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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 1.2.4 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"><-</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"><-</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"><-</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"><-</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"><-</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"><-</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"><-</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"><-</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"><-</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"><-</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"><-</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">|></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">|></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">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> <table class="table"> <thead><tr class="header"> <th align="left"></th> <th align="right">npar</th> <th align="right">AIC</th> <th align="right">BIC</th> <th align="right">Lik</th> </tr></thead> <tbody> <tr class="odd"> <td align="left">SFO const</td> <td align="right">5</td> <td align="right">833.9</td> <td align="right">832.0</td> <td align="right">-412.0</td> </tr> <tr class="even"> <td align="left">SFO tc</td> <td align="right">6</td> <td align="right">831.6</td> <td align="right">829.3</td> <td align="right">-409.8</td> </tr> <tr class="odd"> <td align="left">FOMC const</td> <td align="right">7</td> <td align="right">709.1</td> <td align="right">706.4</td> <td align="right">-347.6</td> </tr> <tr class="even"> <td align="left">FOMC tc</td> <td align="right">8</td> <td align="right">689.2</td> <td align="right">686.1</td> <td align="right">-336.6</td> </tr> <tr class="odd"> <td align="left">DFOP const</td> <td align="right">9</td> <td align="right">703.0</td> <td align="right">699.5</td> <td align="right">-342.5</td> </tr> <tr class="even"> <td align="left">SFORB const</td> <td align="right">9</td> <td align="right">701.3</td> <td align="right">697.8</td> <td align="right">-341.7</td> </tr> <tr class="odd"> <td align="left">HS const</td> <td align="right">9</td> <td align="right">718.6</td> <td align="right">715.1</td> <td align="right">-350.3</td> </tr> <tr class="even"> <td align="left">DFOP tc</td> <td align="right">10</td> <td align="right">703.1</td> <td align="right">699.2</td> <td align="right">-341.6</td> </tr> <tr class="odd"> <td align="left">SFORB tc</td> <td align="right">10</td> <td align="right">700.0</td> <td align="right">696.1</td> <td align="right">-340.0</td> </tr> <tr class="even"> <td align="left">HS tc</td> <td align="right">10</td> <td align="right">716.7</td> <td align="right">712.8</td> <td align="right">-348.3</td> </tr> </tbody> </table> <p>Model comparison based on AIC and BIC indicates that the two-component error model is preferable for all parent models with the exception of DFOP. The lowest AIC and BIC values are are obtained with the FOMC model, followed by SFORB and DFOP.</p> <div class="sourceCode" id="cb8"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">stopCluster</a></span><span class="op">(</span><span class="va">cl</span><span class="op">)</span></span></code></pre></div> </div> <div class="section level2"> <h2 id="pathway-fits">Pathway fits<a class="anchor" aria-label="anchor" href="#pathway-fits"></a> </h2> <div class="section level3"> <h3 id="evaluations-with-pathway-established-previously">Evaluations with pathway established previously<a class="anchor" aria-label="anchor" href="#evaluations-with-pathway-established-previously"></a> </h3> <p>To test the technical feasibility of coupling the relevant parent degradation models with different transformation pathway models, a list of <code>mkinmod</code> models is set up below. As in the EU evaluation, parallel formation of metabolites JCZ38 and J9Z38 and secondary formation of metabolite JSE76 from JCZ38 is used.</p> <div class="sourceCode" id="cb9"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="kw">if</span> <span class="op">(</span><span class="op">!</span><span class="fu"><a href="https://rdrr.io/r/base/files2.html" class="external-link">dir.exists</a></span><span class="op">(</span><span class="st">"cyan_dlls"</span><span class="op">)</span><span class="op">)</span> <span class="fu"><a href="https://rdrr.io/r/base/files2.html" class="external-link">dir.create</a></span><span class="op">(</span><span class="st">"cyan_dlls"</span><span class="op">)</span></span> <span><span class="va">cyan_path_1</span> <span class="op"><-</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"><-</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"><-</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">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> <table class="table"> <thead><tr class="header"> <th align="left"></th> <th align="left">Nambsheim</th> <th align="left">Tama</th> <th align="left">Gross-Umstadt</th> <th align="left">Sassafras</th> <th align="left">Lleida</th> </tr></thead> <tbody> <tr class="odd"> <td align="left">sfo_path_1</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">C</td> <td align="left">OK</td> </tr> <tr class="even"> <td align="left">fomc_path_1</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> </tr> <tr class="odd"> <td align="left">dfop_path_1</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> </tr> <tr class="even"> <td align="left">sforb_path_1</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> </tr> <tr class="odd"> <td align="left">hs_path_1</td> <td align="left">C</td> <td align="left">C</td> <td align="left">C</td> <td align="left">C</td> <td align="left">C</td> </tr> </tbody> </table> <div class="sourceCode" id="cb11"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">f_sep_1_tc</span> <span class="op"><-</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">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> <table class="table"> <thead><tr class="header"> <th align="left"></th> <th align="left">Nambsheim</th> <th align="left">Tama</th> <th align="left">Gross-Umstadt</th> <th align="left">Sassafras</th> <th align="left">Lleida</th> </tr></thead> <tbody> <tr class="odd"> <td align="left">sfo_path_1</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> </tr> <tr class="even"> <td align="left">fomc_path_1</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> </tr> <tr class="odd"> <td align="left">dfop_path_1</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> </tr> <tr class="even"> <td align="left">sforb_path_1</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> </tr> <tr class="odd"> <td align="left">hs_path_1</td> <td align="left">C</td> <td align="left">OK</td> <td align="left">C</td> <td align="left">OK</td> <td align="left">C</td> </tr> </tbody> </table> <p>Most separate fits converged successfully. The biggest convergence problems are seen when using the HS model with constant variance.</p> <p>For the hierarchical pathway fits, those random effects that could not be quantified in the corresponding parent data analyses are excluded.</p> <p>In the code below, the output of the <code>illparms</code> function for the parent only fits is used as an argument <code>no_random_effect</code> to the <code>mhmkin</code> function. The possibility to do so was introduced in mkin version <code>1.2.2</code> which is currently under development.</p> <div class="sourceCode" id="cb12"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">f_saem_1</span> <span class="op"><-</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">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> <table class="table"> <thead><tr class="header"> <th align="left"></th> <th align="left">const</th> <th align="left">tc</th> </tr></thead> <tbody> <tr class="odd"> <td align="left">sfo_path_1</td> <td align="left">FO</td> <td align="left">Fth, FO</td> </tr> <tr class="even"> <td align="left">fomc_path_1</td> <td align="left">OK</td> <td align="left">Fth, FO</td> </tr> <tr class="odd"> <td align="left">dfop_path_1</td> <td align="left">Fth, FO</td> <td align="left">Fth, FO</td> </tr> <tr class="even"> <td align="left">sforb_path_1</td> <td align="left">Fth, FO</td> <td align="left">Fth, FO</td> </tr> <tr class="odd"> <td align="left">hs_path_1</td> <td align="left">FO</td> <td align="left">E</td> </tr> </tbody> </table> <p>The status information from the individual fits shows that all fits completed successfully. The matrix entries Fth and FO indicate that the Fisher Information Matrix could not be inverted for the fixed effects (theta) and the random effects (Omega), respectively. For the affected fits, ill-defined parameters cannot be determined using the <code>illparms</code> function, because it relies on the Fisher Information Matrix.</p> <div class="sourceCode" id="cb14"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> <table class="table"> <colgroup> <col width="18%"> <col width="77%"> <col width="4%"> </colgroup> <thead><tr class="header"> <th align="left"></th> <th align="left">const</th> <th align="left">tc</th> </tr></thead> <tbody> <tr class="odd"> <td align="left">sfo_path_1</td> <td align="left">NA</td> <td align="left">NA</td> </tr> <tr class="even"> <td align="left">fomc_path_1</td> <td align="left">sd(log_k_J9Z38), sd(f_cyan_ilr_2), sd(f_JCZ38_qlogis)</td> <td align="left">NA</td> </tr> <tr class="odd"> <td align="left">dfop_path_1</td> <td align="left">NA</td> <td align="left">NA</td> </tr> <tr class="even"> <td align="left">sforb_path_1</td> <td align="left">NA</td> <td align="left">NA</td> </tr> <tr class="odd"> <td align="left">hs_path_1</td> <td align="left">NA</td> <td align="left">E</td> </tr> </tbody> </table> <p>The model 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">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> <table class="table"> <thead><tr class="header"> <th align="left"></th> <th align="right">npar</th> <th align="right">AIC</th> <th align="right">BIC</th> <th align="right">Lik</th> </tr></thead> <tbody> <tr class="odd"> <td align="left">sfo_path_1 const</td> <td align="right">16</td> <td align="right">2693.0</td> <td align="right">2686.8</td> <td align="right">-1330.5</td> </tr> <tr class="even"> <td align="left">sfo_path_1 tc</td> <td align="right">17</td> <td align="right">2657.6</td> <td align="right">2651.0</td> <td align="right">-1311.8</td> </tr> <tr class="odd"> <td align="left">fomc_path_1 const</td> <td align="right">18</td> <td align="right">2427.9</td> <td align="right">2420.9</td> <td align="right">-1196.0</td> </tr> <tr class="even"> <td align="left">fomc_path_1 tc</td> <td align="right">19</td> <td align="right">2423.6</td> <td align="right">2416.2</td> <td align="right">-1192.8</td> </tr> <tr class="odd"> <td align="left">dfop_path_1 const</td> <td align="right">20</td> <td align="right">2403.2</td> <td align="right">2395.4</td> <td align="right">-1181.6</td> </tr> <tr class="even"> <td align="left">sforb_path_1 const</td> <td align="right">20</td> <td align="right">2401.4</td> <td align="right">2393.6</td> <td align="right">-1180.7</td> </tr> <tr class="odd"> <td align="left">hs_path_1 const</td> <td align="right">20</td> <td align="right">2427.2</td> <td align="right">2419.4</td> <td align="right">-1193.6</td> </tr> <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">2390.1</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">2399.9</td> <td align="right">2392.1</td> <td align="right">-1180.0</td> </tr> </tbody> </table> <p>For these two parent model, successful fits are shown below. Plots of the fits with the other parent models are shown in the Appendix.