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| author | Johannes Ranke <johannes.ranke@jrwb.de> | 2025-02-13 16:30:31 +0100 |
|---|---|---|
| committer | Johannes Ranke <johannes.ranke@jrwb.de> | 2025-02-13 19:20:04 +0100 |
| commit | 6476f5f49b373cd4cf05f2e73389df83e437d597 (patch) | |
| tree | d0ef15c0d2ab42d246f7c8ebaeb4e63f4a928699 /docs/dev/articles/prebuilt | |
| parent | 786e50724d9d7cc8fe04171d28ed09ea8d698cc3 (diff) | |
Axis legend formatting, update vignettes
Diffstat (limited to 'docs/dev/articles/prebuilt')
38 files changed, 0 insertions, 9940 deletions
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</li> - <li> - <a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> - </li> - </ul> -</li> -<li> - <a href="../../news/index.html">News</a> -</li> - </ul> -<ul class="nav navbar-nav navbar-right"> -<li> - <a href="https://github.com/jranke/mkin/" class="external-link"> - <span class="fab fa-github fa-lg"></span> - - </a> -</li> - </ul> -</div> -<!--/.nav-collapse --> - </div> -<!--/.container --> -</div> -<!--/.navbar --> - - - - </header><div class="row"> - <div class="col-md-9 contents"> - <div class="page-header toc-ignore"> - <h1 data-toc-skip>Testing hierarchical pathway kinetics with -residue data on cyantraniliprole</h1> - <h4 data-toc-skip class="author">Johannes -Ranke</h4> - - <h4 data-toc-skip class="date">Last change on 20 April 2023, -last compiled on 20 April 2023</h4> - - <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/prebuilt/2022_cyan_pathway.rmd" class="external-link"><code>vignettes/prebuilt/2022_cyan_pathway.rmd</code></a></small> - <div class="hidden name"><code>2022_cyan_pathway.rmd</code></div> - - </div> - - - -<div class="section level2"> -<h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#introduction"></a> -</h2> -<p>The purpose of this document is to test demonstrate how nonlinear -hierarchical models (NLHM) based on the parent degradation models SFO, -FOMC, DFOP and HS, with serial formation of two or more metabolites can -be fitted with the mkin package.</p> -<p>It was assembled in the course of work package 1.2 of Project Number -173340 (Application of nonlinear hierarchical models to the kinetic -evaluation of chemical degradation data) of the German Environment -Agency carried out in 2022 and 2023.</p> -<p>The mkin package is used in version 1.2.4 which is currently under -development. The newly introduced functionality that is used here is a -simplification of excluding random effects for a set of fits based on a -related set of fits with a reduced model, and the documentation of the -starting parameters of the fit, so that all starting parameters of -<code>saem</code> fits are now listed in the summary. The -<code>saemix</code> package is used as a backend for fitting the NLHM, -but is also loaded to make the convergence plot function available.</p> -<p>This document is processed with the <code>knitr</code> package, which -also provides the <code>kable</code> function that is used to improve -the display of tabular data in R markdown documents. For parallel -processing, the <code>parallel</code> package is used.</p> -<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://pkgdown.jrwb.de/mkin/">mkin</a></span><span class="op">)</span></span> -<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://yihui.org/knitr/" class="external-link">knitr</a></span><span class="op">)</span></span> -<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">saemix</span><span class="op">)</span></span> -<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">parallel</span><span class="op">)</span></span> -<span><span class="va">n_cores</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/detectCores.html" class="external-link">detectCores</a></span><span class="op">(</span><span class="op">)</span></span> -<span></span> -<span><span class="co"># We need to start a new cluster after defining a compiled model that is</span></span> -<span><span class="co"># saved as a DLL to the user directory, therefore we define a function</span></span> -<span><span class="co"># This is used again after defining the pathway model</span></span> -<span><span class="va">start_cluster</span> <span class="op"><-</span> <span class="kw">function</span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span> <span class="op">{</span></span> -<span> <span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/Sys.info.html" class="external-link">Sys.info</a></span><span class="op">(</span><span class="op">)</span><span class="op">[</span><span class="st">"sysname"</span><span class="op">]</span> <span class="op">==</span> <span class="st">"Windows"</span><span class="op">)</span> <span class="op">{</span></span> -<span> <span class="va">ret</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makePSOCKcluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> -<span> <span class="op">}</span> <span class="kw">else</span> <span class="op">{</span></span> -<span> <span class="va">ret</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makeForkCluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> -<span> <span class="op">}</span></span> -<span> <span class="kw"><a href="https://rdrr.io/r/base/function.html" class="external-link">return</a></span><span class="op">(</span><span class="va">ret</span><span class="op">)</span></span> -<span><span class="op">}</span></span> -<span><span class="va">cl</span> <span class="op"><-</span> <span class="fu">start_cluster</span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span></code></pre></div> -<div class="section level3"> -<h3 id="test-data">Test data<a class="anchor" aria-label="anchor" href="#test-data"></a> -</h3> -<p>The example data are taken from the final addendum to the DAR from -2014 and are distributed with the mkin package. Residue data and time -step normalisation factors are read in using the function -<code>read_spreadsheet</code> from the mkin package. This function also -performs the time step normalisation.</p> -<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">data_file</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.file.html" class="external-link">system.file</a></span><span class="op">(</span></span> -<span> <span class="st">"testdata"</span>, <span class="st">"cyantraniliprole_soil_efsa_2014.xlsx"</span>,</span> -<span> package <span class="op">=</span> <span class="st">"mkin"</span><span class="op">)</span></span> -<span><span class="va">cyan_ds</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/read_spreadsheet.html">read_spreadsheet</a></span><span class="op">(</span><span class="va">data_file</span>, parent_only <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div> -<p>The following tables show the covariate data and the 5 datasets that -were read in from the spreadsheet file.</p> -<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">pH</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/attr.html" class="external-link">attr</a></span><span class="op">(</span><span class="va">cyan_ds</span>, <span class="st">"covariates"</span><span class="op">)</span></span> -<span><span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="va">pH</span>, caption <span class="op">=</span> <span class="st">"Covariate data"</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<caption>Covariate data</caption> -<thead><tr class="header"> -<th align="left"></th> -<th align="right">pH</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">Nambsheim</td> -<td align="right">7.90</td> -</tr> -<tr class="even"> -<td align="left">Tama</td> -<td align="right">6.20</td> -</tr> -<tr class="odd"> -<td align="left">Gross-Umstadt</td> -<td align="right">7.04</td> -</tr> -<tr class="even"> -<td align="left">Sassafras</td> -<td align="right">4.62</td> -</tr> -<tr class="odd"> -<td align="left">Lleida</td> -<td align="right">8.05</td> -</tr> -</tbody> -</table> -<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="kw">for</span> <span class="op">(</span><span class="va">ds_name</span> <span class="kw">in</span> <span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">cyan_ds</span><span class="op">)</span><span class="op">)</span> <span class="op">{</span></span> -<span> <span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span></span> -<span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="fu"><a href="../../reference/mkin_long_to_wide.html">mkin_long_to_wide</a></span><span class="op">(</span><span class="va">cyan_ds</span><span class="op">[[</span><span class="va">ds_name</span><span class="op">]</span><span class="op">]</span><span class="op">)</span>,</span> -<span> caption <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste</a></span><span class="op">(</span><span class="st">"Dataset"</span>, <span class="va">ds_name</span><span class="op">)</span>,</span> -<span> booktabs <span class="op">=</span> <span class="cn">TRUE</span>, row.names <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">)</span></span> -<span> <span class="fu"><a href="https://rdrr.io/r/base/cat.html" class="external-link">cat</a></span><span class="op">(</span><span class="st">"\n\\clearpage\n"</span><span class="op">)</span></span> -<span><span class="op">}</span></span></code></pre></div> -<table class="table"> -<caption>Dataset Nambsheim</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">cyan</th> -<th align="right">JCZ38</th> -<th align="right">J9C38</th> -<th align="right">JSE76</th> -<th align="right">J9Z38</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.000000</td> -<td align="right">105.79</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">3.210424</td> -<td align="right">77.26</td> -<td align="right">7.92</td> -<td align="right">11.94</td> -<td align="right">5.58</td> -<td align="right">9.12</td> -</tr> -<tr class="odd"> -<td align="right">7.490988</td> -<td align="right">57.13</td> -<td align="right">15.46</td> -<td align="right">16.58</td> -<td align="right">12.59</td> -<td align="right">11.74</td> -</tr> -<tr class="even"> -<td align="right">17.122259</td> -<td align="right">37.74</td> -<td align="right">15.98</td> -<td align="right">13.36</td> -<td align="right">26.05</td> -<td align="right">10.77</td> -</tr> -<tr class="odd"> -<td align="right">23.543105</td> -<td align="right">31.47</td> -<td align="right">6.05</td> -<td align="right">14.49</td> -<td align="right">34.71</td> -<td align="right">4.96</td> -</tr> -<tr class="even"> -<td align="right">43.875788</td> -<td align="right">16.74</td> -<td align="right">6.07</td> -<td align="right">7.57</td> -<td align="right">40.38</td> -<td align="right">6.52</td> -</tr> -<tr class="odd"> -<td align="right">67.418893</td> -<td align="right">8.85</td> -<td align="right">10.34</td> -<td align="right">6.39</td> -<td align="right">30.71</td> -<td align="right">8.90</td> -</tr> -<tr class="even"> -<td align="right">107.014116</td> -<td align="right">5.19</td> -<td align="right">9.61</td> -<td align="right">1.95</td> -<td align="right">20.41</td> -<td align="right">12.93</td> -</tr> -<tr class="odd"> -<td align="right">129.487080</td> -<td align="right">3.45</td> -<td align="right">6.18</td> -<td align="right">1.36</td> -<td align="right">21.78</td> -<td align="right">6.99</td> -</tr> -<tr class="even"> -<td align="right">195.835832</td> -<td align="right">2.15</td> -<td align="right">9.13</td> -<td align="right">0.95</td> -<td align="right">16.29</td> -<td align="right">7.69</td> -</tr> -<tr class="odd"> -<td align="right">254.693596</td> -<td align="right">1.92</td> -<td align="right">6.92</td> -<td align="right">0.20</td> -<td align="right">13.57</td> -<td align="right">7.16</td> -</tr> -<tr