.3131 0.09841 0.5277
+SD.log_k_cyan_free_bound    0.8850 0.29909 1.4710
+SD.log_k_cyan_bound_free    0.6167 0.20391 1.0295
+SD.log_k_JCZ38              1.3555 0.49101 2.2200
+SD.log_k_J9Z38              0.7200 0.16166 1.2783
+SD.log_k_JSE76              0.6252 0.14619 1.1042
+SD.f_cyan_ilr_1             0.3386 0.11447 0.5627
+SD.f_cyan_ilr_2             0.4699 0.09810 0.8417
+
+Correlation is not available
+
+Random effects:
+                           est.   lower  upper
+SD.log_k_cyan_free       0.3131 0.09841 0.5277
+SD.log_k_cyan_free_bound 0.8850 0.29909 1.4710
+SD.log_k_cyan_bound_free 0.6167 0.20391 1.0295
+SD.log_k_JCZ38           1.3555 0.49101 2.2200
+SD.log_k_J9Z38           0.7200 0.16166 1.2783
+SD.log_k_JSE76           0.6252 0.14619 1.1042
+SD.f_cyan_ilr_1          0.3386 0.11447 0.5627
+SD.f_cyan_ilr_2          0.4699 0.09810 0.8417
+
+Variance model:
+     est. lower upper
+a.1 2.746 2.555 2.938
+
+Backtransformed parameters:
+                          est. lower upper
+cyan_free_0          1.026e+02    NA    NA
+k_cyan_free          5.767e-02    NA    NA
+k_cyan_free_bound    6.777e-02    NA    NA
+k_cyan_bound_free    3.010e-02    NA    NA
+k_JCZ38              5.267e-02    NA    NA
+k_J9Z38              6.012e-03    NA    NA
+k_JSE76              2.606e-02    NA    NA
+f_cyan_free_to_JCZ38 6.089e-01    NA    NA
+f_cyan_free_to_J9Z38 2.299e-01    NA    NA
+f_JCZ38_to_JSE76     1.000e+00    NA    NA
+f_JSE76_to_JCZ38     8.761e-01    NA    NA
+
+Estimated Eigenvalues of SFORB model(s):
+cyan_b1 cyan_b2  cyan_g 
+ 0.1434  0.0121  0.3469 
+
+Resulting formation fractions:
+                    ff
+cyan_free_JCZ38 0.6089
+cyan_free_J9Z38 0.2299
+cyan_free_sink  0.1612
+cyan_free       1.0000
+JCZ38_JSE76     1.0000
+JCZ38_sink      0.0000
+JSE76_JCZ38     0.8761
+JSE76_sink      0.1239
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_cyan_b1 DT50_cyan_b2
+cyan   23.94 155.06    46.68        4.832        57.28
+JCZ38  13.16  43.71       NA           NA           NA
+J9Z38 115.30 383.02       NA           NA           NA
+JSE76  26.59  88.35       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:      3.2 
+mkin version used for pre-fitting:  1.2.3 
+R version used for fitting:         4.2.3 
+Date of fit:     Thu Apr 20 08:16:19 2023 
+Date of summary: Thu Apr 20 20:01:31 2023 
+
+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 887.343 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 
+              101.751                -2.837                -3.016 
+log_k_cyan_bound_free           log_k_JCZ38           log_k_J9Z38 
+               -3.660                -2.299                -5.313 
+          log_k_JSE76          f_cyan_ilr_1          f_cyan_ilr_2 
+               -3.699                 0.672                 5.873 
+       f_JCZ38_qlogis        f_JSE76_qlogis 
+               13.216                13.338 
+
+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         0.00           0.00           0.00
+log_k_cyan_free             0.0000         0.00           0.00           0.00
+log_k_cyan_free_bound       0.0000         0.00           0.00           0.00
+log_k_cyan_bound_free       0.0000         0.00           0.00           0.00
+log_k_JCZ38                 0.0000         0.00           0.00           0.00
+log_k_J9Z38                 0.0000         0.00           0.00           0.00
+log_k_JSE76                 0.0000         0.00           0.00           0.00
+f_cyan_ilr_1                0.6519         0.00           0.00           0.00
+f_cyan_ilr_2                0.0000        10.78           0.00           0.00
+f_JCZ38_qlogis              0.0000         0.00          13.96           0.00
+f_JSE76_qlogis              0.0000         0.00           0.00          14.69
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2236 2228  -1098
+
+Optimised parameters:
+                              est.   lower   upper
