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class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/prebuilt/2022_cyan_pathway.rmd" class="external-link"><code>vignettes/prebuilt/2022_cyan_pathway.rmd</code></a></small> <div class="hidden name"><code>2022_cyan_pathway.rmd</code></div> </div> <div class="section level2"> <h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#introduction"></a> </h2> <p>The purpose of this document is to test demonstrate how nonlinear hierarchical models (NLHM) based on the parent degradation models SFO, FOMC, DFOP and HS, with serial formation of two or more metabolites can be fitted with the mkin package.</p> <p>It was assembled in the course of work package 1.2 of Project Number 173340 (Application of nonlinear hierarchical models to the kinetic evaluation of chemical degradation data) of the German Environment Agency carried out in 2022 and 2023.</p> <p>The mkin package is used in version 1.2.3 which is currently under development. The newly introduced functionality that is used here is a simplification of excluding random effects for a set of fits based on a related set of fits with a reduced model, and the documentation of the starting parameters of the fit, so that all starting parameters of <code>saem</code> fits are now listed in the summary. The <code>saemix</code> package is used as a backend for fitting the NLHM, but is also loaded to make the convergence plot function available.</p> <p>This document is processed with the <code>knitr</code> package, which also provides the <code>kable</code> function that is used to improve the display of tabular data in R markdown documents. For parallel processing, the <code>parallel</code> package is used.</p> <div class="sourceCode" id="cb1"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://pkgdown.jrwb.de/mkin/">mkin</a></span><span class="op">)</span></span> <span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://yihui.org/knitr/" class="external-link">knitr</a></span><span class="op">)</span></span> <span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">saemix</span><span class="op">)</span></span> <span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">parallel</span><span class="op">)</span></span> <span><span class="va">n_cores</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/detectCores.html" class="external-link">detectCores</a></span><span class="op">(</span><span class="op">)</span></span> <span><span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/Sys.info.html" class="external-link">Sys.info</a></span><span class="op">(</span><span class="op">)</span><span class="op">[</span><span class="st">"sysname"</span><span class="op">]</span> <span class="op">==</span> <span class="st">"Windows"</span><span class="op">)</span> <span class="op">{</span></span> <span> <span class="va">cl</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makePSOCKcluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> <span><span class="op">}</span> <span class="kw">else</span> <span class="op">{</span></span> <span> <span class="va">cl</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makeForkCluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> <span><span class="op">}</span></span></code></pre></div> <div class="section level3"> <h3 id="test-data">Test data<a class="anchor" aria-label="anchor" href="#test-data"></a> </h3> <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">700.1</td> <td align="right">696.2</td> <td align="right">-340.1</td> </tr> <tr class="even"> <td align="left">HS tc</td> <td align="right">10</td> <td align="right">716.7</td> <td align="right">712.8</td> <td align="right">-348.3</td> </tr> </tbody> </table> <p>Model comparison based on AIC and BIC indicates that the two-component error model is preferable for all parent models with the exception of DFOP. The lowest AIC and BIC values are are obtained with the FOMC model, followed by SFORB and DFOP.</p> </div> <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="cb8"><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></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="cb9"><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</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">OK</td> <td align="left">OK</td> </tr> <tr class="even"> <td align="left">fomc_path_1</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> </tr> <tr class="odd"> <td align="left">dfop_path_1</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> </tr> <tr class="even"> <td align="left">sforb_path_1</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> </tr> <tr class="odd"> <td align="left">hs_path_1</td> <td align="left">C</td> <td align="left">C</td> <td align="left">C</td> <td align="left">C</td> <td align="left">C</td> </tr> </tbody> </table> <div class="sourceCode" id="cb10"><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">C</td> </tr> <tr class="odd"> <td align="left">dfop_path_1</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> </tr> <tr class="even"> <td align="left">sforb_path_1</td> <td align="left">OK</td> <td align="left">C</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> </tr> <tr class="odd"> <td align="left">hs_path_1</td> <td align="left">C</td> <td align="left">OK</td> <td align="left">C</td> <td align="left">OK</td> <td align="left">OK</td> </tr> </tbody> </table> <p>Most separate fits converged successfully. The biggest convergence problems are seen when using the HS model with constant variance.</p> <p>For the hierarchical pathway fits, those random effects that could not be quantified in the corresponding parent data analyses are excluded.</p> <p>In the code below, the output of the <code>illparms</code> function for the parent only fits is used as an argument <code>no_random_effect</code> to the <code>mhmkin</code> function. The possibility to do so was introduced in mkin version <code>1.2.2</code> which is currently under development.</p> <div class="sourceCode" id="cb11"><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</span><span class="op">)</span></span></code></pre></div> <div class="sourceCode" id="cb12"><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">Fth, FO</td> <td align="left">Fth, FO</td> </tr> <tr class="even"> <td align="left">fomc_path_1</td> <td align="left">OK</td> <td align="left">Fth, FO</td> </tr> <tr class="odd"> <td align="left">dfop_path_1</td> <td align="left">Fth, FO</td> <td align="left">Fth, FO</td> </tr> <tr class="even"> <td align="left">sforb_path_1</td> <td align="left">Fth, FO</td> <td align="left">Fth, FO</td> </tr> <tr class="odd"> <td align="left">hs_path_1</td> <td align="left">Fth, FO</td> <td align="left">Fth, FO</td> </tr> </tbody> </table> <p>The status information from the individual fits shows that all fits completed successfully. The matrix entries Fth and FO indicate that the Fisher Information Matrix could not be inverted for the fixed effects (theta) and the random effects (Omega), respectively. For the affected fits, ill-defined parameters cannot be determined using the <code>illparms</code> function, because it relies on the Fisher Information Matrix.</p> <div class="sourceCode" id="cb13"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> <table class="table"> <colgroup> <col width="18%"> <col width="77%"> <col width="4%"> </colgroup> <thead><tr class="header"> <th align="left"></th> <th align="left">const</th> <th align="left">tc</th> </tr></thead> <tbody> <tr class="odd"> <td align="left">sfo_path_1</td> <td align="left">NA</td> <td align="left">NA</td> </tr> <tr class="even"> <td align="left">fomc_path_1</td> <td align="left">sd(log_k_J9Z38), sd(f_cyan_ilr_2), sd(f_JCZ38_qlogis)</td> <td align="left">NA</td> </tr> <tr class="odd"> <td align="left">dfop_path_1</td> <td align="left">NA</td> <td align="left">NA</td> </tr> <tr class="even"> <td align="left">sforb_path_1</td> <td align="left">NA</td> <td align="left">NA</td> </tr> <tr class="odd"> <td align="left">hs_path_1</td> <td align="left">NA</td> <td align="left">NA</td> </tr> </tbody> </table> <p>The model comparison below suggests that the pathway fits using DFOP or SFORB for the parent compound provide the best fit.</p> <div class="sourceCode" id="cb14"><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">2692.8</td> <td align="right">2686.6</td> <td align="right">-1330.4</td> </tr> <tr class="even"> <td align="left">sfo_path_1 tc</td> <td align="right">17</td> <td align="right">2657.7</td> <td align="right">2651.1</td> <td align="right">-1311.9</td> </tr> <tr class="odd"> <td align="left">fomc_path_1 const</td> <td align="right">18</td> <td align="right">2427.8</td> <td align="right">2420.8</td> <td align="right">-1195.9</td> </tr> <tr class="even"> <td align="left">fomc_path_1 tc</td> <td align="right">19</td> <td align="right">2423.4</td> <td align="right">2416.0</td> <td align="right">-1192.7</td> </tr> <tr class="odd"> <td align="left">dfop_path_1 const</td> <td align="right">20</td> <td align="right">2403.2</td> <td align="right">2395.4</td> <td align="right">-1181.6</td> </tr> <tr class="even"> <td align="left">sforb_path_1 const</td> <td align="right">20</td> <td align="right">2401.4</td> <td align="right">2393.6</td> <td align="right">-1180.7</td> </tr> <tr class="odd"> <td align="left">hs_path_1 const</td> <td align="right">20</td> <td align="right">2427.3</td> <td align="right">2419.5</td> <td align="right">-1193.7</td> </tr> <tr class="even"> <td align="left">dfop_path_1 tc</td> <td align="right">20</td> <td align="right">2398.0</td> <td align="right">2390.2</td> <td align="right">-1179.0</td> </tr> <tr class="odd"> <td align="left">sforb_path_1 tc</td> <td align="right">20</td> <td align="right">2399.8</td> <td align="right">2392.0</td> <td align="right">-1179.9</td> </tr> <tr class="even"> <td align="left">hs_path_1 tc</td> <td align="right">21</td> <td align="right">2422.3</td> <td align="right">2414.1</td> <td align="right">-1190.2</td> </tr> </tbody> </table> <p>For these two parent model, successful fits are shown below. Plots of the fits with the other parent models are shown in the Appendix.</p> <div class="sourceCode" id="cb15"><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-6-1.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="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">"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-7-1.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> <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="cb17"><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 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</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">C</td> <td align="left">OK</td> </tr> </tbody> </table> <p>Using constant variance, separate fits converge with the exception of the fits to the Sassafras soil data.</p> <div class="sourceCode" id="cb18"><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">C</td> <td align="left">OK</td> <td align="left">C</td> <td align="left">OK</td> </tr> <tr class="even"> <td align="left">dfop_path_2</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">C</td> <td align="left">OK</td> </tr> <tr class="odd"> <td align="left">sforb_path_2</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> <td align="left">OK</td> </tr> </tbody> </table> <p>Using the two-component error model, all separate fits converge with the exception of the alternative pathway fit with DFOP used for the parent and the Sassafras dataset.</p> <div class="sourceCode" id="cb19"><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</span><span class="op">)</span></span></code></pre></div> <div class="sourceCode" id="cb20"><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">OK</td> <td align="left">FO</td> </tr> <tr class="even"> <td align="left">dfop_path_2</td> <td align="left">OK</td> <td align="left">OK</td> </tr> <tr class="odd"> <td align="left">sforb_path_2</td> <td align="left">OK</td> <td align="left">OK</td> </tr> </tbody> </table> <p>The hierarchical fits for the alternative pathway completed successfully.