class="even"> -<td align="right">321.042348</td> -<td align="right">2.26</td> -<td align="right">7.02</td> -<td align="right">NA</td> -<td align="right">11.12</td> -<td align="right">8.66</td> -</tr> -<tr class="odd"> -<td align="right">383.110535</td> -<td align="right">NA</td> -<td align="right">5.05</td> -<td align="right">NA</td> -<td align="right">10.64</td> -<td align="right">5.56</td> -</tr> -<tr class="even"> -<td align="right">0.000000</td> -<td align="right">105.57</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">3.210424</td> -<td align="right">78.88</td> -<td align="right">12.77</td> -<td align="right">11.94</td> -<td align="right">5.47</td> -<td align="right">9.12</td> -</tr> -<tr class="even"> -<td align="right">7.490988</td> -<td align="right">59.94</td> -<td align="right">15.27</td> -<td align="right">16.58</td> -<td align="right">13.60</td> -<td align="right">11.74</td> -</tr> -<tr class="odd"> -<td align="right">17.122259</td> -<td align="right">39.67</td> -<td align="right">14.26</td> -<td align="right">13.36</td> -<td align="right">29.44</td> -<td align="right">10.77</td> -</tr> -<tr class="even"> -<td align="right">23.543105</td> -<td align="right">30.21</td> -<td align="right">16.07</td> -<td align="right">14.49</td> -<td align="right">35.90</td> -<td align="right">4.96</td> -</tr> -<tr class="odd"> -<td align="right">43.875788</td> -<td align="right">18.06</td> -<td align="right">9.44</td> -<td align="right">7.57</td> -<td align="right">42.30</td> -<td align="right">6.52</td> -</tr> -<tr class="even"> -<td align="right">67.418893</td> -<td align="right">8.54</td> -<td align="right">5.78</td> -<td align="right">6.39</td> -<td align="right">34.70</td> -<td align="right">8.90</td> -</tr> -<tr class="odd"> -<td align="right">107.014116</td> -<td align="right">7.26</td> -<td align="right">4.54</td> -<td align="right">1.95</td> -<td align="right">23.33</td> -<td align="right">12.93</td> -</tr> -<tr class="even"> -<td align="right">129.487080</td> -<td align="right">3.60</td> -<td align="right">4.22</td> -<td align="right">1.36</td> -<td align="right">23.56</td> -<td align="right">6.99</td> -</tr> -<tr class="odd"> -<td align="right">195.835832</td> -<td align="right">2.84</td> -<td align="right">3.05</td> -<td align="right">0.95</td> -<td align="right">16.21</td> -<td align="right">7.69</td> -</tr> -<tr class="even"> -<td align="right">254.693596</td> -<td align="right">2.00</td> -<td align="right">2.90</td> -<td align="right">0.20</td> -<td align="right">15.53</td> -<td align="right">7.16</td> -</tr> -<tr class="odd"> -<td align="right">321.042348</td> -<td align="right">1.79</td> -<td align="right">0.94</td> -<td align="right">NA</td> -<td align="right">9.80</td> -<td align="right">8.66</td> -</tr> -<tr class="even"> -<td align="right">383.110535</td> -<td align="right">NA</td> -<td align="right">1.82</td> -<td align="right">NA</td> -<td align="right">9.49</td> -<td align="right">5.56</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset Tama</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">cyan</th> -<th align="right">JCZ38</th> -<th align="right">J9Z38</th> -<th align="right">JSE76</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.000000</td> -<td align="right">106.14</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">2.400833</td> -<td align="right">93.47</td> -<td align="right">6.46</td> -<td align="right">2.85</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">5.601943</td> -<td align="right">88.39</td> -<td align="right">10.86</td> -<td align="right">4.65</td> -<td align="right">3.85</td> -</tr> -<tr class="even"> -<td align="right">12.804442</td> -<td align="right">72.29</td> -<td align="right">11.97</td> -<td align="right">4.91</td> -<td align="right">11.24</td> -</tr> -<tr class="odd"> -<td align="right">17.606108</td> -<td align="right">65.79</td> -<td align="right">13.11</td> -<td align="right">6.63</td> -<td align="right">13.79</td> -</tr> -<tr class="even"> -<td align="right">32.811382</td> -<td align="right">53.16</td> -<td align="right">11.24</td> -<td align="right">8.90</td> -<td align="right">23.40</td> -</tr> -<tr class="odd"> -<td align="right">50.417490</td> -<td align="right">44.01</td> -<td align="right">11.34</td> -<td align="right">9.98</td> -<td align="right">29.56</td> -</tr> -<tr class="even"> -<td align="right">80.027761</td> -<td align="right">33.23</td> -<td align="right">8.82</td> -<td align="right">11.31</td> -<td align="right">35.63</td> -</tr> -<tr class="odd"> -<td align="right">96.833591</td> -<td align="right">40.68</td> -<td align="right">5.94</td> -<td align="right">8.32</td> -<td align="right">29.09</td> -</tr> -<tr class="even"> -<td align="right">146.450803</td> -<td align="right">20.65</td> -<td align="right">4.49</td> -<td align="right">8.72</td> -<td align="right">36.88</td> -</tr> -<tr class="odd"> -<td align="right">190.466072</td> -<td align="right">17.71</td> -<td align="right">4.66</td> -<td align="right">11.10</td> -<td align="right">40.97</td> -</tr> -<tr class="even"> -<td align="right">240.083284</td> -<td align="right">14.86</td> -<td align="right">2.27</td> -<td align="right">11.62</td> -<td align="right">40.11</td> -</tr> -<tr class="odd"> -<td align="right">286.499386</td> -<td align="right">12.02</td> -<td align="right">NA</td> -<td align="right">10.73</td> -<td align="right">42.58</td> -</tr> -<tr class="even"> -<td align="right">0.000000</td> -<td align="right">109.11</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">2.400833</td> -<td align="right">96.84</td> -<td align="right">5.52</td> -<td align="right">2.04</td> -<td align="right">2.02</td> -</tr> -<tr class="even"> -<td align="right">5.601943</td> -<td align="right">85.29</td> -<td align="right">9.65</td> -<td align="right">2.99</td> -<td align="right">4.39</td> -</tr> -<tr class="odd"> -<td align="right">12.804442</td> -<td align="right">73.68</td> -<td align="right">12.48</td> -<td align="right">5.05</td> -<td align="right">11.47</td> -</tr> -<tr class="even"> -<td align="right">17.606108</td> -<td align="right">64.89</td> -<td align="right">12.44</td> -<td align="right">6.29</td> -<td align="right">15.00</td> -</tr> -<tr class="odd"> -<td align="right">32.811382</td> -<td align="right">52.27</td> -<td align="right">10.86</td> -<td align="right">7.65</td> -<td align="right">23.30</td> -</tr> -<tr class="even"> -<td align="right">50.417490</td> -<td align="right">42.61</td> -<td align="right">10.54</td> -<td align="right">9.37</td> -<td align="right">31.06</td> -</tr> -<tr class="odd"> -<td align="right">80.027761</td> -<td align="right">34.29</td> -<td align="right">10.02</td> -<td align="right">9.04</td> -<td align="right">37.87</td> -</tr> -<tr class="even"> -<td align="right">96.833591</td> -<td align="right">30.50</td> -<td align="right">6.34</td> -<td align="right">8.14</td> -<td align="right">33.97</td> -</tr> -<tr class="odd"> -<td align="right">146.450803</td> -<td align="right">19.21</td> -<td align="right">6.29</td> -<td align="right">8.52</td> -<td align="right">26.15</td> -</tr> -<tr class="even"> -<td align="right">190.466072</td> -<td align="right">17.55</td> -<td align="right">5.81</td> -<td align="right">9.89</td> -<td align="right">32.08</td> -</tr> -<tr class="odd"> -<td align="right">240.083284</td> -<td align="right">13.22</td> -<td align="right">5.99</td> -<td align="right">10.79</td> -<td align="right">40.66</td> -</tr> -<tr class="even"> -<td align="right">286.499386</td> -<td align="right">11.09</td> -<td align="right">6.05</td> -<td align="right">8.82</td> -<td align="right">42.90</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset Gross-Umstadt</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">cyan</th> -<th align="right">JCZ38</th> -<th align="right">J9Z38</th> -<th align="right">JSE76</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.0000000</td> -<td align="right">103.03</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">2.1014681</td> -<td align="right">87.85</td> -<td align="right">4.79</td> -<td align="right">3.26</td> -<td align="right">0.62</td> -</tr> -<tr class="odd"> -<td align="right">4.9034255</td> -<td align="right">77.35</td> -<td align="right">8.05</td> -<td align="right">9.89</td> -<td align="right">1.32</td> -</tr> -<tr class="even"> -<td align="right">10.5073404</td> -<td align="right">69.33</td> -<td align="right">9.74</td> -<td align="right">12.32</td> -<td align="right">4.74</td> -</tr> -<tr class="odd"> -<td align="right">21.0146807</td> -<td align="right">55.65</td> -<td align="right">14.57</td> -<td align="right">13.59</td> -<td align="right">9.84</td> -</tr> -<tr class="even"> -<td align="right">31.5220211</td> -<td align="right">49.03</td> -<td align="right">14.66</td> -<td align="right">16.71</td> -<td align="right">12.32</td> -</tr> -<tr class="odd"> -<td align="right">42.0293615</td> -<td align="right">41.86</td> -<td align="right">15.97</td> -<td align="right">13.64</td> -<td align="right">15.53</td> -</tr> -<tr class="even"> -<td align="right">63.0440422</td> -<td align="right">34.88</td> -<td align="right">18.20</td> -<td align="right">14.12</td> -<td align="right">22.02</td> -</tr> -<tr class="odd"> -<td align="right">84.0587230</td> -<td align="right">28.26</td> -<td align="right">15.64</td> -<td align="right">14.06</td> -<td align="right">25.60</td> -</tr> -<tr class="even"> -<td align="right">0.0000000</td> -<td align="right">104.05</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">2.1014681</td> -<td align="right">85.25</td> -<td align="right">2.68</td> -<td align="right">7.32</td> -<td align="right">0.69</td> -</tr> -<tr class="even"> -<td align="right">4.9034255</td> -<td align="right">77.22</td> -<td align="right">7.28</td> -<td align="right">8.37</td> -<td align="right">1.45</td> -</tr> -<tr class="odd"> -<td align="right">10.5073404</td> -<td align="right">65.23</td> -<td align="right">10.73</td> -<td align="right">10.93</td> -<td align="right">4.74</td> -</tr> -<tr class="even"> -<td align="right">21.0146807</td> -<td align="right">57.78</td> -<td align="right">12.29</td> -<td align="right">14.80</td> -<td align="right">9.05</td> -</tr> -<tr class="odd"> -<td align="right">31.5220211</td> -<td align="right">54.83</td> -<td align="right">14.05</td> -<td align="right">12.01</td> -<td align="right">11.05</td> -</tr> -<tr class="even"> -<td align="right">42.0293615</td> -<td align="right">45.17</td> -<td align="right">12.12</td> -<td align="right">17.89</td> -<td align="right">15.71</td> -</tr> -<tr class="odd"> -<td align="right">63.0440422</td> -<td align="right">34.83</td> -<td align="right">12.90</td> -<td align="right">15.86</td> -<td align="right">22.52</td> -</tr> -<tr class="even"> -<td align="right">84.0587230</td> -<td align="right">26.59</td> -<td align="right">14.28</td> -<td align="right">14.91</td> -<td align="right">28.48</td> -</tr> -<tr class="odd"> -<td align="right">0.0000000</td> -<td align="right">104.62</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">0.8145225</td> -<td align="right">97.21</td> -<td align="right">NA</td> -<td align="right">4.00</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">1.9005525</td> -<td align="right">89.64</td> -<td align="right">3.59</td> -<td align="right">5.24</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">4.0726125</td> -<td align="right">87.90</td> -<td align="right">4.10</td> -<td align="right">9.58</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">8.1452251</td> -<td align="right">86.90</td> -<td align="right">5.96</td> -<td align="right">9.45</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">12.2178376</td> -<td