+cyan_free_0              100.72760      NA      NA
+log_k_cyan_free           -3.18281      NA      NA
+log_k_cyan_free_bound     -3.37924      NA      NA
+log_k_cyan_bound_free     -3.77107      NA      NA
+log_k_JCZ38               -2.92811      NA      NA
+log_k_J9Z38               -5.02759      NA      NA
+log_k_JSE76               -3.65835      NA      NA
+f_cyan_ilr_1               0.67390      NA      NA
+f_cyan_ilr_2               1.15106      NA      NA
+f_JCZ38_qlogis           827.82299      NA      NA
+f_JSE76_qlogis             1.83064      NA      NA
+a.1                        2.06921 1.84443 2.29399
+b.1                        0.06391 0.05267 0.07515
+SD.log_k_cyan_free         0.50518 0.18962 0.82075
+SD.log_k_cyan_bound_free   0.30991 0.08170 0.53813
+SD.log_k_JCZ38             1.26661 0.46578 2.06744
+SD.log_k_J9Z38             0.88272 0.27813 1.48730
+SD.log_k_JSE76             0.53050 0.12561 0.93538
+SD.f_cyan_ilr_1            0.35547 0.12461 0.58633
+SD.f_cyan_ilr_2            0.91446 0.20131 1.62761
+
+Correlation is not available
+
+Random effects:
+                           est.  lower  upper
+SD.log_k_cyan_free       0.5052 0.1896 0.8207
+SD.log_k_cyan_bound_free 0.3099 0.0817 0.5381
+SD.log_k_JCZ38           1.2666 0.4658 2.0674
+SD.log_k_J9Z38           0.8827 0.2781 1.4873
+SD.log_k_JSE76           0.5305 0.1256 0.9354
+SD.f_cyan_ilr_1          0.3555 0.1246 0.5863
+SD.f_cyan_ilr_2          0.9145 0.2013 1.6276
+
+Variance model:
+       est.   lower   upper
+a.1 2.06921 1.84443 2.29399
+b.1 0.06391 0.05267 0.07515
+
+Backtransformed parameters:
+                          est. lower upper
+cyan_free_0          1.007e+02    NA    NA
+k_cyan_free          4.147e-02    NA    NA
+k_cyan_free_bound    3.407e-02    NA    NA
+k_cyan_bound_free    2.303e-02    NA    NA
+k_JCZ38              5.350e-02    NA    NA
+k_J9Z38              6.555e-03    NA    NA
+k_JSE76              2.578e-02    NA    NA
+f_cyan_free_to_JCZ38 6.505e-01    NA    NA
+f_cyan_free_to_J9Z38 2.508e-01    NA    NA
+f_JCZ38_to_JSE76     1.000e+00    NA    NA
+f_JSE76_to_JCZ38     8.618e-01    NA    NA
+
+Estimated Eigenvalues of SFORB model(s):
+cyan_b1 cyan_b2  cyan_g 
+0.08768 0.01089 0.39821 
+
+Resulting formation fractions:
+                     ff
+cyan_free_JCZ38 0.65053
+cyan_free_J9Z38 0.25082
+cyan_free_sink  0.09864
+cyan_free       1.00000
+JCZ38_JSE76     1.00000
+JCZ38_sink      0.00000
+JSE76_JCZ38     0.86184
+JSE76_sink      0.13816
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_cyan_b1 DT50_cyan_b2
+cyan   25.32 164.79    49.61        7.906        63.64
+JCZ38  12.96  43.04       NA           NA           NA
+J9Z38 105.75 351.29       NA           NA           NA
+JSE76  26.89  89.33       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 4.2.3 (2023-03-15)
+Platform: x86_64-pc-linux-gnu (64-bit)
+Running under: Debian GNU/Linux 12 (bookworm)
+
+Matrix products: default
+BLAS:   /usr/lib/x86_64-linux-gnu/openblas-serial/libblas.so.3
+LAPACK: /usr/lib/x86_64-linux-gnu/openblas-serial/libopenblas-r0.3.21.so
+
+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       
+
+attached base packages:
+[1] parallel  stats     graphics  grDevices utils     datasets  methods  
+[8] base     
+
+other attached packages:
+[1] saemix_3.2 npde_3.3   knitr_1.42 mkin_1.2.3
+
+loaded via a namespace (and not attached):
+ [1] pillar_1.9.0      bslib_0.4.2       compiler_4.2.3    jquerylib_0.1.4  
+ [5] tools_4.2.3       mclust_6.0.0      digest_0.6.31     tibble_3.2.1     
+ [9] jsonlite_1.8.4    evaluate_0.20     memoise_2.0.1     lifecycle_1.0.3  
+[13] nlme_3.1-162      gtable_0.3.3      lattice_0.21-8    pkgconfig_2.0.3  
+[17] rlang_1.1.0       DBI_1.1.3         cli_3.6.1         yaml_2.3.7       
+[21] pkgdown_2.0.7     xfun_0.38         fastmap_1.1.1     gridExtra_2.3    
+[25] dplyr_1.1.1       stringr_1.5.0     generics_0.1.3    desc_1.4.2       