</p> <div class="sourceCode" id="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"><-</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"><-</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"><-</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">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> <table class="table"> <thead><tr class="header"> <th align="left"></th> <th align="left">Nambsheim</th> <th align="left">Tama</th> <th align="left">Gross-Umstadt</th> <th align="left">Sassafras</th> <th align="left">Lleida</th> </tr></thead> <tbody> <tr class="odd"> <td align="left">fomc_path_2</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">C</td> <td align="left">OK</td> </tr> <tr class="even"> <td align="left">dfop_path_2</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">C</td> <td align="left">OK</td> </tr> <tr class="odd"> <td align="left">sforb_path_2</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> </tr> </tbody> </table> <p>Using constant variance, separate fits converge with the exception of the fits to the Sassafras soil data.</p> <div class="sourceCode" id="cb20"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">f_sep_2_tc</span> <span class="op"><-</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">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> <table class="table"> <thead><tr class="header"> <th align="left"></th> <th align="left">Nambsheim</th> <th align="left">Tama</th> <th align="left">Gross-Umstadt</th> <th align="left">Sassafras</th> <th align="left">Lleida</th> </tr></thead> <tbody> <tr class="odd"> <td align="left">fomc_path_2</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">C</td> <td align="left">OK</td> </tr> <tr class="even"> <td align="left">dfop_path_2</td> <td align="left">OK</td> <td align="left">C</td> <td align="left">OK</td> <td align="left">C</td> <td align="left">OK</td> </tr> <tr class="odd"> <td align="left">sforb_path_2</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">C</td> <td align="left">OK</td> </tr> </tbody> </table> <p>Using the two-component error model, all separate fits converge with the exception of the alternative pathway fit with DFOP used for the parent and the Sassafras dataset.</p> <div class="sourceCode" id="cb21"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">f_saem_2</span> <span class="op"><-</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">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> <table class="table"> <thead><tr class="header"> <th align="left"></th> <th align="left">const</th> <th align="left">tc</th> </tr></thead> <tbody> <tr class="odd"> <td align="left">fomc_path_2</td> <td align="left">E</td> <td align="left">OK</td> </tr> <tr class="even"> <td align="left">dfop_path_2</td> <td align="left">OK</td> <td align="left">OK</td> </tr> <tr class="odd"> <td align="left">sforb_path_2</td> <td align="left">OK</td> <td align="left">OK</td> </tr> </tbody> </table> <p>The hierarchical fits for the alternative pathway completed successfully.</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">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> <table class="table"> <colgroup> <col width="14%"> <col width="42%"> <col width="42%"> </colgroup> <thead><tr class="header"> <th align="left"></th> <th align="left">const</th> <th align="left">tc</th> </tr></thead> <tbody> <tr class="odd"> <td align="left">fomc_path_2</td> <td align="left">E</td> <td align="left">sd(f_JSE76_qlogis)</td> </tr> <tr class="even"> <td align="left">dfop_path_2</td> <td align="left">sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)</td> <td align="left">sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)</td> </tr> <tr class="odd"> <td align="left">sforb_path_2</td> <td align="left">sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)</td> <td align="left">sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)</td> </tr> </tbody> </table> <p>In 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">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> <table class="table"> <thead><tr class="header"> <th align="left"></th> <th align="right">npar</th> <th align="right">AIC</th> <th align="right">BIC</th> <th align="right">Lik</th> </tr></thead> <tbody> <tr class="odd"> <td align="left">fomc_path_2 tc</td> <td align="right">21</td> <td align="right">2249.0</td> <td align="right">2240.8</td> <td align="right">-1103.5</td> </tr> <tr class="even"> <td align="left">dfop_path_2 const</td> <td align="right">22</td> <td align="right">2288.4</td> <td align="right">2279.8</td> <td align="right">-1122.2</td> </tr> <tr class="odd"> <td align="left">sforb_path_2 const</td> <td align="right">22</td> <td align="right">2283.3</td> <td align="right">2274.7</td> <td align="right">-1119.7</td> </tr> <tr class="even"> <td align="left">dfop_path_2 tc</td> <td align="right">22</td> <td align="right">2234.4</td> <td align="right">2225.8</td> <td align="right">-1095.2</td> </tr> <tr class="odd"> <td align="left">sforb_path_2 tc</td> <td align="right">22</td> <td align="right">2239.7</td> <td align="right">2231.1</td> <td align="right">-1097.9</td> </tr> </tbody> </table> <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"><-</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"><-</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"><-</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"><-</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"><-</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"><-</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"><-</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"><-</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">|></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">|></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">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> <table class="table"> <thead><tr class="header"> <th align="left"></th> <th align="right">npar</th> <th align="right">AIC</th> <th align="right">BIC</th> <th align="right">Lik</th> </tr></thead> <tbody> <tr class="odd"> <td align="left">fomc_path_2 tc</td> <td align="right">19</td> <td align="right">2249.1</td> <td align="right">2241.6</td> <td align="right">-1105.5</td> </tr> <tr class="even"> <td align="left">dfop_path_2 const</td> <td align="right">20</td> <td align="right">2282.2</td> <td align="right">2274.4</td> <td align="right">-1121.1</td> </tr> <tr class="odd"> <td align="left">sforb_path_2 const</td> <td align="right">20</td> <td align="right">2279.7</td> <td align="right">2271.9</td> <td align="right">-1119.9</td> </tr> <tr class="even"> <td align="left">dfop_path_2 tc</td> <td align="right">20</td> <td align="right">2237.3</td> <td align="right">2229.5</td> <td align="right">-1098.6</td> </tr> <tr class="odd"> <td align="left">sforb_path_2 tc</td> <td align="right">20</td> <td align="right">2241.3</td> <td align="right">2233.5</td> <td align="right">-1100.7</td> </tr> </tbody> </table> <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: 1.2.4 R version used for fitting: 4.3.0 Date of fit: Fri May 19 09:27:54 2023 Date of summary: Fri May 19 09:57:33 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 422.743 s Using 300, 100 iterations and 10 chains Variance model: Constant variance Starting values for degradation parameters: cyan_0 log_k_cyan log_k_JCZ38 log_k_J9Z38 log_k_JSE76 95.3304 -3.8459 -3.1305 -5.0678 -5.3196 f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis 0.8158 23.5335 11.8774 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_0 log_k_cyan log_k_JCZ38 log_k_J9Z38 log_k_JSE76 cyan_0 4.797 0.0000 0.000 0.000 0.0000 log_k_cyan 0.000 0.9619 0.000 0.000 0.0000 log_k_JCZ38 0.000 0.0000 2.139 0.000 0.0000 log_k_J9Z38 0.000 0.0000 0.000 1.639 0.0000 log_k_JSE76 0.000 0.0000 0.000 0.000 0.7894 f_cyan_ilr_1 0.000 0.0000 0.000 0.000 0.0000 f_cyan_ilr_2 0.000 0.0000 0.000 0.000 0.0000 f_JCZ38_qlogis 0.000 0.0000 0.000 0.000 0.0000 f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis cyan_0 0.0000 0.000 0.00 log_k_cyan 0.0000 0.000 0.00 log_k_JCZ38 0.0000 0.000 0.00 log_k_J9Z38 0.0000 0.000 0.00 log_k_JSE76 0.0000 0.000 0.00 f_cyan_ilr_1 0.7714 0.000 0.00 f_cyan_ilr_2 0.0000 9.247 0.00 f_JCZ38_qlogis 0.0000 0.000 16.61 Starting values for error model parameters: a.1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2693 2687 -1331 Optimised parameters: est. lower upper cyan_0 95.1279 9.354e+01 9.671e+01 log_k_cyan -3.8527 -4.367e+00 -3.338e+00 log_k_JCZ38 -3.0381 -4.187e+00 -1.889e+00 log_k_J9Z38 -5.0095 -5.623e+00 -4.396e+00 log_k_JSE76 -5.3357 -6.025e+00 -4.646e+00 f_cyan_ilr_1 0.8050 5.174e-01 1.093e+00 f_cyan_ilr_2 12.4820 -1.050e+06 1.051e+06 f_JCZ38_qlogis 1.2912 3.561e-01 2.226e+00 a.1 4.8393 NA NA SD.log_k_cyan 0.5840 NA NA SD.log_k_JCZ38 1.2740 NA NA SD.log_k_J9Z38 0.3172 NA NA SD.log_k_JSE76 0.5677 NA NA SD.f_cyan_ilr_1 0.2623 NA NA SD.f_cyan_ilr_2 1.3724 NA NA SD.f_JCZ38_qlogis 0.1464 NA NA Correlation is not available Random effects: est. lower upper SD.log_k_cyan 0.5840 NA NA SD.log_k_JCZ38 1.2740 NA NA SD.log_k_J9Z38 0.3172 NA NA SD.log_k_JSE76 0.5677 NA NA SD.f_cyan_ilr_1 0.2623 NA NA SD.f_cyan_ilr_2 1.3724 NA NA SD.f_JCZ38_qlogis 0.1464 NA NA Variance model: est. lower upper a.1 4.839 NA NA Backtransformed parameters: est. lower upper cyan_0 95.127935 93.542456 96.713413 k_cyan 0.021221 0.012687 0.035497 k_JCZ38 0.047924 0.015189 0.151213 k_J9Z38 0.006674 0.003612 0.012332 k_JSE76 0.004817 0.002417 0.009601 f_cyan_to_JCZ38 0.757402 NA NA f_cyan_to_J9Z38 0.242597 NA NA f_JCZ38_to_JSE76 0.784347 0.588098 0.902582 Resulting formation fractions: ff cyan_JCZ38 7.574e-01 cyan_J9Z38 2.426e-01 cyan_sink 9.839e-08 JCZ38_JSE76 7.843e-01 JCZ38_sink 2.157e-01 Estimated disappearance times: DT50 DT90 cyan 32.66 108.50 JCZ38 14.46 48.05 J9Z38 103.86 345.00 JSE76 143.91 478.04 </code></pre> <p></p> <caption> Hierarchical SFO path 1 fit with two-component error </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.4 R version used for fitting: 4.3.0 Date of fit: Fri May 19 09:27:49 2023 Date of summary: Fri May 19 09:57:33 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 417.436 s Using 300, 100 iterations and 10 chains Variance model: Two-component variance function Starting values for degradation parameters: cyan_0 log_k_cyan log_k_JCZ38 log_k_J9Z38 log_k_JSE76 96.0039 -3.8907 -3.1276 -5.0069 -4.9367 f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis 0.7937 22.3422 17.8932 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_0 log_k_cyan log_k_JCZ38 log_k_J9Z38 log_k_JSE76 cyan_0 4.859 0.000 0.00 0.00 0.0000 log_k_cyan 0.000 0.962 0.00 0.00 0.0000 log_k_JCZ38 0.000 0.000 2.04 0.00 0.0000 log_k_J9Z38 0.000 0.000 0.00 1.72 0.0000 log_k_JSE76 0.000 0.000 0.00 0.00 0.9076 f_cyan_ilr_1 0.000 0.000 0.00 0.00 0.0000 f_cyan_ilr_2 0.000 0.000 0.00 0.00 0.0000 f_JCZ38_qlogis 0.000 0.000 0.00 0.00 0.0000 f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis cyan_0 0.0000 0.000 0.00 log_k_cyan 0.0000 0.000 0.00 log_k_JCZ38 0.0000 0.000 0.00 log_k_J9Z38 0.0000 0.000 0.00 log_k_JSE76 0.0000 0.000 0.00 f_cyan_ilr_1 0.7598 0.000 0.00 f_cyan_ilr_2 0.0000 8.939 0.00 f_JCZ38_qlogis 0.0000 0.000 14.49 Starting values for error model parameters: a.1 b.1 1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2658 2651 -1312 Optimised parameters: est. lower upper cyan_0 94.81681 NA NA log_k_cyan -3.91558 NA NA log_k_JCZ38 -3.12715 NA NA log_k_J9Z38 -5.04840 NA NA log_k_JSE76 -5.10443 NA NA f_cyan_ilr_1 0.80760 NA NA f_cyan_ilr_2 48.66960 NA NA f_JCZ38_qlogis 3.03397 NA NA a.1 3.93879 NA NA b.1 0.08057 NA NA SD.log_k_cyan 0.58921 NA NA SD.log_k_JCZ38 1.29813 NA NA SD.log_k_J9Z38 0.68372 NA NA SD.log_k_JSE76 0.35128 NA NA SD.f_cyan_ilr_1 0.38352 NA NA SD.f_cyan_ilr_2 4.98884 NA NA SD.f_JCZ38_qlogis 1.75636 NA NA