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authorJohannes Ranke <jranke@uni-bremen.de>2023-04-20 20:17:12 +0200
committerJohannes Ranke <jranke@uni-bremen.de>2023-04-20 20:17:12 +0200
commit7b7c4bf493ba15824ea43bed764661678b4aca03 (patch)
tree48de1e32327c36ee49fc476dc76ece8397ab55c6 /docs/articles/prebuilt
parent842998b688037c007d8876d7e1110c929fe2374c (diff)
parent9ae42bd20bc2543a94cf1581ba9820c2f9e3afbd (diff)
Merge branch 'v1.2.3_pkgdown'
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+ <a href="../../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a>
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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>
+
+
+
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+ <p></p>
+<p>Developed by Johannes Ranke.</p>
+</div>
+
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+<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p>
+</div>
+
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+</div>
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+</html>
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+ <a href="../../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a>
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+ <a href="../../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a>
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+ <a href="../../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a>
+ </li>
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+ <a href="../../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a>
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+ <div class="page-header toc-ignore">
+ <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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+ <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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