</p> <div class="sourceCode" id="cb21"><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">sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)</td> <td align="left">NA</td> </tr> <tr class="even"> <td align="left">dfop_path_2</td> <td align="left">sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)</td> <td align="left">sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)</td> </tr> <tr class="odd"> <td align="left">sforb_path_2</td> <td align="left">sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)</td> <td align="left">sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)</td> </tr> </tbody> </table> <p>In both fits, the random effects for the formation fractions for the pathways from JCZ38 to JSE76, and for the reverse pathway from JSE76 to JCZ38 are ill-defined.</p> <div class="sourceCode" id="cb22"><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 const</td> <td align="right">20</td> <td align="right">2308.3</td> <td align="right">2300.5</td> <td align="right">-1134.2</td> </tr> <tr class="even"> <td align="left">fomc_path_2 tc</td> <td align="right">21</td> <td align="right">2248.3</td> <td align="right">2240.1</td> <td align="right">-1103.2</td> </tr> <tr class="odd"> <td align="left">dfop_path_2 const</td> <td align="right">22</td> <td align="right">2289.6</td> <td align="right">2281.0</td> <td align="right">-1122.8</td> </tr> <tr class="even"> <td align="left">sforb_path_2 const</td> <td align="right">22</td> <td align="right">2284.1</td> <td align="right">2275.5</td> <td align="right">-1120.0</td> </tr> <tr class="odd"> <td align="left">dfop_path_2 tc</td> <td align="right">22</td> <td align="right">2234.4</td> <td align="right">2225.8</td> <td align="right">-1095.2</td> </tr> <tr class="even"> <td align="left">sforb_path_2 tc</td> <td align="right">22</td> <td align="right">2240.4</td> <td align="right">2231.8</td> <td align="right">-1098.2</td> </tr> </tbody> </table> <p>The variants using the biexponential models DFOP and SFORB for the parent compound and the two-component error model give the lowest AIC and BIC values and are plotted below. Compared with the original pathway, the AIC and BIC values indicate a large improvement. This is confirmed by the plots, which show that the metabolite JCZ38 is fitted much better with this model.</p> <div class="sourceCode" id="cb23"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">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-11-1.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="cb24"><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-12-1.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="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">"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-13-1.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="cb26"><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</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</span><span class="op">)</span></span></code></pre></div> <div class="sourceCode" id="cb27"><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="cb28"><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="cb29"><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">2250.9</td> <td align="right">2243.5</td> <td align="right">-1106.5</td> </tr> <tr class="even"> <td align="left">dfop_path_2 const</td> <td align="right">20</td> <td align="right">2281.7</td> <td align="right">2273.9</td> <td align="right">-1120.8</td> </tr> <tr class="odd"> <td align="left">sforb_path_2 const</td> <td align="right">20</td> <td align="right">2279.5</td> <td align="right">2271.7</td> <td align="right">-1119.7</td> </tr> <tr class="even"> <td align="left">dfop_path_2 tc</td> <td align="right">20</td> <td align="right">2231.5</td> <td align="right">2223.7</td> <td align="right">-1095.8</td> </tr> <tr class="odd"> <td align="left">sforb_path_2 tc</td> <td align="right">20</td> <td align="right">2235.7</td> <td align="right">2227.9</td> <td align="right">-1097.9</td> </tr> </tbody> </table> <p>While the AIC and BIC values of the best fit (DFOP pathway fit with two-component error) are lower than in the previous fits with the alternative pathway, the practical value of these refined evaluations is limited as no confidence intervals are obtained.</p> </div> </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="cb30"><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-17-1.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="cb31"><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-18-1.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="cb32"><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-19-1.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: 1.2.2 R version used for fitting: 4.2.2 Date of fit: Sat Jan 28 10:07:38 2023 Date of summary: Fri Feb 17 22:24:33 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 1088.473 s Using 300, 100 iterations and 10 chains Variance model: Constant variance Starting values for degradation parameters: cyan_0 log_k_cyan log_k_JCZ38 log_k_J9Z38 log_k_JSE76 95.3304 -3.8459 -3.1305 -5.0678 -5.3196 f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis 0.8158 22.5404 10.4289 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_0 log_k_cyan log_k_JCZ38 log_k_J9Z38 log_k_JSE76 cyan_0 4.797 0.0000 0.000 0.000 0.0000 log_k_cyan 0.000 0.9619 0.000 0.000 0.0000 log_k_JCZ38 0.000 0.0000 2.139 0.000 0.0000 log_k_J9Z38 0.000 0.0000 0.000 1.639 0.0000 log_k_JSE76 0.000 0.0000 0.000 0.000 0.7894 f_cyan_ilr_1 0.000 0.0000 0.000 0.000 0.0000 f_cyan_ilr_2 0.000 0.0000 0.000 0.000 0.0000 f_JCZ38_qlogis 0.000 0.0000 0.000 0.000 0.0000 f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis cyan_0 0.0000 0.000 0.00 log_k_cyan 0.0000 0.000 0.00 log_k_JCZ38 0.0000 0.000 0.00 log_k_J9Z38 0.0000 0.000 0.00 log_k_JSE76 0.0000 0.000 0.00 f_cyan_ilr_1 0.7714 0.000 0.00 f_cyan_ilr_2 0.0000 8.684 0.00 f_JCZ38_qlogis 0.0000 0.000 13.48 Starting values for error model parameters: a.1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2693 2687 -1330 Optimised parameters: est. lower upper cyan_0 95.0946 NA NA log_k_cyan -3.8544 NA NA log_k_JCZ38 -3.0402 NA NA log_k_J9Z38 -5.0109 NA NA log_k_JSE76 -5.2857 NA NA f_cyan_ilr_1 0.8069 NA NA f_cyan_ilr_2 16.6623 NA NA f_JCZ38_qlogis 1.3602 NA NA a.1 4.8326 NA NA SD.log_k_cyan 0.5842 NA NA SD.log_k_JCZ38 1.2680 NA NA SD.log_k_J9Z38 0.3626 NA NA SD.log_k_JSE76 0.5244 NA NA SD.f_cyan_ilr_1 0.2752 NA NA SD.f_cyan_ilr_2 2.3556 NA NA SD.f_JCZ38_qlogis 0.2400 NA NA Correlation is not available Random effects: est. lower upper SD.log_k_cyan 0.5842 NA NA SD.log_k_JCZ38 1.2680 NA NA SD.log_k_J9Z38 0.3626 NA NA SD.log_k_JSE76 0.5244 NA NA SD.f_cyan_ilr_1 0.2752 NA NA SD.f_cyan_ilr_2 2.3556 NA NA SD.f_JCZ38_qlogis 0.2400 NA NA Variance model: est. lower upper a.1 4.833 NA NA Backtransformed parameters: est. lower upper cyan_0 95.094581 NA NA k_cyan 0.021186 NA NA k_JCZ38 0.047825 NA NA k_J9Z38 0.006665 NA NA k_JSE76 0.005063 NA NA f_cyan_to_JCZ38 0.757885 NA NA f_cyan_to_J9Z38 0.242115 NA NA f_JCZ38_to_JSE76 0.795792 NA NA Resulting formation fractions: ff cyan_JCZ38 7.579e-01 cyan_J9Z38 2.421e-01 cyan_sink 5.877e-10 JCZ38_JSE76 7.958e-01 JCZ38_sink 2.042e-01 Estimated disappearance times: DT50 DT90 cyan 32.72 108.68 JCZ38 14.49 48.15 J9Z38 103.99 345.46 JSE76 136.90 454.76 </code></pre> <p></p> <caption> Hierarchical SFO path 1 fit with two-component error </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.2 R version used for fitting: 4.2.2 Date of fit: Sat Jan 28 10:08:17 2023 Date of summary: Fri Feb 17 22:24:33 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 1127.552 s Using 300, 100 iterations and 10 chains Variance model: Two-component variance function Starting values for degradation parameters: cyan_0 log_k_cyan log_k_JCZ38 log_k_J9Z38 log_k_JSE76 96.0039 -3.8907 -3.1276 -5.0069 -4.9367 f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis 0.7937 20.0030 15.1336 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_0 log_k_cyan log_k_JCZ38 log_k_J9Z38 log_k_JSE76 cyan_0 4.859 0.000 0.00 0.00 0.0000 log_k_cyan 0.000 0.962 0.00 0.00 0.0000 log_k_JCZ38 0.000 0.000 2.04 0.00 0.0000 log_k_J9Z38 0.000 0.000 0.00 1.72 0.0000 log_k_JSE76 0.000 0.000 0.00 0.00 0.9076 f_cyan_ilr_1 0.000 0.000 0.00 0.00 0.0000 f_cyan_ilr_2 0.000 0.000 0.00 0.00 0.0000 f_JCZ38_qlogis 0.000 0.000 0.00 0.00 0.0000 f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis cyan_0 0.0000 0.000 0.00 log_k_cyan 0.0000 0.000 0.00 log_k_JCZ38 0.0000 0.000 0.00 log_k_J9Z38 0.0000 0.000 0.00 log_k_JSE76 0.0000 0.000 0.00 f_cyan_ilr_1 0.7598 0.000 0.00 f_cyan_ilr_2 0.0000 7.334 0.00 f_JCZ38_qlogis 0.0000 0.000 11.78 Starting values for error model parameters: a.1 b.1 1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2658 2651 -1312 Optimised parameters: est. lower upper cyan_0 94.72923 NA NA log_k_cyan -3.91670 NA NA log_k_JCZ38 -3.12917 NA NA log_k_J9Z38 -5.06070 NA NA log_k_JSE76 -5.09254 NA NA f_cyan_ilr_1 0.81116 NA NA f_cyan_ilr_2 39.97850 NA NA f_JCZ38_qlogis 3.09728 NA NA a.1 3.95044 NA NA b.1 0.07998 NA NA SD.log_k_cyan 0.58855 NA NA SD.log_k_JCZ38 1.29753 NA NA SD.log_k_J9Z38 0.62851 NA NA SD.log_k_JSE76 0.37235 NA NA SD.f_cyan_ilr_1 0.37346 NA NA SD.f_cyan_ilr_2 1.41667 NA NA SD.f_JCZ38_qlogis 1.81467 NA NA Correlation is not available Random effects: est. lower upper SD.log_k_cyan 0.5886 NA NA SD.log_k_JCZ38 1.2975 NA NA SD.log_k_J9Z38 0.6285 NA NA SD.log_k_JSE76 0.3724 NA NA SD.f_cyan_ilr_1 0.3735 NA NA SD.f_cyan_ilr_2 1.4167 NA NA SD.f_JCZ38_qlogis 1.8147 NA NA Variance model: est. lower upper a.1 3.95044 NA NA b.1 0.07998 NA NA Backtransformed parameters: est. lower upper cyan_0 94.729229 NA NA k_cyan 0.019907 NA NA k_JCZ38 0.043754 NA NA k_J9Z38 0.006341 NA NA k_JSE76 0.006142 NA NA f_cyan_to_JCZ38 0.758991 NA NA f_cyan_to_J9Z38 0.241009 NA NA f_JCZ38_to_JSE76 0.956781 NA NA Resulting formation fractions: ff cyan_JCZ38 0.75899 cyan_J9Z38 0.24101 cyan_sink 0.00000 JCZ38_JSE76 0.95678 JCZ38_sink 0.04322 Estimated disappearance times: DT50 DT90 cyan 34.82 115.67 JCZ38 15.84 52.63 J9Z38 109.31 363.12 JSE76 112.85 374.87 </code></pre> <p></p> <caption> Hierarchical FOMC path 1 fit with constant variance </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.2 R version used for fitting: 4.2.2 Date of fit: Sat Jan 28 10:09:12 2023 Date of summary: Fri Feb 17 22:24:33 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 1182.258 s Using 300, 100 iterations and 10 chains Variance model: Constant variance Starting values for degradation parameters: cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 101.2314 -3.3680 -5.1108 -5.9416 0.7144 f_cyan_ilr_2 f_JCZ38_qlogis log_alpha log_beta 7.3870 15.7604 -0.1791 2.9811 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 cyan_0 5.416 0.000 0.0 0.000 0.0000 log_k_JCZ38 0.000 2.439 0.0 0.000 0.0000 log_k_J9Z38 0.000 0.000 1.7 0.000 0.0000 log_k_JSE76 0.000 0.000 0.0 1.856 0.0000 f_cyan_ilr_1 0.000 0.000 0.0 0.000 0.7164 f_cyan_ilr_2 0.000 0.000 0.0 0.000 0.0000 f_JCZ38_qlogis 0.000 0.000 0.0 0.000 0.0000 log_alpha 0.000 0.000 0.0 0.000 0.0000 log_beta 0.000 0.000 0.0 0.000 0.0000 f_cyan_ilr_2 f_JCZ38_qlogis log_alpha log_beta cyan_0 0.00 0.00 0.0000 0.0000 log_k_JCZ38 0.00 0.00 0.0000 0.0000 log_k_J9Z38 0.00 0.00 0.0000 0.0000 log_k_JSE76 0.00 0.00 0.0000 0.0000 f_cyan_ilr_1 0.00 0.00 0.0000 0.0000 f_cyan_ilr_2 12.33 0.00 0.0000 0.0000 f_JCZ38_qlogis 0.00 20.42 0.0000 0.0000 log_alpha 0.00 0.00 0.4144 0.0000 log_beta 0.00 0.00 0.0000 0.5077 Starting values for error model parameters: a.1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2428 2421 -1196 Optimised parameters: est. lower upper cyan_0 101.0225 98.306270 103.7387 log_k_JCZ38 -3.3786 -4.770657 -1.9866 log_k_J9Z38 -5.2603 -5.902085 -4.6186 log_k_JSE76 -6.1427 -7.318336 -4.9671 f_cyan_ilr_1 0.7437 0.421215 1.0663 f_cyan_ilr_2 0.9108 0.267977 1.5537 f_JCZ38_qlogis 2.0487 0.524897 3.5724 log_alpha -0.2268 -0.618049 0.1644 log_beta 2.8986 2.700701 3.0964 a.1 3.4058 3.169913 3.6416 SD.cyan_0 2.5279 0.454190 4.6016 SD.log_k_JCZ38 1.5636 0.572824 2.5543 SD.log_k_J9Z38 0.5316 -0.004405 1.0677 SD.log_k_JSE76 0.9903 0.106325 1.8742 SD.f_cyan_ilr_1 0.3464 0.112066 0.5807 SD.f_cyan_ilr_2 0.2804 -0.393900 0.9546 SD.f_JCZ38_qlogis 0.9416 -0.152986 2.0362 SD.log_alpha 0.4273 0.161044 0.6936 Correlation: cyan_0 l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 log_lph log_k_JCZ38 -0.0156 log_k_J9Z38 -0.0493 0.0073 log_k_JSE76 -0.0329 0.0018 0.0069 f_cyan_ilr_1 -0.0086 0.0180 -0.1406 0.0012 f_cyan_ilr_2 -0.2629 0.0779 0.2826 0.0274 0.0099 f_JCZ38_qlogis 0.0713 -0.0747 -0.0505 0.1169 -0.1022 -0.4893 log_alpha -0.0556 0.0120 0.0336 0.0193 0.0036 0.0840 -0.0489 log_beta -0.2898 0.0460 0.1305 0.0768 0.0190 0.4071 -0.1981 0.2772 Random effects: est. lower upper SD.cyan_0 2.5279 0.454190 4.6016 SD.log_k_JCZ38 1.5636 0.572824 