Correlation is not available Random effects: est. lower upper SD.log_k_cyan 0.5892 NA NA SD.log_k_JCZ38 1.2981 NA NA SD.log_k_J9Z38 0.6837 NA NA SD.log_k_JSE76 0.3513 NA NA SD.f_cyan_ilr_1 0.3835 NA NA SD.f_cyan_ilr_2 4.9888 NA NA SD.f_JCZ38_qlogis 1.7564 NA NA Variance model: est. lower upper a.1 3.93879 NA NA b.1 0.08057 NA NA Backtransformed parameters: est. lower upper cyan_0 94.81681 NA NA k_cyan 0.01993 NA NA k_JCZ38 0.04384 NA NA k_J9Z38 0.00642 NA NA k_JSE76 0.00607 NA NA f_cyan_to_JCZ38 0.75807 NA NA f_cyan_to_J9Z38 0.24193 NA NA f_JCZ38_to_JSE76 0.95409 NA NA Resulting formation fractions: ff cyan_JCZ38 0.75807 cyan_J9Z38 0.24193 cyan_sink 0.00000 JCZ38_JSE76 0.95409 JCZ38_sink 0.04591 Estimated disappearance times: DT50 DT90 cyan 34.78 115.54 JCZ38 15.81 52.52 J9Z38 107.97 358.68 JSE76 114.20 379.35 </code></pre> <p></p> <caption> Hierarchical FOMC path 1 fit with constant variance </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.4 R version used for fitting: 4.3.0 Date of fit: Fri May 19 09:28:29 2023 Date of summary: Fri May 19 09:57:33 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 457.122 s Using 300, 100 iterations and 10 chains Variance model: Constant variance Starting values for degradation parameters: cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 101.2314 -3.3680 -5.1108 -5.9416 0.7144 f_cyan_ilr_2 f_JCZ38_qlogis log_alpha log_beta 7.0229 14.9234 -0.1791 2.9811 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 cyan_0 5.416 0.000 0.0 0.000 0.0000 log_k_JCZ38 0.000 2.439 0.0 0.000 0.0000 log_k_J9Z38 0.000 0.000 1.7 0.000 0.0000 log_k_JSE76 0.000 0.000 0.0 1.856 0.0000 f_cyan_ilr_1 0.000 0.000 0.0 0.000 0.7164 f_cyan_ilr_2 0.000 0.000 0.0 0.000 0.0000 f_JCZ38_qlogis 0.000 0.000 0.0 0.000 0.0000 log_alpha 0.000 0.000 0.0 0.000 0.0000 log_beta 0.000 0.000 0.0 0.000 0.0000 f_cyan_ilr_2 f_JCZ38_qlogis log_alpha log_beta cyan_0 0.00 0.00 0.0000 0.0000 log_k_JCZ38 0.00 0.00 0.0000 0.0000 log_k_J9Z38 0.00 0.00 0.0000 0.0000 log_k_JSE76 0.00 0.00 0.0000 0.0000 f_cyan_ilr_1 0.00 0.00 0.0000 0.0000 f_cyan_ilr_2 11.57 0.00 0.0000 0.0000 f_JCZ38_qlogis 0.00 18.81 0.0000 0.0000 log_alpha 0.00 0.00 0.4144 0.0000 log_beta 0.00 0.00 0.0000 0.5077 Starting values for error model parameters: a.1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2428 2421 -1196 Optimised parameters: est. lower upper cyan_0 101.1664 98.51265 103.8202 log_k_JCZ38 -3.3883 -4.78250 -1.9941 log_k_J9Z38 -5.3087 -5.91564 -4.7017 log_k_JSE76 -6.1313 -7.30061 -4.9619 f_cyan_ilr_1 0.7456 0.43782 1.0534 f_cyan_ilr_2 0.8181 0.24956 1.3866 f_JCZ38_qlogis 2.0467 0.61165 3.4817 log_alpha -0.2391 -0.62806 0.1499 log_beta 2.8739 2.67664 3.0711 a.1 3.4160 3.17960 3.6525 SD.cyan_0 2.4355 0.40399 4.4671 SD.log_k_JCZ38 1.5654 0.57311 2.5576 SD.log_k_J9Z38 0.4645 -0.06533 0.9943 SD.log_k_JSE76 0.9841 0.10738 1.8609 SD.f_cyan_ilr_1 0.3285 0.10546 0.5515 SD.f_cyan_ilr_2 0.2276 -0.38711 0.8424 SD.f_JCZ38_qlogis 0.8340 -0.20970 1.8777 SD.log_alpha 0.4250 0.16017 0.6898 Correlation: cyan_0 l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 log_lph log_k_JCZ38 -0.0159 log_k_J9Z38 -0.0546 0.0080 log_k_JSE76 -0.0337 0.0016 0.0074 f_cyan_ilr_1 -0.0095 0.0194 -0.1573 0.0003 f_cyan_ilr_2 -0.2733 0.0799 0.3059 0.0263 0.0125 f_JCZ38_qlogis 0.0755 -0.0783 -0.0516 0.1222 -0.1155 -0.5231 log_alpha -0.0567 0.0120 0.0351 0.0189 0.0040 0.0829 -0.0502 log_beta -0.2980 0.0461 0.1382 0.0758 0.0209 0.4079 -0.2053 0.2759 Random effects: est. lower upper SD.cyan_0 2.4355 0.40399 4.4671 SD.log_k_JCZ38 1.5654 0.57311 2.5576 SD.log_k_J9Z38 0.4645 -0.06533 0.9943 SD.log_k_JSE76 0.9841 0.10738 1.8609 SD.f_cyan_ilr_1 0.3285 0.10546 0.5515 SD.f_cyan_ilr_2 0.2276 -0.38711 0.8424 SD.f_JCZ38_qlogis 0.8340 -0.20970 1.8777 SD.log_alpha 0.4250 0.16017 0.6898 Variance model: est. lower upper a.1 3.416 3.18 3.652 Backtransformed parameters: est. lower upper cyan_0 1.012e+02 9.851e+01 103.82023 k_JCZ38 3.377e-02 8.375e-03 0.13614 k_J9Z38 4.948e-03 2.697e-03 0.00908 k_JSE76 2.174e-03 6.751e-04 0.00700 f_cyan_to_JCZ38 6.389e-01 NA NA f_cyan_to_J9Z38 2.226e-01 NA NA f_JCZ38_to_JSE76 8.856e-01 6.483e-01 0.97016 alpha 7.873e-01 5.336e-01 1.16166 beta 1.771e+01 1.454e+01 21.56509 Resulting formation fractions: ff cyan_JCZ38 0.6389 cyan_J9Z38 0.2226 cyan_sink 0.1385 JCZ38_JSE76 0.8856 JCZ38_sink 0.1144 Estimated disappearance times: DT50 DT90 DT50back cyan 25.00 312.06 93.94 JCZ38 20.53 68.19 NA J9Z38 140.07 465.32 NA JSE76 318.86 1059.22 NA </code></pre> <p></p> <caption> Hierarchical FOMC path 1 fit with two-component error </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.4 R version used for fitting: 4.3.0 Date of fit: Fri May 19 09:28:21 2023 Date of summary: Fri May 19 09:57:33 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 449.531 s Using 300, 100 iterations and 10 chains Variance model: Two-component variance function Starting values for degradation parameters: cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 101.13294 -3.32499 -5.09097 -5.93566 0.71359 f_cyan_ilr_2 f_JCZ38_qlogis log_alpha log_beta 10.30315 14.62272 -0.09633 3.10634 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 cyan_0 5.649 0.000 0.00 0.00 0.0000 log_k_JCZ38 0.000 2.319 0.00 0.00 0.0000 log_k_J9Z38 0.000 0.000 1.73 0.00 0.0000 log_k_JSE76 0.000 0.000 0.00 1.86 0.0000 f_cyan_ilr_1 0.000 0.000 0.00 0.00 0.7183 f_cyan_ilr_2 0.000 0.000 0.00 0.00 0.0000 f_JCZ38_qlogis 0.000 0.000 0.00 0.00 0.0000 log_alpha 0.000 0.000 0.00 0.00 0.0000 log_beta 0.000 0.000 0.00 0.00 0.0000 f_cyan_ilr_2 f_JCZ38_qlogis log_alpha log_beta cyan_0 0.00 0.00 0.0000 0.0000 log_k_JCZ38 0.00 0.00 0.0000 0.0000 log_k_J9Z38 0.00 0.00 0.0000 0.0000 log_k_JSE76 0.00 0.00 0.0000 0.0000 f_cyan_ilr_1 0.00 0.00 0.0000 0.0000 f_cyan_ilr_2 12.85 0.00 0.0000 0.0000 f_JCZ38_qlogis 0.00 18.54 0.0000 0.0000 log_alpha 0.00 0.00 0.3142 0.0000 log_beta 0.00 0.00 0.0000 0.7333 Starting values for error model parameters: a.1 b.1 1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2424 2416 -1193 Optimised parameters: est. lower upper cyan_0 100.65667 NA NA log_k_JCZ38 -3.45782 NA NA log_k_J9Z38 -5.23476 NA NA log_k_JSE76 -5.71827 NA NA f_cyan_ilr_1 0.68389 NA NA f_cyan_ilr_2 0.61027 NA NA f_JCZ38_qlogis 116.27482 NA NA log_alpha -0.14484 NA NA log_beta 3.03220 NA NA a.1 3.11051 NA NA b.1 0.04508 NA NA SD.log_k_JCZ38 1.39961 NA NA SD.log_k_J9Z38 0.57920 NA NA SD.log_k_JSE76 0.68364 NA NA SD.f_cyan_ilr_1 0.31477 NA NA SD.f_cyan_ilr_2 0.37716 NA NA SD.f_JCZ38_qlogis 5.52695 NA NA SD.log_alpha 0.22823 NA NA SD.log_beta 0.39161 NA NA Correlation is not available Random effects: est. lower upper SD.log_k_JCZ38 1.3996 NA NA SD.log_k_J9Z38 0.5792 NA NA SD.log_k_JSE76 0.6836 NA NA SD.f_cyan_ilr_1 0.3148 NA NA SD.f_cyan_ilr_2 0.3772 NA NA SD.f_JCZ38_qlogis 5.5270 NA NA SD.log_alpha 0.2282 NA NA SD.log_beta 0.3916 NA NA Variance model: est. lower upper a.1 3.11051 NA NA b.1 0.04508 NA NA Backtransformed parameters: est. lower upper cyan_0 1.007e+02 NA NA k_JCZ38 3.150e-02 NA NA k_J9Z38 5.328e-03 NA NA k_JSE76 3.285e-03 NA NA f_cyan_to_JCZ38 5.980e-01 NA NA f_cyan_to_J9Z38 2.273e-01 NA NA f_JCZ38_to_JSE76 1.000e+00 NA NA alpha 8.652e-01 NA NA beta 2.074e+01 NA NA Resulting formation fractions: ff cyan_JCZ38 0.5980 cyan_J9Z38 0.2273 cyan_sink 0.1746 JCZ38_JSE76 1.0000 JCZ38_sink 0.0000 Estimated disappearance times: DT50 DT90 DT50back cyan 25.48 276.2 83.15 JCZ38 22.01 73.1 NA J9Z38 130.09 432.2 NA JSE76 210.98 700.9 NA </code></pre> <p></p> <caption> Hierarchical DFOP path 1 fit with constant variance </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.4 R version used for fitting: 4.3.0 Date of fit: Fri May 19 09:29:15 2023 Date of summary: Fri May 19 09:57:33 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 503.737 s Using 300, 100 iterations and 10 chains Variance model: Constant variance Starting values for degradation parameters: cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 102.0643 -3.4008 -5.0024 -5.8612 0.6855 f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 g_qlogis 1.2366 13.6901 -1.8641 -4.5063 -0.6468 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 cyan_0 4.466 0.000 0.000 0.000 0.0000 log_k_JCZ38 0.000 2.382 0.000 0.000 0.0000 log_k_J9Z38 0.000 0.000 1.595 0.000 0.0000 log_k_JSE76 0.000 0.000 0.000 1.245 0.0000 f_cyan_ilr_1 0.000 0.000 0.000 0.000 0.6852 f_cyan_ilr_2 0.000 0.000 0.000 0.000 0.0000 f_JCZ38_qlogis 0.000 0.000 0.000 0.000 0.0000 log_k1 0.000 0.000 0.000 0.000 0.0000 log_k2 0.000 0.000 0.000 0.000 0.0000 g_qlogis 0.000 0.000 0.000 0.000 0.0000 f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 g_qlogis cyan_0 0.00 0.00 0.0000 0.0000 0.000 log_k_JCZ38 0.00 0.00 0.0000 0.0000 0.000 log_k_J9Z38 0.00 0.00 0.0000 0.0000 0.000 log_k_JSE76 0.00 0.00 0.0000 0.0000 0.000 f_cyan_ilr_1 0.00 0.00 0.0000 0.0000 0.000 f_cyan_ilr_2 1.28 0.00 0.0000 0.0000 0.000 f_JCZ38_qlogis 0.00 16.08 0.0000 0.0000 0.000 log_k1 0.00 0.00 0.9866 0.0000 0.000 log_k2 0.00 0.00 0.0000 0.5953 0.000 g_qlogis 0.00 0.00 0.0000 0.0000 1.583 Starting values for error model parameters: a.1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2403 2395 -1182 Optimised parameters: est. lower upper cyan_0 102.5565 NA NA log_k_JCZ38 -3.4729 NA NA log_k_J9Z38 -5.1533 NA NA log_k_JSE76 -5.6669 NA NA f_cyan_ilr_1 0.6665 NA NA f_cyan_ilr_2 0.5191 NA NA f_JCZ38_qlogis 37.0113 NA NA log_k1 -1.8497 NA NA log_k2 -4.4931 NA NA g_qlogis -0.6383 NA NA a.1 3.2397 NA NA SD.log_k_JCZ38 1.4286 NA NA SD.log_k_J9Z38 0.5312 NA NA SD.log_k_JSE76 0.6627 NA NA SD.f_cyan_ilr_1 0.3013 NA NA SD.f_cyan_ilr_2 0.2980 NA NA SD.f_JCZ38_qlogis 0.1637 NA NA SD.log_k1 0.5069 NA NA SD.log_k2 0.3828 NA NA SD.g_qlogis 0.8641 NA NA Correlation is not available Random effects: est. lower upper SD.log_k_JCZ38 1.4286 NA NA SD.log_k_J9Z38 0.5312 NA NA SD.log_k_JSE76 0.6627 NA NA SD.f_cyan_ilr_1 0.3013 NA NA SD.f_cyan_ilr_2 0.2980 NA NA SD.f_JCZ38_qlogis 0.1637 NA NA SD.log_k1 0.5069 NA NA SD.log_k2 0.3828 NA NA SD.g_qlogis 0.8641 NA NA Variance model: est. lower upper a.1 3.24 NA NA Backtransformed parameters: est. lower upper cyan_0 1.026e+02 NA NA k_JCZ38 3.103e-02 NA NA k_J9Z38 5.780e-03 NA NA k_JSE76 3.459e-03 NA NA f_cyan_to_JCZ38 5.813e-01 NA NA f_cyan_to_J9Z38 2.265e-01 NA NA f_JCZ38_to_JSE76 1.000e+00 NA NA k1 1.573e-01 NA NA k2 1.119e-02 NA NA g 3.456e-01 NA NA Resulting formation fractions: ff cyan_JCZ38 0.5813 cyan_J9Z38 0.2265 cyan_sink 0.1922 JCZ38_JSE76 1.0000 JCZ38_sink 0.0000 Estimated disappearance times: DT50 DT90 DT50back DT50_k1 DT50_k2 cyan 25.23 167.94 50.55 4.407 61.97 JCZ38 22.34 74.22 NA NA NA J9Z38 119.92 398.36 NA NA NA JSE76 200.41 665.76 NA NA NA </code></pre> <p></p> <caption> Hierarchical DFOP path 1 fit with two-component error </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.4 R version used for fitting: 4.3.0 Date of fit: Fri May 19 09:31:24 2023 Date of summary: Fri May 19 09:57:33 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 632.55 s Using 300, 100 iterations and 10 chains Variance model: Two-component variance function Starting values for degradation parameters: cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 101.3964 -3.3626 -4.9792 -5.8727 0.6814 f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 g_qlogis 6.8713 13.6901 -1.9222 -4.5035 -0.7172 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 cyan_0 5.317 0.000 0.000 0.000 0.0000 log_k_JCZ38 0.000 2.272 0.000 0.000 0.0000 log_k_J9Z38 0.000 0.000 1.633 0.000 0.0000 log_k_JSE76 0.000 0.000 0.000 1.271 0.0000 f_cyan_ilr_1 0.000 0.000 0.000 0.000 0.6839 f_cyan_ilr_2 0.000 0.000 0.000 0.000 0.0000 f_JCZ38_qlogis 0.000 0.000 0.000 0.000 0.0000 log_k1 0.000 0.000 0.000 0.000 0.0000 log_k2 0.000 0.000 0.000 0.000 0.0000 g_qlogis 0.000 0.000 0.000 0.000 0.0000 f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 