+[29] fs_1.6.1          vctrs_0.6.1       sass_0.4.5        systemfonts_1.0.4
+[33] tidyselect_1.2.0  rprojroot_2.0.3   lmtest_0.9-40     grid_4.2.3       
+[37] inline_0.3.19     glue_1.6.2        R6_2.5.1          textshaping_0.3.6
+[41] fansi_1.0.4       rmarkdown_2.21    purrr_1.0.1       ggplot2_3.4.2    
+[45] magrittr_2.0.3    scales_1.2.1      htmltools_0.5.5   colorspace_2.1-0 
+[49] ragg_1.2.5        utf8_1.2.3        stringi_1.7.12    munsell_0.5.0    
+[53] cachem_1.0.7      zoo_1.8-12       </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:       64936316 kB</code></pre>
+</div>
+</div>
+  </div>
+
+  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
+
+        <nav id="toc" data-toggle="toc"><h2 data-toc-skip>Contents</h2>
+    </nav>
+</div>
+
+</div>
+
+
+
+      <footer><div class="copyright">
+  <p></p>
+<p>Developed by Johannes Ranke.</p>
+</div>
+
+<div class="pkgdown">
+  <p></p>
+<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p>
+</div>
+
+      </footer>
+</div>
+
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+  
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+  </body>
+</html>
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+      <h1 data-toc-skip>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 20 April 2023</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="hidden 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 1.2.3. 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">C</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">C</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">720.4</td>
+<td align="right">718.8</td>
+<td align="right">-352.2</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">665.5</td>
+<td align="right">663.4</td>
+<td align="right">-322.8</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="37%">
+<col width="6%">
+<col width="8%">
+<col width="8%">
+<col width="9%">
+<col width="9%">
+<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">663.8</td>
+<td align="right">661.9</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">665.5</td>
+<td align="right">663.4</td>
+<td align="right">-322.8</td>
+<td align="right">0.2809</td>
+<td align="right">1</td>
+<td align="right">0.5961</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:      3.2 
+mkin version used for pre-fitting:  1.2.3 
+R version used for fitting:         4.2.3 
+Date of fit:     Thu Apr 20 14:07:09 2023 
+Date of summary: Thu Apr 20 14:07:10 2023 
+
+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 4.175 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+   DMTA_0        k1        k2         g 
+98.759266  0.087034  0.009933  0.930827 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 k1 k2 g
+DMTA_0  98.76  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
+  663.8 661.9 -322.9
+
+Optimised parameters:
+               est.     lower     upper
+DMTA_0    98.228939 96.285869 100.17201
+k1         0.064063  0.033477   0.09465
+k2         0.008297  0.005824   0.01077
+g          0.953821  0.914328   0.99331
+a.1        1.068479  0.869538   1.26742
+b.1        0.029424  0.022406   0.03644
+SD.DMTA_0  2.030437  0.404824   3.65605
+SD.k1      0.594692  0.256660   0.93272
+SD.g       1.006754  0.361327   1.65218
+
+Correlation: 
+   DMTA_0  k1      k2     
+k1  0.0218                
+k2  0.0556  0.0355        
+g  -0.0516 -0.0284 -0.2800
+
+Random effects:
+            est.  lower  upper
+SD.DMTA_0 2.0304 0.4048 3.6560
+SD.k1     0.5947 0.2567 0.9327
+SD.g      1.0068 0.3613 1.6522
+
+Variance model:
+       est.   lower   upper
+a.1 1.06848 0.86954 1.26742
+b.1 0.02942 0.02241 0.03644
+
+Estimated disappearance times:
+      DT50 DT90 DT50back DT50_k1 DT50_k2
+DMTA 11.45 41.4    12.46   10.82   83.54</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:      3.2 
+mkin version used for pre-fitting:  1.2.3 
+R version used for fitting:         4.2.3 
+Date of fit:     Thu Apr 20 14:07:02 2023 