2.5543 SD.log_k_J9Z38 0.5316 -0.004405 1.0677 SD.log_k_JSE76 0.9903 0.106325 1.8742 SD.f_cyan_ilr_1 0.3464 0.112066 0.5807 SD.f_cyan_ilr_2 0.2804 -0.393900 0.9546 SD.f_JCZ38_qlogis 0.9416 -0.152986 2.0362 SD.log_alpha 0.4273 0.161044 0.6936 Variance model: est. lower upper a.1 3.406 3.17 3.642 Backtransformed parameters: est. lower upper cyan_0 1.010e+02 9.831e+01 1.037e+02 k_JCZ38 3.409e-02 8.475e-03 1.372e-01 k_J9Z38 5.194e-03 2.734e-03 9.867e-03 k_JSE76 2.149e-03 6.633e-04 6.963e-03 f_cyan_to_JCZ38 6.481e-01 NA NA f_cyan_to_J9Z38 2.264e-01 NA NA f_JCZ38_to_JSE76 8.858e-01 6.283e-01 9.727e-01 alpha 7.971e-01 5.390e-01 1.179e+00 beta 1.815e+01 1.489e+01 2.212e+01 Resulting formation fractions: ff cyan_JCZ38 0.6481 cyan_J9Z38 0.2264 cyan_sink 0.1255 JCZ38_JSE76 0.8858 JCZ38_sink 0.1142 Estimated disappearance times: DT50 DT90 DT50back cyan 25.15 308.01 92.72 JCZ38 20.33 67.54 NA J9Z38 133.46 443.35 NA JSE76 322.53 1071.42 NA </code></pre> <p></p> <caption> Hierarchical FOMC path 1 fit with two-component error </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.2 R version used for fitting: 4.2.2 Date of fit: Sat Jan 28 10:09:18 2023 Date of summary: Fri Feb 17 22:24:33 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 1188.041 s Using 300, 100 iterations and 10 chains Variance model: Two-component variance function Starting values for degradation parameters: cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 101.13827 -3.32493 -5.08921 -5.93478 0.71330 f_cyan_ilr_2 f_JCZ38_qlogis log_alpha log_beta 10.05989 12.79248 -0.09621 3.10646 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 cyan_0 5.643 0.000 0.000 0.00 0.0000 log_k_JCZ38 0.000 2.319 0.000 0.00 0.0000 log_k_J9Z38 0.000 0.000 1.731 0.00 0.0000 log_k_JSE76 0.000 0.000 0.000 1.86 0.0000 f_cyan_ilr_1 0.000 0.000 0.000 0.00 0.7186 f_cyan_ilr_2 0.000 0.000 0.000 0.00 0.0000 f_JCZ38_qlogis 0.000 0.000 0.000 0.00 0.0000 log_alpha 0.000 0.000 0.000 0.00 0.0000 log_beta 0.000 0.000 0.000 0.00 0.0000 f_cyan_ilr_2 f_JCZ38_qlogis log_alpha log_beta cyan_0 0.00 0.00 0.0000 0.0000 log_k_JCZ38 0.00 0.00 0.0000 0.0000 log_k_J9Z38 0.00 0.00 0.0000 0.0000 log_k_JSE76 0.00 0.00 0.0000 0.0000 f_cyan_ilr_1 0.00 0.00 0.0000 0.0000 f_cyan_ilr_2 12.49 0.00 0.0000 0.0000 f_JCZ38_qlogis 0.00 20.19 0.0000 0.0000 log_alpha 0.00 0.00 0.3142 0.0000 log_beta 0.00 0.00 0.0000 0.7331 Starting values for error model parameters: a.1 b.1 1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2423 2416 -1193 Optimised parameters: est. lower upper cyan_0 100.57649 NA NA log_k_JCZ38 -3.46250 NA NA log_k_J9Z38 -5.24442 NA NA log_k_JSE76 -5.75229 NA NA f_cyan_ilr_1 0.68480 NA NA f_cyan_ilr_2 0.61670 NA NA f_JCZ38_qlogis 87.97407 NA NA log_alpha -0.15699 NA NA log_beta 3.01540 NA NA a.1 3.11518 NA NA b.1 0.04445 NA NA SD.log_k_JCZ38 1.40732 NA NA SD.log_k_J9Z38 0.56510 NA NA SD.log_k_JSE76 0.72067 NA NA SD.f_cyan_ilr_1 0.31199 NA NA SD.f_cyan_ilr_2 0.36894 NA NA SD.f_JCZ38_qlogis 6.92892 NA NA SD.log_alpha 0.25662 NA NA SD.log_beta 0.35845 NA NA Correlation is not available Random effects: est. lower upper SD.log_k_JCZ38 1.4073 NA NA SD.log_k_J9Z38 0.5651 NA NA SD.log_k_JSE76 0.7207 NA NA SD.f_cyan_ilr_1 0.3120 NA NA SD.f_cyan_ilr_2 0.3689 NA NA SD.f_JCZ38_qlogis 6.9289 NA NA SD.log_alpha 0.2566 NA NA SD.log_beta 0.3585 NA NA Variance model: est. lower upper a.1 3.11518 NA NA b.1 0.04445 NA NA Backtransformed parameters: est. lower upper cyan_0 1.006e+02 NA NA k_JCZ38 3.135e-02 NA NA k_J9Z38 5.277e-03 NA NA k_JSE76 3.175e-03 NA NA f_cyan_to_JCZ38 5.991e-01 NA NA f_cyan_to_J9Z38 2.275e-01 NA NA f_JCZ38_to_JSE76 1.000e+00 NA NA alpha 8.547e-01 NA NA beta 2.040e+01 NA NA Resulting formation fractions: ff cyan_JCZ38 0.5991 cyan_J9Z38 0.2275 cyan_sink 0.1734 JCZ38_JSE76 1.0000 JCZ38_sink 0.0000 Estimated disappearance times: DT50 DT90 DT50back cyan 25.50 281.29 84.68 JCZ38 22.11 73.44 NA J9Z38 131.36 436.35 NA JSE76 218.28 725.11 NA </code></pre> <p></p> <caption> Hierarchical DFOP path 1 fit with constant variance </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.2 R version used for fitting: 4.2.2 Date of fit: Sat Jan 28 10:10:30 2023 Date of summary: Fri Feb 17 22:24:33 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 1260.905 s Using 300, 100 iterations and 10 chains Variance model: Constant variance Starting values for degradation parameters: cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 102.0644 -3.4008 -5.0024 -5.8613 0.6855 f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 g_qlogis 1.2365 13.7245 -1.8641 -4.5063 -0.6468 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 cyan_0 4.466 0.000 0.000 0.000 0.0000 log_k_JCZ38 0.000 2.382 0.000 0.000 0.0000 log_k_J9Z38 0.000 0.000 1.595 0.000 0.0000 log_k_JSE76 0.000 0.000 0.000 1.245 0.0000 f_cyan_ilr_1 0.000 0.000 0.000 0.000 0.6852 f_cyan_ilr_2 0.000 0.000 0.000 0.000 0.0000 f_JCZ38_qlogis 0.000 0.000 0.000 0.000 0.0000 log_k1 0.000 0.000 0.000 0.000 0.0000 log_k2 0.000 0.000 0.000 0.000 0.0000 g_qlogis 0.000 0.000 0.000 0.000 0.0000 f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 g_qlogis cyan_0 0.00 0.00 0.0000 0.0000 0.000 log_k_JCZ38 0.00 0.00 0.0000 0.0000 0.000 log_k_J9Z38 0.00 0.00 0.0000 0.0000 0.000 log_k_JSE76 0.00 0.00 0.0000 0.0000 0.000 f_cyan_ilr_1 0.00 0.00 0.0000 0.0000 0.000 f_cyan_ilr_2 1.28 0.00 0.0000 0.0000 0.000 f_JCZ38_qlogis 0.00 16.11 0.0000 0.0000 0.000 log_k1 0.00 0.00 0.9866 0.0000 0.000 log_k2 0.00 0.00 0.0000 0.5953 0.000 g_qlogis 0.00 0.00 0.0000 0.0000 1.583 Starting values for error model parameters: a.1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2403 2395 -1182 Optimised parameters: est. lower upper cyan_0 102.6079 NA NA log_k_JCZ38 -3.4855 NA NA log_k_J9Z38 -5.1686 NA NA log_k_JSE76 -5.6697 NA NA f_cyan_ilr_1 0.6714 NA NA f_cyan_ilr_2 0.4986 NA NA f_JCZ38_qlogis 55.4760 NA NA log_k1 -1.8409 NA NA log_k2 -4.4915 NA NA g_qlogis -0.6403 NA NA a.1 3.2387 NA NA SD.log_k_JCZ38 1.4524 NA NA SD.log_k_J9Z38 0.5151 NA NA SD.log_k_JSE76 0.6514 NA NA SD.f_cyan_ilr_1 0.3023 NA NA SD.f_cyan_ilr_2 0.2959 NA NA SD.f_JCZ38_qlogis 1.9984 NA NA SD.log_k1 0.5188 NA NA SD.log_k2 0.3894 NA NA SD.g_qlogis 0.8579 NA NA Correlation is not available Random effects: est. lower upper SD.log_k_JCZ38 1.4524 NA NA SD.log_k_J9Z38 0.5151 NA NA SD.log_k_JSE76 0.6514 NA NA SD.f_cyan_ilr_1 0.3023 NA NA SD.f_cyan_ilr_2 0.2959 NA NA SD.f_JCZ38_qlogis 1.9984 NA NA SD.log_k1 0.5188 NA NA SD.log_k2 0.3894 NA NA SD.g_qlogis 0.8579 NA NA Variance model: est. lower upper a.1 3.239 NA NA Backtransformed parameters: est. lower upper cyan_0 1.026e+02 NA NA k_JCZ38 3.064e-02 NA NA k_J9Z38 5.692e-03 NA NA k_JSE76 3.449e-03 NA NA f_cyan_to_JCZ38 5.798e-01 NA NA f_cyan_to_J9Z38 2.243e-01 NA NA f_JCZ38_to_JSE76 1.000e+00 NA NA k1 1.587e-01 NA NA k2 1.120e-02 NA NA g 3.452e-01 NA NA Resulting formation fractions: ff cyan_JCZ38 0.5798 cyan_J9Z38 0.2243 cyan_sink 0.1958 JCZ38_JSE76 1.0000 JCZ38_sink 0.0000 Estimated disappearance times: DT50 DT90 DT50back DT50_k1 DT50_k2 cyan 25.21 167.73 50.49 4.368 61.87 JCZ38 22.62 75.15 NA NA NA J9Z38 121.77 404.50 NA NA NA JSE76 200.98 667.64 NA NA NA </code></pre> <p></p> <caption> Hierarchical DFOP path 1 fit with two-component error </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.2 R version used for fitting: 4.2.2 Date of fit: Sat Jan 28 10:16:28 2023 Date of summary: Fri Feb 17 22:24:33 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 1617.774 s Using 300, 100 iterations and 10 chains Variance model: Two-component variance function Starting values for degradation parameters: cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 101.3964 -3.3626 -4.9792 -5.8727 0.6814 f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 g_qlogis 6.7799 13.7245 -1.9222 -4.5035 -0.7172 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 cyan_0 5.317 0.000 0.000 0.000 0.0000 log_k_JCZ38 0.000 2.272 0.000 0.000 0.0000 log_k_J9Z38 0.000 0.000 1.633 0.000 0.0000 log_k_JSE76 0.000 0.000 0.000 1.271 0.0000 f_cyan_ilr_1 0.000 0.000 0.000 0.000 0.6838 f_cyan_ilr_2 0.000 0.000 0.000 0.000 0.0000 f_JCZ38_qlogis 0.000 0.000 0.000 0.000 0.0000 log_k1 0.000 0.000 0.000 0.000 0.0000 log_k2 0.000 0.000 0.000 0.000 0.0000 g_qlogis 0.000 0.000 0.000 0.000 0.0000 f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 g_qlogis cyan_0 0.00 0.00 0.0000 0.0000 0.000 log_k_JCZ38 0.00 0.00 0.0000 0.0000 0.000 log_k_J9Z38 0.00 0.00 0.0000 0.0000 0.000 log_k_JSE76 0.00 0.00 0.0000 0.0000 0.000 f_cyan_ilr_1 0.00 0.00 0.0000 0.0000 0.000 f_cyan_ilr_2 11.77 0.00 0.0000 0.0000 0.000 f_JCZ38_qlogis 0.00 16.11 0.0000 0.0000 0.000 log_k1 0.00 0.00 0.9496 0.0000 0.000 log_k2 0.00 0.00 0.0000 0.5846 0.000 g_qlogis 0.00 0.00 0.0000 0.0000 1.719 Starting values for error model parameters: a.1 b.1 1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2398 2390 -1179 Optimised parameters: est. lower upper cyan_0 100.8076 NA NA log_k_JCZ38 -3.4684 NA NA log_k_J9Z38 -5.0844 NA NA log_k_JSE76 -5.5743 NA NA f_cyan_ilr_1 0.6669 NA NA f_cyan_ilr_2 0.7912 NA NA f_JCZ38_qlogis 84.1825 NA NA log_k1 -2.1671 NA NA log_k2 -4.5447 NA NA g_qlogis -0.5631 NA NA a.1 2.9627 NA NA b.1 0.0444 NA NA SD.log_k_JCZ38 1.4044 NA NA SD.log_k_J9Z38 0.6410 NA NA SD.log_k_JSE76 0.5391 NA NA SD.f_cyan_ilr_1 0.3203 NA NA SD.f_cyan_ilr_2 0.5038 NA NA SD.f_JCZ38_qlogis 3.5865 NA NA SD.log_k2 0.3119 NA NA SD.g_qlogis 0.8276 NA NA Correlation is not available Random effects: est. lower upper SD.log_k_JCZ38 1.4044 NA NA SD.log_k_J9Z38 0.6410 NA NA SD.log_k_JSE76 0.5391 NA NA SD.f_cyan_ilr_1 0.3203 NA NA SD.f_cyan_ilr_2 0.5038 NA NA SD.f_JCZ38_qlogis 3.5865 NA NA SD.log_k2 0.3119 NA NA SD.g_qlogis 0.8276 NA NA Variance model: est. lower upper a.1 2.9627 NA NA b.1 0.0444 NA NA Backtransformed parameters: est. lower upper cyan_0 1.008e+02 NA NA k_JCZ38 3.117e-02 NA NA k_J9Z38 6.193e-03 NA NA k_JSE76 3.794e-03 NA NA f_cyan_to_JCZ38 6.149e-01 NA NA f_cyan_to_J9Z38 2.395e-01 NA NA f_JCZ38_to_JSE76 1.000e+00 NA NA k1 1.145e-01 NA NA k2 1.062e-02 NA NA g 3.628e-01 NA NA Resulting formation fractions: ff cyan_JCZ38 0.6149 cyan_J9Z38 0.2395 cyan_sink 0.1456 JCZ38_JSE76 1.0000 JCZ38_sink 0.0000 Estimated disappearance times: DT50 DT90 DT50back DT50_k1 DT50_k2 cyan 26.26 174.32 52.47 6.053 65.25 JCZ38 22.24 73.88 NA NA NA J9Z38 111.93 371.82 NA NA NA JSE76 182.69 606.88 NA NA NA </code></pre> <p></p> <caption> Hierarchical SFORB path 1 fit with constant variance </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.2 R version used for fitting: 4.2.2 Date of fit: Sat Jan 28 10:10:49 2023 Date of summary: Fri Feb 17 22:24:33 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 1279.472 s Using 300, 100 iterations and 10 chains Variance model: Constant variance Starting values for degradation parameters: cyan_free_0 log_k_cyan_free log_k_cyan_free_bound 102.0643 -2.8987 -2.7077 log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 -3.4717 -3.4008 -5.0024 log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 -5.8613 0.6855 1.2366 f_JCZ38_qlogis 13.7418 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_free_0 log_k_cyan_free log_k_cyan_free_bound cyan_free_0 4.466 0.0000 0.000 log_k_cyan_free 0.000 0.6158 0.000 log_k_cyan_free_bound 0.000 0.0000 1.463 log_k_cyan_bound_free 0.000 0.0000 0.000 log_k_JCZ38 0.000 0.0000 0.000 log_k_J9Z38 0.000 0.0000 0.000 log_k_JSE76 0.000 0.0000 0.000 f_cyan_ilr_1 0.000 0.0000 0.000 f_cyan_ilr_2 0.000 0.0000 0.000 f_JCZ38_qlogis 0.000 0.0000 0.000 log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 cyan_free_0 0.000 0.000 0.000 0.000 log_k_cyan_free 0.000 0.000 0.000 0.000 log_k_cyan_free_bound 0.000 0.000 0.000 0.000 log_k_cyan_bound_free 1.058 0.000 0.000 0.000 log_k_JCZ38 0.000 2.382 0.000 0.000 log_k_J9Z38 0.000 0.000 1.595 0.000 log_k_JSE76 0.000 0.000 0.000 1.245 f_cyan_ilr_1 0.000 0.000 0.000 0.000 f_cyan_ilr_2 0.000 0.000 0.000 0.000 f_JCZ38_qlogis 0.000 0.000 0.000 0.000 f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis cyan_free_0 0.0000 0.00 0.00 log_k_cyan_free 0.0000 0.00 0.00 log_k_cyan_free_bound 0.0000 0.00 0.00 log_k_cyan_bound_free 0.0000 0.00 0.00 log_k_JCZ38 0.0000 0.00 0.00 log_k_J9Z38 0.0000 0.00 0.00 log_k_JSE76 0.0000 0.00 0.00 f_cyan_ilr_1 0.6852 0.00 0.00 f_cyan_ilr_2 0.0000 1.28 0.00 f_JCZ38_qlogis 0.0000 0.00 16.14 Starting values for error model parameters: a.1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2401 2394 -1181 Optimised parameters: est. lower upper cyan_free_0 102.7803 NA NA log_k_cyan_free -2.8068 NA NA log_k_cyan_free_bound -2.5714 NA NA log_k_cyan_bound_free -3.4426 NA NA log_k_JCZ38 -3.4994 NA NA log_k_J9Z38 -5.1148 NA NA log_k_JSE76 -5.6335 NA NA f_cyan_ilr_1 0.6597 NA NA f_cyan_ilr_2 0.5132 NA NA f_JCZ38_qlogis 37.2090 NA NA a.1 3.2367 NA NA SD.log_k_cyan_free 0.3161 NA NA SD.log_k_cyan_free_bound 0.8103 NA NA SD.log_k_cyan_bound_free 0.5554 NA NA SD.log_k_JCZ38 1.4858 NA NA SD.log_k_J9Z38 0.5859 NA NA SD.log_k_JSE76 0.6195 NA NA SD.f_cyan_ilr_1 0.3118 NA NA SD.f_cyan_ilr_2 0.3344 NA NA SD.f_JCZ38_qlogis 0.5518 NA NA Correlation is not available Random effects: est. lower upper SD.log_k_cyan_free 0.3161 NA NA SD.log_k_cyan_free_bound 0.8103 NA NA SD.log_k_cyan_bound_free 0.5554 NA NA SD.log_k_JCZ38 1.4858 NA NA SD.log_k_J9Z38 0.5859 NA NA SD.log_k_JSE76 0.6195 NA NA SD.f_cyan_ilr_1 0.3118 NA NA SD.f_cyan_ilr_2 0.3344 NA NA SD.f_JCZ38_qlogis 0.5518 NA NA Variance model: est. lower upper a.1 3.237 NA NA Backtransformed parameters: est. lower upper cyan_free_0 1.028e+02 NA NA k_cyan_free 6.040e-02 NA NA k_cyan_free_bound 7.643e-02 NA NA k_cyan_bound_free 3.198e-02 NA NA k_JCZ38 3.022e-02 NA NA k_J9Z38 6.007e-03 NA NA k_JSE76 3.576e-03 NA NA f_cyan_free_to_JCZ38 5.787e-01 NA NA f_cyan_free_to_J9Z38 2.277e-01 NA NA f_JCZ38_to_JSE76 1.000e+00 NA NA Estimated Eigenvalues of SFORB model(s): cyan_b1 cyan_b2 cyan_g 0.15646 0.01235 0.33341 Resulting formation fractions: ff cyan_free_JCZ38 0.5787 cyan_free_J9Z38 0.2277 cyan_free_sink 0.1936 cyan_free 1.0000 JCZ38_JSE76 1.0000 JCZ38_sink 0.0000 Estimated disappearance times: DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 cyan 24.48 153.7 46.26 4.43 56.15 JCZ38 22.94 76.2 NA NA NA J9Z38 115.39 383.3 NA NA NA JSE76 193.84 643.9 NA NA NA </code></pre> <p></p> <caption> Hierarchical SFORB path 1 fit with two-component error </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.2 R version used for fitting: 4.2.2 Date of fit: Sat Jan 28 10:17:00 2023 Date of summary: Fri Feb 17 22:24:33 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 1649.941 s Using 300, 100 iterations and 10 chains Variance model: Two-component variance function Starting values for degradation parameters: cyan_free_0 log_k_cyan_free log_k_cyan_free_bound 101.3964 -2.9881 -2.7949 log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 -3.4376 -3.3626 -4.9792 log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 -5.8727 0.6814 6.8139 f_JCZ38_qlogis 13.7419 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_free_0 log_k_cyan_free log_k_cyan_free_bound cyan_free_0 5.317 0.0000 0.000 log_k_cyan_free 0.000 0.7301 0.000 log_k_cyan_free_bound 0.000 0.0000 1.384 log_k_cyan_bound_free 0.000 0.0000 0.000 log_k_JCZ38 0.000 0.0000 0.000 log_k_J9Z38 0.000 0.0000 0.000 log_k_JSE76 0.000 0.0000 0.000 f_cyan_ilr_1 0.000 0.0000 0.000 f_cyan_ilr_2 0.000 0.0000 0.000 f_JCZ38_qlogis 0.000 0.0000 0.000 log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 cyan_free_0 0.000 0.000 0.000 0.000 log_k_cyan_free 0.000 0.000 0.000 0.000 log_k_cyan_free_bound 0.000 0.000 0.000 0.000 log_k_cyan_bound_free 1.109 0.000 0.000 0.000 log_k_JCZ38 0.000 2.272 0.000 0.000 log_k_J9Z38 0.000 0.000 1.633 0.000 log_k_JSE76 0.000 0.000 0.000 1.271 f_cyan_ilr_1 0.000 0.000 0.000 0.000 f_cyan_ilr_2 0.000 0.000 0.000 0.000 f_JCZ38_qlogis 0.000 0.000 0.000 0.000 f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis cyan_free_0 0.0000 0.00 0.00 log_k_cyan_free 0.0000 0.00 0.00 log_k_cyan_free_bound 0.0000 0.00 0.00 log_k_cyan_bound_free 0.0000 0.00 0.00 log_k_JCZ38 0.0000 0.00 0.00 log_k_J9Z38 0.0000 0.00 0.00 log_k_JSE76 0.0000 0.00 0.00 f_cyan_ilr_1 0.6838 0.00 0.00 f_cyan_ilr_2 0.0000 11.84 0.00 f_JCZ38_qlogis 0.0000 0.00 16.14 Starting values for error model parameters: a.1 b.1 1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2400 2392 -1180 Optimised parameters: est. lower upper cyan_free_0 100.69983 NA NA log_k_cyan_free -3.11584 NA NA log_k_cyan_free_bound -3.15216 NA NA log_k_cyan_bound_free -3.65986 NA NA log_k_JCZ38 -3.47811 NA NA log_k_J9Z38 -5.08835 NA NA log_k_JSE76 -5.55514 NA NA f_cyan_ilr_1 0.66764 NA NA f_cyan_ilr_2 0.78329 NA NA f_JCZ38_qlogis 25.35245 NA NA a.1 2.99088 NA NA b.1 0.04346 NA NA SD.log_k_cyan_free 0.48797 NA NA SD.log_k_cyan_bound_free 0.27243 NA NA SD.log_k_JCZ38 1.42450 NA NA SD.log_k_J9Z38 0.63496 NA NA SD.log_k_JSE76 0.55951 NA NA SD.f_cyan_ilr_1 0.32687 NA NA SD.f_cyan_ilr_2 0.48056 NA NA SD.f_JCZ38_qlogis 0.43818 NA NA Correlation is not available Random effects: est. lower upper SD.log_k_cyan_free 0.4880 NA NA SD.log_k_cyan_bound_free 0.2724 NA NA SD.log_k_JCZ38 1.4245 NA NA SD.log_k_J9Z38 0.6350 NA NA SD.log_k_JSE76 0.5595 NA NA SD.f_cyan_ilr_1 0.3269 NA NA SD.f_cyan_ilr_2 0.4806 NA NA SD.f_JCZ38_qlogis 0.4382 NA NA Variance model: est. lower upper a.1 2.99088 NA NA b.1 0.04346 NA NA Backtransformed parameters: est. lower upper cyan_free_0 1.007e+02 NA NA k_cyan_free 4.434e-02 NA NA k_cyan_free_bound 4.276e-02 NA NA k_cyan_bound_free 2.574e-02 NA NA k_JCZ38 3.087e-02 NA NA k_J9Z38 6.168e-03 NA NA k_JSE76 3.868e-03 NA NA f_cyan_free_to_JCZ38 6.143e-01 NA NA f_cyan_free_to_J9Z38 2.389e-01 NA NA f_JCZ38_to_JSE76 1.000e+00 NA NA Estimated Eigenvalues of SFORB model(s): cyan_b1 cyan_b2 cyan_g 0.10161 0.01123 0.36636 Resulting formation fractions: ff cyan_free_JCZ38 6.143e-01 cyan_free_J9Z38 2.389e-01 cyan_free_sink 1.468e-01 cyan_free 1.000e+00 JCZ38_JSE76 1.000e+00 JCZ38_sink 9.763e-12 Estimated disappearance times: DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 cyan 25.91 164.4 49.49 6.822 61.72 JCZ38 22.46 74.6 NA NA NA J9Z38 112.37 373.3 NA NA NA JSE76 179.22 595.4 NA NA NA </code></pre> <p></p> <caption> Hierarchical HS path 1 fit with constant variance </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.2 R version used for fitting: 4.2.2 Date of fit: Sat Jan 28 10:11:04 2023 Date of summary: Fri Feb 17 22:24:33 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 1294.259 s Using 300, 100 iterations and 10 chains Variance model: Constant variance Starting values for degradation parameters: cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 102.8738 -3.4490 -4.9348 -5.5989 0.6469 f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 log_tb 1.2854 9.7193 -2.9084 -4.1810 1.7813 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 cyan_0 5.409 0.00 0.00 0.000 0.0000 log_k_JCZ38 0.000 2.33 0.00 0.000 0.0000 log_k_J9Z38 0.000 0.00 1.59 0.000 0.0000 log_k_JSE76 0.000 0.00 0.00 1.006 0.0000 f_cyan_ilr_1 0.000 0.00 0.00 0.000 0.6371 f_cyan_ilr_2 0.000 0.00 0.00 0.000 0.0000 f_JCZ38_qlogis 0.000 0.00 0.00 0.000 0.0000 log_k1 0.000 0.00 0.00 0.000 0.0000 log_k2 0.000 0.00 0.00 0.000 0.0000 log_tb 0.000 0.00 0.00 0.000 0.0000 f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 log_tb cyan_0 0.000 0.00 0.0000 0.0000 0.0000 log_k_JCZ38 0.000 0.00 0.0000 0.0000 0.0000 log_k_J9Z38 0.000 0.00 0.0000 0.0000 0.0000 log_k_JSE76 0.000 0.00 0.0000 0.0000 0.0000 f_cyan_ilr_1 0.000 0.00 0.0000 0.0000 0.0000 f_cyan_ilr_2 2.167 0.00 0.0000 0.0000 0.0000 f_JCZ38_qlogis 0.000 10.22 0.0000 0.0000 0.0000 log_k1 0.000 0.00 0.7003 0.0000 0.0000 log_k2 0.000 0.00 0.0000 0.8928 0.0000 log_tb 0.000 0.00 0.0000 0.0000 0.6774 Starting values for error model parameters: a.1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2427 2420 -1194 Optimised parameters: est. lower upper cyan_0 101.84849 NA NA log_k_JCZ38 -3.47365 NA NA log_k_J9Z38 -5.10562 NA NA log_k_JSE76 -5.60318 NA NA f_cyan_ilr_1 0.66127 NA NA f_cyan_ilr_2 0.60283 NA NA f_JCZ38_qlogis 45.06408 NA NA log_k1 -3.10124 NA NA log_k2 -4.39028 NA NA log_tb 2.32256 NA NA a.1 3.32683 NA NA SD.log_k_JCZ38 1.41427 NA NA SD.log_k_J9Z38 0.54767 NA NA SD.log_k_JSE76 0.62147 NA NA SD.f_cyan_ilr_1 0.30189 NA NA SD.f_cyan_ilr_2 0.34960 NA NA SD.f_JCZ38_qlogis 0.04644 NA NA SD.log_k1 0.39534 NA NA SD.log_k2 0.43468 NA NA SD.log_tb 0.60781 NA NA Correlation is not available Random effects: est. lower upper SD.log_k_JCZ38 1.41427 NA NA SD.log_k_J9Z38 0.54767 NA NA SD.log_k_JSE76 0.62147 NA NA SD.f_cyan_ilr_1 0.30189 NA NA SD.f_cyan_ilr_2 0.34960 NA NA SD.f_JCZ38_qlogis 0.04644 NA NA SD.log_k1 0.39534 NA NA SD.log_k2 0.43468 NA NA SD.log_tb 0.60781 NA NA Variance model: est. lower upper a.1 3.327 NA NA Backtransformed parameters: est. lower upper cyan_0 1.018e+02 NA NA k_JCZ38 3.100e-02 NA NA k_J9Z38 6.063e-03 NA NA k_JSE76 3.686e-03 NA NA f_cyan_to_JCZ38 5.910e-01 NA NA f_cyan_to_J9Z38 2.320e-01 NA NA f_JCZ38_to_JSE76 1.000e+00 NA NA k1 4.499e-02 NA NA k2 1.240e-02 NA NA tb 1.020e+01 NA NA Resulting formation fractions: ff cyan_JCZ38 0.591 cyan_J9Z38 0.232 cyan_sink 0.177 JCZ38_JSE76 1.000 JCZ38_sink 0.000 Estimated disappearance times: DT50 DT90 DT50back DT50_k1 DT50_k2 cyan 29.09 158.91 47.84 15.41 55.91 JCZ38 22.36 74.27 NA NA NA J9Z38 114.33 379.80 NA NA NA JSE76 188.04 624.66 NA NA NA </code></pre> <p></p> <caption> Hierarchical HS path 1 fit with two-component error </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.2 R version used for fitting: 4.2.2 Date of fit: Sat Jan 28 10:11:24 2023 Date of summary: Fri Feb 17 22:24:33 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 1313.805 s Using 300, 100 iterations and 10 chains Variance model: Two-component variance function Starting values for degradation parameters: cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 101.168 -3.358 -4.941 -5.794 0.676 f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 log_tb 5.740 13.863 -3.147 -4.262 2.173 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 cyan_0 5.79 0.000 0.000 0.000 0.0000 log_k_JCZ38 0.00 2.271 0.000 0.000 0.0000 log_k_J9Z38 0.00 0.000 1.614 0.000 0.0000 log_k_JSE76 0.00 0.000 0.000 1.264 0.0000 f_cyan_ilr_1 0.00 0.000 0.000 0.000 0.6761 f_cyan_ilr_2 0.00 0.000 0.000 0.000 0.0000 f_JCZ38_qlogis 0.00 0.000 0.000 0.000 0.0000 log_k1 0.00 0.000 0.000 0.000 0.0000 log_k2 0.00 0.000 0.000 0.000 0.0000 log_tb 0.00 0.000 0.000 0.000 0.0000 f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 log_tb cyan_0 0.000 0.00 0.0000 0.0000 0.000 log_k_JCZ38 0.000 0.00 0.0000 0.0000 0.000 log_k_J9Z38 0.000 0.00 0.0000 0.0000 0.000 log_k_JSE76 0.000 0.00 0.0000 0.0000 0.000 f_cyan_ilr_1 0.000 0.00 0.0000 0.0000 0.000 f_cyan_ilr_2 9.572 0.00 0.0000 0.0000 0.000 f_JCZ38_qlogis 0.000 19.19 0.0000 0.0000 0.000 log_k1 0.000 0.00 0.8705 0.0000 0.000 log_k2 0.000 0.00 0.0000 0.9288 0.000 log_tb 0.000 0.00 0.0000 0.0000 1.065 Starting values for error model parameters: a.1 b.1 1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2422 2414 -1190 Optimised parameters: est. lower upper cyan_0 100.9521 NA NA log_k_JCZ38 -3.4629 NA NA log_k_J9Z38 -5.0346 NA NA log_k_JSE76 -5.5722 NA NA f_cyan_ilr_1 0.6560 NA NA f_cyan_ilr_2 0.7983 NA NA f_JCZ38_qlogis 42.7949 NA NA log_k1 -3.1721 NA NA log_k2 -4.4039 NA NA log_tb 2.3994 NA NA a.1 3.0586 NA NA b.1 0.0380 NA NA SD.log_k_JCZ38 1.3754 NA NA SD.log_k_J9Z38 0.6703 NA NA SD.log_k_JSE76 0.5876 NA NA SD.f_cyan_ilr_1 0.3272 NA NA SD.f_cyan_ilr_2 0.5300 NA NA SD.f_JCZ38_qlogis 6.4465 NA NA SD.log_k1 0.4135 NA NA SD.log_k2 0.4182 NA NA SD.log_tb 0.6035 NA NA Correlation is not available Random effects: est. lower upper SD.log_k_JCZ38 1.3754 NA NA SD.log_k_J9Z38 0.6703 NA NA SD.log_k_JSE76 0.5876 NA NA SD.f_cyan_ilr_1 0.3272 NA NA SD.f_cyan_ilr_2 0.5300 NA NA SD.f_JCZ38_qlogis 6.4465 NA NA SD.log_k1 0.4135 NA NA SD.log_k2 0.4182 NA NA SD.log_tb 0.6035 NA NA Variance model: est. lower upper a.1 3.059 NA NA b.1 0.038 NA NA Backtransformed parameters: est. lower upper cyan_0 1.010e+02 NA NA k_JCZ38 3.134e-02 NA NA k_J9Z38 6.509e-03 NA NA k_JSE76 3.802e-03 NA NA f_cyan_to_JCZ38 6.127e-01 NA NA f_cyan_to_J9Z38 2.423e-01 NA NA f_JCZ38_to_JSE76 1.000e+00 NA NA k1 4.191e-02 NA NA k2 1.223e-02 NA NA tb 1.102e+01 NA NA Resulting formation fractions: ff cyan_JCZ38 0.6127 cyan_J9Z38 0.2423 cyan_sink 0.1449 JCZ38_JSE76 1.0000 JCZ38_sink 0.0000 Estimated disappearance times: DT50 DT90 DT50back DT50_k1 DT50_k2 cyan 29.94 161.54 48.63 16.54 56.68 JCZ38 22.12 73.47 NA NA NA J9Z38 106.50 353.77 NA NA NA JSE76 182.30 605.60 NA NA NA </code></pre> <p></p> </div> <div class="section level4"> <h4 id="pathway-2">Pathway 2<a class="anchor" aria-label="anchor" href="#pathway-2"></a> </h4> <caption> Hierarchical FOMC path 2 fit with constant variance </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.2 R version used for fitting: 4.2.2 Date of fit: Sat Jan 28 10:34:28 2023 Date of summary: Fri Feb 17 22:24:33 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 