g_qlogis cyan_0 0.00 0.00 0.0000 0.0000 0.000 log_k_JCZ38 0.00 0.00 0.0000 0.0000 0.000 log_k_J9Z38 0.00 0.00 0.0000 0.0000 0.000 log_k_JSE76 0.00 0.00 0.0000 0.0000 0.000 f_cyan_ilr_1 0.00 0.00 0.0000 0.0000 0.000 f_cyan_ilr_2 11.95 0.00 0.0000 0.0000 0.000 f_JCZ38_qlogis 0.00 16.08 0.0000 0.0000 0.000 log_k1 0.00 0.00 0.9496 0.0000 0.000 log_k2 0.00 0.00 0.0000 0.5846 0.000 g_qlogis 0.00 0.00 0.0000 0.0000 1.719 Starting values for error model parameters: a.1 b.1 1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2398 2390 -1179 Optimised parameters: est. lower upper cyan_0 100.69709 NA NA log_k_JCZ38 -3.46669 NA NA log_k_J9Z38 -5.05076 NA NA log_k_JSE76 -5.55558 NA NA f_cyan_ilr_1 0.66045 NA NA f_cyan_ilr_2 0.84275 NA NA f_JCZ38_qlogis 64.22404 NA NA log_k1 -2.17715 NA NA log_k2 -4.55002 NA NA g_qlogis -0.55920 NA NA a.1 2.95785 NA NA b.1 0.04456 NA NA SD.log_k_JCZ38 1.39881 NA NA SD.log_k_J9Z38 0.67788 NA NA SD.log_k_JSE76 0.52603 NA NA SD.f_cyan_ilr_1 0.32490 NA NA SD.f_cyan_ilr_2 0.53923 NA NA SD.f_JCZ38_qlogis 2.75576 NA NA SD.log_k2 0.30694 NA NA SD.g_qlogis 0.83619 NA NA Correlation is not available Random effects: est. lower upper SD.log_k_JCZ38 1.3988 NA NA SD.log_k_J9Z38 0.6779 NA NA SD.log_k_JSE76 0.5260 NA NA SD.f_cyan_ilr_1 0.3249 NA NA SD.f_cyan_ilr_2 0.5392 NA NA SD.f_JCZ38_qlogis 2.7558 NA NA SD.log_k2 0.3069 NA NA SD.g_qlogis 0.8362 NA NA Variance model: est. lower upper a.1 2.95785 NA NA b.1 0.04456 NA NA Backtransformed parameters: est. lower upper cyan_0 1.007e+02 NA NA k_JCZ38 3.122e-02 NA NA k_J9Z38 6.404e-03 NA NA k_JSE76 3.866e-03 NA NA f_cyan_to_JCZ38 6.187e-01 NA NA f_cyan_to_J9Z38 2.431e-01 NA NA f_JCZ38_to_JSE76 1.000e+00 NA NA k1 1.134e-01 NA NA k2 1.057e-02 NA NA g 3.637e-01 NA NA Resulting formation fractions: ff cyan_JCZ38 0.6187 cyan_J9Z38 0.2431 cyan_sink 0.1382 JCZ38_JSE76 1.0000 JCZ38_sink 0.0000 Estimated disappearance times: DT50 DT90 DT50back DT50_k1 DT50_k2 cyan 26.35 175.12 52.72 6.114 65.6 JCZ38 22.20 73.75 NA NA NA J9Z38 108.23 359.53 NA NA NA JSE76 179.30 595.62 NA NA NA </code></pre> <p></p> <caption> Hierarchical SFORB path 1 fit with constant variance </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.4 R version used for fitting: 4.3.0 Date of fit: Fri May 19 09:29:23 2023 Date of summary: Fri May 19 09:57:33 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 511.715 s Using 300, 100 iterations and 10 chains Variance model: Constant variance Starting values for degradation parameters: cyan_free_0 log_k_cyan_free log_k_cyan_free_bound 102.0643 -2.8987 -2.7077 log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 -3.4717 -3.4008 -5.0024 log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 -5.8613 0.6855 1.2366 f_JCZ38_qlogis 13.7395 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_free_0 log_k_cyan_free log_k_cyan_free_bound cyan_free_0 4.466 0.0000 0.000 log_k_cyan_free 0.000 0.6158 0.000 log_k_cyan_free_bound 0.000 0.0000 1.463 log_k_cyan_bound_free 0.000 0.0000 0.000 log_k_JCZ38 0.000 0.0000 0.000 log_k_J9Z38 0.000 0.0000 0.000 log_k_JSE76 0.000 0.0000 0.000 f_cyan_ilr_1 0.000 0.0000 0.000 f_cyan_ilr_2 0.000 0.0000 0.000 f_JCZ38_qlogis 0.000 0.0000 0.000 log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 cyan_free_0 0.000 0.000 0.000 0.000 log_k_cyan_free 0.000 0.000 0.000 0.000 log_k_cyan_free_bound 0.000 0.000 0.000 0.000 log_k_cyan_bound_free 1.058 0.000 0.000 0.000 log_k_JCZ38 0.000 2.382 0.000 0.000 log_k_J9Z38 0.000 0.000 1.595 0.000 log_k_JSE76 0.000 0.000 0.000 1.245 f_cyan_ilr_1 0.000 0.000 0.000 0.000 f_cyan_ilr_2 0.000 0.000 0.000 0.000 f_JCZ38_qlogis 0.000 0.000 0.000 0.000 f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis cyan_free_0 0.0000 0.00 0.00 log_k_cyan_free 0.0000 0.00 0.00 log_k_cyan_free_bound 0.0000 0.00 0.00 log_k_cyan_bound_free 0.0000 0.00 0.00 log_k_JCZ38 0.0000 0.00 0.00 log_k_J9Z38 0.0000 0.00 0.00 log_k_JSE76 0.0000 0.00 0.00 f_cyan_ilr_1 0.6852 0.00 0.00 f_cyan_ilr_2 0.0000 1.28 0.00 f_JCZ38_qlogis 0.0000 0.00 16.13 Starting values for error model parameters: a.1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2401 2394 -1181 Optimised parameters: est. lower upper cyan_free_0 102.8136 NA NA log_k_cyan_free -2.7935 NA NA log_k_cyan_free_bound -2.5440 NA NA log_k_cyan_bound_free -3.4303 NA NA log_k_JCZ38 -3.5010 NA NA log_k_J9Z38 -5.1226 NA NA log_k_JSE76 -5.6314 NA NA f_cyan_ilr_1 0.6609 NA NA f_cyan_ilr_2 0.5085 NA NA f_JCZ38_qlogis 44.0153 NA NA a.1 3.2318 NA NA SD.log_k_cyan_free 0.3211 NA NA SD.log_k_cyan_free_bound 0.8408 NA NA SD.log_k_cyan_bound_free 0.5724 NA NA SD.log_k_JCZ38 1.4925 NA NA SD.log_k_J9Z38 0.5816 NA NA SD.log_k_JSE76 0.6037 NA NA SD.f_cyan_ilr_1 0.3115 NA NA SD.f_cyan_ilr_2 0.3436 NA NA SD.f_JCZ38_qlogis 4.8937 NA NA Correlation is not available Random effects: est. lower upper SD.log_k_cyan_free 0.3211 NA NA SD.log_k_cyan_free_bound 0.8408 NA NA SD.log_k_cyan_bound_free 0.5724 NA NA SD.log_k_JCZ38 1.4925 NA NA SD.log_k_J9Z38 0.5816 NA NA SD.log_k_JSE76 0.6037 NA NA SD.f_cyan_ilr_1 0.3115 NA NA SD.f_cyan_ilr_2 0.3436 NA NA SD.f_JCZ38_qlogis 4.8937 NA NA Variance model: est. lower upper a.1 3.232 NA NA Backtransformed parameters: est. lower upper cyan_free_0 1.028e+02 NA NA k_cyan_free 6.120e-02 NA NA k_cyan_free_bound 7.855e-02 NA NA k_cyan_bound_free 3.238e-02 NA NA k_JCZ38 3.017e-02 NA NA k_J9Z38 5.961e-03 NA NA k_JSE76 3.584e-03 NA NA f_cyan_free_to_JCZ38 5.784e-01 NA NA f_cyan_free_to_J9Z38 2.271e-01 NA NA f_JCZ38_to_JSE76 1.000e+00 NA NA Estimated Eigenvalues of SFORB model(s): cyan_b1 cyan_b2 cyan_g 0.15973 0.01241 0.33124 Resulting formation fractions: ff cyan_free_JCZ38 0.5784 cyan_free_J9Z38 0.2271 cyan_free_sink 0.1945 cyan_free 1.0000 JCZ38_JSE76 1.0000 JCZ38_sink 0.0000 Estimated disappearance times: DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 cyan 24.51 153.18 46.11 4.34 55.87 JCZ38 22.98 76.33 NA NA NA J9Z38 116.28 386.29 NA NA NA JSE76 193.42 642.53 NA NA NA </code></pre> <p></p> <caption> Hierarchical SFORB path 1 fit with two-component error </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.4 R version used for fitting: 4.3.0 Date of fit: Fri May 19 09:31:23 2023 Date of summary: Fri May 19 09:57:33 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 630.627 s Using 300, 100 iterations and 10 chains Variance model: Two-component variance function Starting values for degradation parameters: cyan_free_0 log_k_cyan_free log_k_cyan_free_bound 101.3964 -2.9881 -2.7949 log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 -3.4376 -3.3626 -4.9792 log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 -5.8727 0.6814 6.7399 f_JCZ38_qlogis 13.7395 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_free_0 log_k_cyan_free log_k_cyan_free_bound cyan_free_0 5.317 0.0000 0.000 log_k_cyan_free 0.000 0.7301 0.000 log_k_cyan_free_bound 0.000 0.0000 1.384 log_k_cyan_bound_free 0.000 0.0000 0.000 log_k_JCZ38 0.000 0.0000 0.000 log_k_J9Z38 0.000 0.0000 0.000 log_k_JSE76 0.000 0.0000 0.000 f_cyan_ilr_1 0.000 0.0000 0.000 f_cyan_ilr_2 0.000 0.0000 0.000 f_JCZ38_qlogis 0.000 0.0000 0.000 log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 cyan_free_0 0.000 0.000 0.000 0.000 log_k_cyan_free 0.000 0.000 0.000 0.000 log_k_cyan_free_bound 0.000 0.000 0.000 0.000 log_k_cyan_bound_free 1.109 0.000 0.000 0.000 log_k_JCZ38 0.000 2.272 0.000 0.000 log_k_J9Z38 0.000 0.000 1.633 0.000 log_k_JSE76 0.000 0.000 0.000 1.271 f_cyan_ilr_1 0.000 0.000 0.000 0.000 f_cyan_ilr_2 0.000 0.000 0.000 0.000 f_JCZ38_qlogis 0.000 0.000 0.000 0.000 f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis cyan_free_0 0.0000 0.00 0.00 log_k_cyan_free 0.0000 0.00 0.00 log_k_cyan_free_bound 0.0000 0.00 0.00 log_k_cyan_bound_free 0.0000 0.00 0.00 log_k_JCZ38 0.0000 0.00 0.00 log_k_J9Z38 0.0000 0.00 0.00 log_k_JSE76 0.0000 0.00 0.00 f_cyan_ilr_1 0.6838 0.00 0.00 f_cyan_ilr_2 0.0000 11.69 0.00 f_JCZ38_qlogis 0.0000 0.00 16.13 Starting values for error model parameters: a.1 b.1 1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2400 2392 -1180 Optimised parameters: est. lower upper cyan_free_0 100.56004 NA NA log_k_cyan_free -3.12657 NA NA log_k_cyan_free_bound -3.16825 NA NA log_k_cyan_bound_free -3.66003 NA NA log_k_JCZ38 -3.47278 NA NA log_k_J9Z38 -5.06823 NA NA log_k_JSE76 -5.54327 NA NA f_cyan_ilr_1 0.66631 NA NA f_cyan_ilr_2 0.82898 NA NA f_JCZ38_qlogis 38.31115 NA NA a.1 2.98352 NA NA b.1 0.04388 NA NA SD.log_k_cyan_free 0.49145 NA NA SD.log_k_cyan_bound_free 0.27347 NA NA SD.log_k_JCZ38 1.41193 NA NA SD.log_k_J9Z38 0.66073 NA NA SD.log_k_JSE76 0.55885 NA NA SD.f_cyan_ilr_1 0.33020 NA NA SD.f_cyan_ilr_2 0.51367 NA NA SD.f_JCZ38_qlogis 5.52122 NA NA Correlation is not available Random effects: est. lower upper SD.log_k_cyan_free 0.4914 NA NA SD.log_k_cyan_bound_free 0.2735 NA NA SD.log_k_JCZ38 1.4119 NA NA SD.log_k_J9Z38 0.6607 NA NA SD.log_k_JSE76 0.5589 NA NA SD.f_cyan_ilr_1 0.3302 NA NA SD.f_cyan_ilr_2 0.5137 NA NA SD.f_JCZ38_qlogis 5.5212 NA NA Variance model: est. lower upper a.1 2.98352 NA NA b.1 0.04388 NA NA Backtransformed parameters: est. lower upper cyan_free_0 1.006e+02 NA NA k_cyan_free 4.387e-02 NA NA k_cyan_free_bound 4.208e-02 NA NA k_cyan_bound_free 2.573e-02 NA NA k_JCZ38 3.103e-02 NA NA k_J9Z38 6.294e-03 NA NA k_JSE76 3.914e-03 NA NA f_cyan_free_to_JCZ38 6.188e-01 NA NA f_cyan_free_to_J9Z38 2.412e-01 NA NA f_JCZ38_to_JSE76 1.000e+00 NA NA Estimated Eigenvalues of SFORB model(s): cyan_b1 cyan_b2 cyan_g 0.10044 0.01124 0.36580 Resulting formation fractions: ff cyan_free_JCZ38 0.6188 cyan_free_J9Z38 0.2412 cyan_free_sink 0.1400 cyan_free 1.0000 JCZ38_JSE76 1.0000 JCZ38_sink 0.0000 Estimated disappearance times: DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 cyan 26.05 164.4 49.48 6.901 61.67 JCZ38 22.34 74.2 NA NA NA J9Z38 110.14 365.9 NA NA NA JSE76 177.11 588.3 NA NA NA </code></pre> <p></p> <caption> Hierarchical HS path 1 fit with constant variance </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.4 R version used for fitting: 4.3.0 Date of fit: Fri May 19 09:28:57 2023 Date of summary: Fri May 19 09:57:33 2023 Equations: d_cyan/dt = - ifelse(time <= tb, k1, k2) * cyan d_JCZ38/dt = + f_cyan_to_JCZ38 * ifelse(time <= tb, k1, k2) * cyan - k_JCZ38 * JCZ38 d_J9Z38/dt = + f_cyan_to_J9Z38 * ifelse(time <= 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 485.304 s Using 300, 100 iterations and 10 chains Variance model: Constant variance Starting values for degradation parameters: cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 102.8845 -3.4495 -4.9355 -5.6040 0.6468 f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 log_tb 1.2396 9.7220 -2.9079 -4.1810 1.7813 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 cyan_0 5.406 0.00 0.00 0.000 0.0000 log_k_JCZ38 0.000 2.33 0.00 0.000 0.0000 log_k_J9Z38 0.000 0.00 1.59 0.000 0.0000 log_k_JSE76 0.000 0.00 0.00 1.013 0.0000 f_cyan_ilr_1 0.000 0.00 0.00 0.000 0.6367 f_cyan_ilr_2 0.000 0.00 0.00 0.000 0.0000 f_JCZ38_qlogis 0.000 0.00 0.00 0.000 0.0000 log_k1 0.000 0.00 0.00 0.000 0.0000 log_k2 0.000 0.00 0.00 0.000 0.0000 log_tb 0.000 0.00 0.00 0.000 0.0000 f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 log_tb cyan_0 0.000 0.00 0.0000 0.0000 0.0000 log_k_JCZ38 0.000 0.00 0.0000 0.0000 0.0000 log_k_J9Z38 0.000 0.00 0.0000 0.0000 0.0000 log_k_JSE76 0.000 0.00 0.0000 0.0000 0.0000 f_cyan_ilr_1 0.000 0.00 0.0000 0.0000 0.0000 f_cyan_ilr_2 2.038 0.00 0.0000 0.0000 0.0000 f_JCZ38_qlogis 0.000 10.33 0.0000 0.0000 0.0000 log_k1 0.000 0.00 0.7006 0.0000 0.0000 log_k2 0.000 0.00 0.0000 0.8928 0.0000 log_tb 0.000 0.00 0.0000 0.0000 0.6773 Starting values for error model parameters: a.1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2427 2419 -1194 Optimised parameters: est. lower upper cyan_0 101.9660 1.005e+02 1.035e+02 log_k_JCZ38 -3.4698 -4.716e+00 -2.224e+00 log_k_J9Z38 -5.0947 -5.740e+00 -4.450e+00 log_k_JSE76 -5.5977 -6.321e+00 -4.875e+00 f_cyan_ilr_1 0.6595 3.734e-01 9.456e-01 f_cyan_ilr_2 0.5905 1.664e-01 1.015e+00 f_JCZ38_qlogis 25.8627 -4.224e+05 4.225e+05 log_k1 -3.0884 -3.453e+00 -2.723e+00 log_k2 -4.3877 -4.778e+00 -3.998e+00 log_tb 2.3057 1.715e+00 2.896e+00 a.1 3.3228 NA NA SD.log_k_JCZ38 1.4071 NA NA SD.log_k_J9Z38 0.5774 NA NA SD.log_k_JSE76 0.6214 NA NA SD.f_cyan_ilr_1 0.3058 NA NA SD.f_cyan_ilr_2 0.3470 NA NA SD.f_JCZ38_qlogis 0.0644 NA NA SD.log_k1 0.3994 NA NA SD.log_k2 0.4373 NA NA SD.log_tb 0.6419 NA NA Correlation is not available Random effects: est. lower upper SD.log_k_JCZ38 1.4071 NA NA SD.log_k_J9Z38 0.5774 NA NA SD.log_k_JSE76 0.6214 NA NA SD.f_cyan_ilr_1 0.3058 NA NA SD.f_cyan_ilr_2 0.3470 NA NA SD.f_JCZ38_qlogis 0.0644 NA NA SD.log_k1 0.3994 NA NA SD.log_k2 0.4373 NA NA SD.log_tb 0.6419 NA NA Variance model: est. lower upper a.1 3.323 NA NA Backtransformed parameters: est. lower upper cyan_0 1.020e+02 1.005e+02 1.035e+02 k_JCZ38 3.112e-02 8.951e-03 1.082e-01 k_J9Z38 6.129e-03 3.216e-03 1.168e-02 k_JSE76 3.706e-03 1.798e-03 7.639e-03 f_cyan_to_JCZ38 5.890e-01 NA NA f_cyan_to_J9Z38 2.318e-01 NA NA f_JCZ38_to_JSE76 1.000e+00 0.000e+00 1.000e+00 k1 4.558e-02 3.164e-02 6.565e-02 k2 1.243e-02 8.417e-03 1.835e-02 tb 1.003e+01 5.557e+00 1.811e+01 Resulting formation fractions: ff cyan_JCZ38 5.890e-01 cyan_J9Z38 2.318e-01 cyan_sink 1.793e-01 JCZ38_JSE76 1.000e+00 JCZ38_sink 5.861e-12 Estimated disappearance times: DT50 DT90 DT50back DT50_k1 DT50_k2 cyan 29.02 158.51 47.72 15.21 55.77 JCZ38 22.27 73.98 NA NA NA J9Z38 113.09 375.69 NA NA NA JSE76 187.01 621.23 NA NA NA </code></pre> <p></p> </div> <div class="section level4"> <h4 id="pathway-2">Pathway 2<a class="anchor" aria-label="anchor" href="#pathway-2"></a> </h4> <caption> Hierarchical FOMC path 2 fit with two-component error </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.4 R version used for fitting: 4.3.0 Date of fit: Fri May 19 09:39:30 2023 Date of summary: Fri May 19 09:57:33 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 474.942 s Using 300, 100 iterations and 10 chains Variance model: Two-component variance function Starting values for degradation parameters: cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 102.4477 -1.8631 -5.1087 -2.5114 0.6826 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta 4.7944 15.9616 13.1566 -0.1564 2.9781 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 cyan_0 7.701 0.000 0.000 0.000 0.0000 log_k_JCZ38 0.000 1.448 0.000 0.000 0.0000 log_k_J9Z38 0.000 0.000 1.724 0.000 0.0000 log_k_JSE76 0.000 0.000 0.000 3.659 0.0000 f_cyan_ilr_1 0.000 0.000 0.000 0.000 0.6356 f_cyan_ilr_2 0.000 0.000 0.000 0.000 0.0000 f_JCZ38_qlogis 0.000 0.000 0.000 0.000 0.0000 f_JSE76_qlogis 0.000 0.000 0.000 0.000 0.0000 log_alpha 0.000 0.000 0.000 0.000 0.0000 log_beta 0.000 0.000 0.000 0.000 0.0000 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta cyan_0 0.00 0.00 0.00 0.0000 0.0000 log_k_JCZ38 0.00 0.00 0.00 0.0000 0.0000 log_k_J9Z38 0.00 0.00 0.00 0.0000 0.0000 log_k_JSE76 0.00 0.00 0.00 0.0000 0.0000 f_cyan_ilr_1 0.00 0.00 0.00 0.0000 0.0000 f_cyan_ilr_2 10.32 0.00 0.00 0.0000 0.0000 f_JCZ38_qlogis 0.00 12.23 0.00 0.0000 0.0000 f_JSE76_qlogis 0.00 0.00 14.99 0.0000 0.0000 log_alpha 0.00 0.00 0.00 0.3924 0.0000 log_beta 0.00 0.00 0.00 0.0000 0.5639 Starting values for error model parameters: a.1 b.1 1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2249 2241 -1104 Optimised parameters: est. lower upper cyan_0 101.55265 9.920e+01 103.90593 log_k_JCZ38 -2.32302 -2.832e+00 -1.81416 log_k_J9Z38 -5.13082 -5.942e+00 -4.31990 log_k_JSE76 -3.01756 -4.262e+00 -1.77360 f_cyan_ilr_1 0.70850 3.657e-01 1.05135 f_cyan_ilr_2 0.95775 2.612e-01 1.65432 f_JCZ38_qlogis 3.86105 9.248e-01 6.79733 f_JSE76_qlogis 7.51583 -1.120e+02 127.03921 log_alpha -0.15308 -4.508e-01 0.14462 log_beta 2.99165 2.711e+00 3.27202 a.1 2.04034 1.811e+00 2.26968 b.1 0.06924 5.745e-02 0.08104 SD.log_k_JCZ38 0.50818 1.390e-01 0.87736 SD.log_k_J9Z38 0.86597 2.652e-01 1.46671 SD.log_k_JSE76 1.38092 4.864e-01 2.27541 SD.f_cyan_ilr_1 0.38204 1.354e-01 0.62864 SD.f_cyan_ilr_2 0.55129 7.198e-02 1.03060 SD.f_JCZ38_qlogis 1.88457 1.710e-02 3.75205 SD.f_JSE76_qlogis 2.64018 -2.450e+03 2455.27887 SD.log_alpha 0.31860 1.047e-01 0.53249 SD.log_beta 0.24195 1.273e-02 0.47117 Correlation: cyan_0 l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76 log_k_JCZ38 -0.0235 log_k_J9Z38 -0.0442 0.0047 log_k_JSE76 -0.0023 0.0966 0.0006 f_cyan_ilr_1 -0.0032 0.0070 -0.0536 -0.0001 f_cyan_ilr_2 -0.5189 0.0452 0.1152 0.0013 -0.0304 f_JCZ38_qlogis 0.1088 -0.0848 -0.0240 0.0040 -0.0384 -0.2303 f_JSE76_qlogis -0.0545 0.1315 0.0195 0.0020 0.0252 0.1737 -0.5939 log_alpha -0.0445 0.0056 0.0261 0.0019 -0.0055 0.0586 -0.0239 -0.0284 log_beta -0.2388 0.0163 0.0566 0.0040 -0.0078 0.2183 -0.0714 -0.0332 log_lph log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta 0.2135 Random effects: est. lower upper SD.log_k_JCZ38 0.5082 1.390e-01 0.8774 SD.log_k_J9Z38 0.8660 2.652e-01 1.4667 SD.log_k_JSE76 1.3809 4.864e-01 2.2754 SD.f_cyan_ilr_1 0.3820 1.354e-01 0.6286 SD.f_cyan_ilr_2 0.5513 7.198e-02 1.0306 SD.f_JCZ38_qlogis 1.8846 1.710e-02 3.7520 SD.f_JSE76_qlogis 2.6402 -2.450e+03 2455.2789 SD.log_alpha 0.3186 1.047e-01 0.5325 SD.log_beta 0.2420 1.273e-02 0.4712 Variance model: est. lower upper a.1 2.04034 1.81101 2.26968 b.1 0.06924 0.05745 0.08104 Backtransformed parameters: est. lower upper cyan_0 1.016e+02 9.920e+01 103.9059 k_JCZ38 9.798e-02 5.890e-02 0.1630 k_J9Z38 5.912e-03 2.627e-03 0.0133 k_JSE76 4.892e-02 1.410e-02 0.1697 f_cyan_to_JCZ38 6.432e-01 NA NA f_cyan_to_J9Z38 2.362e-01 NA NA f_JCZ38_to_JSE76 9.794e-01 7.160e-01 0.9989 f_JSE76_to_JCZ38 9.995e-01 2.268e-49 1.0000 alpha 8.581e-01 6.371e-01 1.1556 beta 1.992e+01 1.505e+01 26.3646 Resulting formation fractions: ff cyan_JCZ38 0.6432301 cyan_J9Z38 0.2361657 cyan_sink 0.1206042 JCZ38_JSE76 0.9793879 JCZ38_sink 0.0206121 JSE76_JCZ38 0.9994559 JSE76_sink 0.0005441 Estimated disappearance times: DT50 DT90 DT50back cyan 24.759 271.61 81.76 JCZ38 7.075 23.50 NA J9Z38 117.249 389.49 NA JSE76 14.169 47.07 NA </code></pre> <p></p> <caption> Hierarchical DFOP path 2 fit with constant variance </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.4 R version used for fitting: 4.3.0 Date of fit: Fri May 19 09:40:29 2023 Date of summary: Fri May 19 09:57:33 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 533.901 s Using 300, 100 iterations and 10 chains Variance model: Constant variance Starting values for degradation parameters: cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 102.4380 -2.3107 -5.3123 -3.7120 0.6757 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 1.1439 13.1194 12.3492 -1.9317 -4.4557 g_qlogis -0.5644 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 cyan_0 4.591 0.0000 0.000 0.0 0.0000 log_k_JCZ38 0.000 0.7966 0.000 0.0 0.0000 log_k_J9Z38 0.000 0.0000 1.561 0.0 0.0000 log_k_JSE76 0.000 0.0000 0.000 0.8 0.0000 f_cyan_ilr_1 0.000 0.0000 0.000 0.0 0.6349 f_cyan_ilr_2 0.000 0.0000 0.000 0.0 0.0000 f_JCZ38_qlogis 0.000 0.0000 0.000 0.0 0.0000 f_JSE76_qlogis 0.000 0.0000 0.000 0.0 0.0000 log_k1 0.000 0.0000 0.000 0.0 0.0000 log_k2 0.000 0.0000 0.000 0.0 0.0000 g_qlogis 0.000 0.0000 0.000 0.0 0.0000 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 cyan_0 0.000 0.00 0.00 0.000 0.0000 log_k_JCZ38 0.000 0.00 0.00 0.000 0.0000 log_k_J9Z38 0.000 0.00 0.00 0.000 0.0000 log_k_JSE76 0.000 0.00 0.00 0.000 0.0000 f_cyan_ilr_1 0.000 0.00 0.00 0.000 0.0000 f_cyan_ilr_2 1.797 0.00 0.00 0.000 0.0000 f_JCZ38_qlogis 0.000 13.86 0.00 0.000 0.0000 f_JSE76_qlogis 0.000 0.00 13.91 0.000 0.0000 log_k1 0.000 0.00 0.00 1.106 0.0000 log_k2 0.000 0.00 0.00 0.000 0.6141 g_qlogis 0.000 0.00 0.00 0.000 0.0000 g_qlogis cyan_0 0.000 log_k_JCZ38 0.000 log_k_J9Z38 0.000 log_k_JSE76 0.000 f_cyan_ilr_1 0.000 f_cyan_ilr_2 0.000 f_JCZ38_qlogis 0.000 f_JSE76_qlogis 0.000 log_k1 0.000 log_k2 0.000 g_qlogis 1.595 Starting values for error model parameters: a.1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2288 2280 -1122 Optimised parameters: est. lower upper cyan_0 102.7204 1.014e+02 1.040e+02 log_k_JCZ38 -2.8925 -4.044e+00 -1.741e+00 log_k_J9Z38 -5.1430 -5.828e+00 -4.457e+00 log_k_JSE76 -3.5577 -4.174e+00 -2.941e+00 f_cyan_ilr_1 0.6929 3.788e-01 1.007e+00 f_cyan_ilr_2 0.6066 5.342e-02 1.160e+00 f_JCZ38_qlogis 9.8071 -2.819e+03 2.838e+03 f_JSE76_qlogis 2.2229 5.684e-01 3.877e+00 log_k1 -1.9339 -2.609e+00 -1.258e+00 log_k2 -4.4709 -4.935e+00 -4.007e+00 g_qlogis -0.4987 -1.373e+00 3.757e-01 a.1 2.7368 2.545e+00 2.928e+00 SD.log_k_JCZ38 1.2747 4.577e-01 2.092e+00 SD.log_k_J9Z38 0.6758 1.418e-01 1.210e+00 SD.log_k_JSE76 0.5869 1.169e-01 1.057e+00 SD.f_cyan_ilr_1 0.3392 1.161e-01 5.622e-01 SD.f_cyan_ilr_2 0.4200 8.501e-02 7.550e-01 SD.f_JCZ38_qlogis 0.8511 -1.137e+06 1.137e+06 SD.f_JSE76_qlogis 0.3767 -5.238e-01 1.277e+00 SD.log_k1 0.7475 2.601e-01 1.235e+00 SD.log_k2 0.5179 1.837e-01 8.521e-01 SD.g_qlogis 0.9817 3.553e-01 1.608e+00 Correlation: cyan_0 l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76 log_k_JCZ38 -0.0351 log_k_J9Z38 -0.0541 0.0043 log_k_JSE76 -0.0078 0.0900 -0.0014 f_cyan_ilr_1 -0.0249 0.0268 -0.0962 0.0000 f_cyan_ilr_2 -0.3560 0.0848 0.1545 -0.0022 0.0463 f_JCZ38_qlogis 0.2005 -0.1226 -0.0347 0.0514 -0.1840 -0.5906 f_JSE76_qlogis -0.1638 0.1307 0.0266 0.0001 0.1645 0.5181 -0.9297 log_k1 0.0881 -0.0071 0.0005 -0.0070 -0.0064 -0.0346 0.0316 -0.0341 log_k2 0.0238 -0.0003 0.0082 -0.0022 -0.0017 -0.0017 -0.0002 -0.0076 g_qlogis 0.0198 -0.0002 -0.0109 0.0034 0.0017 -0.0176 0.0044 0.0051 log_k1 log_k2 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 0.0276 g_qlogis -0.0283 -0.0309 Random effects: est. lower upper SD.log_k_JCZ38 1.2747 4.577e-01 2.092e+00 SD.log_k_J9Z38 0.6758 1.418e-01 1.210e+00 SD.log_k_JSE76 0.5869 1.169e-01 1.057e+00 SD.f_cyan_ilr_1 0.3392 1.161e-01 5.622e-01 SD.f_cyan_ilr_2 0.4200 8.501e-02 7.550e-01 SD.f_JCZ38_qlogis 0.8511 -1.137e+06 1.137e+06 SD.f_JSE76_qlogis 0.3767 -5.238e-01 1.277e+00 SD.log_k1 0.7475 2.601e-01 1.235e+00 SD.log_k2 0.5179 1.837e-01 8.521e-01 SD.g_qlogis 0.9817 3.553e-01 1.608e+00 Variance model: est. lower upper a.1 2.737 2.545 2.928 Backtransformed parameters: est. lower upper cyan_0 102.72037 1.014e+02 104.00464 k_JCZ38 0.05544 1.752e-02 0.17539 k_J9Z38 0.00584 2.942e-03 0.01159 k_JSE76 0.02850 1.539e-02 0.05279 f_cyan_to_JCZ38 0.59995 NA NA f_cyan_to_J9Z38 0.22519 NA NA f_JCZ38_to_JSE76 0.99994 0.000e+00 1.00000 f_JSE76_to_JCZ38 0.90229 6.384e-01 0.97971 k1 0.14459 7.357e-02 0.28414 k2 0.01144 7.192e-03 0.01819 g 0.37784 2.021e-01 0.59284 Resulting formation fractions: ff cyan_JCZ38 5.999e-01 cyan_J9Z38 2.252e-01 cyan_sink 1.749e-01 JCZ38_JSE76 9.999e-01 JCZ38_sink 5.506e-05 JSE76_JCZ38 9.023e-01 JSE76_sink 9.771e-02 Estimated disappearance times: DT50 DT90 DT50back DT50_k1 DT50_k2 cyan 21.93 159.83 48.11 4.794 60.6 JCZ38 12.50 41.53 NA NA NA J9Z38 118.69 394.27 NA NA NA JSE76 24.32 80.78 NA NA NA </code></pre> <p></p> <caption> Hierarchical DFOP path 2 fit with two-component error </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.4 R version used for fitting: 4.3.0 Date of fit: Fri May 19 09:43:04 2023 Date of summary: Fri May 19 09:57:33 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 688.913 s Using 300, 100 iterations and 10 chains Variance model: Two-component variance function Starting values for degradation parameters: cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 101.7393 -1.4493 -5.0118 -2.1269 0.6720 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 7.3362 13.4423 13.2659 -2.0061 -4.5527 g_qlogis -0.5806 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 cyan_0 5.604 0.00 0.000 0.000 0.0000 log_k_JCZ38 