+Date of summary: Thu Apr 20 14:08:16 2023 
+
+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 0.982 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:      3.2 
+mkin version used for pre-fitting:  1.2.3 
+R version used for fitting:         4.2.3 
+Date of fit:     Thu Apr 20 14:07:03 2023 
+Date of summary: Thu Apr 20 14:08:16 2023 
+
+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 2.398 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 95.703157 98.84049
+k_DMTA     0.056638  0.029110  0.08417
+a.1        2.660081  2.230398  3.08976
+b.1        0.001665 -0.006911  0.01024
+SD.DMTA_0  1.545520  0.145035  2.94601
+SD.k_DMTA  0.606422  0.262274  0.95057
+
+Correlation: 
+       DMTA_0
+k_DMTA 0.0169
+
+Random effects:
+            est.  lower  upper
+SD.DMTA_0 1.5455 0.1450 2.9460
+SD.k_DMTA 0.6064 0.2623 0.9506
+
+Variance model:
+        est.     lower   upper
+a.1 2.660081  2.230398 3.08976
+b.1 0.001665 -0.006911 0.01024
+
+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:      3.2 
+mkin version used for pre-fitting:  1.2.3 
+R version used for fitting:         4.2.3 
+Date of fit:     Thu Apr 20 14:07:02 2023 
+Date of summary: Thu Apr 20 14:08:16 2023 
+
+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 1.398 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      112.8746 34.8816 190.868
+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:      3.2 
+mkin version used for pre-fitting:  1.2.3 
+R version used for fitting:         4.2.3 
+Date of fit:     Thu Apr 20 14:07:04 2023 
+Date of summary: Thu Apr 20 14:08:16 2023 
+
+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 3.044 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
+  720.4 718.8 -352.2
+
+Optimised parameters:
+              est.    lower     upper
+DMTA_0    98.99136 97.26011 100.72261
+alpha      5.86312  2.57485   9.15138
+beta      88.55571 29.20889 147.90254
+a.1        1.51063  1.24384   1.77741
+b.1        0.02824  0.02040   0.03609
+SD.DMTA_0  1.57436 -0.04867   3.19739
+SD.alpha   0.59871  0.17132   1.02611
+SD.beta    0.72994  0.22849   1.23139
+
+Correlation: 
+      DMTA_0  alpha  
+alpha -0.1363        
+beta  -0.1414  0.2542
+
+Random effects:
+            est.    lower upper
+SD.DMTA_0 1.5744 -0.04867 3.197
+SD.alpha  0.5987  0.17132 1.026
+SD.beta   0.7299  0.22849 1.231
+
+Variance model:
+       est.  lower   upper
+a.1 1.51063 1.2438 1.77741
+b.1 0.02824 0.0204 0.03609
+
+Estimated disappearance times:
+      DT50 DT90 DT50back
+DMTA 11.11 42.6    12.82
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical mkin fit of the DFOP model with error model const
+</caption>
+<pre><code>
+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.3 
+R version used for fitting:         4.2.3 
+Date of fit:     Thu Apr 20 14:07:02 2023 
+Date of summary: Thu Apr 20 14:08:16 2023 
+
+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 1.838 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 96.573898 99.61106
+k1         0.062499  0.030336  0.09466
+k2         0.009065 -0.005133  0.02326
+g          0.948967  0.862079  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:      3.2 
+mkin version used for pre-fitting:  1.2.3 
+R version used for fitting:         4.2.3 
+Date of fit:     Thu Apr 20 14:07:04 2023 
+Date of summary: Thu Apr 20 14:08:16 2023 
+
+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 3.297 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+   DMTA_0        k1        k2         g 
+98.759266  0.087034  0.009933  0.930827 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 k1 k2 g
+DMTA_0  98.76  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
+  665.5 663.4 -322.8
+
+Optimised parameters:
+               est.     lower     upper
+DMTA_0    98.377019 96.447952 100.30609
+k1         0.064843  0.034607   0.09508
+k2         0.008895  0.006368   0.01142
+g          0.949696  0.903815   0.99558
+a.1        1.065241  0.865754   1.26473