align="right">74.74</td> -<td align="right">7.83</td> -<td align="right">15.03</td> -<td align="right">5.33</td> -</tr> -<tr class="odd"> -<td align="right">16.2904502</td> -<td align="right">74.13</td> -<td align="right">8.84</td> -<td align="right">14.41</td> -<td align="right">5.10</td> -</tr> -<tr class="even"> -<td align="right">24.4356753</td> -<td align="right">65.26</td> -<td align="right">11.84</td> -<td align="right">18.33</td> -<td align="right">6.71</td> -</tr> -<tr class="odd"> -<td align="right">32.5809004</td> -<td align="right">57.70</td> -<td align="right">12.74</td> -<td align="right">19.93</td> -<td align="right">9.74</td> -</tr> -<tr class="even"> -<td align="right">0.0000000</td> -<td align="right">101.94</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">0.8145225</td> -<td align="right">99.94</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">1.9005525</td> -<td align="right">94.87</td> -<td align="right">NA</td> -<td align="right">4.56</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">4.0726125</td> -<td align="right">86.96</td> -<td align="right">6.75</td> -<td align="right">6.90</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">8.1452251</td> -<td align="right">80.51</td> -<td align="right">10.68</td> -<td align="right">7.43</td> -<td align="right">2.58</td> -</tr> -<tr class="odd"> -<td align="right">12.2178376</td> -<td align="right">78.38</td> -<td align="right">10.35</td> -<td align="right">9.46</td> -<td align="right">3.69</td> -</tr> -<tr class="even"> -<td align="right">16.2904502</td> -<td align="right">70.05</td> -<td align="right">13.73</td> -<td align="right">9.27</td> -<td align="right">7.18</td> -</tr> -<tr class="odd"> -<td align="right">24.4356753</td> -<td align="right">61.28</td> -<td align="right">12.57</td> -<td align="right">13.28</td> -<td align="right">13.19</td> -</tr> -<tr class="even"> -<td align="right">32.5809004</td> -<td align="right">52.85</td> -<td align="right">12.67</td> -<td align="right">12.95</td> -<td align="right">13.69</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset Sassafras</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">cyan</th> -<th align="right">JCZ38</th> -<th align="right">J9Z38</th> -<th align="right">JSE76</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.000000</td> -<td align="right">102.17</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">2.216719</td> -<td align="right">95.49</td> -<td align="right">1.11</td> -<td align="right">0.10</td> -<td align="right">0.83</td> -</tr> -<tr class="odd"> -<td align="right">5.172343</td> -<td align="right">83.35</td> -<td align="right">6.43</td> -<td align="right">2.89</td> -<td align="right">3.30</td> -</tr> -<tr class="even"> -<td align="right">11.083593</td> -<td align="right">78.18</td> -<td align="right">10.00</td> -<td align="right">5.59</td> -<td align="right">0.81</td> -</tr> -<tr class="odd"> -<td align="right">22.167186</td> -<td align="right">70.44</td> -<td align="right">17.21</td> -<td align="right">4.23</td> -<td align="right">1.09</td> -</tr> -<tr class="even"> -<td align="right">33.250779</td> -<td align="right">68.00</td> -<td align="right">20.45</td> -<td align="right">5.86</td> -<td align="right">1.17</td> -</tr> -<tr class="odd"> -<td align="right">44.334371</td> -<td align="right">59.64</td> -<td align="right">24.64</td> -<td align="right">3.17</td> -<td align="right">2.72</td> -</tr> -<tr class="even"> -<td align="right">66.501557</td> -<td align="right">50.73</td> -<td align="right">27.50</td> -<td align="right">6.19</td> -<td align="right">1.27</td> -</tr> -<tr class="odd"> -<td align="right">88.668742</td> -<td align="right">45.65</td> -<td align="right">32.77</td> -<td align="right">5.69</td> -<td align="right">4.54</td> -</tr> -<tr class="even"> -<td align="right">0.000000</td> -<td align="right">100.43</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">2.216719</td> -<td align="right">95.34</td> -<td align="right">3.21</td> -<td align="right">0.14</td> -<td align="right">0.46</td> -</tr> -<tr class="even"> -<td align="right">5.172343</td> -<td align="right">84.38</td> -<td align="right">5.73</td> -<td align="right">4.75</td> -<td align="right">0.62</td> -</tr> -<tr class="odd"> -<td align="right">11.083593</td> -<td align="right">78.50</td> -<td align="right">11.89</td> -<td align="right">3.99</td> -<td align="right">0.73</td> -</tr> -<tr class="even"> -<td align="right">22.167186</td> -<td align="right">71.17</td> -<td align="right">17.28</td> -<td align="right">4.39</td> -<td align="right">0.66</td> -</tr> -<tr class="odd"> -<td align="right">33.250779</td> -<td align="right">59.41</td> -<td align="right">18.73</td> -<td align="right">11.85</td> -<td align="right">2.65</td> -</tr> -<tr class="even"> -<td align="right">44.334371</td> -<td align="right">64.57</td> -<td align="right">22.93</td> -<td align="right">5.13</td> -<td align="right">2.01</td> -</tr> -<tr class="odd"> -<td align="right">66.501557</td> -<td align="right">49.08</td> -<td align="right">33.39</td> -<td align="right">5.67</td> -<td align="right">3.63</td> -</tr> -<tr class="even"> -<td align="right">88.668742</td> -<td align="right">40.41</td> -<td align="right">39.60</td> -<td align="right">5.93</td> -<td align="right">6.17</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset Lleida</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">cyan</th> -<th align="right">JCZ38</th> -<th align="right">J9Z38</th> -<th align="right">JSE76</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.000000</td> -<td align="right">102.71</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">2.821051</td> -<td align="right">79.11</td> -<td align="right">5.70</td> -<td align="right">8.07</td> -<td align="right">0.97</td> -</tr> -<tr class="odd"> -<td align="right">6.582451</td> -<td align="right">70.03</td> -<td align="right">7.17</td> -<td align="right">11.31</td> -<td align="right">4.72</td> -</tr> -<tr class="even"> -<td align="right">14.105253</td> -<td align="right">50.93</td> -<td align="right">10.25</td> -<td align="right">14.84</td> -<td align="right">9.95</td> -</tr> -<tr class="odd"> -<td align="right">28.210505</td> -<td align="right">33.43</td> -<td align="right">10.40</td> -<td align="right">14.82</td> -<td align="right">24.06</td> -</tr> -<tr class="even"> -<td align="right">42.315758</td> -<td align="right">24.69</td> -<td align="right">9.75</td> -<td align="right">16.38</td> -<td align="right">29.38</td> -</tr> -<tr class="odd"> -<td align="right">56.421010</td> -<td align="right">22.99</td> -<td align="right">10.06</td> -<td align="right">15.51</td> -<td align="right">29.25</td> -</tr> -<tr class="even"> -<td align="right">84.631516</td> -<td align="right">14.63</td> -<td align="right">5.63</td> -<td align="right">14.74</td> -<td align="right">31.04</td> -</tr> -<tr class="odd"> -<td align="right">112.842021</td> -<td align="right">12.43</td> -<td align="right">4.17</td> -<td align="right">13.53</td> -<td align="right">33.28</td> -</tr> -<tr class="even"> -<td align="right">0.000000</td> -<td align="right">99.31</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">2.821051</td> -<td align="right">82.07</td> -<td align="right">6.55</td> -<td align="right">5.60</td> -<td align="right">1.12</td> -</tr> -<tr class="even"> -<td align="right">6.582451</td> -<td align="right">70.65</td> -<td align="right">7.61</td> -<td align="right">8.01</td> -<td align="right">3.21</td> -</tr> -<tr class="odd"> -<td align="right">14.105253</td> -<td align="right">53.52</td> -<td align="right">11.48</td> -<td align="right">10.82</td> -<td align="right">12.24</td> -</tr> -<tr class="even"> -<td align="right">28.210505</td> -<td align="right">35.60</td> -<td align="right">11.19</td> -<td align="right">15.43</td> -<td align="right">23.53</td> -</tr> -<tr class="odd"> -<td align="right">42.315758</td> -<td align="right">34.26</td> -<td align="right">11.09</td> -<td align="right">13.26</td> -<td align="right">27.42</td> -</tr> -<tr class="even"> -<td align="right">56.421010</td> -<td align="right">21.79</td> -<td align="right">4.80</td> -<td align="right">18.30</td> -<td align="right">30.20</td> -</tr> -<tr class="odd"> -<td align="right">84.631516</td> -<td align="right">14.06</td> -<td align="right">6.30</td> -<td align="right">16.35</td> -<td align="right">32.32</td> -</tr> -<tr class="even"> -<td align="right">112.842021</td> -<td align="right">11.51</td> -<td align="right">5.57</td> -<td align="right">12.64</td> -<td align="right">32.51</td> -</tr> -</tbody> -</table> -</div> -</div> -<div class="section level2"> -<h2 id="parent-only-evaluations">Parent only evaluations<a class="anchor" aria-label="anchor" href="#parent-only-evaluations"></a> -</h2> -<p>As the pathway fits have very long run times, evaluations of the -parent data are performed first, in order to determine for each -hierarchical parent degradation model which random effects on the -degradation model parameters are ill-defined.</p> -<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">cyan_sep_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>, <span class="st">"SFORB"</span>, <span class="st">"HS"</span><span class="op">)</span>,</span> -<span> <span class="va">cyan_ds</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>, cores <span class="op">=</span> <span class="va">n_cores</span><span class="op">)</span></span> -<span><span class="va">cyan_sep_tc</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">cyan_sep_const</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span> -<span><span class="va">cyan_saem_full</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mhmkin.html">mhmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">cyan_sep_const</span>, <span class="va">cyan_sep_tc</span><span class="op">)</span><span class="op">)</span></span> -<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">cyan_saem_full</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">const</th> -<th align="left">tc</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">SFO</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">FOMC</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">DFOP</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">SFORB</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">HS</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -</tbody> -</table> -<p>All fits converged successfully.</p> -<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">cyan_saem_full</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">const</th> -<th align="left">tc</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">SFO</td> -<td align="left">sd(cyan_0)</td> -<td align="left">sd(cyan_0)</td> -</tr> -<tr class="even"> -<td align="left">FOMC</td> -<td align="left">sd(log_beta)</td> -<td align="left">sd(cyan_0)</td> -</tr> -<tr class="odd"> -<td align="left">DFOP</td> -<td align="left">sd(cyan_0)</td> -<td align="left">sd(cyan_0), sd(log_k1)</td> -</tr> -<tr class="even"> -<td align="left">SFORB</td> -<td align="left">sd(cyan_free_0)</td> -<td align="left">sd(cyan_free_0), sd(log_k_cyan_free_bound)</td> -</tr> -<tr class="odd"> -<td align="left">HS</td> -<td align="left">sd(cyan_0)</td> -<td align="left">sd(cyan_0)</td> -</tr> -</tbody> -</table> -<p>In almost all models, the random effect for the initial concentration -of the parent compound is ill-defined. For the biexponential models DFOP -and SFORB, the random effect of one additional parameter is ill-defined -when the two-component error model is used.