0.000 2.77 0.000 0.000 0.0000 log_k_J9Z38 0.000 0.00 1.662 0.000 0.0000 log_k_JSE76 0.000 0.00 0.000 5.021 0.0000 f_cyan_ilr_1 0.000 0.00 0.000 0.000 0.6519 f_cyan_ilr_2 0.000 0.00 0.000 0.000 0.0000 f_JCZ38_qlogis 0.000 0.00 0.000 0.000 0.0000 f_JSE76_qlogis 0.000 0.00 0.000 0.000 0.0000 log_k1 0.000 0.00 0.000 0.000 0.0000 log_k2 0.000 0.00 0.000 0.000 0.0000 g_qlogis 0.000 0.00 0.000 0.000 0.0000 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 cyan_0 0.00 0.00 0.00 0.0000 0.0000 log_k_JCZ38 0.00 0.00 0.00 0.0000 0.0000 log_k_J9Z38 0.00 0.00 0.00 0.0000 0.0000 log_k_JSE76 0.00 0.00 0.00 0.0000 0.0000 f_cyan_ilr_1 0.00 0.00 0.00 0.0000 0.0000 f_cyan_ilr_2 13.37 0.00 0.00 0.0000 0.0000 f_JCZ38_qlogis 0.00 14.21 0.00 0.0000 0.0000 f_JSE76_qlogis 0.00 0.00 14.58 0.0000 0.0000 log_k1 0.00 0.00 0.00 0.8453 0.0000 log_k2 0.00 0.00 0.00 0.0000 0.5969 g_qlogis 0.00 0.00 0.00 0.0000 0.0000 g_qlogis cyan_0 0.00 log_k_JCZ38 0.00 log_k_J9Z38 0.00 log_k_JSE76 0.00 f_cyan_ilr_1 0.00 f_cyan_ilr_2 0.00 f_JCZ38_qlogis 0.00 f_JSE76_qlogis 0.00 log_k1 0.00 log_k2 0.00 g_qlogis 1.69 Starting values for error model parameters: a.1 b.1 1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2234 2226 -1095 Optimised parameters: est. lower upper cyan_0 101.25496 99.14662 103.36331 log_k_JCZ38 -2.55593 -3.32972 -1.78215 log_k_J9Z38 -5.07103 -5.85423 -4.28783 log_k_JSE76 -3.25468 -4.17577 -2.33360 f_cyan_ilr_1 0.70139 0.35924 1.04355 f_cyan_ilr_2 1.07712 0.17789 1.97636 f_JCZ38_qlogis 3.57483 0.05990 7.08976 f_JSE76_qlogis 4.54884 -7.25628 16.35395 log_k1 -2.38201 -2.51639 -2.24763 log_k2 -4.66741 -4.91865 -4.41617 g_qlogis -0.28446 -1.14192 0.57300 a.1 2.05925 1.83267 2.28582 b.1 0.06172 0.05076 0.07268 SD.log_k_JCZ38 0.81137 0.25296 1.36977 SD.log_k_J9Z38 0.83542 0.25396 1.41689 SD.log_k_JSE76 0.97903 0.30100 1.65707 SD.f_cyan_ilr_1 0.37878 0.13374 0.62382 SD.f_cyan_ilr_2 0.67274 0.10102 1.24446 SD.f_JCZ38_qlogis 1.35327 -0.42361 3.13015 SD.f_JSE76_qlogis 1.43956 -19.15140 22.03052 SD.log_k2 0.25329 0.07521 0.43138 SD.g_qlogis 0.95167 0.35149 1.55184 Correlation: cyan_0 l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76 log_k_JCZ38 -0.0265 log_k_J9Z38 -0.0392 0.0024 log_k_JSE76 0.0011 0.1220 -0.0016 f_cyan_ilr_1 -0.0161 0.0217 -0.0552 0.0034 f_cyan_ilr_2 -0.4718 0.0829 0.1102 0.0042 0.0095 f_JCZ38_qlogis 0.1609 -0.1318 -0.0277 0.0081 -0.1040 -0.4559 f_JSE76_qlogis -0.1289 0.1494 0.0219 0.0012 0.1004 0.4309 -0.8543 log_k1 0.2618 -0.0739 -0.0167 -0.0148 -0.0444 -0.2768 0.3518 -0.3818 log_k2 0.0603 -0.0217 0.0174 -0.0058 -0.0197 -0.0533 0.0923 -0.1281 g_qlogis 0.0362 0.0115 -0.0111 0.0040 0.0095 -0.0116 -0.0439 0.0651 log_k1 log_k2 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 0.3269 g_qlogis -0.1656 -0.0928 Random effects: est. lower upper SD.log_k_JCZ38 0.8114 0.25296 1.3698 SD.log_k_J9Z38 0.8354 0.25396 1.4169 SD.log_k_JSE76 0.9790 0.30100 1.6571 SD.f_cyan_ilr_1 0.3788 0.13374 0.6238 SD.f_cyan_ilr_2 0.6727 0.10102 1.2445 SD.f_JCZ38_qlogis 1.3533 -0.42361 3.1301 SD.f_JSE76_qlogis 1.4396 -19.15140 22.0305 SD.log_k2 0.2533 0.07521 0.4314 SD.g_qlogis 0.9517 0.35149 1.5518 Variance model: est. lower upper a.1 2.05925 1.83267 2.28582 b.1 0.06172 0.05076 0.07268 Backtransformed parameters: est. lower upper cyan_0 1.013e+02 9.915e+01 103.36331 k_JCZ38 7.762e-02 3.580e-02 0.16828 k_J9Z38 6.276e-03 2.868e-03 0.01373 k_JSE76 3.859e-02 1.536e-02 0.09695 f_cyan_to_JCZ38 6.520e-01 NA NA f_cyan_to_J9Z38 2.418e-01 NA NA f_JCZ38_to_JSE76 9.727e-01 5.150e-01 0.99917 f_JSE76_to_JCZ38 9.895e-01 7.052e-04 1.00000 k1 9.236e-02 8.075e-02 0.10565 k2 9.397e-03 7.309e-03 0.01208 g 4.294e-01 2.420e-01 0.63945 Resulting formation fractions: ff cyan_JCZ38 0.65203 cyan_J9Z38 0.24181 cyan_sink 0.10616 JCZ38_JSE76 0.97274 JCZ38_sink 0.02726 JSE76_JCZ38 0.98953 JSE76_sink 0.01047 Estimated disappearance times: DT50 DT90 DT50back DT50_k1 DT50_k2 cyan 24.26 185.34 55.79 7.504 73.77 JCZ38 8.93 29.66 NA NA NA J9Z38 110.45 366.89 NA NA NA JSE76 17.96 59.66 NA NA NA </code></pre> <p></p> <caption> Hierarchical SFORB path 2 fit with constant variance </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.4 R version used for fitting: 4.3.0 Date of fit: Fri May 19 09:40:32 2023 Date of summary: Fri May 19 09:57:33 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 536.94 s Using 300, 100 iterations and 10 chains Variance model: Constant variance Starting values for degradation parameters: cyan_free_0 log_k_cyan_free log_k_cyan_free_bound 102.4395 -2.7673 -2.8942 log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 -3.6201 -2.3107 -5.3123 log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 -3.7120 0.6754 1.1448 f_JCZ38_qlogis f_JSE76_qlogis 14.8408 15.4734 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_free_0 log_k_cyan_free log_k_cyan_free_bound cyan_free_0 4.589 0.0000 0.00 log_k_cyan_free 0.000 0.4849 0.00 log_k_cyan_free_bound 0.000 0.0000 1.62 log_k_cyan_bound_free 0.000 0.0000 0.00 log_k_JCZ38 0.000 0.0000 0.00 log_k_J9Z38 0.000 0.0000 0.00 log_k_JSE76 0.000 0.0000 0.00 f_cyan_ilr_1 0.000 0.0000 0.00 f_cyan_ilr_2 0.000 0.0000 0.00 f_JCZ38_qlogis 0.000 0.0000 0.00 f_JSE76_qlogis 0.000 0.0000 0.00 log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 cyan_free_0 0.000 0.0000 0.000 0.0 log_k_cyan_free 0.000 0.0000 0.000 0.0 log_k_cyan_free_bound 0.000 0.0000 0.000 0.0 log_k_cyan_bound_free 1.197 0.0000 0.000 0.0 log_k_JCZ38 0.000 0.7966 0.000 0.0 log_k_J9Z38 0.000 0.0000 1.561 0.0 log_k_JSE76 0.000 0.0000 0.000 0.8 f_cyan_ilr_1 0.000 0.0000 0.000 0.0 f_cyan_ilr_2 0.000 0.0000 0.000 0.0 f_JCZ38_qlogis 0.000 0.0000 0.000 0.0 f_JSE76_qlogis 0.000 0.0000 0.000 0.0 f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis cyan_free_0 0.0000 0.000 0.0 0.00 log_k_cyan_free 0.0000 0.000 0.0 0.00 log_k_cyan_free_bound 0.0000 0.000 0.0 0.00 log_k_cyan_bound_free 0.0000 0.000 0.0 0.00 log_k_JCZ38 0.0000 0.000 0.0 0.00 log_k_J9Z38 0.0000 0.000 0.0 0.00 log_k_JSE76 0.0000 0.000 0.0 0.00 f_cyan_ilr_1 0.6349 0.000 0.0 0.00 f_cyan_ilr_2 0.0000 1.797 0.0 0.00 f_JCZ38_qlogis 0.0000 0.000 15.6 0.00 f_JSE76_qlogis 0.0000 0.000 0.0 17.52 Starting values for error model parameters: a.1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2283 2275 -1120 Optimised parameters: est. lower upper cyan_free_0 102.6517 101.40815 103.8952 log_k_cyan_free -2.8729 -3.18649 -2.5593 log_k_cyan_free_bound -2.7803 -3.60525 -1.9552 log_k_cyan_bound_free -3.5845 -4.16644 -3.0026 log_k_JCZ38 -2.3411 -2.89698 -1.7852 log_k_J9Z38 -5.2487 -6.01271 -4.4847 log_k_JSE76 -3.0259 -4.28274 -1.7690 f_cyan_ilr_1 0.7289 0.38214 1.0756 f_cyan_ilr_2 0.6891 0.18277 1.1954 f_JCZ38_qlogis 4.2162 0.47015 7.9622 f_JSE76_qlogis 5.8911 -20.19088 31.9730 a.1 2.7159 2.52587 2.9060 SD.log_k_cyan_free 0.3354 0.10979 0.5610 SD.log_k_cyan_free_bound 0.9061 0.30969 1.5025 SD.log_k_cyan_bound_free 0.6376 0.21229 1.0628 SD.log_k_JCZ38 0.5499 0.14533 0.9545 SD.log_k_J9Z38 0.7457 0.15106 1.3404 SD.log_k_JSE76 1.3822 0.47329 2.2912 SD.f_cyan_ilr_1 0.3820 0.13280 0.6313 SD.f_cyan_ilr_2 0.4317 0.06803 0.7953 SD.f_JCZ38_qlogis 1.8258 -0.25423 3.9059 SD.f_JSE76_qlogis 2.2348 -83.33679 87.8065 Correlation: cyn_f_0 lg_k_c_ lg_k_cyn_f_ lg_k_cyn_b_ l__JCZ3 l__J9Z3 log_k_cyan_free 0.1944 log_k_cyan_free_bound 0.0815 0.0814 log_k_cyan_bound_free 0.0106 0.0426 0.0585 log_k_JCZ38 -0.0231 -0.0106 -0.0089 -0.0051 log_k_J9Z38 -0.0457 -0.0108 0.0019 0.0129 0.0032 log_k_JSE76 -0.0054 -0.0024 -0.0017 -0.0005 0.1108 0.0009 f_cyan_ilr_1 0.0051 -0.0005 -0.0035 -0.0056 0.0131 -0.0967 f_cyan_ilr_2 -0.3182 -0.0771 -0.0309 -0.0038 0.0680 0.1643 f_JCZ38_qlogis 0.0834 0.0369 0.0302 0.0172 -0.1145 -0.0204 f_JSE76_qlogis -0.0553 -0.0365 -0.0441 -0.0414 0.1579 0.0175 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 log_k_cyan_free log_k_cyan_free_bound log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 -0.0002 f_cyan_ilr_2 0.0020 -0.0415 f_JCZ38_qlogis 0.0052 -0.0665 -0.3437 f_JSE76_qlogis 0.0066 0.0635 0.3491 -0.7487 Random effects: est. lower upper SD.log_k_cyan_free 0.3354 0.10979 0.5610 SD.log_k_cyan_free_bound 0.9061 0.30969 1.5025 SD.log_k_cyan_bound_free 0.6376 0.21229 1.0628 SD.log_k_JCZ38 0.5499 0.14533 0.9545 SD.log_k_J9Z38 0.7457 0.15106 1.3404 SD.log_k_JSE76 1.3822 0.47329 2.2912 SD.f_cyan_ilr_1 0.3820 0.13280 0.6313 SD.f_cyan_ilr_2 0.4317 0.06803 0.7953 SD.f_JCZ38_qlogis 1.8258 -0.25423 3.9059 SD.f_JSE76_qlogis 2.2348 -83.33679 87.8065 Variance model: est. lower upper a.1 2.716 2.526 2.906 Backtransformed parameters: est. lower upper cyan_free_0 1.027e+02 1.014e+02 103.89517 k_cyan_free 5.654e-02 4.132e-02 0.07736 k_cyan_free_bound 6.202e-02 2.718e-02 0.14153 k_cyan_bound_free 2.775e-02 1.551e-02 0.04966 k_JCZ38 9.622e-02 5.519e-02 0.16777 k_J9Z38 5.254e-03 2.447e-03 0.01128 k_JSE76 4.852e-02 1.380e-02 0.17051 f_cyan_free_to_JCZ38 6.197e-01 5.643e-01 0.84429 f_cyan_free_to_J9Z38 2.211e-01 5.643e-01 0.84429 f_JCZ38_to_JSE76 9.855e-01 6.154e-01 0.99965 f_JSE76_to_JCZ38 9.972e-01 1.703e-09 1.00000 Estimated Eigenvalues of SFORB model(s): cyan_b1 cyan_b2 cyan_g 0.13466 0.01165 0.36490 Resulting formation fractions: ff cyan_free_JCZ38 0.619745 cyan_free_J9Z38 0.221083 cyan_free_sink 0.159172 cyan_free 1.000000 JCZ38_JSE76 0.985460 JCZ38_sink 0.014540 JSE76_JCZ38 0.997244 JSE76_sink 0.002756 Estimated disappearance times: DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 cyan 23.293 158.67 47.77 5.147 59.5 JCZ38 7.203 23.93 NA NA NA J9Z38 131.918 438.22 NA NA NA JSE76 14.287 47.46 NA NA NA </code></pre> <p></p> <caption> Hierarchical SFORB path 2 fit with two-component error </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.4 R version used for fitting: 4.3.0 Date of fit: Fri May 19 09:42:47 2023 Date of summary: Fri May 19 09:57:33 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 671.849 s Using 300, 100 iterations and 10 chains Variance model: Two-component variance function Starting values for degradation parameters: cyan_free_0 log_k_cyan_free log_k_cyan_free_bound 101.7511 -2.8370 -3.0162 log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 -3.6600 -2.2988 -5.3129 log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 -3.6991 0.6722 4.8596 f_JCZ38_qlogis f_JSE76_qlogis 13.4678 14.2149 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_free_0 log_k_cyan_free log_k_cyan_free_bound cyan_free_0 5.629 0.000 0.000 log_k_cyan_free 0.000 0.446 0.000 log_k_cyan_free_bound 0.000 0.000 1.449 log_k_cyan_bound_free 0.000 0.000 0.000 log_k_JCZ38 0.000 0.000 0.000 log_k_J9Z38 0.000 0.000 0.000 log_k_JSE76 0.000 0.000 0.000 f_cyan_ilr_1 0.000 0.000 0.000 f_cyan_ilr_2 0.000 0.000 0.000 f_JCZ38_qlogis 0.000 0.000 0.000 f_JSE76_qlogis 0.000 0.000 0.000 log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 cyan_free_0 0.000 0.0000 0.000 0.0000 log_k_cyan_free 0.000 0.0000 0.000 0.0000 log_k_cyan_free_bound 0.000 0.0000 0.000 0.0000 log_k_cyan_bound_free 1.213 0.0000 0.000 0.0000 log_k_JCZ38 0.000 0.7801 0.000 0.0000 log_k_J9Z38 0.000 0.0000 1.575 0.0000 log_k_JSE76 0.000 0.0000 0.000 0.8078 f_cyan_ilr_1 0.000 0.0000 0.000 0.0000 f_cyan_ilr_2 0.000 0.0000 0.000 0.0000 f_JCZ38_qlogis 0.000 0.0000 0.000 0.0000 f_JSE76_qlogis 0.000 0.0000 0.000 0.0000 f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis cyan_free_0 0.0000 0.000 0.00 0.00 log_k_cyan_free 0.0000 0.000 0.00 0.00 log_k_cyan_free_bound 0.0000 0.000 0.00 0.00 log_k_cyan_bound_free 0.0000 0.000 0.00 0.00 log_k_JCZ38 0.0000 0.000 0.00 0.00 log_k_J9Z38 0.0000 0.000 0.00 0.00 log_k_JSE76 0.0000 0.000 0.00 0.00 f_cyan_ilr_1 0.6518 0.000 0.00 0.00 f_cyan_ilr_2 0.0000 9.981 0.00 0.00 f_JCZ38_qlogis 0.0000 0.000 14.26 0.00 f_JSE76_qlogis 0.0000 0.000 0.00 16.17 Starting values for error model parameters: a.1 b.1 1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2240 2231 -1098 Optimised parameters: est. lower upper