+b.1        0.029340  0.022336   0.03634
+SD.DMTA_0  2.007754  0.387982   3.62753
+SD.k1      0.580473  0.250286   0.91066
+SD.k2      0.006105 -4.920337   4.93255
+SD.g       1.097149  0.412779   1.78152
+
+Correlation: 
+   DMTA_0  k1      k2     
+k1  0.0235                
+k2  0.0595  0.0424        
+g  -0.0470 -0.0278 -0.2731
+
+Random effects:
+              est.   lower  upper
+SD.DMTA_0 2.007754  0.3880 3.6275
+SD.k1     0.580473  0.2503 0.9107
+SD.k2     0.006105 -4.9203 4.9325
+SD.g      1.097149  0.4128 1.7815
+
+Variance model:
+       est.   lower   upper
+a.1 1.06524 0.86575 1.26473
+b.1 0.02934 0.02234 0.03634
+
+Estimated disappearance times:
+      DT50  DT90 DT50back DT50_k1 DT50_k2
+DMTA 11.36 41.32    12.44   10.69   77.92
+
+</code></pre>
+<p></p>
+<caption>
+Hierarchical mkin fit of the HS model with error model const
+</caption>
+<pre><code>
+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.3 
+R version used for fitting:         4.2.3 
+Date of fit:     Thu Apr 20 14:07:03 2023 
+Date of summary: Thu Apr 20 14:08:16 2023 
+
+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 1.972 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:      3.2 
+mkin version used for pre-fitting:  1.2.3 
+R version used for fitting:         4.2.3 
+Date of fit:     Thu Apr 20 14:07:04 2023 
+Date of summary: Thu Apr 20 14:08:16 2023 
+
+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 3.378 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    97.76570 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  0.88590  1.29080
+b.1        0.02964  0.02257  0.03671
+SD.DMTA_0  2.04877  0.42607  3.67147
+SD.k1      0.59166  0.25621  0.92711
+SD.k2      0.30698  0.09561  0.51835
+SD.tb      0.01274 -0.10914  0.13462
+
+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  0.42607 3.6715
+SD.k1     0.59166  0.25621 0.9271
+SD.k2     0.30698  0.09561 0.5183
+SD.tb     0.01274 -0.10914 0.1346
+
+Variance model:
+       est.   lower   upper
+a.1 1.08835 0.88590 1.29080
+b.1 0.02964 0.02257 0.03671
+
+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 4.2.3 (2023-03-15)
+Platform: x86_64-pc-linux-gnu (64-bit)
+Running under: Debian GNU/Linux 12 (bookworm)
+
+Matrix products: default
+BLAS:   /usr/lib/x86_64-linux-gnu/openblas-serial/libblas.so.3
+LAPACK: /usr/lib/x86_64-linux-gnu/openblas-serial/libopenblas-r0.3.21.so
+
+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       
+
+attached base packages:
+[1] parallel  stats     graphics  grDevices utils     datasets  methods  
+[8] base     
+
+other attached packages:
+[1] saemix_3.2 npde_3.3   knitr_1.42 mkin_1.2.3
+
+loaded via a namespace (and not attached):
+ [1] highr_0.10        pillar_1.9.0      bslib_0.4.2       compiler_4.2.3   
+ [5] jquerylib_0.1.4   tools_4.2.3       mclust_6.0.0      digest_0.6.31    
+ [9] tibble_3.2.1      jsonlite_1.8.4    evaluate_0.20     memoise_2.0.1    
+[13] lifecycle_1.0.3   nlme_3.1-162      gtable_0.3.3      lattice_0.21-8   
+[17] pkgconfig_2.0.3   rlang_1.1.0       DBI_1.1.3         cli_3.6.1        
+[21] yaml_2.3.7        pkgdown_2.0.7     xfun_0.38         fastmap_1.1.1    
+[25] gridExtra_2.3     dplyr_1.1.1       stringr_1.5.0     generics_0.1.3   
+[29] desc_1.4.2        fs_1.6.1          vctrs_0.6.1       sass_0.4.5       
+[33] systemfonts_1.0.4 tidyselect_1.2.0  rprojroot_2.0.3   lmtest_0.9-40    
+[37] grid_4.2.3        glue_1.6.2        R6_2.5.1          textshaping_0.3.6
+[41] fansi_1.0.4       rmarkdown_2.21    purrr_1.0.1       ggplot2_3.4.2    
+[45] magrittr_2.0.3    codetools_0.2-19  scales_1.2.1      htmltools_0.5.5  
+[49] colorspace_2.1-0  ragg_1.2.5        utf8_1.2.3        stringi_1.7.12   
+[53] munsell_0.5.0     cachem_1.0.7      zoo_1.8-12       </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:       64936316 kB</code></pre>
+</div>
+</div>
+  </div>
+
+  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
+