</p> -<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">cyan_saem_full</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="right">npar</th> -<th align="right">AIC</th> -<th align="right">BIC</th> -<th align="right">Lik</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">SFO const</td> -<td align="right">5</td> -<td align="right">833.9</td> -<td align="right">832.0</td> -<td align="right">-412.0</td> -</tr> -<tr class="even"> -<td align="left">SFO tc</td> -<td align="right">6</td> -<td align="right">831.6</td> -<td align="right">829.3</td> -<td align="right">-409.8</td> -</tr> -<tr class="odd"> -<td align="left">FOMC const</td> -<td align="right">7</td> -<td align="right">709.1</td> -<td align="right">706.4</td> -<td align="right">-347.6</td> -</tr> -<tr class="even"> -<td align="left">FOMC tc</td> -<td align="right">8</td> -<td align="right">689.2</td> -<td align="right">686.1</td> -<td align="right">-336.6</td> -</tr> -<tr class="odd"> -<td align="left">DFOP const</td> -<td align="right">9</td> -<td align="right">703.0</td> -<td align="right">699.5</td> -<td align="right">-342.5</td> -</tr> -<tr class="even"> -<td align="left">SFORB const</td> -<td align="right">9</td> -<td align="right">701.3</td> -<td align="right">697.8</td> -<td align="right">-341.7</td> -</tr> -<tr class="odd"> -<td align="left">HS const</td> -<td align="right">9</td> -<td align="right">718.6</td> -<td align="right">715.1</td> -<td align="right">-350.3</td> -</tr> -<tr class="even"> -<td align="left">DFOP tc</td> -<td align="right">10</td> -<td align="right">703.1</td> -<td align="right">699.2</td> -<td align="right">-341.6</td> -</tr> -<tr class="odd"> -<td align="left">SFORB tc</td> -<td align="right">10</td> -<td align="right">700.1</td> -<td align="right">696.2</td> -<td align="right">-340.1</td> -</tr> -<tr class="even"> -<td align="left">HS tc</td> -<td align="right">10</td> -<td align="right">716.7</td> -<td align="right">712.8</td> -<td align="right">-348.3</td> -</tr> -</tbody> -</table> -<p>Model comparison based on AIC and BIC indicates that the -two-component error model is preferable for all parent models with the -exception of DFOP. The lowest AIC and BIC values are are obtained with -the FOMC model, followed by SFORB and DFOP.</p> -<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">stopCluster</a></span><span class="op">(</span><span class="va">cl</span><span class="op">)</span></span></code></pre></div> -</div> -<div class="section level2"> -<h2 id="pathway-fits">Pathway fits<a class="anchor" aria-label="anchor" href="#pathway-fits"></a> -</h2> -<div class="section level3"> -<h3 id="evaluations-with-pathway-established-previously">Evaluations with pathway established previously<a class="anchor" aria-label="anchor" href="#evaluations-with-pathway-established-previously"></a> -</h3> -<p>To test the technical feasibility of coupling the relevant parent -degradation models with different transformation pathway models, a list -of <code>mkinmod</code> models is set up below. As in the EU evaluation, -parallel formation of metabolites JCZ38 and J9Z38 and secondary -formation of metabolite JSE76 from JCZ38 is used.</p> -<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="kw">if</span> <span class="op">(</span><span class="op">!</span><span class="fu"><a href="https://rdrr.io/r/base/files2.html" class="external-link">dir.exists</a></span><span class="op">(</span><span class="st">"cyan_dlls"</span><span class="op">)</span><span class="op">)</span> <span class="fu"><a href="https://rdrr.io/r/base/files2.html" class="external-link">dir.create</a></span><span class="op">(</span><span class="st">"cyan_dlls"</span><span class="op">)</span></span> -<span><span class="va">cyan_path_1</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span></span> -<span> sfo_path_1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> cyan <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"JCZ38"</span>, <span class="st">"J9Z38"</span><span class="op">)</span><span class="op">)</span>,</span> -<span> JCZ38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JSE76"</span><span class="op">)</span>,</span> -<span> J9Z38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> JSE76 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> name <span class="op">=</span> <span class="st">"sfo_path_1"</span>, dll_dir <span class="op">=</span> <span class="st">"cyan_dlls"</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,</span> -<span> fomc_path_1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> cyan <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"FOMC"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"JCZ38"</span>, <span class="st">"J9Z38"</span><span class="op">)</span><span class="op">)</span>,</span> -<span> JCZ38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JSE76"</span><span class="op">)</span>,</span> -<span> J9Z38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> JSE76 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> name <span class="op">=</span> <span class="st">"fomc_path_1"</span>, dll_dir <span class="op">=</span> <span class="st">"cyan_dlls"</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,</span> -<span> dfop_path_1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> cyan <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"DFOP"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"JCZ38"</span>, <span class="st">"J9Z38"</span><span class="op">)</span><span class="op">)</span>,</span> -<span> JCZ38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JSE76"</span><span class="op">)</span>,</span> -<span> J9Z38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> JSE76 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> name <span class="op">=</span> <span class="st">"dfop_path_1"</span>, dll_dir <span class="op">=</span> <span class="st">"cyan_dlls"</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,</span> -<span> sforb_path_1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> cyan <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"JCZ38"</span>, <span class="st">"J9Z38"</span><span class="op">)</span><span class="op">)</span>,</span> -<span> JCZ38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JSE76"</span><span class="op">)</span>,</span> -<span> J9Z38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> JSE76 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> name <span class="op">=</span> <span class="st">"sforb_path_1"</span>, dll_dir <span class="op">=</span> <span class="st">"cyan_dlls"</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,</span> -<span> hs_path_1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> cyan <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"HS"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"JCZ38"</span>, <span class="st">"J9Z38"</span><span class="op">)</span><span class="op">)</span>,</span> -<span> JCZ38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JSE76"</span><span class="op">)</span>,</span> -<span> J9Z38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> JSE76 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> name <span class="op">=</span> <span class="st">"hs_path_1"</span>, dll_dir <span class="op">=</span> <span class="st">"cyan_dlls"</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<span><span class="op">)</span></span> -<span><span class="va">cl_path_1</span> <span class="op"><-</span> <span class="fu">start_cluster</span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span></code></pre></div> -<p>To obtain suitable starting values for the NLHM fits, separate -pathway fits are performed for all datasets.</p> -<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_sep_1_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span></span> -<span> <span class="va">cyan_path_1</span>,</span> -<span> <span class="va">cyan_ds</span>,</span> -<span> error_model <span class="op">=</span> <span class="st">"const"</span>,</span> -<span> cluster <span class="op">=</span> <span class="va">cl_path_1</span>,</span> -<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_1_const</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">Nambsheim</th> -<th align="left">Tama</th> -<th align="left">Gross-Umstadt</th> -<th align="left">Sassafras</th> -<th align="left">Lleida</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">sfo_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">fomc_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">dfop_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">sforb_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">hs_path_1</td> -<td align="left">C</td> -<td align="left">C</td> -<td align="left">C</td> -<td align="left">C</td> -<td align="left">C</td> -</tr> -</tbody> -</table> -<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_sep_1_tc</span> <span class="op"><-</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="cb12"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_saem_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mhmkin.html">mhmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">f_sep_1_const</span>, <span class="va">f_sep_1_tc</span><span class="op">)</span>,</span> -<span> no_random_effect <span class="op">=</span> <span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">cyan_saem_full</span><span class="op">)</span>,</span> -<span> cluster <span class="op">=</span> <span class="va">cl_path_1</span><span class="op">)</span></span></code></pre></div> -<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">const</th> -<th align="left">tc</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">sfo_path_1</td> -<td align="left">Fth, FO</td> -<td align="left">Fth, FO</td> -</tr> -<tr class="even"> -<td align="left">fomc_path_1</td> -<td align="left">OK</td> -<td align="left">Fth, FO</td> -</tr> -<tr class="odd"> -<td align="left">dfop_path_1</td> -<td align="left">Fth, FO</td> -<td align="left">Fth, FO</td> -</tr> -<tr class="even"> -<td align="left">sforb_path_1</td> -<td align="left">Fth, FO</td> -<td align="left">Fth, FO</td> -</tr> -<tr class="odd"> -<td align="left">hs_path_1</td> -<td align="left">Fth, FO</td> -<td align="left">Fth, FO</td> -</tr> -</tbody> -</table> -<p>The status information from the individual fits shows that all fits -completed successfully. The matrix entries Fth and FO indicate that the -Fisher Information Matrix could not be inverted for the fixed effects -(theta) and the random effects (Omega), respectively. For the affected -fits, ill-defined parameters cannot be determined using the -<code>illparms</code> function, because it relies on the Fisher -Information Matrix.</p> -<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<colgroup> -<col width="18%"> -<col width="77%"> -<col width="4%"> -</colgroup> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">const</th> -<th align="left">tc</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">sfo_path_1</td> -<td align="left">NA</td> -<td align="left">NA</td> -</tr> -<tr class="even"> -<td align="left">fomc_path_1</td> -<td align="left">sd(log_k_J9Z38), sd(f_cyan_ilr_2), -sd(f_JCZ38_qlogis)</td> -<td align="left">NA</td> -</tr> -<tr class="odd"> -<td align="left">dfop_path_1</td> -<td align="left">NA</td> -<td align="left">NA</td> -</tr> -<tr class="even"> -<td align="left">sforb_path_1</td> -<td align="left">NA</td> -<td align="left">NA</td> -</tr> -<tr class="odd"> -<td align="left">hs_path_1</td> -<td align="left">NA</td> -<td align="left">NA</td> -</tr> -</tbody> -</table> -<p>The model comparison below suggests that the pathway fits using DFOP -or SFORB for the parent compound provide the best fit.