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      <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 19 Mai 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 1.2.5 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:  1.2.5 
R version used for fitting:         4.3.0 
Date of fit:     Fri May 19 17:42:02 2023 
Date of summary: Fri May 19 18:14:01 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 443.997 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:  1.2.5 
R version used for fitting:         4.3.0 
Date of fit:     Fri May 19 17:42:01 2023 
Date of summary: Fri May 19 18:14:01 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 442.545 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:  1.2.5 
R version used for fitting:         4.3.0 
Date of fit:     Fri May 19 17:42:38 2023 
Date of summary: Fri May 19 18:14:01 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 479.463 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:  1.2.5 
R version used for fitting:         4.3.0 
Date of fit:     Fri May 19 17:42:53 2023 
Date of summary: Fri May 19 18:14:01 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 494.121 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:  1.2.5 
R version used for fitting:         4.3.0 
Date of fit:     Fri May 19 17:43:22 2023 
Date of summary: Fri May 19 18:14:01 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 523.691 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:  1.2.5 
R version used for fitting:         4.3.0 
Date of fit:     Fri May 19 17:46:08 2023 
Date of summary: Fri May 19 18:14:01 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 689.217 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:  1.2.5 
R version used for fitting:         4.3.0 
Date of fit:     Fri May 19 17:43:37 2023 
Date of summary: Fri May 19 18:14:01 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 538.025 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:  1.2.5 
R version used for fitting:         4.3.0 
Date of fit:     Fri May 19 17:45:51 2023 
Date of summary: Fri May 19 18:14:01 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 672.309 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:  1.2.5 
R version used for fitting:         4.3.0 
Date of fit:     Fri May 19 17:43:26 2023 
Date of summary: Fri May 19 18:14:01 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 526.974 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:  1.2.5 
R version used for fitting:         4.3.0 
Date of fit:     Fri May 19 17:43:29 2023 
Date of summary: Fri May 19 18:14:01 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 529.515 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:  1.2.5 
R version used for fitting:         4.3.0 
Date of fit:     Fri May 19 17:54:58 2023 
Date of summary: Fri May 19 18:14:01 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 519.639 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:  1.2.5 
R version used for fitting:         4.3.0 
Date of fit:     Fri May 19 17:54:41 2023 
Date of summary: Fri May 19 18:14:01 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 503.222 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:  1.2.5 
R version used for fitting:         4.3.0 
Date of fit:     Fri May 19 17:55:53 2023 
Date of summary: Fri May 19 18:14:01 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 574.8 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:  1.2.5 
R version used for fitting:         4.3.0 
Date of fit:     Fri May 19 17:58:32 2023 
Date of summary: Fri May 19 18:14:01 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 733.398 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:  1.2.5 
R version used for fitting:         4.3.0 
Date of fit:     Fri May 19 17:55:51 2023 
Date of summary: Fri May 19 18:14:01 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 572.747 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:  1.2.5 
R version used for fitting:         4.3.0 
Date of fit:     Fri May 19 17:58:21 2023 
Date of summary: Fri May 19 18:14:01 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 722.847 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:  1.2.5 
R version used for fitting:         4.3.0 
Date of fit:     Fri May 19 18:12:10 2023 
Date of summary: Fri May 19 18:14:01 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 816.454 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:  1.2.5 
R version used for fitting:         4.3.0 
Date of fit:     Fri May 19 18:13:38 2023 
Date of summary: Fri May 19 18:14:01 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 904.25 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:  1.2.5 
R version used for fitting:         4.3.0 
Date of fit:     Fri May 19 18:14:00 2023 
Date of summary: Fri May 19 18:14:01 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 926.094 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:  1.2.5 
R version used for fitting:         4.3.0 
Date of fit:     Fri May 19 18:13:34 2023 
Date of summary: Fri May 19 18:14:01 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 900.859 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:  1.2.5 
R version used for fitting:         4.3.0 
Date of fit:     Fri May 19 18:13:37 2023 
Date of summary: Fri May 19 18:14:01 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 903.326 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 4.3.0 (2023-04-21)
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;  LAPACK version 3.11.0

locale:
 [1] LC_CTYPE=de_DE.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=de_DE.UTF-8        LC_COLLATE=de_DE.UTF-8    
 [5] LC_MONETARY=de_DE.UTF-8    LC_MESSAGES=de_DE.UTF-8   
 [7] LC_PAPER=de_DE.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=de_DE.UTF-8 LC_IDENTIFICATION=C       

time zone: Europe/Berlin
tzcode source: system (glibc)

attached base packages:
[1] parallel  stats     graphics  grDevices utils     datasets  methods  
[8] base     

other attached packages:
[1] saemix_3.2 npde_3.3   knitr_1.42 mkin_1.2.5

loaded via a namespace (and not attached):
 [1] sass_0.4.6        utf8_1.2.3        generics_0.1.3    stringi_1.7.12   
 [5] lattice_0.21-8    digest_0.6.31     magrittr_2.0.3    evaluate_0.21    
 [9] grid_4.3.0        fastmap_1.1.1     cellranger_1.1.0  rprojroot_2.0.3  
[13] jsonlite_1.8.4    processx_3.8.1    pkgbuild_1.4.0    deSolve_1.35     
[17] DBI_1.1.3         mclust_6.0.0      ps_1.7.5          gridExtra_2.3    
[21] purrr_1.0.1       fansi_1.0.4       scales_1.2.1      codetools_0.2-19 
[25] textshaping_0.3.6 jquerylib_0.1.4   cli_3.6.1         crayon_1.5.2     
[29] rlang_1.1.1       munsell_0.5.0     cachem_1.0.8      yaml_2.3.7       
[33] inline_0.3.19     tools_4.3.0       memoise_2.0.1     dplyr_1.1.2      
[37] colorspace_2.1-0  ggplot2_3.4.2     vctrs_0.6.2       R6_2.5.1         
[41] zoo_1.8-12        lifecycle_1.0.3   stringr_1.5.0     fs_1.6.2         
[45] ragg_1.2.5        callr_3.7.3       pkgconfig_2.0.3   desc_1.4.2       
[49] pkgdown_2.0.7     bslib_0.4.2       pillar_1.9.0      gtable_0.3.3     
[53] glue_1.6.2        systemfonts_1.0.4 highr_0.10        xfun_0.39        
[57] tibble_3.2.1      lmtest_0.9-40     tidyselect_1.2.0  htmltools_0.5.5  
[61] nlme_3.1-162      rmarkdown_2.21    compiler_4.3.0    prettyunits_1.1.1
[65] readxl_1.4.2     </code></pre>
</div>
<div class="section level3">
<h3 id="hardware-info">Hardware info<a class="anchor" aria-label="anchor" href="#hardware-info"></a>
</h3>
<pre><code>CPU model: AMD Ryzen 9 7950X 16-Core Processor</code></pre>
<pre><code>MemTotal:       64925476 kB</code></pre>
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