+        <nav id="toc" data-toggle="toc"><h2 data-toc-skip>Contents</h2>
+    </nav>
+</div>
+
+</div>
+
+
+
+      <footer><div class="copyright">
+  <p></p>
+<p>Developed by Johannes Ranke.</p>
+</div>
+
+<div class="pkgdown">
+  <p></p>
+<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p>
+</div>
+
+      </footer>
+</div>
+
+  
+
+
+  
+
+  </body>
+</html>
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+      <a href="../../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a>
+    </li>
+    <li class="divider">
+    </li>
+<li class="dropdown-header">Example evaluations with hierarchical models (nonlinear mixed-effects models)</li>
+    <li>
+      <a href="../../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a>
+    </li>
+    <li>
+      <a href="../../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a>
+    </li>
+    <li>
+      <a href="../../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a>
+    </li>
+    <li>
+      <a href="../../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a>
+    </li>
+    <li>
+      <a href="../../articles/web_only/multistart.html">Short demo of the multistart method</a>
+    </li>
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+    </li>
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+      <a href="../../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a>
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+      <a href="../../articles/web_only/benchmarks.html">Benchmark timings for mkin</a>
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+      <a href="../../articles/twa.html">Calculation of time weighted average concentrations with mkin</a>
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+      
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+      </header><div class="row">
+  <div class="col-md-9 contents">
+    <div class="page-header toc-ignore">
+      <h1 data-toc-skip>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 20 April 2023</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="hidden 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 1.2.3, 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">C</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">C</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">C</td>
+<td align="left">OK</td>
+<td align="left">OK</td>
+<td align="left">C</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">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">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="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">OK</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>
+<pre><code>Warning in FUN(X[[i]], ...): Could not obtain log likelihood with 'is' method
+for sforb_path_1 const</code></pre>
+<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">2276.3</td>
+<td align="right">2272.5</td>
+<td align="right">-1120.1</td>
+</tr>
+<tr class="odd">
+<td align="left">fomc_path_1 const</td>
+<td align="right">19</td>
+<td align="right">2099.0</td>
+<td align="right">2095.0</td>
+<td align="right">-1030.5</td>
+</tr>
+<tr class="even">
+<td align="left">fomc_path_1 tc</td>
+<td align="right">20</td>
+<td align="right">1939.6</td>
+<td align="right">1935.5</td>
+<td align="right">-949.8</td>
+</tr>
+<tr class="odd">
+<td align="left">dfop_path_1 const</td>
+<td align="right">21</td>
+<td align="right">2038.8</td>
+<td align="right">2034.4</td>
+<td align="right">-998.4</td>
+</tr>
+<tr class="even">
+<td align="left">hs_path_1 const</td>
+<td align="right">21</td>
+<td align="right">2024.2</td>
+<td align="right">2019.8</td>
+<td align="right">-991.1</td>
+</tr>
+<tr class="odd">
+<td align="left">dfop_path_1 tc</td>
+<td align="right">22</td>
+<td align="right">1879.8</td>
+<td align="right">1875.2</td>
+<td align="right">-917.9</td>
+</tr>
+<tr class="even">
+<td align="left">sforb_path_1 tc</td>
+<td align="right">22</td>
+<td align="right">1832.9</td>
+<td align="right">1828.3</td>