</p> -<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="right">npar</th> -<th align="right">AIC</th> -<th align="right">BIC</th> -<th align="right">Lik</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">sfo_path_1 const</td> -<td align="right">16</td> -<td align="right">2692.8</td> -<td align="right">2686.6</td> -<td align="right">-1330.4</td> -</tr> -<tr class="even"> -<td align="left">sfo_path_1 tc</td> -<td align="right">17</td> -<td align="right">2657.7</td> -<td align="right">2651.1</td> -<td align="right">-1311.9</td> -</tr> -<tr class="odd"> -<td align="left">fomc_path_1 const</td> -<td align="right">18</td> -<td align="right">2427.8</td> -<td align="right">2420.8</td> -<td align="right">-1195.9</td> -</tr> -<tr class="even"> -<td align="left">fomc_path_1 tc</td> -<td align="right">19</td> -<td align="right">2423.4</td> -<td align="right">2416.0</td> -<td align="right">-1192.7</td> -</tr> -<tr class="odd"> -<td align="left">dfop_path_1 const</td> -<td align="right">20</td> -<td align="right">2403.2</td> -<td align="right">2395.4</td> -<td align="right">-1181.6</td> -</tr> -<tr class="even"> -<td align="left">sforb_path_1 const</td> -<td align="right">20</td> -<td align="right">2401.4</td> -<td align="right">2393.6</td> -<td align="right">-1180.7</td> -</tr> -<tr class="odd"> -<td align="left">hs_path_1 const</td> -<td align="right">20</td> -<td align="right">2427.3</td> -<td align="right">2419.5</td> -<td align="right">-1193.7</td> -</tr> -<tr class="even"> -<td align="left">dfop_path_1 tc</td> -<td align="right">20</td> -<td align="right">2398.0</td> -<td align="right">2390.2</td> -<td align="right">-1179.0</td> -</tr> -<tr class="odd"> -<td align="left">sforb_path_1 tc</td> -<td align="right">20</td> -<td align="right">2399.8</td> -<td align="right">2392.0</td> -<td align="right">-1179.9</td> -</tr> -<tr class="even"> -<td align="left">hs_path_1 tc</td> -<td align="right">21</td> -<td align="right">2422.3</td> -<td align="right">2414.1</td> -<td align="right">-1190.2</td> -</tr> -</tbody> -</table> -<p>For these two parent model, successful fits are shown below. Plots of -the fits with the other parent models are shown in the Appendix.</p> -<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">[[</span><span class="st">"dfop_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_cyan_pathway_files/figure-html/unnamed-chunk-7-1.png" alt="DFOP pathway fit with two-component error" width="700"><p class="caption"> -DFOP pathway fit with two-component error -</p> -</div> -<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">[[</span><span class="st">"sforb_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_cyan_pathway_files/figure-html/unnamed-chunk-8-1.png" alt="SFORB pathway fit with two-component error" width="700"><p class="caption"> -SFORB pathway fit with two-component error -</p> -</div> -<p>A closer graphical analysis of these Figures shows that the residues -of transformation product JCZ38 in the soils Tama and Nambsheim observed -at later time points are strongly and systematically underestimated.</p> -<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">stopCluster</a></span><span class="op">(</span><span class="va">cl_path_1</span><span class="op">)</span></span></code></pre></div> -</div> -<div class="section level3"> -<h3 id="alternative-pathway-fits">Alternative pathway fits<a class="anchor" aria-label="anchor" href="#alternative-pathway-fits"></a> -</h3> -<p>To improve the fit for JCZ38, a back-reaction from JSE76 to JCZ38 was -introduced in an alternative version of the transformation pathway, in -analogy to the back-reaction from K5A78 to K5A77. Both pairs of -transformation products are pairs of an organic acid with its -corresponding amide (Addendum 2014, p. 109). As FOMC provided the best -fit for the parent, and the biexponential models DFOP and SFORB provided -the best initial pathway fits, these three parent models are used in the -alternative pathway fits.</p> -<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">cyan_path_2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span></span> -<span> fomc_path_2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> cyan <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"FOMC"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"JCZ38"</span>, <span class="st">"J9Z38"</span><span class="op">)</span><span class="op">)</span>,</span> -<span> JCZ38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JSE76"</span><span class="op">)</span>,</span> -<span> J9Z38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> JSE76 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JCZ38"</span><span class="op">)</span>,</span> -<span> name <span class="op">=</span> <span class="st">"fomc_path_2"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> dll_dir <span class="op">=</span> <span class="st">"cyan_dlls"</span>,</span> -<span> overwrite <span class="op">=</span> <span class="cn">TRUE</span></span> -<span> <span class="op">)</span>,</span> -<span> dfop_path_2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> cyan <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"DFOP"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"JCZ38"</span>, <span class="st">"J9Z38"</span><span class="op">)</span><span class="op">)</span>,</span> -<span> JCZ38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JSE76"</span><span class="op">)</span>,</span> -<span> J9Z38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> JSE76 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JCZ38"</span><span class="op">)</span>,</span> -<span> name <span class="op">=</span> <span class="st">"dfop_path_2"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> dll_dir <span class="op">=</span> <span class="st">"cyan_dlls"</span>,</span> -<span> overwrite <span class="op">=</span> <span class="cn">TRUE</span></span> -<span> <span class="op">)</span>,</span> -<span> sforb_path_2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> cyan <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"JCZ38"</span>, <span class="st">"J9Z38"</span><span class="op">)</span><span class="op">)</span>,</span> -<span> JCZ38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JSE76"</span><span class="op">)</span>,</span> -<span> J9Z38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> JSE76 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JCZ38"</span><span class="op">)</span>,</span> -<span> name <span class="op">=</span> <span class="st">"sforb_path_2"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> dll_dir <span class="op">=</span> <span class="st">"cyan_dlls"</span>,</span> -<span> overwrite <span class="op">=</span> <span class="cn">TRUE</span></span> -<span> <span class="op">)</span></span> -<span><span class="op">)</span></span> -<span></span> -<span><span class="va">cl_path_2</span> <span class="op"><-</span> <span class="fu">start_cluster</span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> -<span><span class="va">f_sep_2_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span></span> -<span> <span class="va">cyan_path_2</span>,</span> -<span> <span class="va">cyan_ds</span>,</span> -<span> error_model <span class="op">=</span> <span class="st">"const"</span>,</span> -<span> cluster <span class="op">=</span> <span class="va">cl_path_2</span>,</span> -<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<span></span> -<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_2_const</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">Nambsheim</th> -<th align="left">Tama</th> -<th align="left">Gross-Umstadt</th> -<th align="left">Sassafras</th> -<th align="left">Lleida</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">fomc_path_2</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">dfop_path_2</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">sforb_path_2</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -</tr> -</tbody> -</table> -<p>Using constant variance, separate fits converge with the exception of -the fits to the Sassafras soil data.</p> -<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_sep_2_tc</span> <span class="op"><-</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="cb21"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_saem_2</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mhmkin.html">mhmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">f_sep_2_const</span>, <span class="va">f_sep_2_tc</span><span class="op">)</span>,</span> -<span> no_random_effect <span class="op">=</span> <span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">cyan_saem_full</span><span class="op">[</span><span class="fl">2</span><span class="op">:</span><span class="fl">4</span>, <span class="op">]</span><span class="op">)</span>,</span> -<span> cluster <span class="op">=</span> <span class="va">cl_path_2</span><span class="op">)</span></span></code></pre></div> -<div class="sourceCode" id="cb22"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">const</th> -<th align="left">tc</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">fomc_path_2</td> -<td align="left">OK</td> -<td align="left">FO</td> -</tr> -<tr class="even"> -<td align="left">dfop_path_2</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">sforb_path_2</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -</tbody> -</table> -<p>The hierarchical fits for the alternative pathway completed -successfully.</p> -<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<colgroup> -<col width="14%"> -<col width="42%"> -<col width="42%"> -</colgroup> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">const</th> -<th align="left">tc</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">fomc_path_2</td> -<td align="left">sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)</td> -<td align="left">NA</td> -</tr> -<tr class="even"> -<td align="left">dfop_path_2</td> -<td align="left">sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)</td> -<td align="left">sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)</td> -</tr> -<tr class="odd"> -<td align="left">sforb_path_2</td> -<td align="left">sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)</td> -<td align="left">sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)</td> -</tr> -</tbody> -</table> -<p>In both fits, the random effects for the formation fractions for the -pathways from JCZ38 to JSE76, and for the reverse pathway from JSE76 to -JCZ38 are ill-defined.</p> -<div class="sourceCode" id="cb24"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="right">npar</th> -<th align="right">AIC</th> -<th align="right">BIC</th> -<th align="right">Lik</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">fomc_path_2 const</td> -<td align="right">20</td> -<td align="right">2308.3</td> -<td align="right">2300.5</td> -<td align="right">-1134.2</td> -</tr> -<tr class="even"> -<td align="left">fomc_path_2 tc</td> -<td align="right">21</td> -<td align="right">2248.3</td> -<td align="right">2240.1</td> -<td align="right">-1103.2</td> -</tr> -<tr class="odd"> -<td align="left">dfop_path_2 const</td> -<td align="right">22</td> -<td align="right">2289.6</td> -<td align="right">2281.0</td> -<td align="right">-1122.8</td> -</tr> -<tr class="even"> -<td align="left">sforb_path_2 const</td> -<td align="right">22</td> -<td align="right">2284.1</td> -<td align="right">2275.5</td> -<td align="right">-1120.0</td> -</tr> -<tr class="odd"> -<td align="left">dfop_path_2 tc</td> -<td align="right">22</td> -<td align="right">2234.4</td> -<td align="right">2225.8</td> -<td align="right">-1095.2</td> -</tr> -<tr class="even"> -<td align="left">sforb_path_2 tc</td> -<td align="right">22</td> -<td align="right">2240.4</td> -<td align="right">2231.8</td> -<td align="right">-1098.2</td> -</tr> -</tbody> -</table> -<p>The variants using the biexponential models DFOP and SFORB for the -parent compound and the two-component error model give the lowest AIC -and BIC values and are plotted below. Compared with the original -pathway, the AIC and BIC values indicate a large improvement. This is -confirmed by the plots, which show that the metabolite JCZ38 is fitted -much better with this model.