1030.246 s Using 300, 100 iterations and 10 chains Variance model: Constant variance Starting values for degradation parameters: cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 101.8173 -1.8998 -5.1449 -2.5415 0.6705 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta 4.4669 16.1281 13.3327 -0.2314 2.8738 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 cyan_0 5.742 0.000 0.000 0.00 0.0000 log_k_JCZ38 0.000 1.402 0.000 0.00 0.0000 log_k_J9Z38 0.000 0.000 1.718 0.00 0.0000 log_k_JSE76 0.000 0.000 0.000 3.57 0.0000 f_cyan_ilr_1 0.000 0.000 0.000 0.00 0.5926 f_cyan_ilr_2 0.000 0.000 0.000 0.00 0.0000 f_JCZ38_qlogis 0.000 0.000 0.000 0.00 0.0000 f_JSE76_qlogis 0.000 0.000 0.000 0.00 0.0000 log_alpha 0.000 0.000 0.000 0.00 0.0000 log_beta 0.000 0.000 0.000 0.00 0.0000 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta cyan_0 0.00 0.00 0.00 0.0000 0.0000 log_k_JCZ38 0.00 0.00 0.00 0.0000 0.0000 log_k_J9Z38 0.00 0.00 0.00 0.0000 0.0000 log_k_JSE76 0.00 0.00 0.00 0.0000 0.0000 f_cyan_ilr_1 0.00 0.00 0.00 0.0000 0.0000 f_cyan_ilr_2 10.56 0.00 0.00 0.0000 0.0000 f_JCZ38_qlogis 0.00 12.04 0.00 0.0000 0.0000 f_JSE76_qlogis 0.00 0.00 15.26 0.0000 0.0000 log_alpha 0.00 0.00 0.00 0.4708 0.0000 log_beta 0.00 0.00 0.00 0.0000 0.4432 Starting values for error model parameters: a.1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2308 2301 -1134 Optimised parameters: est. lower upper cyan_0 101.9586 99.22024 104.69700 log_k_JCZ38 -2.4861 -3.17661 -1.79560 log_k_J9Z38 -5.3926 -6.08842 -4.69684 log_k_JSE76 -3.1193 -4.12904 -2.10962 f_cyan_ilr_1 0.7368 0.42085 1.05276 f_cyan_ilr_2 0.6196 0.06052 1.17861 f_JCZ38_qlogis 4.8970 -4.68003 14.47398 f_JSE76_qlogis 4.4066 -1.02087 9.83398 log_alpha -0.3021 -0.68264 0.07838 log_beta 2.7438 2.57970 2.90786 a.1 2.9008 2.69920 3.10245 SD.cyan_0 2.7081 0.64216 4.77401 SD.log_k_JCZ38 0.7043 0.19951 1.20907 SD.log_k_J9Z38 0.6248 0.05790 1.19180 SD.log_k_JSE76 1.0750 0.33157 1.81839 SD.f_cyan_ilr_1 0.3429 0.11688 0.56892 SD.f_cyan_ilr_2 0.4774 0.09381 0.86097 SD.f_JCZ38_qlogis 1.5565 -7.83970 10.95279 SD.f_JSE76_qlogis 1.6871 -1.25577 4.63000 SD.log_alpha 0.4216 0.15913 0.68405 Correlation: cyan_0 l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76 log_k_JCZ38 -0.0167 log_k_J9Z38 -0.0307 0.0057 log_k_JSE76 -0.0032 0.1358 0.0009 f_cyan_ilr_1 -0.0087 0.0206 -0.1158 -0.0009 f_cyan_ilr_2 -0.1598 0.0690 0.1770 0.0002 -0.0007 f_JCZ38_qlogis 0.0966 -0.1132 -0.0440 0.0182 -0.1385 -0.4583 f_JSE76_qlogis -0.0647 0.1157 0.0333 -0.0026 0.1110 0.3620 -0.8586 log_alpha -0.0389 0.0113 0.0209 0.0021 0.0041 0.0451 -0.0605 0.0412 log_beta -0.2508 0.0533 0.0977 0.0098 0.0220 0.2741 -0.2934 0.1999 log_lph log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta 0.2281 Random effects: est. lower upper SD.cyan_0 2.7081 0.64216 4.7740 SD.log_k_JCZ38 0.7043 0.19951 1.2091 SD.log_k_J9Z38 0.6248 0.05790 1.1918 SD.log_k_JSE76 1.0750 0.33157 1.8184 SD.f_cyan_ilr_1 0.3429 0.11688 0.5689 SD.f_cyan_ilr_2 0.4774 0.09381 0.8610 SD.f_JCZ38_qlogis 1.5565 -7.83970 10.9528 SD.f_JSE76_qlogis 1.6871 -1.25577 4.6300 SD.log_alpha 0.4216 0.15913 0.6840 Variance model: est. lower upper a.1 2.901 2.699 3.102 Backtransformed parameters: est. lower upper cyan_0 101.95862 99.220240 1.047e+02 k_JCZ38 0.08323 0.041727 1.660e-01 k_J9Z38 0.00455 0.002269 9.124e-03 k_JSE76 0.04419 0.016098 1.213e-01 f_cyan_to_JCZ38 0.61318 NA NA f_cyan_to_J9Z38 0.21630 NA NA f_JCZ38_to_JSE76 0.99259 0.009193 1.000e+00 f_JSE76_to_JCZ38 0.98795 0.264857 9.999e-01 alpha 0.73924 0.505281 1.082e+00 beta 15.54568 13.193194 1.832e+01 Resulting formation fractions: ff cyan_JCZ38 0.613182 cyan_J9Z38 0.216298 cyan_sink 0.170519 JCZ38_JSE76 0.992586 JCZ38_sink 0.007414 JSE76_JCZ38 0.987950 JSE76_sink 0.012050 Estimated disappearance times: DT50 DT90 DT50back cyan 24.157 334.68 100.7 JCZ38 8.328 27.66 NA J9Z38 152.341 506.06 NA JSE76 15.687 52.11 NA </code></pre> <p></p> <caption> Hierarchical FOMC path 2 fit with two-component error </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.2 R version used for fitting: 4.2.2 Date of fit: Sat Jan 28 10:37:36 2023 Date of summary: Fri Feb 17 22:24:33 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 1217.619 s Using 300, 100 iterations and 10 chains Variance model: Two-component variance function Starting values for degradation parameters: cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 101.9028 -1.9055 -5.0249 -2.5646 0.6807 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta 4.8883 16.0676 9.3923 -0.1346 3.0364 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 cyan_0 6.321 0.000 0.000 0.000 0.0000 log_k_JCZ38 0.000 1.392 0.000 0.000 0.0000 log_k_J9Z38 0.000 0.000 1.561 0.000 0.0000 log_k_JSE76 0.000 0.000 0.000 3.614 0.0000 f_cyan_ilr_1 0.000 0.000 0.000 0.000 0.6339 f_cyan_ilr_2 0.000 0.000 0.000 0.000 0.0000 f_JCZ38_qlogis 0.000 0.000 0.000 0.000 0.0000 f_JSE76_qlogis 0.000 0.000 0.000 0.000 0.0000 log_alpha 0.000 0.000 0.000 0.000 0.0000 log_beta 0.000 0.000 0.000 0.000 0.0000 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta cyan_0 0.00 0.00 0.00 0.0000 0.0000 log_k_JCZ38 0.00 0.00 0.00 0.0000 0.0000 log_k_J9Z38 0.00 0.00 0.00 0.0000 0.0000 log_k_JSE76 0.00 0.00 0.00 0.0000 0.0000 f_cyan_ilr_1 0.00 0.00 0.00 0.0000 0.0000 f_cyan_ilr_2 10.41 0.00 0.00 0.0000 0.0000 f_JCZ38_qlogis 0.00 12.24 0.00 0.0000 0.0000 f_JSE76_qlogis 0.00 0.00 15.13 0.0000 0.0000 log_alpha 0.00 0.00 0.00 0.3701 0.0000 log_beta 0.00 0.00 0.00 0.0000 0.5662 Starting values for error model parameters: a.1 b.1 1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2248 2240 -1103 Optimised parameters: est. lower upper cyan_0 101.55545 9.920e+01 1.039e+02 log_k_JCZ38 -2.37354 -2.928e+00 -1.819e+00 log_k_J9Z38 -5.14736 -5.960e+00 -4.335e+00 log_k_JSE76 -3.07802 -4.243e+00 -1.913e+00 f_cyan_ilr_1 0.71263 3.655e-01 1.060e+00 f_cyan_ilr_2 0.95202 2.701e-01 1.634e+00 f_JCZ38_qlogis 3.58473 1.251e+00 5.919e+00 f_JSE76_qlogis 19.03623 -1.037e+07 1.037e+07 log_alpha -0.15297 -4.490e-01 1.431e-01 log_beta 2.99230 2.706e+00 3.278e+00 a.1 2.04816 NA NA b.1 0.06886 NA NA SD.log_k_JCZ38 0.56174 NA NA SD.log_k_J9Z38 0.86509 NA NA SD.log_k_JSE76 1.28450 NA NA SD.f_cyan_ilr_1 0.38705 NA NA SD.f_cyan_ilr_2 0.54153 NA NA SD.f_JCZ38_qlogis 1.65311 NA NA SD.f_JSE76_qlogis 7.51468 NA NA SD.log_alpha 0.31586 NA NA SD.log_beta 0.24696 NA NA Correlation is not available Random effects: est. lower upper SD.log_k_JCZ38 0.5617 NA NA SD.log_k_J9Z38 0.8651 NA NA SD.log_k_JSE76 1.2845 NA NA SD.f_cyan_ilr_1 0.3870 NA NA SD.f_cyan_ilr_2 0.5415 NA NA SD.f_JCZ38_qlogis 1.6531 NA NA SD.f_JSE76_qlogis 7.5147 NA NA SD.log_alpha 0.3159 NA NA SD.log_beta 0.2470 NA NA Variance model: est. lower upper a.1 2.04816 NA NA b.1 0.06886 NA NA Backtransformed parameters: est. lower upper cyan_0 1.016e+02 99.20301 103.9079 k_JCZ38 9.315e-02 0.05349 0.1622 k_J9Z38 5.815e-03 0.00258 0.0131 k_JSE76 4.605e-02 0.01436 0.1477 f_cyan_to_JCZ38 6.438e-01 NA NA f_cyan_to_J9Z38 2.350e-01 NA NA f_JCZ38_to_JSE76 9.730e-01 0.77745 0.9973 f_JSE76_to_JCZ38 1.000e+00 0.00000 1.0000 alpha 8.582e-01 0.63824 1.1538 beta 1.993e+01 14.97621 26.5262 Resulting formation fractions: ff cyan_JCZ38 6.438e-01 cyan_J9Z38 2.350e-01 cyan_sink 1.212e-01 JCZ38_JSE76 9.730e-01 JCZ38_sink 2.700e-02 JSE76_JCZ38 1.000e+00 JSE76_sink 5.403e-09 Estimated disappearance times: DT50 DT90 DT50back cyan 24.771 271.70 81.79 JCZ38 7.441 24.72 NA J9Z38 119.205 395.99 NA JSE76 15.052 50.00 NA </code></pre> <p></p> <caption> Hierarchical DFOP path 2 fit with constant variance </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.2 R version used for fitting: 4.2.2 Date of fit: Sat Jan 28 10:38:34 2023 Date of summary: Fri Feb 17 22:24:33 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 1276.128 s Using 300, 100 iterations and 10 chains Variance model: Constant variance Starting values for degradation parameters: cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 102.4358 -2.3107 -5.3123 -3.7120 0.6753 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 1.1462 12.4095 12.3630 -1.9317 -4.4557 g_qlogis -0.5648 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 cyan_0 4.594 0.0000 0.000 0.0 0.0000 log_k_JCZ38 0.000 0.7966 0.000 0.0 0.0000 log_k_J9Z38 0.000 0.0000 1.561 0.0 0.0000 log_k_JSE76 0.000 0.0000 0.000 0.8 0.0000 f_cyan_ilr_1 0.000 0.0000 0.000 0.0 0.6349 f_cyan_ilr_2 0.000 0.0000 0.000 0.0 0.0000 f_JCZ38_qlogis 0.000 0.0000 0.000 0.0 0.0000 f_JSE76_qlogis 0.000 0.0000 0.000 0.0 0.0000 log_k1 0.000 0.0000 0.000 0.0 0.0000 log_k2 0.000 0.0000 0.000 0.0 0.0000 g_qlogis 0.000 0.0000 0.000 0.0 0.0000 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 cyan_0 0.000 0.00 0.0 0.000 0.0000 log_k_JCZ38 0.000 0.00 0.0 0.000 0.0000 log_k_J9Z38 0.000 0.00 0.0 0.000 0.0000 log_k_JSE76 0.000 0.00 0.0 0.000 0.0000 f_cyan_ilr_1 0.000 0.00 0.0 0.000 0.0000 f_cyan_ilr_2 1.797 0.00 0.0 0.000 0.0000 f_JCZ38_qlogis 0.000 13.85 0.0 0.000 0.0000 f_JSE76_qlogis 0.000 0.00 14.1 0.000 0.0000 log_k1 0.000 0.00 0.0 1.106 0.0000 log_k2 0.000 0.00 0.0 0.000 0.6141 g_qlogis 0.000 0.00 0.0 0.000 0.0000 g_qlogis cyan_0 0.000 log_k_JCZ38 0.000 log_k_J9Z38 0.000 log_k_JSE76 0.000 f_cyan_ilr_1 0.000 f_cyan_ilr_2 0.000 f_JCZ38_qlogis 0.000 f_JSE76_qlogis 0.000 log_k1 0.000 log_k2 0.000 g_qlogis 1.595 Starting values for error model parameters: a.1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2290 2281 -1123 Optimised parameters: est. lower upper cyan_0 102.6903 101.44420 103.9365 log_k_JCZ38 -2.4018 -2.98058 -1.8230 log_k_J9Z38 -5.1865 -5.92931 -4.4437 log_k_JSE76 -3.0784 -4.25226 -1.9045 f_cyan_ilr_1 0.7157 0.37625 1.0551 f_cyan_ilr_2 0.7073 0.20136 1.2132 f_JCZ38_qlogis 4.6797 0.43240 8.9269 f_JSE76_qlogis 5.0080 -1.01380 11.0299 log_k1 -1.9620 -2.62909 -1.2949 log_k2 -4.4894 -4.94958 -4.0292 g_qlogis -0.4658 -1.34443 0.4129 a.1 2.7158 2.52576 2.9059 SD.log_k_JCZ38 0.5818 0.15679 1.0067 SD.log_k_J9Z38 0.7421 0.16751 1.3167 SD.log_k_JSE76 1.2841 0.43247 2.1356 SD.f_cyan_ilr_1 0.3748 0.13040 0.6192 SD.f_cyan_ilr_2 0.4550 0.08396 0.8261 SD.f_JCZ38_qlogis 2.0862 -0.73390 4.9062 SD.f_JSE76_qlogis 1.9585 -3.14773 7.0647 SD.log_k1 0.7389 0.25761 1.2201 SD.log_k2 0.5132 0.18143 0.8450 SD.g_qlogis 0.9870 0.35773 1.6164 Correlation: cyan_0 l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76 log_k_JCZ38 -0.0170 log_k_J9Z38 -0.0457 0.0016 log_k_JSE76 -0.0046 0.1183 0.0005 f_cyan_ilr_1 0.0079 0.0072 -0.0909 0.0003 f_cyan_ilr_2 -0.3114 0.0343 0.1542 0.0023 -0.0519 f_JCZ38_qlogis 0.0777 -0.0601 -0.0152 0.0080 -0.0520 -0.2524 f_JSE76_qlogis -0.0356 0.0817 0.0073 0.0051 0.0388 0.1959 -0.6236 log_k1 0.0848 -0.0028 0.0010 -0.0010 -0.0014 -0.0245 0.0121 -0.0177 log_k2 0.0274 -0.0001 0.0075 0.0000 -0.0023 -0.0060 0.0000 -0.0130 g_qlogis 0.0159 0.0002 -0.0095 0.0002 0.0029 -0.0140 -0.0001 0.0149 log_k1 log_k2 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 0.0280 g_qlogis -0.0278 -0.0310 Random effects: est. lower upper SD.log_k_JCZ38 0.5818 0.15679 1.0067 SD.log_k_J9Z38 0.7421 0.16751 1.3167 SD.log_k_JSE76 1.2841 0.43247 2.1356 SD.f_cyan_ilr_1 0.3748 0.13040 0.6192 SD.f_cyan_ilr_2 0.4550 0.08396 0.8261 SD.f_JCZ38_qlogis 2.0862 -0.73390 4.9062 SD.f_JSE76_qlogis 1.9585 -3.14773 7.0647 SD.log_k1 0.7389 0.25761 1.2201 SD.log_k2 0.5132 0.18143 0.8450 SD.g_qlogis 0.9870 0.35773 1.6164 Variance model: est. lower upper a.1 2.716 2.526 2.906 Backtransformed parameters: est. lower upper cyan_0 1.027e+02 1.014e+02 103.93649 k_JCZ38 9.056e-02 5.076e-02 0.16154 k_J9Z38 5.591e-03 2.660e-03 0.01175 k_JSE76 4.603e-02 1.423e-02 0.14890 f_cyan_to_JCZ38 6.184e-01 NA NA f_cyan_to_J9Z38 2.248e-01 NA NA f_JCZ38_to_JSE76 9.908e-01 6.064e-01 0.99987 f_JSE76_to_JCZ38 9.934e-01 2.662e-01 0.99998 k1 1.406e-01 7.214e-02 0.27393 k2 1.123e-02 7.086e-03 0.01779 g 3.856e-01 2.068e-01 0.60177 Resulting formation fractions: ff cyan_JCZ38 0.618443 cyan_J9Z38 0.224770 cyan_sink 0.156787 JCZ38_JSE76 0.990803 JCZ38_sink 0.009197 JSE76_JCZ38 0.993360 JSE76_sink 0.006640 Estimated disappearance times: DT50 DT90 DT50back DT50_k1 DT50_k2 cyan 21.674 161.70 48.68 4.931 61.74 JCZ38 7.654 25.43 NA NA NA J9Z38 123.966 411.81 NA NA NA JSE76 15.057 50.02 NA NA NA </code></pre> <p></p> <caption> Hierarchical DFOP path 2 fit with two-component error </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.2 R version used for fitting: 4.2.2 Date of fit: Sat Jan 28 10:45:32 2023 Date of summary: Fri Feb 17 22:24:33 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 1693.767 s Using 300, 100 iterations