+<td align="right">-894.4</td>
+</tr>
+<tr class="odd">
+<td align="left">hs_path_1 tc</td>
+<td align="right">22</td>
+<td align="right">1831.4</td>
+<td align="right">1826.8</td>
+<td align="right">-893.7</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="cb10"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">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"></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="cb11"><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="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">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">1830.3</td>
+<td align="right">1825.9</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">1832.9</td>
+<td align="right">1828.3</td>
+<td align="right">-894.4</td>
+</tr>
+</tbody>
+</table>
+<p>The convergence plot of the refined fit is shown below.</p>
+<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">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="cb14"><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>
+<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 
+15 17 
+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 4.2.3 (2023-03-15)
+Platform: x86_64-pc-linux-gnu (64-bit)
+Running under: Debian GNU/Linux 12 (bookworm)
+
+Matrix products: default
+BLAS:   /usr/lib/x86_64-linux-gnu/openblas-serial/libblas.so.3
+LAPACK: /usr/lib/x86_64-linux-gnu/openblas-serial/libopenblas-r0.3.21.so
+
+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       
+
+attached base packages:
+[1] parallel  stats     graphics  grDevices utils     datasets  methods  
+[8] base     
+
+other attached packages:
+[1] saemix_3.2 npde_3.3   knitr_1.42 mkin_1.2.3
+
+loaded via a namespace (and not attached):
+ [1] deSolve_1.35      zoo_1.8-12        tidyselect_1.2.0  xfun_0.38        
+ [5] bslib_0.4.2       purrr_1.0.1       lattice_0.21-8    colorspace_2.1-0 
+ [9] vctrs_0.6.1       generics_0.1.3    htmltools_0.5.5   yaml_2.3.7       
+[13] utf8_1.2.3        rlang_1.1.0       pkgbuild_1.4.0    pkgdown_2.0.7    
+[17] jquerylib_0.1.4   pillar_1.9.0      glue_1.6.2        DBI_1.1.3        
+[21] lifecycle_1.0.3   stringr_1.5.0     munsell_0.5.0     gtable_0.3.3     
+[25] ragg_1.2.5        codetools_0.2-19  memoise_2.0.1     evaluate_0.20    
+[29] inline_0.3.19     callr_3.7.3       fastmap_1.1.1     ps_1.7.4         
+[33] lmtest_0.9-40     fansi_1.0.4       highr_0.10        scales_1.2.1     
+[37] cachem_1.0.7      desc_1.4.2        jsonlite_1.8.4    systemfonts_1.0.4
+[41] fs_1.6.1          textshaping_0.3.6 gridExtra_2.3     ggplot2_3.4.2    
+[45] digest_0.6.31     stringi_1.7.12    processx_3.8.0    dplyr_1.1.1      
+[49] grid_4.2.3        rprojroot_2.0.3   cli_3.6.1         tools_4.2.3      
+[53] magrittr_2.0.3    sass_0.4.5        tibble_3.2.1      crayon_1.5.2     
+[57] pkgconfig_2.0.3   prettyunits_1.1.1 rmarkdown_2.21    R6_2.5.1         
+[61] mclust_6.0.0      nlme_3.1-162      compiler_4.2.3   </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:       64936316 kB</code></pre>
+</div>
+</div>
+  </div>
+
+  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
+
+        <nav id="toc" data-toggle="toc"><h2 data-toc-skip>Contents</h2>
+    </nav>
+</div>
+
+</div>
+
+
+
+      <footer><div class="copyright">
+  <p></p>
+<p>Developed by Johannes Ranke.</p>
+</div>
+
+<div class="pkgdown">
+  <p></p>
+<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p>
+</div>
+
+      </footer>
+</div>
+
+  
+
+
+  
+
+  </body>
+</html>
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author	Johannes Ranke <jranke@uni-bremen.de>	2023-04-20 20:17:12 +0200
committer	Johannes Ranke <jranke@uni-bremen.de>	2023-04-20 20:17:12 +0200
commit	7b7c4bf493ba15824ea43bed764661678b4aca03 (patch)
tree	48de1e32327c36ee49fc476dc76ece8397ab55c6 /docs/articles/prebuilt
parent	842998b688037c007d8876d7e1110c929fe2374c (diff)
parent	9ae42bd20bc2543a94cf1581ba9820c2f9e3afbd (diff)