</p> -<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"fomc_path_2"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_cyan_pathway_files/figure-html/unnamed-chunk-13-1.png" alt="FOMC pathway fit with two-component error, alternative pathway" width="700"><p class="caption"> -FOMC pathway fit with two-component error, alternative pathway -</p> -</div> -<div class="sourceCode" id="cb26"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"dfop_path_2"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_cyan_pathway_files/figure-html/unnamed-chunk-14-1.png" alt="DFOP pathway fit with two-component error, alternative pathway" width="700"><p class="caption"> -DFOP pathway fit with two-component error, alternative pathway -</p> -</div> -<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"sforb_path_2"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_cyan_pathway_files/figure-html/unnamed-chunk-15-1.png" alt="SFORB pathway fit with two-component error, alternative pathway" width="700"><p class="caption"> -SFORB pathway fit with two-component error, alternative pathway -</p> -</div> -</div> -<div class="section level3"> -<h3 id="refinement-of-alternative-pathway-fits">Refinement of alternative pathway fits<a class="anchor" aria-label="anchor" href="#refinement-of-alternative-pathway-fits"></a> -</h3> -<p>All ill-defined random effects that were identified in the parent -only fits and in the above pathway fits, are excluded for the final -evaluations below. For this purpose, a list of character vectors is -created below that can be indexed by row and column indices, and which -contains the degradation parameter names for which random effects should -be excluded for each of the hierarchical fits contained in -<code>f_saem_2</code>.</p> -<div class="sourceCode" id="cb28"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">no_ranef</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/matrix.html" class="external-link">matrix</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="op">)</span>, nrow <span class="op">=</span> <span class="fl">3</span>, ncol <span class="op">=</span> <span class="fl">2</span>, dimnames <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/dimnames.html" class="external-link">dimnames</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">)</span><span class="op">)</span></span> -<span><span class="va">no_ranef</span><span class="op">[[</span><span class="st">"fomc_path_2"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"log_beta"</span>, <span class="st">"f_JCZ38_qlogis"</span>, <span class="st">"f_JSE76_qlogis"</span><span class="op">)</span></span> -<span><span class="va">no_ranef</span><span class="op">[[</span><span class="st">"fomc_path_2"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"cyan_0"</span>, <span class="st">"f_JCZ38_qlogis"</span>, <span class="st">"f_JSE76_qlogis"</span><span class="op">)</span></span> -<span><span class="va">no_ranef</span><span class="op">[[</span><span class="st">"dfop_path_2"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"cyan_0"</span>, <span class="st">"f_JCZ38_qlogis"</span>, <span class="st">"f_JSE76_qlogis"</span><span class="op">)</span></span> -<span><span class="va">no_ranef</span><span class="op">[[</span><span class="st">"dfop_path_2"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"cyan_0"</span>, <span class="st">"log_k1"</span>, <span class="st">"f_JCZ38_qlogis"</span>, <span class="st">"f_JSE76_qlogis"</span><span class="op">)</span></span> -<span><span class="va">no_ranef</span><span class="op">[[</span><span class="st">"sforb_path_2"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"cyan_free_0"</span>,</span> -<span> <span class="st">"f_JCZ38_qlogis"</span>, <span class="st">"f_JSE76_qlogis"</span><span class="op">)</span></span> -<span><span class="va">no_ranef</span><span class="op">[[</span><span class="st">"sforb_path_2"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"cyan_free_0"</span>, <span class="st">"log_k_cyan_free_bound"</span>,</span> -<span> <span class="st">"f_JCZ38_qlogis"</span>, <span class="st">"f_JSE76_qlogis"</span><span class="op">)</span></span> -<span><span class="fu"><a href="https://rdrr.io/r/parallel/clusterApply.html" class="external-link">clusterExport</a></span><span class="op">(</span><span class="va">cl_path_2</span>, <span class="st">"no_ranef"</span><span class="op">)</span></span> -<span></span> -<span><span class="va">f_saem_3</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_saem_2</span>,</span> -<span> no_random_effect <span class="op">=</span> <span class="va">no_ranef</span>,</span> -<span> cluster <span class="op">=</span> <span class="va">cl_path_2</span><span class="op">)</span></span></code></pre></div> -<div class="sourceCode" id="cb29"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_saem_3</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">const</th> -<th align="left">tc</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">fomc_path_2</td> -<td align="left">E</td> -<td align="left">Fth</td> -</tr> -<tr class="even"> -<td align="left">dfop_path_2</td> -<td align="left">Fth</td> -<td align="left">Fth</td> -</tr> -<tr class="odd"> -<td align="left">sforb_path_2</td> -<td align="left">Fth</td> -<td align="left">Fth</td> -</tr> -</tbody> -</table> -<p>With the exception of the FOMC pathway fit with constant variance, -all updated fits completed successfully. However, the Fisher Information -Matrix for the fixed effects (Fth) could not be inverted, so no -confidence intervals for the optimised parameters are available.</p> -<div class="sourceCode" id="cb30"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_3</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">const</th> -<th align="left">tc</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">fomc_path_2</td> -<td align="left">E</td> -<td align="left"></td> -</tr> -<tr class="even"> -<td align="left">dfop_path_2</td> -<td align="left"></td> -<td align="left"></td> -</tr> -<tr class="odd"> -<td align="left">sforb_path_2</td> -<td align="left"></td> -<td align="left"></td> -</tr> -</tbody> -</table> -<div class="sourceCode" id="cb31"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_3</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="right">npar</th> -<th align="right">AIC</th> -<th align="right">BIC</th> -<th align="right">Lik</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">fomc_path_2 tc</td> -<td align="right">19</td> -<td align="right">2250.9</td> -<td align="right">2243.5</td> -<td align="right">-1106.5</td> -</tr> -<tr class="even"> -<td align="left">dfop_path_2 const</td> -<td align="right">20</td> -<td align="right">2281.7</td> -<td align="right">2273.9</td> -<td align="right">-1120.8</td> -</tr> -<tr class="odd"> -<td align="left">sforb_path_2 const</td> -<td align="right">20</td> -<td align="right">2279.5</td> -<td align="right">2271.7</td> -<td align="right">-1119.7</td> -</tr> -<tr class="even"> -<td align="left">dfop_path_2 tc</td> -<td align="right">20</td> -<td align="right">2231.5</td> -<td align="right">2223.7</td> -<td align="right">-1095.8</td> -</tr> -<tr class="odd"> -<td align="left">sforb_path_2 tc</td> -<td align="right">20</td> -<td align="right">2235.7</td> -<td align="right">2227.9</td> -<td align="right">-1097.9</td> -</tr> -</tbody> -</table> -<p>While the AIC and BIC values of the best fit (DFOP pathway fit with -two-component error) are lower than in the previous fits with the -alternative pathway, the practical value of these refined evaluations is -limited as no confidence intervals are obtained.</p> -<div class="sourceCode" id="cb32"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">stopCluster</a></span><span class="op">(</span><span class="va">cl_path_2</span><span class="op">)</span></span></code></pre></div> -</div> -</div> -<div class="section level2"> -<h2 id="conclusion">Conclusion<a class="anchor" aria-label="anchor" href="#conclusion"></a> -</h2> -<p>It was demonstrated that a relatively complex transformation pathway -with parallel formation of two primary metabolites and one secondary -metabolite can be fitted even if the data in the individual datasets are -quite different and partly only cover the formation phase.</p> -<p>The run times of the pathway fits were several hours, limiting the -practical feasibility of iterative refinements based on ill-defined -parameters and of alternative checks of parameter identifiability based -on multistart runs.</p> -</div> -<div class="section level2"> -<h2 id="acknowledgements">Acknowledgements<a class="anchor" aria-label="anchor" href="#acknowledgements"></a> -</h2> -<p>The helpful comments by Janina Wöltjen of the German Environment -Agency are gratefully acknowledged.</p> -</div> -<div class="section level2"> -<h2 id="appendix">Appendix<a class="anchor" aria-label="anchor" href="#appendix"></a> -</h2> -<div class="section level3"> -<h3 id="plots-of-fits-that-were-not-refined-further">Plots of fits that were not refined further<a class="anchor" aria-label="anchor" href="#plots-of-fits-that-were-not-refined-further"></a> -</h3> -<div class="sourceCode" id="cb33"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">[[</span><span class="st">"sfo_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_cyan_pathway_files/figure-html/unnamed-chunk-20-1.png" alt="SFO pathway fit with two-component error" width="700"><p class="caption"> -SFO pathway fit with two-component error -</p> -</div> -<div class="sourceCode" id="cb34"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">[[</span><span class="st">"fomc_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_cyan_pathway_files/figure-html/unnamed-chunk-21-1.png" alt="FOMC pathway fit with two-component error" width="700"><p class="caption"> -FOMC pathway fit with two-component error -</p> -</div> -<div class="sourceCode" id="cb35"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">[[</span><span class="st">"sforb_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_cyan_pathway_files/figure-html/unnamed-chunk-22-1.png" alt="HS pathway fit with two-component error" width="700"><p class="caption"> -HS pathway fit with two-component error -</p> -</div> -</div> -<div class="section level3"> -<h3 id="hierarchical-fit-listings">Hierarchical fit listings<a class="anchor" aria-label="anchor" href="#hierarchical-fit-listings"></a> -</h3> -<div class="section level4"> -<h4 id="pathway-1">Pathway 1<a class="anchor" aria-label="anchor" href="#pathway-1"></a> -</h4> -<caption> -Hierarchical SFO path 1 fit with constant variance -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 20:33:05 2023 -Date of summary: Thu Apr 20 21:04:34 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 438.011 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: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 20:32:55 2023 -Date of summary: Thu Apr 20 21:04:34 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 427.249 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: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 20:33:49 2023 -Date of summary: Thu Apr 20 21:04:34 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 481.497 