and 10 chains Variance model: Two-component variance function Starting values for degradation parameters: cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 101.7523 -1.5948 -5.0119 -2.2723 0.6719 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 5.1681 12.8238 12.4130 -2.0057 -4.5526 g_qlogis -0.5805 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 cyan_0 5.627 0.000 0.000 0.000 0.0000 log_k_JCZ38 0.000 2.327 0.000 0.000 0.0000 log_k_J9Z38 0.000 0.000 1.664 0.000 0.0000 log_k_JSE76 0.000 0.000 0.000 4.566 0.0000 f_cyan_ilr_1 0.000 0.000 0.000 0.000 0.6519 f_cyan_ilr_2 0.000 0.000 0.000 0.000 0.0000 f_JCZ38_qlogis 0.000 0.000 0.000 0.000 0.0000 f_JSE76_qlogis 0.000 0.000 0.000 0.000 0.0000 log_k1 0.000 0.000 0.000 0.000 0.0000 log_k2 0.000 0.000 0.000 0.000 0.0000 g_qlogis 0.000 0.000 0.000 0.000 0.0000 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 cyan_0 0.0 0.00 0.00 0.0000 0.0000 log_k_JCZ38 0.0 0.00 0.00 0.0000 0.0000 log_k_J9Z38 0.0 0.00 0.00 0.0000 0.0000 log_k_JSE76 0.0 0.00 0.00 0.0000 0.0000 f_cyan_ilr_1 0.0 0.00 0.00 0.0000 0.0000 f_cyan_ilr_2 10.1 0.00 0.00 0.0000 0.0000 f_JCZ38_qlogis 0.0 13.99 0.00 0.0000 0.0000 f_JSE76_qlogis 0.0 0.00 14.15 0.0000 0.0000 log_k1 0.0 0.00 0.00 0.8452 0.0000 log_k2 0.0 0.00 0.00 0.0000 0.5968 g_qlogis 0.0 0.00 0.00 0.0000 0.0000 g_qlogis cyan_0 0.000 log_k_JCZ38 0.000 log_k_J9Z38 0.000 log_k_JSE76 0.000 f_cyan_ilr_1 0.000 f_cyan_ilr_2 0.000 f_JCZ38_qlogis 0.000 f_JSE76_qlogis 0.000 log_k1 0.000 log_k2 0.000 g_qlogis 1.691 Starting values for error model parameters: a.1 b.1 1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2234 2226 -1095 Optimised parameters: est. lower upper cyan_0 101.10667 9.903e+01 103.18265 log_k_JCZ38 -2.49437 -3.297e+00 -1.69221 log_k_J9Z38 -5.08171 -5.875e+00 -4.28846 log_k_JSE76 -3.20072 -4.180e+00 -2.22163 f_cyan_ilr_1 0.71059 3.639e-01 1.05727 f_cyan_ilr_2 1.15398 2.981e-01 2.00984 f_JCZ38_qlogis 3.18027 1.056e+00 5.30452 f_JSE76_qlogis 5.61578 -2.505e+01 36.28077 log_k1 -2.38875 -2.517e+00 -2.26045 log_k2 -4.67246 -4.928e+00 -4.41715 g_qlogis -0.28231 -1.135e+00 0.57058 a.1 2.08190 1.856e+00 2.30785 b.1 0.06114 5.015e-02 0.07214 SD.log_k_JCZ38 0.84622 2.637e-01 1.42873 SD.log_k_J9Z38 0.84564 2.566e-01 1.43464 SD.log_k_JSE76 1.04385 3.242e-01 1.76351 SD.f_cyan_ilr_1 0.38568 1.362e-01 0.63514 SD.f_cyan_ilr_2 0.68046 7.166e-02 1.28925 SD.f_JCZ38_qlogis 1.25244 -4.213e-02 2.54700 SD.f_JSE76_qlogis 0.28202 -1.515e+03 1515.87968 SD.log_k2 0.25749 7.655e-02 0.43843 SD.g_qlogis 0.94535 3.490e-01 1.54174 Correlation: cyan_0 l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76 log_k_JCZ38 -0.0086 log_k_J9Z38 -0.0363 -0.0007 log_k_JSE76 0.0015 0.1210 -0.0017 f_cyan_ilr_1 -0.0048 0.0095 -0.0572 0.0030 f_cyan_ilr_2 -0.4788 0.0328 0.1143 0.0027 -0.0316 f_JCZ38_qlogis 0.0736 -0.0664 -0.0137 0.0145 -0.0444 -0.2175 f_JSE76_qlogis -0.0137 0.0971 0.0035 0.0009 0.0293 0.1333 -0.6767 log_k1 0.2345 -0.0350 -0.0099 -0.0113 -0.0126 -0.1652 0.1756 -0.2161 log_k2 0.0440 -0.0133 0.0199 -0.0040 -0.0097 -0.0119 0.0604 -0.1306 g_qlogis 0.0438 0.0078 -0.0123 0.0029 0.0046 -0.0363 -0.0318 0.0736 log_k1 log_k2 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 0.3198 g_qlogis -0.1666 -0.0954 Random effects: est. lower upper SD.log_k_JCZ38 0.8462 2.637e-01 1.4287 SD.log_k_J9Z38 0.8456 2.566e-01 1.4346 SD.log_k_JSE76 1.0439 3.242e-01 1.7635 SD.f_cyan_ilr_1 0.3857 1.362e-01 0.6351 SD.f_cyan_ilr_2 0.6805 7.166e-02 1.2893 SD.f_JCZ38_qlogis 1.2524 -4.213e-02 2.5470 SD.f_JSE76_qlogis 0.2820 -1.515e+03 1515.8797 SD.log_k2 0.2575 7.655e-02 0.4384 SD.g_qlogis 0.9453 3.490e-01 1.5417 Variance model: est. lower upper a.1 2.08190 1.85595 2.30785 b.1 0.06114 0.05015 0.07214 Backtransformed parameters: est. lower upper cyan_0 1.011e+02 9.903e+01 103.18265 k_JCZ38 8.255e-02 3.701e-02 0.18411 k_J9Z38 6.209e-03 2.809e-03 0.01373 k_JSE76 4.073e-02 1.530e-02 0.10843 f_cyan_to_JCZ38 6.608e-01 NA NA f_cyan_to_J9Z38 2.419e-01 NA NA f_JCZ38_to_JSE76 9.601e-01 7.419e-01 0.99506 f_JSE76_to_JCZ38 9.964e-01 1.322e-11 1.00000 k1 9.174e-02 8.070e-02 0.10430 k2 9.349e-03 7.243e-03 0.01207 g 4.299e-01 2.432e-01 0.63890 Resulting formation fractions: ff cyan_JCZ38 0.660808 cyan_J9Z38 0.241904 cyan_sink 0.097288 JCZ38_JSE76 0.960085 JCZ38_sink 0.039915 JSE76_JCZ38 0.996373 JSE76_sink 0.003627 Estimated disappearance times: DT50 DT90 DT50back DT50_k1 DT50_k2 cyan 24.359 186.18 56.05 7.555 74.14 JCZ38 8.397 27.89 NA NA NA J9Z38 111.631 370.83 NA NA NA JSE76 17.017 56.53 NA NA NA </code></pre> <p></p> <caption> Hierarchical SFORB path 2 fit with constant variance </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.2 R version used for fitting: 4.2.2 Date of fit: Sat Jan 28 10:38:37 2023 Date of summary: Fri Feb 17 22:24:33 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 1279.102 s Using 300, 100 iterations and 10 chains Variance model: Constant variance Starting values for degradation parameters: cyan_free_0 log_k_cyan_free log_k_cyan_free_bound 102.4394 -2.7673 -2.8942 log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 -3.6201 -2.3107 -5.3123 log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 -3.7120 0.6754 1.1448 f_JCZ38_qlogis f_JSE76_qlogis 13.2672 13.3538 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_free_0 log_k_cyan_free log_k_cyan_free_bound cyan_free_0 4.589 0.0000 0.00 log_k_cyan_free 0.000 0.4849 0.00 log_k_cyan_free_bound 0.000 0.0000 1.62 log_k_cyan_bound_free 0.000 0.0000 0.00 log_k_JCZ38 0.000 0.0000 0.00 log_k_J9Z38 0.000 0.0000 0.00 log_k_JSE76 0.000 0.0000 0.00 f_cyan_ilr_1 0.000 0.0000 0.00 f_cyan_ilr_2 0.000 0.0000 0.00 f_JCZ38_qlogis 0.000 0.0000 0.00 f_JSE76_qlogis 0.000 0.0000 0.00 log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 cyan_free_0 0.000 0.0000 0.000 0.0 log_k_cyan_free 0.000 0.0000 0.000 0.0 log_k_cyan_free_bound 0.000 0.0000 0.000 0.0 log_k_cyan_bound_free 1.197 0.0000 0.000 0.0 log_k_JCZ38 0.000 0.7966 0.000 0.0 log_k_J9Z38 0.000 0.0000 1.561 0.0 log_k_JSE76 0.000 0.0000 0.000 0.8 f_cyan_ilr_1 0.000 0.0000 0.000 0.0 f_cyan_ilr_2 0.000 0.0000 0.000 0.0 f_JCZ38_qlogis 0.000 0.0000 0.000 0.0 f_JSE76_qlogis 0.000 0.0000 0.000 0.0 f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis cyan_free_0 0.0000 0.000 0.00 0.00 log_k_cyan_free 0.0000 0.000 0.00 0.00 log_k_cyan_free_bound 0.0000 0.000 0.00 0.00 log_k_cyan_bound_free 0.0000 0.000 0.00 0.00 log_k_JCZ38 0.0000 0.000 0.00 0.00 log_k_J9Z38 0.0000 0.000 0.00 0.00 log_k_JSE76 0.0000 0.000 0.00 0.00 f_cyan_ilr_1 0.6349 0.000 0.00 0.00 f_cyan_ilr_2 0.0000 1.797 0.00 0.00 f_JCZ38_qlogis 0.0000 0.000 13.84 0.00 f_JSE76_qlogis 0.0000 0.000 0.00 14.66 Starting values for error model parameters: a.1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2284 2275 -1120 Optimised parameters: est. lower upper cyan_free_0 102.7730 1.015e+02 1.041e+02 log_k_cyan_free -2.8530 -3.167e+00 -2.539e+00 log_k_cyan_free_bound -2.7326 -3.543e+00 -1.922e+00 log_k_cyan_bound_free -3.5582 -4.126e+00 -2.990e+00 log_k_JCZ38 -2.3810 -2.921e+00 -1.841e+00 log_k_J9Z38 -5.2301 -5.963e+00 -4.497e+00 log_k_JSE76 -3.0286 -4.286e+00 -1.771e+00 f_cyan_ilr_1 0.7081 3.733e-01 1.043e+00 f_cyan_ilr_2 0.5847 7.846e-03 1.162e+00 f_JCZ38_qlogis 9.5676 -1.323e+03 1.342e+03 f_JSE76_qlogis 3.7042 7.254e-02 7.336e+00 a.1 2.7222 2.532e+00 2.913e+00 SD.log_k_cyan_free 0.3338 1.086e-01 5.589e-01 SD.log_k_cyan_free_bound 0.8888 3.023e-01 1.475e+00 SD.log_k_cyan_bound_free 0.6220 2.063e-01 1.038e+00 SD.log_k_JCZ38 0.5221 1.334e-01 9.108e-01 SD.log_k_J9Z38 0.7104 1.371e-01 1.284e+00 SD.log_k_JSE76 1.3837 4.753e-01 2.292e+00 SD.f_cyan_ilr_1 0.3620 1.248e-01 5.992e-01 SD.f_cyan_ilr_2 0.4259 8.145e-02 7.704e-01 SD.f_JCZ38_qlogis 3.5332 -1.037e+05 1.037e+05 SD.f_JSE76_qlogis 1.6990 -2.771e-01 3.675e+00 Correlation: cyn_f_0 lg_k_c_ lg_k_cyn_f_ lg_k_cyn_b_ l__JCZ3 l__J9Z3 log_k_cyan_free 0.2126 log_k_cyan_free_bound 0.0894 0.0871 log_k_cyan_bound_free 0.0033 0.0410 0.0583 log_k_JCZ38 -0.0708 -0.0280 -0.0147 0.0019 log_k_J9Z38 -0.0535 -0.0138 0.0012 0.0148 0.0085 log_k_JSE76 -0.0066 -0.0030 -0.0021 -0.0005 0.1090 0.0010 f_cyan_ilr_1 -0.0364 -0.0157 -0.0095 -0.0015 0.0458 -0.0960 f_cyan_ilr_2 -0.3814 -0.1104 -0.0423 0.0146 0.1540 0.1526 f_JCZ38_qlogis 0.2507 0.0969 0.0482 -0.0097 -0.2282 -0.0363 f_JSE76_qlogis -0.1648 -0.0710 -0.0443 -0.0087 0.2002 0.0226 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 log_k_cyan_free log_k_cyan_free_bound log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 0.0001 f_cyan_ilr_2 0.0031 0.0586 f_JCZ38_qlogis 0.0023 -0.1867 -0.6255 f_JSE76_qlogis 0.0082 0.1356 0.4519 -0.7951 Random effects: est. lower upper SD.log_k_cyan_free 0.3338 1.086e-01 5.589e-01 SD.log_k_cyan_free_bound 0.8888 3.023e-01 1.475e+00 SD.log_k_cyan_bound_free 0.6220 2.063e-01 1.038e+00 SD.log_k_JCZ38 0.5221 1.334e-01 9.108e-01 SD.log_k_J9Z38 0.7104 1.371e-01 1.284e+00 SD.log_k_JSE76 1.3837 4.753e-01 2.292e+00 SD.f_cyan_ilr_1 0.3620 1.248e-01 5.992e-01 SD.f_cyan_ilr_2 0.4259 8.145e-02 7.704e-01 SD.f_JCZ38_qlogis 3.5332 -1.037e+05 1.037e+05 SD.f_JSE76_qlogis 1.6990 -2.771e-01 3.675e+00 Variance model: est. lower upper a.1 2.722 2.532 2.913 Backtransformed parameters: est. lower upper cyan_free_0 1.028e+02 1.015e+02 104.06475 k_cyan_free 5.767e-02 4.213e-02 0.07894 k_cyan_free_bound 6.505e-02 2.892e-02 0.14633 k_cyan_bound_free 2.849e-02 1.614e-02 0.05028 k_JCZ38 9.246e-02 5.390e-02 0.15859 k_J9Z38 5.353e-03 2.572e-03 0.01114 k_JSE76 4.838e-02 1.376e-02 0.17009 f_cyan_free_to_JCZ38 6.011e-01 5.028e-01 0.83792 f_cyan_free_to_J9Z38 2.208e-01 5.028e-01 0.83792 f_JCZ38_to_JSE76 9.999e-01 0.000e+00 1.00000 f_JSE76_to_JCZ38 9.760e-01 5.181e-01 0.99935 Estimated Eigenvalues of SFORB model(s): cyan_b1 cyan_b2 cyan_g 0.13942 0.01178 0.35948 Resulting formation fractions: ff cyan_free_JCZ38 6.011e-01 cyan_free_J9Z38 2.208e-01 cyan_free_sink 1.780e-01 cyan_free 1.000e+00 JCZ38_JSE76 9.999e-01 JCZ38_sink 6.996e-05 JSE76_JCZ38 9.760e-01 JSE76_sink 2.403e-02 Estimated disappearance times: DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 cyan 23.390 157.60 47.44 4.971 58.82 JCZ38 7.497 24.90 NA NA NA J9Z38 129.482 430.13 NA NA NA JSE76 14.326 47.59 NA NA NA </code></pre> <p></p> <caption> Hierarchical SFORB path 2 fit with two-component error </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.2 R version used for fitting: 4.2.2 Date of fit: Sat Jan 28 10:46:02 2023 Date of summary: Fri Feb 17 22:24:33 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 1723.343 s Using 300, 100 iterations and 10 chains Variance model: Two-component variance function Starting values for degradation parameters: cyan_free_0 log_k_cyan_free log_k_cyan_free_bound 101.751 -2.837 -3.016 log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 -3.660 -2.299 -5.313 log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 -3.699 0.672 5.873 f_JCZ38_qlogis f_JSE76_qlogis 13.216 13.338 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_free_0 log_k_cyan_free log_k_cyan_free_bound cyan_free_0 5.629 0.000 0.000 log_k_cyan_free 0.000 0.446 0.000 log_k_cyan_free_bound 0.000 0.000 1.449 log_k_cyan_bound_free 0.000 0.000 0.000 log_k_JCZ38 0.000 0.000 0.000 log_k_J9Z38 0.000 0.000 0.000 log_k_JSE76 0.000 0.000 0.000 f_cyan_ilr_1 0.000 0.000 0.000 f_cyan_ilr_2 0.000 0.000 0.000 f_JCZ38_qlogis 0.000 0.000 0.000 f_JSE76_qlogis 0.000 0.000 0.000 log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 cyan_free_0 0.000 0.0000 0.000 0.0000 log_k_cyan_free 0.000 0.0000 0.000 0.0000 log_k_cyan_free_bound 0.000 0.0000 0.000 0.0000 log_k_cyan_bound_free 1.213 0.0000 0.000 0.0000 log_k_JCZ38 0.000 0.7801 0.000 0.0000 log_k_J9Z38 0.000 0.0000 1.575 0.0000 log_k_JSE76 0.000 0.0000 0.000 0.8078 f_cyan_ilr_1 0.000 0.0000 0.000 0.0000 f_cyan_ilr_2 0.000 0.0000 0.000 0.0000 f_JCZ38_qlogis 0.000 0.0000 0.000 0.0000 f_JSE76_qlogis 0.000 0.0000 0.000 0.0000 f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis cyan_free_0 0.0000 0.00 0.00 0.00 log_k_cyan_free 0.0000 0.00 0.00 0.00 log_k_cyan_free_bound 0.0000 0.00 0.00 0.00 log_k_cyan_bound_free 0.0000 0.00 0.00 0.00 log_k_JCZ38 0.0000 0.00 0.00 0.00 log_k_J9Z38 0.0000 0.00 0.00 0.00 log_k_JSE76 0.0000 0.00 0.00 0.00 f_cyan_ilr_1 0.6519 0.00 0.00 0.00 f_cyan_ilr_2 0.0000 10.78 0.00 0.00 f_JCZ38_qlogis 0.0000 0.00 13.96 0.00 f_JSE76_qlogis 0.0000 0.00 0.00 14.69 Starting values for error model parameters: a.1 b.1 1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2240 2232 -1098 Optimised parameters: est. lower upper cyan_free_0 101.10205 98.99221 