cyan_free_0 100.73014 9.873e+01 1.027e+02 log_k_cyan_free -3.19634 -3.641e+00 -2.752e+00 log_k_cyan_free_bound -3.43533 -3.674e+00 -3.197e+00 log_k_cyan_bound_free -3.83282 -4.163e+00 -3.503e+00 log_k_JCZ38 -2.51065 -3.225e+00 -1.796e+00 log_k_J9Z38 -5.02539 -5.825e+00 -4.226e+00 log_k_JSE76 -3.24777 -4.163e+00 -2.333e+00 f_cyan_ilr_1 0.70640 3.562e-01 1.057e+00 f_cyan_ilr_2 1.42704 3.170e-01 2.537e+00 f_JCZ38_qlogis 2.84779 1.042e+00 4.654e+00 f_JSE76_qlogis 8.63674 -6.407e+02 6.580e+02 a.1 2.07082 1.846e+00 2.296e+00 b.1 0.06227 5.120e-02 7.334e-02 SD.log_k_cyan_free 0.49674 1.865e-01 8.069e-01 SD.log_k_cyan_bound_free 0.28537 6.808e-02 5.027e-01 SD.log_k_JCZ38 0.74846 2.305e-01 1.266e+00 SD.log_k_J9Z38 0.86077 2.713e-01 1.450e+00 SD.log_k_JSE76 0.97613 3.030e-01 1.649e+00 SD.f_cyan_ilr_1 0.38994 1.382e-01 6.417e-01 SD.f_cyan_ilr_2 0.82869 3.917e-02 1.618e+00 SD.f_JCZ38_qlogis 1.05000 -2.809e-02 2.128e+00 SD.f_JSE76_qlogis 0.44681 -3.986e+05 3.986e+05 Correlation: cyn_f_0 lg_k_c_ lg_k_cyn_f_ lg_k_cyn_b_ l__JCZ3 l__J9Z3 log_k_cyan_free 0.0936 log_k_cyan_free_bound 0.1302 0.1627 log_k_cyan_bound_free 0.0029 0.0525 0.5181 log_k_JCZ38 -0.0116 -0.0077 -0.0430 -0.0236 log_k_J9Z38 -0.0192 -0.0077 -0.0048 0.0229 -0.0005 log_k_JSE76 0.0007 -0.0020 -0.0134 -0.0072 0.1225 -0.0016 f_cyan_ilr_1 -0.0118 -0.0027 -0.0132 -0.0118 0.0127 -0.0505 f_cyan_ilr_2 -0.4643 -0.0762 -0.1245 0.0137 0.0497 0.1003 f_JCZ38_qlogis 0.0710 0.0371 0.1826 0.0925 -0.0869 -0.0130 f_JSE76_qlogis -0.0367 -0.0270 -0.2274 -0.1865 0.1244 0.0098 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 log_k_cyan_free log_k_cyan_free_bound log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 0.0036 f_cyan_ilr_2 0.0050 -0.0201 f_JCZ38_qlogis 0.0142 -0.0529 -0.2698 f_JSE76_qlogis 0.0064 0.0345 0.2015 -0.7058 Random effects: est. lower upper SD.log_k_cyan_free 0.4967 1.865e-01 8.069e-01 SD.log_k_cyan_bound_free 0.2854 6.808e-02 5.027e-01 SD.log_k_JCZ38 0.7485 2.305e-01 1.266e+00 SD.log_k_J9Z38 0.8608 2.713e-01 1.450e+00 SD.log_k_JSE76 0.9761 3.030e-01 1.649e+00 SD.f_cyan_ilr_1 0.3899 1.382e-01 6.417e-01 SD.f_cyan_ilr_2 0.8287 3.917e-02 1.618e+00 SD.f_JCZ38_qlogis 1.0500 -2.809e-02 2.128e+00 SD.f_JSE76_qlogis 0.4468 -3.986e+05 3.986e+05 Variance model: est. lower upper a.1 2.07082 1.8458 2.29588 b.1 0.06227 0.0512 0.07334 Backtransformed parameters: est. lower upper cyan_free_0 1.007e+02 9.873e+01 102.72898 k_cyan_free 4.091e-02 2.623e-02 0.06382 k_cyan_free_bound 3.221e-02 2.537e-02 0.04090 k_cyan_bound_free 2.165e-02 1.557e-02 0.03011 k_JCZ38 8.122e-02 3.975e-02 0.16594 k_J9Z38 6.569e-03 2.954e-03 0.01461 k_JSE76 3.886e-02 1.556e-02 0.09703 f_cyan_free_to_JCZ38 6.785e-01 6.102e-01 0.97309 f_cyan_free_to_J9Z38 2.498e-01 6.102e-01 0.97309 f_JCZ38_to_JSE76 9.452e-01 7.392e-01 0.99056 f_JSE76_to_JCZ38 9.998e-01 5.580e-279 1.00000 Estimated Eigenvalues of SFORB model(s): cyan_b1 cyan_b2 cyan_g 0.08426 0.01051 0.41220 Resulting formation fractions: ff cyan_free_JCZ38 0.6784541 cyan_free_J9Z38 0.2498405 cyan_free_sink 0.0717054 cyan_free 1.0000000 JCZ38_JSE76 0.9452043 JCZ38_sink 0.0547957 JSE76_JCZ38 0.9998226 JSE76_sink 0.0001774 Estimated disappearance times: DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 cyan 25.237 168.51 50.73 8.226 65.95 JCZ38 8.535 28.35 NA NA NA J9Z38 105.517 350.52 NA NA NA JSE76 17.837 59.25 NA NA NA </code></pre> <p></p> </div> <div class="section level4"> <h4 id="pathway-2-refined-fits">Pathway 2, refined fits<a class="anchor" aria-label="anchor" href="#pathway-2-refined-fits"></a> </h4> <caption> Hierarchical FOMC path 2 fit with reduced random effects, two-component error </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.4 R version used for fitting: 4.3.0 Date of fit: Fri May 19 09:55:35 2023 Date of summary: Fri May 19 09:57:33 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 748.54 s Using 300, 100 iterations and 10 chains Variance model: Two-component variance function Starting values for degradation parameters: cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 102.4477 -1.8631 -5.1087 -2.5114 0.6826 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta 4.7944 15.9616 13.1566 -0.1564 2.9781 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 cyan_0 7.701 0.000 0.000 0.000 0.0000 log_k_JCZ38 0.000 1.448 0.000 0.000 0.0000 log_k_J9Z38 0.000 0.000 1.724 0.000 0.0000 log_k_JSE76 0.000 0.000 0.000 3.659 0.0000 f_cyan_ilr_1 0.000 0.000 0.000 0.000 0.6356 f_cyan_ilr_2 0.000 0.000 0.000 0.000 0.0000 f_JCZ38_qlogis 0.000 0.000 0.000 0.000 0.0000 f_JSE76_qlogis 0.000 0.000 0.000 0.000 0.0000 log_alpha 0.000 0.000 0.000 0.000 0.0000 log_beta 0.000 0.000 0.000 0.000 0.0000 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta cyan_0 0.00 0.00 0.00 0.0000 0.0000 log_k_JCZ38 0.00 0.00 0.00 0.0000 0.0000 log_k_J9Z38 0.00 0.00 0.00 0.0000 0.0000 log_k_JSE76 0.00 0.00 0.00 0.0000 0.0000 f_cyan_ilr_1 0.00 0.00 0.00 0.0000 0.0000 f_cyan_ilr_2 10.32 0.00 0.00 0.0000 0.0000 f_JCZ38_qlogis 0.00 12.23 0.00 0.0000 0.0000 f_JSE76_qlogis 0.00 0.00 14.99 0.0000 0.0000 log_alpha 0.00 0.00 0.00 0.3924 0.0000 log_beta 0.00 0.00 0.00 0.0000 0.5639 Starting values for error model parameters: a.1 b.1 1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2249 2242 -1106 Optimised parameters: est. lower upper cyan_0 101.24524 NA NA log_k_JCZ38 -2.85375 NA NA log_k_J9Z38 -5.07729 NA NA log_k_JSE76 -3.53511 NA NA f_cyan_ilr_1 0.67478 NA NA f_cyan_ilr_2 0.97152 NA NA f_JCZ38_qlogis 213.48001 NA NA f_JSE76_qlogis 2.02040 NA NA log_alpha -0.11041 NA NA log_beta 3.06575 NA NA a.1 2.05279 1.82393 2.28166 b.1 0.07116 0.05910 0.08322 SD.log_k_JCZ38 1.21713 0.44160 1.99266 SD.log_k_J9Z38 0.88268 0.27541 1.48995 SD.log_k_JSE76 0.59452 0.15005 1.03898 SD.f_cyan_ilr_1 0.35370 0.12409 0.58331 SD.f_cyan_ilr_2 0.78186 0.18547 1.37824 SD.log_alpha 0.27781 0.08168 0.47394 SD.log_beta 0.32608 0.06490 0.58726 Correlation is not available Random effects: est. lower upper SD.log_k_JCZ38 1.2171 0.44160 1.9927 SD.log_k_J9Z38 0.8827 0.27541 1.4900 SD.log_k_JSE76 0.5945 0.15005 1.0390 SD.f_cyan_ilr_1 0.3537 0.12409 0.5833 SD.f_cyan_ilr_2 0.7819 0.18547 1.3782 SD.log_alpha 0.2778 0.08168 0.4739 SD.log_beta 0.3261 0.06490 0.5873 Variance model: est. lower upper a.1 2.05279 1.8239 2.28166 b.1 0.07116 0.0591 0.08322 Backtransformed parameters: est. lower upper cyan_0 1.012e+02 NA NA k_JCZ38 5.763e-02 NA NA k_J9Z38 6.237e-03 NA NA k_JSE76 2.916e-02 NA NA f_cyan_to_JCZ38 6.354e-01 NA NA f_cyan_to_J9Z38 2.447e-01 NA NA f_JCZ38_to_JSE76 1.000e+00 NA NA f_JSE76_to_JCZ38 8.829e-01 NA NA alpha 8.955e-01 NA NA beta 2.145e+01 NA NA Resulting formation fractions: ff cyan_JCZ38 0.6354 cyan_J9Z38 0.2447 cyan_sink 0.1200 JCZ38_JSE76 1.0000 JCZ38_sink 0.0000 JSE76_JCZ38 0.8829 JSE76_sink 0.1171 Estimated disappearance times: DT50 DT90 DT50back cyan 25.07 259.21 78.03 JCZ38 12.03 39.96 NA J9Z38 111.14 369.19 NA JSE76 23.77 78.98 NA </code></pre> <p></p> <caption> Hierarchical DFOP path 2 fit with reduced random effects, constant variance </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.4 R version used for fitting: 4.3.0 Date of fit: Fri May 19 09:57:10 2023 Date of summary: Fri May 19 09:57:33 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 843.793 s Using 300, 100 iterations and 10 chains Variance model: Constant variance Starting values for degradation parameters: cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 102.4380 -2.3107 -5.3123 -3.7120 0.6757 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 1.1439 13.1194 12.3492 -1.9317 -4.4557 g_qlogis -0.5644 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 cyan_0 4.591 0.0000 0.000 0.0 0.0000 log_k_JCZ38 0.000 0.7966 0.000 0.0 0.0000 log_k_J9Z38 0.000 0.0000 1.561 0.0 0.0000 log_k_JSE76 0.000 0.0000 0.000 0.8 0.0000 f_cyan_ilr_1 0.000 0.0000 0.000 0.0 0.6349 f_cyan_ilr_2 0.000 0.0000 0.000 0.0 0.0000 f_JCZ38_qlogis 0.000 0.0000 0.000 0.0 0.0000 f_JSE76_qlogis 0.000 0.0000 0.000 0.0 0.0000 log_k1 0.000 0.0000 0.000 0.0 0.0000 log_k2 0.000 0.0000 0.000 0.0 0.0000 g_qlogis 0.000 0.0000 0.000 0.0 0.0000 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 cyan_0 0.000 0.00 0.00 0.000 0.0000 log_k_JCZ38 0.000 0.00 0.00 0.000 0.0000 log_k_J9Z38 0.000 0.00 0.00 0.000 0.0000 log_k_JSE76 0.000 0.00 0.00 0.000 0.0000 f_cyan_ilr_1 0.000 0.00 0.00 0.000 0.0000 f_cyan_ilr_2 1.797 0.00 0.00 0.000 0.0000 f_JCZ38_qlogis 0.000 13.86 0.00 0.000 0.0000 f_JSE76_qlogis 0.000 0.00 13.91 0.000 0.0000 log_k1 0.000 0.00 0.00 1.106 0.0000 log_k2 0.000 0.00 0.00 0.000 0.6141 g_qlogis 0.000 0.00 0.00 0.000 0.0000 g_qlogis cyan_0 0.000 log_k_JCZ38 0.000 log_k_J9Z38 0.000 log_k_JSE76 0.000 f_cyan_ilr_1 0.000 f_cyan_ilr_2 0.000 f_JCZ38_qlogis 0.000 f_JSE76_qlogis 0.000 log_k1 0.000 log_k2 0.000 g_qlogis 1.595 Starting values for error model parameters: a.1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2282 2274 -1121 Optimised parameters: est. lower upper cyan_0 102.6036 NA NA log_k_JCZ38 -2.9348 NA NA log_k_J9Z38 -5.1617 NA NA log_k_JSE76 -3.6396 NA NA f_cyan_ilr_1 0.6991 NA NA f_cyan_ilr_2 0.6341 NA NA f_JCZ38_qlogis 4232.3011 NA NA f_JSE76_qlogis 1.9658 NA NA log_k1 -1.9503 NA NA log_k2 -4.4745 NA NA g_qlogis -0.4967 NA NA a.1 2.7461 2.59274 2.8994 SD.log_k_JCZ38 1.3178 0.47602 2.1596 SD.log_k_J9Z38 0.7022 0.15061 1.2538 SD.log_k_JSE76 0.6566 0.15613 1.1570 SD.f_cyan_ilr_1 0.3409 0.11666 0.5652 SD.f_cyan_ilr_2 0.4385 0.09482 0.7821 SD.log_k1 0.7381 0.25599 1.2202 SD.log_k2 0.5133 0.18152 0.8450 SD.g_qlogis 0.9866 0.35681 1.6164 Correlation is not available Random effects: est. lower upper SD.log_k_JCZ38 1.3178 0.47602 2.1596 SD.log_k_J9Z38 0.7022 0.15061 1.2538 SD.log_k_JSE76 0.6566 0.15613 1.1570 SD.f_cyan_ilr_1 0.3409 0.11666 0.5652 SD.f_cyan_ilr_2 0.4385 0.09482 0.7821 SD.log_k1 0.7381 0.25599 1.2202 SD.log_k2 0.5133 0.18152 0.8450 SD.g_qlogis 0.9866 0.35681 1.6164 Variance model: est. lower upper a.1 2.746 2.593 2.899 Backtransformed parameters: est. lower upper cyan_0 1.026e+02 NA NA k_JCZ38 5.314e-02 NA NA k_J9Z38 5.732e-03 NA NA k_JSE76 2.626e-02 NA NA f_cyan_to_JCZ38 6.051e-01 NA NA f_cyan_to_J9Z38 2.251e-01 NA NA f_JCZ38_to_JSE76 1.000e+00 NA NA f_JSE76_to_JCZ38 8.772e-01 NA NA k1 1.422e-01 NA NA k2 1.140e-02 NA NA g 3.783e-01 NA NA Resulting formation fractions: ff cyan_JCZ38 0.6051 cyan_J9Z38 0.2251 cyan_sink 0.1698 JCZ38_JSE76 1.0000 JCZ38_sink 0.0000 JSE76_JCZ38 0.8772 JSE76_sink 0.1228 Estimated disappearance times: DT50 DT90 DT50back DT50_k1 DT50_k2 cyan 22.05 160.35 48.27 4.873 60.83 JCZ38 13.04 43.33 NA NA NA J9Z38 120.93 401.73 NA NA NA JSE76 26.39 87.68 NA NA NA </code></pre> <p></p> <caption> Hierarchical DFOP path 2 fit with reduced random effects, two-component error </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.4 R version used for fitting: 4.3.0 Date of fit: Fri May 19 09:57:32 2023 Date of summary: Fri May 19 09:57:33 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 865.636 s Using 300, 100 iterations and 10 chains Variance model: Two-component variance function Starting values for degradation parameters: cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 101.7393 -1.4493 -5.0118 -2.1269 0.6720 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 7.3362 13.4423 13.2659 -2.0061 -4.5527 g_qlogis -0.5806 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 cyan_0 5.604 0.00 0.000 0.000 0.0000 log_k_JCZ38 0.000 2.77 0.000 0.000 0.0000 log_k_J9Z38 0.000 0.00 1.662 0.000 0.0000 log_k_JSE76 0.000 0.00 0.000 5.021 0.0000 f_cyan_ilr_1 0.000 0.00 0.000 0.000 0.6519 f_cyan_ilr_2 0.000 0.00 0.000 0.000 0.0000 f_JCZ38_qlogis 0.000 0.00 0.000 0.000 0.0000 f_JSE76_qlogis 0.000 0.00 0.000 0.000 0.0000 log_k1 0.000 0.00 0.000 0.000 0.0000 log_k2 0.000 0.00 0.000 0.000 0.0000 g_qlogis 0.000 0.00 0.000 0.000 0.0000 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 