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: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 20:33:59 2023 -Date of summary: Thu Apr 20 21:04:34 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 491.071 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: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 20:34:33 2023 -Date of summary: Thu Apr 20 21:04:34 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 525.551 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: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 20:37:03 2023 -Date of summary: Thu Apr 20 21:04:34 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 675.804 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: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 20:34:43 2023 -Date of summary: Thu Apr 20 21:04:34 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 535.818 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: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 20:37:02 2023 -Date of summary: Thu Apr 20 21:04:34 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 674.859 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: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 20:34:41 2023 -Date of summary: Thu Apr 20 21:04:34 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 533.787 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: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 20:34:39 2023 -Date of summary: Thu Apr 20 21:04:34 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 531.084 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: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 20:45:51 2023 -Date of summary: Thu Apr 20 21:04:34 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 517.002 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: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 20:45:39 2023 -Date of summary: Thu Apr 20 21:04:34 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 505.619 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: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 20:46:46 2023 -Date of summary: Thu Apr 20 21:04:34 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 572.382 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: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 20:49:18 2023 -Date of summary: Thu Apr 20 21:04:34 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 724.515 s -Using 300, 100 iterations and 10 chains - -Variance model: Two-component variance function - -Starting values for degradation parameters: - cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 - 101.7523 -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: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 20:46:33 2023 -Date of summary: Thu Apr 20 21:04:34 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 559.097 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: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 20:49:20 2023 -Date of summary: Thu Apr 20 21:04:34 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 726.293 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: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 21:02:39 2023 -Date of summary: Thu Apr 20 21:04:34 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 796.615 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: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 21:04:15 2023 -Date of summary: Thu Apr 20 21:04:34 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 893.328 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: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 21:04:33 2023 -Date of summary: Thu Apr 20 21:04:34 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 910.788 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: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 21:04:09 2023 -Date of summary: Thu Apr 20 21:04:34 2023 - -Equations: -d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound * - cyan_free + k_cyan_bound_free * cyan_bound -d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free * - cyan_bound -d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38 - * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76 -d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38 - * J9Z38 -d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 - -Data: -433 observations of 4 variable(s) grouped in 5 datasets - -Model predictions using solution type deSolve - -Fitted in 887.369 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: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 21:04:32 2023 -Date of summary: Thu Apr 20 21:04:34 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 910.017 s -Using 300, 100 iterations and 10 chains - -Variance model: Two-component variance function - -Starting values for degradation parameters: - cyan_free_0 log_k_cyan_free log_k_cyan_free_bound - 101.751 -2.837 -3.016 -log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 - -3.660 -2.299 -5.313 - log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 - -3.699 0.672 5.873 - f_JCZ38_qlogis f_JSE76_qlogis - 13.216 13.338 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - cyan_free_0 log_k_cyan_free log_k_cyan_free_bound -cyan_free_0 5.629 0.000 0.000 -log_k_cyan_free 0.000 0.446 0.000 -log_k_cyan_free_bound 0.000 0.000 1.449 -log_k_cyan_bound_free 0.000 0.000 0.000 -log_k_JCZ38 0.000 0.000 0.000 -log_k_J9Z38 0.000 0.000 0.000 -log_k_JSE76 0.000 0.000 0.000 -f_cyan_ilr_1 0.000 0.000 0.000 -f_cyan_ilr_2 0.000 0.000 0.000 -f_JCZ38_qlogis 0.000 0.000 0.000 -f_JSE76_qlogis 0.000 0.000 0.000 - log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 -cyan_free_0 0.000 0.0000 0.000 0.0000 -log_k_cyan_free 0.000 0.0000 0.000 0.0000 -log_k_cyan_free_bound 0.000 0.0000 0.000 0.0000 -log_k_cyan_bound_free 1.213 0.0000 0.000 0.0000 -log_k_JCZ38 0.000 0.7801 0.000 0.0000 -log_k_J9Z38 0.000 0.0000 1.575 0.0000 -log_k_JSE76 0.000 0.0000 0.000 0.8078 -f_cyan_ilr_1 0.000 0.0000 0.000 0.0000 -f_cyan_ilr_2 0.000 0.0000 0.000 0.0000 -f_JCZ38_qlogis 0.000 0.0000 0.000 0.0000 -f_JSE76_qlogis 0.000 0.0000 0.000 0.0000 - f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis -cyan_free_0 0.0000 0.00 0.00 0.00 -log_k_cyan_free 0.0000 0.00 0.00 0.00 -log_k_cyan_free_bound 0.0000 0.00 0.00 0.00 -log_k_cyan_bound_free 0.0000 0.00 0.00 0.00 -log_k_JCZ38 0.0000 0.00 0.00 0.00 -log_k_J9Z38 0.0000 0.00 0.00 0.00 -log_k_JSE76 0.0000 0.00 0.00 0.00 -f_cyan_ilr_1 0.6519 0.00 0.00 0.00 -f_cyan_ilr_2 0.0000 10.78 0.00 0.00 -f_JCZ38_qlogis 0.0000 0.00 13.96 0.00 -f_JSE76_qlogis 0.0000 0.00 0.00 14.69 - -Starting values for error model parameters: -a.1 b.1 - 1 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 2236 2228 -1098 - -Optimised parameters: - est. lower upper -cyan_free_0 100.72760 NA NA -log_k_cyan_free -3.18281 NA NA -log_k_cyan_free_bound -3.37924 NA NA -log_k_cyan_bound_free -3.77107 NA NA -log_k_JCZ38 -2.92811 NA NA -log_k_J9Z38 -5.02759 NA NA -log_k_JSE76 -3.65835 NA NA -f_cyan_ilr_1 0.67390 NA NA -f_cyan_ilr_2 1.15106 NA NA -f_JCZ38_qlogis 827.82299 NA NA -f_JSE76_qlogis 1.83064 NA NA -a.1 2.06921 1.84443 2.29399 -b.1 0.06391 0.05267 0.07515 -SD.log_k_cyan_free 0.50518 0.18962 0.82075 -SD.log_k_cyan_bound_free 0.30991 0.08170 0.53813 -SD.log_k_JCZ38 1.26661 0.46578 2.06744 -SD.log_k_J9Z38 0.88272 0.27813 1.48730 -SD.log_k_JSE76 0.53050 0.12561 0.93538 -SD.f_cyan_ilr_1 0.35547 0.12461 0.58633 -SD.f_cyan_ilr_2 0.91446 0.20131 1.62761 - -Correlation is not available - -Random effects: - est. lower upper -SD.log_k_cyan_free 0.5052 0.1896 0.8207 -SD.log_k_cyan_bound_free 0.3099 0.0817 0.5381 -SD.log_k_JCZ38 1.2666 0.4658 2.0674 -SD.log_k_J9Z38 0.8827 0.2781 1.4873 -SD.log_k_JSE76 0.5305 0.1256 0.9354 -SD.f_cyan_ilr_1 0.3555 0.1246 0.5863 -SD.f_cyan_ilr_2 0.9145 0.2013 1.6276 - -Variance model: - est. lower upper -a.1 2.06921 1.84443 2.29399 -b.1 0.06391 0.05267 0.07515 - -Backtransformed parameters: - est. lower upper -cyan_free_0 1.007e+02 NA NA -k_cyan_free 4.147e-02 NA NA -k_cyan_free_bound 3.407e-02 NA NA -k_cyan_bound_free 2.303e-02 NA NA -k_JCZ38 5.350e-02 NA NA -k_J9Z38 6.555e-03 NA NA -k_JSE76 2.578e-02 NA NA -f_cyan_free_to_JCZ38 6.505e-01 NA NA -f_cyan_free_to_J9Z38 2.508e-01 NA NA -f_JCZ38_to_JSE76 1.000e+00 NA NA -f_JSE76_to_JCZ38 8.618e-01 NA NA - -Estimated Eigenvalues of SFORB model(s): -cyan_b1 cyan_b2 cyan_g -0.08768 0.01089 0.39821 - -Resulting formation fractions: - ff -cyan_free_JCZ38 0.65053 -cyan_free_J9Z38 0.25082 -cyan_free_sink 0.09864 -cyan_free 1.00000 -JCZ38_JSE76 1.00000 -JCZ38_sink 0.00000 -JSE76_JCZ38 0.86184 -JSE76_sink 0.13816 - -Estimated disappearance times: - DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 -cyan 25.32 164.79 49.61 7.906 63.64 -JCZ38 12.96 43.04 NA NA NA -J9Z38 105.75 351.29 NA NA NA -JSE76 26.89 89.33 NA NA NA - -</code></pre> -<p></p> -</div> -</div> -<div class="section level3"> -<h3 id="session-info">Session info<a class="anchor" aria-label="anchor" href="#session-info"></a> -</h3> -<pre><code>R version 4.2.3 (2023-03-15) -Platform: x86_64-pc-linux-gnu (64-bit) -Running under: Debian GNU/Linux 12 (bookworm) - -Matrix products: default -BLAS: /usr/lib/x86_64-linux-gnu/openblas-serial/libblas.so.3 -LAPACK: /usr/lib/x86_64-linux-gnu/openblas-serial/libopenblas-r0.3.21.so - -locale: - [1] LC_CTYPE=de_DE.UTF-8 LC_NUMERIC=C - [3] LC_TIME=de_DE.UTF-8 LC_COLLATE=de_DE.UTF-8 - [5] LC_MONETARY=de_DE.UTF-8 LC_MESSAGES=de_DE.UTF-8 - [7] LC_PAPER=de_DE.UTF-8 LC_NAME=C - [9] LC_ADDRESS=C LC_TELEPHONE=C -[11] LC_MEASUREMENT=de_DE.UTF-8 LC_IDENTIFICATION=C - -attached base packages: -[1] parallel stats graphics grDevices utils datasets methods -[8] base - -other attached packages: -[1] saemix_3.2 npde_3.3 knitr_1.42 mkin_1.2.4 - -loaded via a namespace (and not attached): - [1] deSolve_1.35 zoo_1.8-12 tidyselect_1.2.0 xfun_0.38 - [5] bslib_0.4.2 purrr_1.0.1 lattice_0.21-8 colorspace_2.1-0 - [9] vctrs_0.6.1 generics_0.1.3 htmltools_0.5.5 yaml_2.3.7 -[13] utf8_1.2.3 rlang_1.1.0 pkgbuild_1.4.0 pkgdown_2.0.7 -[17] jquerylib_0.1.4 pillar_1.9.0 glue_1.6.2 DBI_1.1.3 -[21] readxl_1.4.2 lifecycle_1.0.3 stringr_1.5.0 munsell_0.5.0 -[25] gtable_0.3.3 cellranger_1.1.0 ragg_1.2.5 codetools_0.2-19 -[29] memoise_2.0.1 evaluate_0.20 inline_0.3.19 callr_3.7.3 -[33] fastmap_1.1.1 ps_1.7.4 lmtest_0.9-40 fansi_1.0.4 -[37] highr_0.10 scales_1.2.1 cachem_1.0.7 desc_1.4.2 -[41] jsonlite_1.8.4 systemfonts_1.0.4 fs_1.6.1 textshaping_0.3.6 -[45] gridExtra_2.3 ggplot2_3.4.2 digest_0.6.31 stringi_1.7.12 -[49] processx_3.8.0 dplyr_1.1.1 grid_4.2.3 rprojroot_2.0.3 -[53] cli_3.6.1 tools_4.2.3 magrittr_2.0.3 sass_0.4.5 -[57] tibble_3.2.1 crayon_1.5.2 pkgconfig_2.0.3 prettyunits_1.1.1 -[61] rmarkdown_2.21 R6_2.5.1 mclust_6.0.0 nlme_3.1-162 -[65] compiler_4.2.3 </code></pre> -</div> -<div class="section level3"> -<h3 id="hardware-info">Hardware info<a class="anchor" aria-label="anchor" href="#hardware-info"></a> -</h3> -<pre><code>CPU model: AMD Ryzen 9 7950X 16-Core Processor</code></pre> -<pre><code>MemTotal: 64936316 kB</code></pre> -</div> -</div> - </div> - - <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar"> - - <nav id="toc" data-toggle="toc"><h2 data-toc-skip>Contents</h2> - </nav> -</div> - -</div> - - - - <footer><div class="copyright"> - <p></p> -<p>Developed by Johannes Ranke.