103.2119 log_k_cyan_free -3.16929 -3.61395 -2.7246 log_k_cyan_free_bound -3.38259 -3.63022 -3.1350 log_k_cyan_bound_free -3.81075 -4.13888 -3.4826 log_k_JCZ38 -2.42057 -3.00756 -1.8336 log_k_J9Z38 -5.07501 -5.85138 -4.2986 log_k_JSE76 -3.12442 -4.21277 -2.0361 f_cyan_ilr_1 0.70577 0.35788 1.0537 f_cyan_ilr_2 1.14824 0.15810 2.1384 f_JCZ38_qlogis 3.52245 0.43257 6.6123 f_JSE76_qlogis 5.65140 -21.22295 32.5257 a.1 2.07062 1.84329 2.2980 b.1 0.06227 0.05124 0.0733 SD.log_k_cyan_free 0.49468 0.18566 0.8037 SD.log_k_cyan_bound_free 0.28972 0.07188 0.5076 SD.log_k_JCZ38 0.58852 0.16800 1.0090 SD.log_k_J9Z38 0.82500 0.24730 1.4027 SD.log_k_JSE76 1.19201 0.40313 1.9809 SD.f_cyan_ilr_1 0.38534 0.13640 0.6343 SD.f_cyan_ilr_2 0.72463 0.10076 1.3485 SD.f_JCZ38_qlogis 1.38223 -0.20997 2.9744 SD.f_JSE76_qlogis 2.07989 -72.53027 76.6901 Correlation: cyn_f_0 lg_k_c_ lg_k_cyn_f_ lg_k_cyn_b_ l__JCZ3 l__J9Z3 log_k_cyan_free 0.1117 log_k_cyan_free_bound 0.1763 0.1828 log_k_cyan_bound_free 0.0120 0.0593 0.5030 log_k_JCZ38 -0.0459 -0.0230 -0.0931 -0.0337 log_k_J9Z38 -0.0381 -0.0123 -0.0139 0.0237 0.0063 log_k_JSE76 -0.0044 -0.0038 -0.0175 -0.0072 0.1120 0.0003 f_cyan_ilr_1 -0.0199 -0.0087 -0.0407 -0.0233 0.0268 -0.0552 f_cyan_ilr_2 -0.4806 -0.1015 -0.2291 -0.0269 0.1156 0.1113 f_JCZ38_qlogis 0.1805 0.0825 0.3085 0.0963 -0.1674 -0.0314 f_JSE76_qlogis -0.1586 -0.0810 -0.3560 -0.1563 0.2025 0.0278 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 log_k_cyan_free log_k_cyan_free_bound log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 0.0024 f_cyan_ilr_2 0.0087 0.0172 f_JCZ38_qlogis -0.0016 -0.1047 -0.4656 f_JSE76_qlogis 0.0119 0.1034 0.4584 -0.8137 Random effects: est. lower upper SD.log_k_cyan_free 0.4947 0.18566 0.8037 SD.log_k_cyan_bound_free 0.2897 0.07188 0.5076 SD.log_k_JCZ38 0.5885 0.16800 1.0090 SD.log_k_J9Z38 0.8250 0.24730 1.4027 SD.log_k_JSE76 1.1920 0.40313 1.9809 SD.f_cyan_ilr_1 0.3853 0.13640 0.6343 SD.f_cyan_ilr_2 0.7246 0.10076 1.3485 SD.f_JCZ38_qlogis 1.3822 -0.20997 2.9744 SD.f_JSE76_qlogis 2.0799 -72.53027 76.6901 Variance model: est. lower upper a.1 2.07062 1.84329 2.2980 b.1 0.06227 0.05124 0.0733 Backtransformed parameters: est. lower upper cyan_free_0 1.011e+02 9.899e+01 103.21190 k_cyan_free 4.203e-02 2.695e-02 0.06557 k_cyan_free_bound 3.396e-02 2.651e-02 0.04350 k_cyan_bound_free 2.213e-02 1.594e-02 0.03073 k_JCZ38 8.887e-02 4.941e-02 0.15984 k_J9Z38 6.251e-03 2.876e-03 0.01359 k_JSE76 4.396e-02 1.481e-02 0.13054 f_cyan_free_to_JCZ38 6.590e-01 5.557e-01 0.95365 f_cyan_free_to_J9Z38 2.429e-01 5.557e-01 0.95365 f_JCZ38_to_JSE76 9.713e-01 6.065e-01 0.99866 f_JSE76_to_JCZ38 9.965e-01 6.067e-10 1.00000 Estimated Eigenvalues of SFORB model(s): cyan_b1 cyan_b2 cyan_g 0.08749 0.01063 0.40855 Resulting formation fractions: ff cyan_free_JCZ38 0.65905 cyan_free_J9Z38 0.24291 cyan_free_sink 0.09805 cyan_free 1.00000 JCZ38_JSE76 0.97132 JCZ38_sink 0.02868 JSE76_JCZ38 0.99650 JSE76_sink 0.00350 Estimated disappearance times: DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 cyan 24.91 167.16 50.32 7.922 65.19 JCZ38 7.80 25.91 NA NA NA J9Z38 110.89 368.36 NA NA NA JSE76 15.77 52.38 NA NA NA </code></pre> <p></p> </div> <div class="section level4"> <h4 id="pathway-2-refined-fits">Pathway 2, refined fits<a class="anchor" aria-label="anchor" href="#pathway-2-refined-fits"></a> </h4> <caption> Hierarchical FOMC path 2 fit with reduced random effects, two-component error </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.2 R version used for fitting: 4.2.2 Date of fit: Sat Jan 28 11:18:41 2023 Date of summary: Fri Feb 17 22:24:33 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 1957.271 s Using 300, 100 iterations and 10 chains Variance model: Two-component variance function Starting values for degradation parameters: cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 101.9028 -1.9055 -5.0249 -2.5646 0.6807 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta 4.8883 16.0676 9.3923 -0.1346 3.0364 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 cyan_0 6.321 0.000 0.000 0.000 0.0000 log_k_JCZ38 0.000 1.392 0.000 0.000 0.0000 log_k_J9Z38 0.000 0.000 1.561 0.000 0.0000 log_k_JSE76 0.000 0.000 0.000 3.614 0.0000 f_cyan_ilr_1 0.000 0.000 0.000 0.000 0.6339 f_cyan_ilr_2 0.000 0.000 0.000 0.000 0.0000 f_JCZ38_qlogis 0.000 0.000 0.000 0.000 0.0000 f_JSE76_qlogis 0.000 0.000 0.000 0.000 0.0000 log_alpha 0.000 0.000 0.000 0.000 0.0000 log_beta 0.000 0.000 0.000 0.000 0.0000 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta cyan_0 0.00 0.00 0.00 0.0000 0.0000 log_k_JCZ38 0.00 0.00 0.00 0.0000 0.0000 log_k_J9Z38 0.00 0.00 0.00 0.0000 0.0000 log_k_JSE76 0.00 0.00 0.00 0.0000 0.0000 f_cyan_ilr_1 0.00 0.00 0.00 0.0000 0.0000 f_cyan_ilr_2 10.41 0.00 0.00 0.0000 0.0000 f_JCZ38_qlogis 0.00 12.24 0.00 0.0000 0.0000 f_JSE76_qlogis 0.00 0.00 15.13 0.0000 0.0000 log_alpha 0.00 0.00 0.00 0.3701 0.0000 log_beta 0.00 0.00 0.00 0.0000 0.5662 Starting values for error model parameters: a.1 b.1 1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2251 2244 -1106 Optimised parameters: est. lower upper cyan_0 101.05768 NA NA log_k_JCZ38 -2.73252 NA NA log_k_J9Z38 -5.07399 NA NA log_k_JSE76 -3.52863 NA NA f_cyan_ilr_1 0.72176 NA NA f_cyan_ilr_2 1.34610 NA NA f_JCZ38_qlogis 2.08337 NA NA f_JSE76_qlogis 1590.31880 NA NA log_alpha -0.09336 NA NA log_beta 3.10191 NA NA a.1 2.08557 1.85439 2.31675 b.1 0.06998 0.05800 0.08197 SD.log_k_JCZ38 1.20053 0.43329 1.96777 SD.log_k_J9Z38 0.85854 0.26708 1.45000 SD.log_k_JSE76 0.62528 0.16061 1.08995 SD.f_cyan_ilr_1 0.35190 0.12340 0.58039 SD.f_cyan_ilr_2 0.85385 0.15391 1.55378 SD.log_alpha 0.28971 0.08718 0.49225 SD.log_beta 0.31614 0.05938 0.57290 Correlation is not available Random effects: est. lower upper SD.log_k_JCZ38 1.2005 0.43329 1.9678 SD.log_k_J9Z38 0.8585 0.26708 1.4500 SD.log_k_JSE76 0.6253 0.16061 1.0900 SD.f_cyan_ilr_1 0.3519 0.12340 0.5804 SD.f_cyan_ilr_2 0.8538 0.15391 1.5538 SD.log_alpha 0.2897 0.08718 0.4923 SD.log_beta 0.3161 0.05938 0.5729 Variance model: est. lower upper a.1 2.08557 1.854 2.31675 b.1 0.06998 0.058 0.08197 Backtransformed parameters: est. lower upper cyan_0 1.011e+02 NA NA k_JCZ38 6.506e-02 NA NA k_J9Z38 6.257e-03 NA NA k_JSE76 2.935e-02 NA NA f_cyan_to_JCZ38 6.776e-01 NA NA f_cyan_to_J9Z38 2.442e-01 NA NA f_JCZ38_to_JSE76 8.893e-01 NA NA f_JSE76_to_JCZ38 1.000e+00 NA NA alpha 9.109e-01 NA NA beta 2.224e+01 NA NA Resulting formation fractions: ff cyan_JCZ38 0.67761 cyan_J9Z38 0.24417 cyan_sink 0.07822 JCZ38_JSE76 0.88928 JCZ38_sink 0.11072 JSE76_JCZ38 1.00000 JSE76_sink 0.00000 Estimated disappearance times: DT50 DT90 DT50back cyan 25.36 256.37 77.18 JCZ38 10.65 35.39 NA J9Z38 110.77 367.98 NA JSE76 23.62 78.47 NA </code></pre> <p></p> <caption> Hierarchical DFOP path 2 fit with reduced random effects, constant variance </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.2 R version used for fitting: 4.2.2 Date of fit: Sat Jan 28 11:16:32 2023 Date of summary: Fri Feb 17 22:24:33 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 1828.403 s Using 300, 100 iterations and 10 chains Variance model: Constant variance Starting values for degradation parameters: cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 102.4358 -2.3107 -5.3123 -3.7120 0.6753 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 1.1462 12.4095 12.3630 -1.9317 -4.4557 g_qlogis -0.5648 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 cyan_0 4.594 0.0000 0.000 0.0 0.0000 log_k_JCZ38 0.000 0.7966 0.000 0.0 0.0000 log_k_J9Z38 0.000 0.0000 1.561 0.0 0.0000 log_k_JSE76 0.000 0.0000 0.000 0.8 0.0000 f_cyan_ilr_1 0.000 0.0000 0.000 0.0 0.6349 f_cyan_ilr_2 0.000 0.0000 0.000 0.0 0.0000 f_JCZ38_qlogis 0.000 0.0000 0.000 0.0 0.0000 f_JSE76_qlogis 0.000 0.0000 0.000 0.0 0.0000 log_k1 0.000 0.0000 0.000 0.0 0.0000 log_k2 0.000 0.0000 0.000 0.0 0.0000 g_qlogis 0.000 0.0000 0.000 0.0 0.0000 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 cyan_0 0.000 0.00 0.0 0.000 0.0000 log_k_JCZ38 0.000 0.00 0.0 0.000 0.0000 log_k_J9Z38 0.000 0.00 0.0 0.000 0.0000 log_k_JSE76 0.000 0.00 0.0 0.000 0.0000 f_cyan_ilr_1 0.000 0.00 0.0 0.000 0.0000 f_cyan_ilr_2 1.797 0.00 0.0 0.000 0.0000 f_JCZ38_qlogis 0.000 13.85 0.0 0.000 0.0000 f_JSE76_qlogis 0.000 0.00 14.1 0.000 0.0000 log_k1 0.000 0.00 0.0 1.106 0.0000 log_k2 0.000 0.00 0.0 0.000 0.6141 g_qlogis 0.000 0.00 0.0 0.000 0.0000 g_qlogis cyan_0 0.000 log_k_JCZ38 0.000 log_k_J9Z38 0.000 log_k_JSE76 0.000 f_cyan_ilr_1 0.000 f_cyan_ilr_2 0.000 f_JCZ38_qlogis 0.000 f_JSE76_qlogis 0.000 log_k1 0.000 log_k2 0.000 g_qlogis 1.595 Starting values for error model parameters: a.1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2282 2274 -1121 Optimised parameters: est. lower upper cyan_0 102.5254 NA NA log_k_JCZ38 -2.9358 NA NA log_k_J9Z38 -5.1424 NA NA log_k_JSE76 -3.6458 NA NA f_cyan_ilr_1 0.6957 NA NA f_cyan_ilr_2 0.6635 NA NA f_JCZ38_qlogis 4984.8163 NA NA f_JSE76_qlogis 1.9415 NA NA log_k1 -1.9456 NA NA log_k2 -4.4705 NA NA g_qlogis -0.5117 NA NA a.1 2.7455 2.55392 2.9370 SD.log_k_JCZ38 1.3163 0.47635 2.1563 SD.log_k_J9Z38 0.7162 0.16133 1.2711 SD.log_k_JSE76 0.6457 0.15249 1.1390 SD.f_cyan_ilr_1 0.3424 0.11714 0.5677 SD.f_cyan_ilr_2 0.4524 0.09709 0.8077 SD.log_k1 0.7353 0.25445 1.2161 SD.log_k2 0.5137 0.18206 0.8453 SD.g_qlogis 0.9857 0.35651 1.6148 Correlation is not available Random effects: est. lower upper SD.log_k_JCZ38 1.3163 0.47635 2.1563 SD.log_k_J9Z38 0.7162 0.16133 1.2711 SD.log_k_JSE76 0.6457 0.15249 1.1390 SD.f_cyan_ilr_1 0.3424 0.11714 0.5677 SD.f_cyan_ilr_2 0.4524 0.09709 0.8077 SD.log_k1 0.7353 0.25445 1.2161 SD.log_k2 0.5137 0.18206 0.8453 SD.g_qlogis 0.9857 0.35651 1.6148 Variance model: est. lower upper a.1 2.745 2.554 2.937 Backtransformed parameters: est. lower upper cyan_0 1.025e+02 NA NA k_JCZ38 5.309e-02 NA NA k_J9Z38 5.844e-03 NA NA k_JSE76 2.610e-02 NA NA f_cyan_to_JCZ38 6.079e-01 NA NA f_cyan_to_J9Z38 2.272e-01 NA NA f_JCZ38_to_JSE76 1.000e+00 NA NA f_JSE76_to_JCZ38 8.745e-01 NA NA k1 1.429e-01 NA NA k2 1.144e-02 NA NA g 3.748e-01 NA NA Resulting formation fractions: ff cyan_JCZ38 0.6079 cyan_J9Z38 0.2272 cyan_sink 0.1649 JCZ38_JSE76 1.0000 JCZ38_sink 0.0000 JSE76_JCZ38 0.8745 JSE76_sink 0.1255 Estimated disappearance times: DT50 DT90 DT50back DT50_k1 DT50_k2 cyan 22.29 160.20 48.22 4.85 60.58 JCZ38 13.06 43.37 NA NA NA J9Z38 118.61 394.02 NA NA NA JSE76 26.56 88.22 NA NA NA </code></pre> <p></p> <caption> Hierarchical DFOP path 2 fit with reduced random effects, two-component error </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.2 R version used for fitting: 4.2.2 Date of fit: Sat Jan 28 11:22:28 2023 Date of summary: Fri Feb 17 22:24:33 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 2183.989 s Using 300, 100 iterations and 10 chains Variance model: Two-component variance function Starting values for degradation parameters: cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 101.7523 -1.5948 -5.0119 -2.2723 0.6719 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 5.1681 12.8238 12.4130 -2.0057 -4.5526 g_qlogis -0.5805 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 cyan_0 5.627 0.000 0.000 0.000 0.0000 log_k_JCZ38 0.000 2.327 0.000 0.000 0.0000 log_k_J9Z38 0.000 0.000 1.664 0.000 0.0000 log_k_JSE76 0.000 0.000 0.000 4.566 0.0000 f_cyan_ilr_1 0.000 0.000 0.000 0.000 0.6519 f_cyan_ilr_2 0.000 0.000 0.000 0.000 0.0000 f_JCZ38_qlogis 0.000 0.000 0.000 0.000 0.0000 f_JSE76_qlogis 0.000 0.000 0.000 0.000 0.0000 log_k1 0.000 0.000 0.000 0.000 0.0000 log_k2 0.000 0.000 0.000 0.000 0.0000 g_qlogis 0.000 0.000 0.000 0.000 0.0000 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 cyan_0 0.0 0.00 0.00 0.0000 0.0000 log_k_JCZ38 0.0 0.00 0.00 0.0000 0.0000 log_k_J9Z38 0.0 0.00 0.00 0.0000 0.0000 log_k_JSE76 0.0 0.00 0.00 0.0000 0.0000 f_cyan_ilr_1 0.0 0.00 0.00 0.0000 0.0000 f_cyan_ilr_2 10.1 0.00 0.00 0.0000 0.0000 f_JCZ38_qlogis 0.0 13.99 0.00 0.0000 0.0000 f_JSE76_qlogis 0.0 0.00 14.15 0.0000 0.0000 log_k1 0.0 0.00 0.00 0.8452 0.0000 log_k2 0.0 0.00 0.00 0.0000 0.5968 g_qlogis 0.0 0.00 0.00 0.0000 0.0000 g_qlogis cyan_0 0.000 log_k_JCZ38 0.000 log_k_J9Z38 0.000 log_k_JSE76 0.000 f_cyan_ilr_1 0.000 f_cyan_ilr_2 0.000 f_JCZ38_qlogis 0.000 f_JSE76_qlogis 0.000 log_k1 0.000 log_k2 0.000 g_qlogis 1.691 Starting values for error model parameters: a.1 b.1 1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2232 2224 -1096 Optimised parameters: est. lower upper cyan_0 101.20051 NA NA log_k_JCZ38 -2.93542 NA NA log_k_J9Z38 -5.03151 NA NA