cyan_0 0.00 0.00 0.00 0.0000 0.0000 log_k_JCZ38 0.00 0.00 0.00 0.0000 0.0000 log_k_J9Z38 0.00 0.00 0.00 0.0000 0.0000 log_k_JSE76 0.00 0.00 0.00 0.0000 0.0000 f_cyan_ilr_1 0.00 0.00 0.00 0.0000 0.0000 f_cyan_ilr_2 13.37 0.00 0.00 0.0000 0.0000 f_JCZ38_qlogis 0.00 14.21 0.00 0.0000 0.0000 f_JSE76_qlogis 0.00 0.00 14.58 0.0000 0.0000 log_k1 0.00 0.00 0.00 0.8453 0.0000 log_k2 0.00 0.00 0.00 0.0000 0.5969 g_qlogis 0.00 0.00 0.00 0.0000 0.0000 g_qlogis cyan_0 0.00 log_k_JCZ38 0.00 log_k_J9Z38 0.00 log_k_JSE76 0.00 f_cyan_ilr_1 0.00 f_cyan_ilr_2 0.00 f_JCZ38_qlogis 0.00 f_JSE76_qlogis 0.00 log_k1 0.00 log_k2 0.00 g_qlogis 1.69 Starting values for error model parameters: a.1 b.1 1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2237 2229 -1099 Optimised parameters: est. lower upper cyan_0 101.00243 NA NA log_k_JCZ38 -2.80828 NA NA log_k_J9Z38 -5.04449 NA NA log_k_JSE76 -3.66981 NA NA f_cyan_ilr_1 0.72564 NA NA f_cyan_ilr_2 1.37978 NA NA f_JCZ38_qlogis 1.98726 NA NA f_JSE76_qlogis 414.80884 NA NA log_k1 -2.38601 NA NA log_k2 -4.63632 NA NA g_qlogis -0.33920 NA NA a.1 2.10837 1.88051 2.33623 b.1 0.06223 0.05108 0.07338 SD.log_k_JCZ38 1.30902 0.48128 2.13675 SD.log_k_J9Z38 0.83882 0.25790 1.41974 SD.log_k_JSE76 0.58104 0.14201 1.02008 SD.f_cyan_ilr_1 0.35421 0.12398 0.58443 SD.f_cyan_ilr_2 0.79373 0.12007 1.46740 SD.log_k2 0.27476 0.08557 0.46394 SD.g_qlogis 0.96170 0.35463 1.56878 Correlation is not available Random effects: est. lower upper SD.log_k_JCZ38 1.3090 0.48128 2.1367 SD.log_k_J9Z38 0.8388 0.25790 1.4197 SD.log_k_JSE76 0.5810 0.14201 1.0201 SD.f_cyan_ilr_1 0.3542 0.12398 0.5844 SD.f_cyan_ilr_2 0.7937 0.12007 1.4674 SD.log_k2 0.2748 0.08557 0.4639 SD.g_qlogis 0.9617 0.35463 1.5688 Variance model: est. lower upper a.1 2.10837 1.88051 2.33623 b.1 0.06223 0.05108 0.07338 Backtransformed parameters: est. lower upper cyan_0 1.010e+02 NA NA k_JCZ38 6.031e-02 NA NA k_J9Z38 6.445e-03 NA NA k_JSE76 2.548e-02 NA NA f_cyan_to_JCZ38 6.808e-01 NA NA f_cyan_to_J9Z38 2.440e-01 NA NA f_JCZ38_to_JSE76 8.795e-01 NA NA f_JSE76_to_JCZ38 1.000e+00 NA NA k1 9.200e-02 NA NA k2 9.693e-03 NA NA g 4.160e-01 NA NA Resulting formation fractions: ff cyan_JCZ38 0.68081 cyan_J9Z38 0.24398 cyan_sink 0.07521 JCZ38_JSE76 0.87945 JCZ38_sink 0.12055 JSE76_JCZ38 1.00000 JSE76_sink 0.00000 Estimated disappearance times: DT50 DT90 DT50back DT50_k1 DT50_k2 cyan 25.00 182.05 54.8 7.535 71.51 JCZ38 11.49 38.18 NA NA NA J9Z38 107.55 357.28 NA NA NA JSE76 27.20 90.36 NA NA NA </code></pre> <p></p> <caption> Hierarchical SFORB path 2 fit with reduced random effects, constant variance </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.4 R version used for fitting: 4.3.0 Date of fit: Fri May 19 09:57:01 2023 Date of summary: Fri May 19 09:57:33 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 834.906 s Using 300, 100 iterations and 10 chains Variance model: Constant variance Starting values for degradation parameters: cyan_free_0 log_k_cyan_free log_k_cyan_free_bound 102.4395 -2.7673 -2.8942 log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 -3.6201 -2.3107 -5.3123 log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 -3.7120 0.6754 1.1448 f_JCZ38_qlogis f_JSE76_qlogis 14.8408 15.4734 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_free_0 log_k_cyan_free log_k_cyan_free_bound cyan_free_0 4.589 0.0000 0.00 log_k_cyan_free 0.000 0.4849 0.00 log_k_cyan_free_bound 0.000 0.0000 1.62 log_k_cyan_bound_free 0.000 0.0000 0.00 log_k_JCZ38 0.000 0.0000 0.00 log_k_J9Z38 0.000 0.0000 0.00 log_k_JSE76 0.000 0.0000 0.00 f_cyan_ilr_1 0.000 0.0000 0.00 f_cyan_ilr_2 0.000 0.0000 0.00 f_JCZ38_qlogis 0.000 0.0000 0.00 f_JSE76_qlogis 0.000 0.0000 0.00 log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 cyan_free_0 0.000 0.0000 0.000 0.0 log_k_cyan_free 0.000 0.0000 0.000 0.0 log_k_cyan_free_bound 0.000 0.0000 0.000 0.0 log_k_cyan_bound_free 1.197 0.0000 0.000 0.0 log_k_JCZ38 0.000 0.7966 0.000 0.0 log_k_J9Z38 0.000 0.0000 1.561 0.0 log_k_JSE76 0.000 0.0000 0.000 0.8 f_cyan_ilr_1 0.000 0.0000 0.000 0.0 f_cyan_ilr_2 0.000 0.0000 0.000 0.0 f_JCZ38_qlogis 0.000 0.0000 0.000 0.0 f_JSE76_qlogis 0.000 0.0000 0.000 0.0 f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis cyan_free_0 0.0000 0.000 0.0 0.00 log_k_cyan_free 0.0000 0.000 0.0 0.00 log_k_cyan_free_bound 0.0000 0.000 0.0 0.00 log_k_cyan_bound_free 0.0000 0.000 0.0 0.00 log_k_JCZ38 0.0000 0.000 0.0 0.00 log_k_J9Z38 0.0000 0.000 0.0 0.00 log_k_JSE76 0.0000 0.000 0.0 0.00 f_cyan_ilr_1 0.6349 0.000 0.0 0.00 f_cyan_ilr_2 0.0000 1.797 0.0 0.00 f_JCZ38_qlogis 0.0000 0.000 15.6 0.00 f_JSE76_qlogis 0.0000 0.000 0.0 17.52 Starting values for error model parameters: a.1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2280 2272 -1120 Optimised parameters: est. lower upper cyan_free_0 102.6532 NA NA log_k_cyan_free -2.8547 NA NA log_k_cyan_free_bound -2.7004 NA NA log_k_cyan_bound_free -3.5078 NA NA log_k_JCZ38 -2.9255 NA NA log_k_J9Z38 -5.1089 NA NA log_k_JSE76 -3.6263 NA NA f_cyan_ilr_1 0.6873 NA NA f_cyan_ilr_2 0.6498 NA NA f_JCZ38_qlogis 3624.2149 NA NA f_JSE76_qlogis 1.9991 NA NA a.1 2.7472 2.55559 2.9388 SD.log_k_cyan_free 0.3227 0.10296 0.5423 SD.log_k_cyan_free_bound 0.8757 0.29525 1.4562 SD.log_k_cyan_bound_free 0.6128 0.20220 1.0233 SD.log_k_JCZ38 1.3431 0.48474 2.2014 SD.log_k_J9Z38 0.6881 0.14714 1.2291 SD.log_k_JSE76 0.6461 0.15321 1.1390 SD.f_cyan_ilr_1 0.3361 0.11376 0.5585 SD.f_cyan_ilr_2 0.4286 0.08419 0.7730 Correlation is not available Random effects: est. lower upper SD.log_k_cyan_free 0.3227 0.10296 0.5423 SD.log_k_cyan_free_bound 0.8757 0.29525 1.4562 SD.log_k_cyan_bound_free 0.6128 0.20220 1.0233 SD.log_k_JCZ38 1.3431 0.48474 2.2014 SD.log_k_J9Z38 0.6881 0.14714 1.2291 SD.log_k_JSE76 0.6461 0.15321 1.1390 SD.f_cyan_ilr_1 0.3361 0.11376 0.5585 SD.f_cyan_ilr_2 0.4286 0.08419 0.7730 Variance model: est. lower upper a.1 2.747 2.556 2.939 Backtransformed parameters: est. lower upper cyan_free_0 1.027e+02 NA NA k_cyan_free 5.758e-02 NA NA k_cyan_free_bound 6.718e-02 NA NA k_cyan_bound_free 2.996e-02 NA NA k_JCZ38 5.364e-02 NA NA k_J9Z38 6.042e-03 NA NA k_JSE76 2.662e-02 NA NA f_cyan_free_to_JCZ38 6.039e-01 NA NA f_cyan_free_to_J9Z38 2.285e-01 NA NA f_JCZ38_to_JSE76 1.000e+00 NA NA f_JSE76_to_JCZ38 8.807e-01 NA NA Estimated Eigenvalues of SFORB model(s): cyan_b1 cyan_b2 cyan_g 0.1426 0.0121 0.3484 Resulting formation fractions: ff cyan_free_JCZ38 0.6039 cyan_free_J9Z38 0.2285 cyan_free_sink 0.1676 cyan_free 1.0000 JCZ38_JSE76 1.0000 JCZ38_sink 0.0000 JSE76_JCZ38 0.8807 JSE76_sink 0.1193 Estimated disappearance times: DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 cyan 23.84 154.95 46.65 4.86 57.31 JCZ38 12.92 42.93 NA NA NA J9Z38 114.71 381.07 NA NA NA JSE76 26.04 86.51 NA NA NA </code></pre> <p></p> <caption> Hierarchical SFORB path 2 fit with reduced random effects, two-component error </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.4 R version used for fitting: 4.3.0 Date of fit: Fri May 19 09:57:17 2023 Date of summary: Fri May 19 09:57:33 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 850.751 s Using 300, 100 iterations and 10 chains Variance model: Two-component variance function Starting values for degradation parameters: cyan_free_0 log_k_cyan_free log_k_cyan_free_bound 101.7511 -2.8370 -3.0162 log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 -3.6600 -2.2988 -5.3129 log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 -3.6991 0.6722 4.8596 f_JCZ38_qlogis f_JSE76_qlogis 13.4678 14.2149 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_free_0 log_k_cyan_free log_k_cyan_free_bound cyan_free_0 5.629 0.000 0.000 log_k_cyan_free 0.000 0.446 0.000 log_k_cyan_free_bound 0.000 0.000 1.449 log_k_cyan_bound_free 0.000 0.000 0.000 log_k_JCZ38 0.000 0.000 0.000 log_k_J9Z38 0.000 0.000 0.000 log_k_JSE76 0.000 0.000 0.000 f_cyan_ilr_1 0.000 0.000 0.000 f_cyan_ilr_2 0.000 0.000 0.000 f_JCZ38_qlogis 0.000 0.000 0.000 f_JSE76_qlogis 0.000 0.000 0.000 log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 cyan_free_0 0.000 0.0000 0.000 0.0000 log_k_cyan_free 0.000 0.0000 0.000 0.0000 log_k_cyan_free_bound 0.000 0.0000 0.000 0.0000 log_k_cyan_bound_free 1.213 0.0000 0.000 0.0000 log_k_JCZ38 0.000 0.7801 0.000 0.0000 log_k_J9Z38 0.000 0.0000 1.575 0.0000 log_k_JSE76 0.000 0.0000 0.000 0.8078 f_cyan_ilr_1 0.000 0.0000 0.000 0.0000 f_cyan_ilr_2 0.000 0.0000 0.000 0.0000 f_JCZ38_qlogis 0.000 0.0000 0.000 0.0000 f_JSE76_qlogis 0.000 0.0000 0.000 0.0000 f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis cyan_free_0 0.0000 0.000 0.00 0.00 log_k_cyan_free 0.0000 0.000 0.00 0.00 log_k_cyan_free_bound 0.0000 0.000 0.00 0.00 log_k_cyan_bound_free 0.0000 0.000 0.00 0.00 log_k_JCZ38 0.0000 0.000 0.00 0.00 log_k_J9Z38 0.0000 0.000 0.00 0.00 log_k_JSE76 0.0000 0.000 0.00 0.00 f_cyan_ilr_1 0.6518 0.000 0.00 0.00 f_cyan_ilr_2 0.0000 9.981 0.00 0.00 f_JCZ38_qlogis 0.0000 0.000 14.26 0.00 f_JSE76_qlogis 0.0000 0.000 0.00 16.17 Starting values for error model parameters: a.1 b.1 1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2241 2233 -1101 Optimised parameters: est. lower upper cyan_free_0 100.95469 NA NA log_k_cyan_free -3.18706 NA NA log_k_cyan_free_bound -3.38455 NA NA log_k_cyan_bound_free -3.75788 NA NA log_k_JCZ38 -2.77024 NA NA log_k_J9Z38 -5.03665 NA NA log_k_JSE76 -3.60289 NA NA f_cyan_ilr_1 0.72263 NA NA f_cyan_ilr_2 1.45352 NA NA f_JCZ38_qlogis 2.00778 NA NA f_JSE76_qlogis 941.58570 NA NA a.1 2.11130 1.88299 2.33960 b.1 0.06299 0.05176 0.07421 SD.log_k_cyan_free 0.50098 0.18805 0.81390 SD.log_k_cyan_bound_free 0.31671 0.08467 0.54875 SD.log_k_JCZ38 1.25865 0.45932 2.05798 SD.log_k_J9Z38 0.86833 0.27222 1.46444 SD.log_k_JSE76 0.59325 0.14711 1.03940 SD.f_cyan_ilr_1 0.35705 0.12521 0.58890 SD.f_cyan_ilr_2 0.88541 0.13797 1.63286 Correlation is not available Random effects: est. lower upper SD.log_k_cyan_free 0.5010 0.18805 0.8139 SD.log_k_cyan_bound_free 0.3167 0.08467 0.5488 SD.log_k_JCZ38 1.2587 0.45932 2.0580 SD.log_k_J9Z38 0.8683 0.27222 1.4644 SD.log_k_JSE76 0.5933 0.14711 1.0394 SD.f_cyan_ilr_1 0.3571 0.12521 0.5889 SD.f_cyan_ilr_2 0.8854 0.13797 1.6329 Variance model: est. lower upper a.1 2.11130 1.88299 2.33960 b.1 0.06299 0.05176 0.07421 Backtransformed parameters: est. lower upper cyan_free_0 1.010e+02 NA NA k_cyan_free 4.129e-02 NA NA k_cyan_free_bound 3.389e-02 NA NA k_cyan_bound_free 2.333e-02 NA NA k_JCZ38 6.265e-02 NA NA k_J9Z38 6.495e-03 NA NA k_JSE76 2.724e-02 NA NA f_cyan_free_to_JCZ38 6.844e-01 NA NA f_cyan_free_to_J9Z38 2.463e-01 NA NA f_JCZ38_to_JSE76 8.816e-01 NA NA f_JSE76_to_JCZ38 1.000e+00 NA NA Estimated Eigenvalues of SFORB model(s): cyan_b1 cyan_b2 cyan_g 0.08751 0.01101 0.39586 Resulting formation fractions: ff cyan_free_JCZ38 0.68444 cyan_free_J9Z38 0.24633 cyan_free_sink 0.06923 cyan_free 1.00000 JCZ38_JSE76 0.88161 JCZ38_sink 0.11839 JSE76_JCZ38 1.00000 JSE76_sink 0.00000 Estimated disappearance times: DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 cyan 25.36 163.36 49.18 7.921 62.95 JCZ38 11.06 36.75 NA NA NA J9Z38 106.71 354.49 NA NA NA JSE76 25.44 84.51 NA NA NA </code></pre> <p></p> </div> </div> <div class="section level3"> <h3 id="session-info">Session info<a class="anchor" aria-label="anchor" href="#session-info"></a> </h3> <pre><code>R version 4.3.0 Patched (2023-05-18 r84448) Platform: x86_64-pc-linux-gnu (64-bit) Running under: Debian GNU/Linux 12 (bookworm) Matrix products: default BLAS: /home/jranke/svn/R/r-patched/build/lib/libRblas.so LAPACK: /usr/lib/x86_64-linux-gnu/openblas-serial/liblapack.so.3; 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_1.2.4 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> </div> </div> </div> <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar"> <nav 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