log_k_JSE76 -3.67679 NA NA f_cyan_ilr_1 0.67290 NA NA f_cyan_ilr_2 0.99787 NA NA f_JCZ38_qlogis 348.32484 NA NA f_JSE76_qlogis 1.87846 NA NA log_k1 -2.32738 NA NA log_k2 -4.61295 NA NA g_qlogis -0.38342 NA NA a.1 2.06184 1.83746 2.28622 b.1 0.06329 0.05211 0.07447 SD.log_k_JCZ38 1.29042 0.47468 2.10617 SD.log_k_J9Z38 0.84235 0.25903 1.42566 SD.log_k_JSE76 0.56930 0.13934 0.99926 SD.f_cyan_ilr_1 0.35183 0.12298 0.58068 SD.f_cyan_ilr_2 0.77269 0.17908 1.36631 SD.log_k2 0.28549 0.09210 0.47888 SD.g_qlogis 0.93830 0.34568 1.53093 Correlation is not available Random effects: est. lower upper SD.log_k_JCZ38 1.2904 0.4747 2.1062 SD.log_k_J9Z38 0.8423 0.2590 1.4257 SD.log_k_JSE76 0.5693 0.1393 0.9993 SD.f_cyan_ilr_1 0.3518 0.1230 0.5807 SD.f_cyan_ilr_2 0.7727 0.1791 1.3663 SD.log_k2 0.2855 0.0921 0.4789 SD.g_qlogis 0.9383 0.3457 1.5309 Variance model: est. lower upper a.1 2.06184 1.83746 2.28622 b.1 0.06329 0.05211 0.07447 Backtransformed parameters: est. lower upper cyan_0 1.012e+02 NA NA k_JCZ38 5.311e-02 NA NA k_J9Z38 6.529e-03 NA NA k_JSE76 2.530e-02 NA NA f_cyan_to_JCZ38 6.373e-01 NA NA f_cyan_to_J9Z38 2.461e-01 NA NA f_JCZ38_to_JSE76 1.000e+00 NA NA f_JSE76_to_JCZ38 8.674e-01 NA NA k1 9.755e-02 NA NA k2 9.922e-03 NA NA g 4.053e-01 NA NA Resulting formation fractions: ff cyan_JCZ38 0.6373 cyan_J9Z38 0.2461 cyan_sink 0.1167 JCZ38_JSE76 1.0000 JCZ38_sink 0.0000 JSE76_JCZ38 0.8674 JSE76_sink 0.1326 Estimated disappearance times: DT50 DT90 DT50back DT50_k1 DT50_k2 cyan 24.93 179.68 54.09 7.105 69.86 JCZ38 13.05 43.36 NA NA NA J9Z38 106.16 352.67 NA NA NA JSE76 27.39 91.00 NA NA NA </code></pre> <p></p> <caption> Hierarchical SFORB path 2 fit with reduced random effects, constant variance </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.2 R version used for fitting: 4.2.2 Date of fit: Sat Jan 28 11:17:37 2023 Date of summary: Fri Feb 17 22:24:33 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 1893.29 s Using 300, 100 iterations and 10 chains Variance model: Constant variance Starting values for degradation parameters: cyan_free_0 log_k_cyan_free log_k_cyan_free_bound 102.4394 -2.7673 -2.8942 log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 -3.6201 -2.3107 -5.3123 log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 -3.7120 0.6754 1.1448 f_JCZ38_qlogis f_JSE76_qlogis 13.2672 13.3538 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_free_0 log_k_cyan_free log_k_cyan_free_bound cyan_free_0 4.589 0.0000 0.00 log_k_cyan_free 0.000 0.4849 0.00 log_k_cyan_free_bound 0.000 0.0000 1.62 log_k_cyan_bound_free 0.000 0.0000 0.00 log_k_JCZ38 0.000 0.0000 0.00 log_k_J9Z38 0.000 0.0000 0.00 log_k_JSE76 0.000 0.0000 0.00 f_cyan_ilr_1 0.000 0.0000 0.00 f_cyan_ilr_2 0.000 0.0000 0.00 f_JCZ38_qlogis 0.000 0.0000 0.00 f_JSE76_qlogis 0.000 0.0000 0.00 log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 cyan_free_0 0.000 0.0000 0.000 0.0 log_k_cyan_free 0.000 0.0000 0.000 0.0 log_k_cyan_free_bound 0.000 0.0000 0.000 0.0 log_k_cyan_bound_free 1.197 0.0000 0.000 0.0 log_k_JCZ38 0.000 0.7966 0.000 0.0 log_k_J9Z38 0.000 0.0000 1.561 0.0 log_k_JSE76 0.000 0.0000 0.000 0.8 f_cyan_ilr_1 0.000 0.0000 0.000 0.0 f_cyan_ilr_2 0.000 0.0000 0.000 0.0 f_JCZ38_qlogis 0.000 0.0000 0.000 0.0 f_JSE76_qlogis 0.000 0.0000 0.000 0.0 f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis cyan_free_0 0.0000 0.000 0.00 0.00 log_k_cyan_free 0.0000 0.000 0.00 0.00 log_k_cyan_free_bound 0.0000 0.000 0.00 0.00 log_k_cyan_bound_free 0.0000 0.000 0.00 0.00 log_k_JCZ38 0.0000 0.000 0.00 0.00 log_k_J9Z38 0.0000 0.000 0.00 0.00 log_k_JSE76 0.0000 0.000 0.00 0.00 f_cyan_ilr_1 0.6349 0.000 0.00 0.00 f_cyan_ilr_2 0.0000 1.797 0.00 0.00 f_JCZ38_qlogis 0.0000 0.000 13.84 0.00 f_JSE76_qlogis 0.0000 0.000 0.00 14.66 Starting values for error model parameters: a.1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2279 2272 -1120 Optimised parameters: est. lower upper cyan_free_0 102.5621 NA NA log_k_cyan_free -2.8531 NA NA log_k_cyan_free_bound -2.6916 NA NA log_k_cyan_bound_free -3.5032 NA NA log_k_JCZ38 -2.9436 NA NA log_k_J9Z38 -5.1140 NA NA log_k_JSE76 -3.6472 NA NA f_cyan_ilr_1 0.6887 NA NA f_cyan_ilr_2 0.6874 NA NA f_JCZ38_qlogis 4063.6389 NA NA f_JSE76_qlogis 1.9556 NA NA a.1 2.7460 2.55451 2.9376 SD.log_k_cyan_free 0.3131 0.09841 0.5277 SD.log_k_cyan_free_bound 0.8850 0.29909 1.4710 SD.log_k_cyan_bound_free 0.6167 0.20391 1.0295 SD.log_k_JCZ38 1.3555 0.49101 2.2200 SD.log_k_J9Z38 0.7200 0.16166 1.2783 SD.log_k_JSE76 0.6252 0.14619 1.1042 SD.f_cyan_ilr_1 0.3386 0.11447 0.5627 SD.f_cyan_ilr_2 0.4699 0.09810 0.8417 Correlation is not available Random effects: est. lower upper SD.log_k_cyan_free 0.3131 0.09841 0.5277 SD.log_k_cyan_free_bound 0.8850 0.29909 1.4710 SD.log_k_cyan_bound_free 0.6167 0.20391 1.0295 SD.log_k_JCZ38 1.3555 0.49101 2.2200 SD.log_k_J9Z38 0.7200 0.16166 1.2783 SD.log_k_JSE76 0.6252 0.14619 1.1042 SD.f_cyan_ilr_1 0.3386 0.11447 0.5627 SD.f_cyan_ilr_2 0.4699 0.09810 0.8417 Variance model: est. lower upper a.1 2.746 2.555 2.938 Backtransformed parameters: est. lower upper cyan_free_0 1.026e+02 NA NA k_cyan_free 5.767e-02 NA NA k_cyan_free_bound 6.777e-02 NA NA k_cyan_bound_free 3.010e-02 NA NA k_JCZ38 5.267e-02 NA NA k_J9Z38 6.012e-03 NA NA k_JSE76 2.606e-02 NA NA f_cyan_free_to_JCZ38 6.089e-01 NA NA f_cyan_free_to_J9Z38 2.299e-01 NA NA f_JCZ38_to_JSE76 1.000e+00 NA NA f_JSE76_to_JCZ38 8.761e-01 NA NA Estimated Eigenvalues of SFORB model(s): cyan_b1 cyan_b2 cyan_g 0.1434 0.0121 0.3469 Resulting formation fractions: ff cyan_free_JCZ38 0.6089 cyan_free_J9Z38 0.2299 cyan_free_sink 0.1612 cyan_free 1.0000 JCZ38_JSE76 1.0000 JCZ38_sink 0.0000 JSE76_JCZ38 0.8761 JSE76_sink 0.1239 Estimated disappearance times: DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 cyan 23.94 155.06 46.68 4.832 57.28 JCZ38 13.16 43.71 NA NA NA J9Z38 115.30 383.02 NA NA NA JSE76 26.59 88.35 NA NA NA </code></pre> <p></p> <caption> Hierarchical SFORB path 2 fit with reduced random effects, two-component error </caption> <pre><code> saemix version used for fitting: 3.2 mkin version used for pre-fitting: 1.2.2 R version used for fitting: 4.2.2 Date of fit: Sat Jan 28 11:21:01 2023 Date of summary: Fri Feb 17 22:24:33 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 2097.842 s Using 300, 100 iterations and 10 chains Variance model: Two-component variance function Starting values for degradation parameters: cyan_free_0 log_k_cyan_free log_k_cyan_free_bound 101.751 -2.837 -3.016 log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 -3.660 -2.299 -5.313 log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 -3.699 0.672 5.873 f_JCZ38_qlogis f_JSE76_qlogis 13.216 13.338 Fixed degradation parameter values: None Starting values for random effects (square root of initial entries in omega): cyan_free_0 log_k_cyan_free log_k_cyan_free_bound cyan_free_0 5.629 0.000 0.000 log_k_cyan_free 0.000 0.446 0.000 log_k_cyan_free_bound 0.000 0.000 1.449 log_k_cyan_bound_free 0.000 0.000 0.000 log_k_JCZ38 0.000 0.000 0.000 log_k_J9Z38 0.000 0.000 0.000 log_k_JSE76 0.000 0.000 0.000 f_cyan_ilr_1 0.000 0.000 0.000 f_cyan_ilr_2 0.000 0.000 0.000 f_JCZ38_qlogis 0.000 0.000 0.000 f_JSE76_qlogis 0.000 0.000 0.000 log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 cyan_free_0 0.000 0.0000 0.000 0.0000 log_k_cyan_free 0.000 0.0000 0.000 0.0000 log_k_cyan_free_bound 0.000 0.0000 0.000 0.0000 log_k_cyan_bound_free 1.213 0.0000 0.000 0.0000 log_k_JCZ38 0.000 0.7801 0.000 0.0000 log_k_J9Z38 0.000 0.0000 1.575 0.0000 log_k_JSE76 0.000 0.0000 0.000 0.8078 f_cyan_ilr_1 0.000 0.0000 0.000 0.0000 f_cyan_ilr_2 0.000 0.0000 0.000 0.0000 f_JCZ38_qlogis 0.000 0.0000 0.000 0.0000 f_JSE76_qlogis 0.000 0.0000 0.000 0.0000 f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis cyan_free_0 0.0000 0.00 0.00 0.00 log_k_cyan_free 0.0000 0.00 0.00 0.00 log_k_cyan_free_bound 0.0000 0.00 0.00 0.00 log_k_cyan_bound_free 0.0000 0.00 0.00 0.00 log_k_JCZ38 0.0000 0.00 0.00 0.00 log_k_J9Z38 0.0000 0.00 0.00 0.00 log_k_JSE76 0.0000 0.00 0.00 0.00 f_cyan_ilr_1 0.6519 0.00 0.00 0.00 f_cyan_ilr_2 0.0000 10.78 0.00 0.00 f_JCZ38_qlogis 0.0000 0.00 13.96 0.00 f_JSE76_qlogis 0.0000 0.00 0.00 14.69 Starting values for error model parameters: a.1 b.1 1 1 Results: Likelihood computed by importance sampling AIC BIC logLik 2236 2228 -1098 Optimised parameters: est. lower upper cyan_free_0 100.72760 NA NA log_k_cyan_free -3.18281 NA NA log_k_cyan_free_bound -3.37924 NA NA log_k_cyan_bound_free -3.77107 NA NA log_k_JCZ38 -2.92811 NA NA log_k_J9Z38 -5.02759 NA NA log_k_JSE76 -3.65835 NA NA f_cyan_ilr_1 0.67390 NA NA f_cyan_ilr_2 1.15106 NA NA f_JCZ38_qlogis 827.82299 NA NA f_JSE76_qlogis 1.83064 NA NA a.1 2.06921 1.84443 2.29399 b.1 0.06391 0.05267 0.07515 SD.log_k_cyan_free 0.50518 0.18962 0.82075 SD.log_k_cyan_bound_free 0.30991 0.08170 0.53813 SD.log_k_JCZ38 1.26661 0.46578 2.06744 SD.log_k_J9Z38 0.88272 0.27813 1.48730 SD.log_k_JSE76 0.53050 0.12561 0.93538 SD.f_cyan_ilr_1 0.35547 0.12461 0.58633 SD.f_cyan_ilr_2 0.91446 0.20131 1.62761 Correlation is not available Random effects: est. lower upper SD.log_k_cyan_free 0.5052 0.1896 0.8207 SD.log_k_cyan_bound_free 0.3099 0.0817 0.5381 SD.log_k_JCZ38 1.2666 0.4658 2.0674 SD.log_k_J9Z38 0.8827 0.2781 1.4873 SD.log_k_JSE76 0.5305 0.1256 0.9354 SD.f_cyan_ilr_1 0.3555 0.1246 0.5863 SD.f_cyan_ilr_2 0.9145 0.2013 1.6276 Variance model: est. lower upper a.1 2.06921 1.84443 2.29399 b.1 0.06391 0.05267 0.07515 Backtransformed parameters: est. lower upper cyan_free_0 1.007e+02 NA NA k_cyan_free 4.147e-02 NA NA k_cyan_free_bound 3.407e-02 NA NA k_cyan_bound_free 2.303e-02 NA NA k_JCZ38 5.350e-02 NA NA k_J9Z38 6.555e-03 NA NA k_JSE76 2.578e-02 NA NA f_cyan_free_to_JCZ38 6.505e-01 NA NA f_cyan_free_to_J9Z38 2.508e-01 NA NA f_JCZ38_to_JSE76 1.000e+00 NA NA f_JSE76_to_JCZ38 8.618e-01 NA NA Estimated Eigenvalues of SFORB model(s): cyan_b1 cyan_b2 cyan_g 0.08768 0.01089 0.39821 Resulting formation fractions: ff cyan_free_JCZ38 0.65053 cyan_free_J9Z38 0.25082 cyan_free_sink 0.09864 cyan_free 1.00000 JCZ38_JSE76 1.00000 JCZ38_sink 0.00000 JSE76_JCZ38 0.86184 JSE76_sink 0.13816 Estimated disappearance times: DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 cyan 25.32 164.79 49.61 7.906 63.64 JCZ38 12.96 43.04 NA NA NA J9Z38 105.75 351.29 NA NA NA JSE76 26.89 89.33 NA NA NA </code></pre> <p></p> </div> </div> <div class="section level3"> <h3 id="session-info">Session info<a class="anchor" aria-label="anchor" href="#session-info"></a> </h3> <pre><code>R version 4.2.2 Patched (2022-11-10 r83330) Platform: x86_64-pc-linux-gnu (64-bit) Running under: Debian GNU/Linux bookworm/sid Matrix products: default BLAS: /usr/lib/x86_64-linux-gnu/openblas-serial/libblas.so.3 LAPACK: /usr/lib/x86_64-linux-gnu/openblas-serial/libopenblas-r0.3.21.so locale: [1] LC_CTYPE=de_DE.UTF-8 LC_NUMERIC=C [3] LC_TIME=de_DE.UTF-8 LC_COLLATE=de_DE.UTF-8 [5] LC_MONETARY=de_DE.UTF-8 LC_MESSAGES=de_DE.UTF-8 [7] LC_PAPER=de_DE.UTF-8 LC_NAME=C [9] LC_ADDRESS=C LC_TELEPHONE=C [11] LC_MEASUREMENT=de_DE.UTF-8 LC_IDENTIFICATION=C attached base packages: [1] parallel stats graphics grDevices utils datasets methods [8] base other attached packages: [1] saemix_3.2 npde_3.3 knitr_1.41 mkin_1.2.3 loaded via a namespace (and not attached): [1] pillar_1.8.1 bslib_0.4.2 compiler_4.2.2 jquerylib_0.1.4 [5] tools_4.2.2 mclust_6.0.0 digest_0.6.31 tibble_3.1.8 [9] jsonlite_1.8.4 evaluate_0.19 memoise_2.0.1 lifecycle_1.0.3 [13] nlme_3.1-162 gtable_0.3.1 lattice_0.20-45 pkgconfig_2.0.3 [17] rlang_1.0.6 DBI_1.1.3 cli_3.5.0 yaml_2.3.6 [21] pkgdown_2.0.7 xfun_0.35 fastmap_1.1.0 gridExtra_2.3 [25] dplyr_1.0.10 stringr_1.5.0 generics_0.1.3 desc_1.4.2 [29] fs_1.5.2 vctrs_0.5.1 sass_0.4.4 systemfonts_1.0.4 [33] tidyselect_1.2.0 rprojroot_2.0.3 lmtest_0.9-40 grid_4.2.2 [37] inline_0.3.19 glue_1.6.2 R6_2.5.1 textshaping_0.3.6 [41] fansi_1.0.3 rmarkdown_2.19 purrr_1.0.0 ggplot2_3.4.0 [45] magrittr_2.0.3 scales_1.2.1 htmltools_0.5.4 assertthat_0.2.1 [49] colorspace_2.0-3 ragg_1.2.4 utf8_1.2.2 stringi_1.7.8 [53] munsell_0.5.0 cachem_1.0.6 zoo_1.8-11 </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: 64940452 kB</code></pre> </div> </div> </div> <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar"> <nav id="toc" data-toggle="toc"><h2 data-toc-skip>Contents</h2> </nav> </div> </div> <footer><div class="copyright"> <p></p> <p>Developed by Johannes Ranke.</p> </div> <div class="pkgdown"> <p></p> <p>Site built with <a 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