</p> -</div> - -<div class="pkgdown"> - <p></p> -<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p> -</div> - - </footer> -</div> - - - - - - - </body> -</html> diff --git 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evaluations with (generalised) nonlinear least squares</li> - <li> - <a href="../../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a> - </li> - <li> - <a href="../../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a> - </li> - <li> - <a href="../../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> - </li> - <li class="divider"> - </li> -<li class="dropdown-header">Example evaluations with hierarchical models (nonlinear mixed-effects models)</li> - <li> - <a href="../../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a> - </li> - <li> - <a href="../../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a> - </li> - <li> - <a href="../../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a> - </li> - <li> - <a href="../../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a> - </li> - <li> - <a href="../../articles/web_only/multistart.html">Short demo of the multistart method</a> - </li> - <li class="divider"> - </li> -<li class="dropdown-header">Performance</li> - <li> - <a href="../../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> - </li> - <li> - <a href="../../articles/web_only/benchmarks.html">Benchmark timings for mkin</a> - </li> - <li> - <a href="../../articles/web_only/saem_benchmarks.html">Benchmark timings for saem.mmkin</a> - </li> - <li class="divider"> - </li> -<li class="dropdown-header">Miscellaneous</li> - <li> - <a href="../../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> - </li> - <li> - <a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> - </li> - </ul> -</li> -<li> - <a href="../../news/index.html">News</a> -</li> - </ul> -<ul class="nav navbar-nav navbar-right"> -<li> - <a href="https://github.com/jranke/mkin/" class="external-link"> - <span class="fab fa-github fa-lg"></span> - - </a> -</li> - </ul> -</div> -<!--/.nav-collapse --> - </div> -<!--/.container --> -</div> -<!--/.navbar --> - - - - </header><div class="row"> - <div class="col-md-9 contents"> - <div class="page-header toc-ignore"> - <h1 data-toc-skip>Testing hierarchical parent degradation kinetics -with residue data on dimethenamid and dimethenamid-P</h1> - <h4 data-toc-skip class="author">Johannes -Ranke</h4> - - <h4 data-toc-skip class="date">Last change on 5 January -2023, last compiled on 16 April 2023</h4> - - <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/prebuilt/2022_dmta_parent.rmd" class="external-link"><code>vignettes/prebuilt/2022_dmta_parent.rmd</code></a></small> - <div class="hidden name"><code>2022_dmta_parent.rmd</code></div> - - </div> - - - -<div class="section level2"> -<h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#introduction"></a> -</h2> -<p>The purpose of this document is to demonstrate how nonlinear -hierarchical models (NLHM) based on the parent degradation models SFO, -FOMC, DFOP and HS can be fitted with the mkin package.</p> -<p>It was assembled in the course of work package 1.1 of Project Number -173340 (Application of nonlinear hierarchical models to the kinetic -evaluation of chemical degradation data) of the German Environment -Agency carried out in 2022 and 2023.</p> -<p>The mkin package is used in version 1.2.3. It contains the test data -and the functions used in the evaluations. The <code>saemix</code> -package is used as a backend for fitting the NLHM, but is also loaded to -make the convergence plot function available.</p> -<p>This document is processed with the <code>knitr</code> package, which -also provides the <code>kable</code> function that is used to improve -the display of tabular data in R markdown documents. For parallel -processing, the <code>parallel</code> package is used.</p> -<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://pkgdown.jrwb.de/mkin/">mkin</a></span><span class="op">)</span></span> -<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://yihui.org/knitr/" class="external-link">knitr</a></span><span class="op">)</span></span> -<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">saemix</span><span class="op">)</span></span> -<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">parallel</span><span class="op">)</span></span> -<span><span class="va">n_cores</span> <span class="op"><-</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> -<div class="section level2"> -<h2 id="data">Data<a class="anchor" aria-label="anchor" href="#data"></a> -</h2> -<p>The test data are available in the mkin package as an object of class -<code>mkindsg</code> (mkin dataset group) under the identifier -<code>dimethenamid_2018</code>. The following preprocessing steps are -still necessary:</p> -<ul> -<li>The data available for the enantiomer dimethenamid-P (DMTAP) are -renamed to have the same substance name as the data for the racemic -mixture dimethenamid (DMTA). The reason for this is that no difference -between their degradation behaviour was identified in the EU risk -assessment.</li> -<li>The data for transformation products and unnecessary columns are -discarded</li> -<li>The observation times of each dataset are multiplied with the -corresponding normalisation factor also available in the dataset, in -order to make it possible to describe all datasets with a single set of -parameters that are independent of temperature</li> -<li>Finally, datasets observed in the same soil (<code>Elliot 1</code> -and <code>Elliot 2</code>) are combined, resulting in dimethenamid -(DMTA) data from six soils.</li> -</ul> -<p>The following commented R code performs this preprocessing.</p> -<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="co"># Apply a function to each of the seven datasets in the mkindsg object to create a list</span></span> -<span><span class="va">dmta_ds</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">lapply</a></span><span class="op">(</span><span class="fl">1</span><span class="op">:</span><span class="fl">7</span>, <span class="kw">function</span><span class="op">(</span><span class="va">i</span><span class="op">)</span> <span class="op">{</span></span> -<span> <span class="va">ds_i</span> <span class="op"><-</span> <span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">ds</span><span class="op">[[</span><span class="va">i</span><span class="op">]</span><span class="op">]</span><span class="op">$</span><span class="va">data</span> <span class="co"># Get a dataset</span></span> -<span> <span class="va">ds_i</span><span class="op">[</span><span class="va">ds_i</span><span class="op">$</span><span class="va">name</span> <span class="op">==</span> <span class="st">"DMTAP"</span>, <span class="st">"name"</span><span class="op">]</span> <span class="op"><-</span> <span class="st">"DMTA"</span> <span class="co"># Rename DMTAP to DMTA</span></span> -<span> <span class="va">ds_i</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/subset.html" class="external-link">subset</a></span><span class="op">(</span><span class="va">ds_i</span>, <span class="va">name</span> <span class="op">==</span> <span class="st">"DMTA"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"name"</span>, <span class="st">"time"</span>, <span class="st">"value"</span><span class="op">)</span><span class="op">)</span> <span class="co"># Select data</span></span> -<span> <span class="va">ds_i</span><span class="op">$</span><span class="va">time</span> <span class="op"><-</span> <span class="va">ds_i</span><span class="op">$</span><span class="va">time</span> <span class="op">*</span> <span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">f_time_norm</span><span class="op">[</span><span class="va">i</span><span class="op">]</span> <span class="co"># Normalise time</span></span> -<span> <span class="va">ds_i</span> <span class="co"># Return the dataset</span></span> -<span><span class="op">}</span><span class="op">)</span></span> -<span></span> -<span><span class="co"># Use dataset titles as names for the list elements</span></span> -<span><span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">)</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</span><span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">ds</span>, <span class="kw">function</span><span class="op">(</span><span class="va">ds</span><span class="op">)</span> <span class="va">ds</span><span class="op">$</span><span class="va">title</span><span class="op">)</span></span> -<span></span> -<span><span class="co"># Combine data for Elliot soil to obtain a named list with six elements</span></span> -<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/cbind.html" class="external-link">rbind</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 1"</span><span class="op">]</span><span class="op">]</span>, <span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 2"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span> <span class="co">#</span></span> -<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 1"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="cn">NULL</span></span> -<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 2"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="cn">NULL</span></span></code></pre></div> -<p>The following tables show the 6 datasets.</p> -<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="kw">for</span> <span class="op">(</span><span class="va">ds_name</span> <span class="kw">in</span> <span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">)</span><span class="op">)</span> <span class="op">{</span></span> -<span> <span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="fu"><a href="../../reference/mkin_long_to_wide.html">mkin_long_to_wide</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">[[</span><span class="va">ds_name</span><span class="op">]</span><span class="op">]</span><span class="op">)</span>,</span> -<span> caption <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste</a></span><span class="op">(</span><span class="st">"Dataset"</span>, <span class="va">ds_name</span><span class="op">)</span>,</span> -<span> label <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste0</a></span><span class="op">(</span><span class="st">"tab:"</span>, <span class="va">ds_name</span><span class="op">)</span>, booktabs <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span><span class="op">)</span></span> -<span> <span class="fu"><a href="https://rdrr.io/r/base/cat.html" class="external-link">cat</a></span><span class="op">(</span><span class="st">"\n\\clearpage\n"</span><span class="op">)</span></span> -<span><span class="op">}</span></span></code></pre></div> -<table class="table"> -<caption>Dataset Calke</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">DMTA</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0</td> -<td align="right">95.8</td> -</tr> -<tr class="even"> -<td align="right">0</td> -<td align="right">98.7</td> -</tr> -<tr class="odd"> -<td align="right">14</td> -<td align="right">60.5</td> -</tr> -<tr class="even"> -<td align="right">30</td> -<td align="right">39.1</td> -</tr> -<tr class="odd"> -<td align="right">59</td> -<td align="right">15.2</td> -</tr> -<tr class="even"> -<td align="right">120</td> -<td align="right">4.8</td> -</tr> -<tr class="odd"> -<td align="right">120</td> -<td align="right">4.6</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset Borstel</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">DMTA</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.000000</td> -<td align="right">100.5</td> -</tr> -<tr class="even"> -<td align="right">0.000000</td> -<td align="right">99.6</td> -</tr> -<tr class="odd"> -<td align="right">1.941295</td> -<td align="right">91.9</td> -</tr> -<tr class="even"> -<td align="right">1.941295</td> -<td align="right">91.3</td> -</tr> -<tr class="odd"> -<td align="right">6.794534</td> -<td align="right">81.8</td> -</tr> -<tr class="even"> -<td align="right">6.794534</td> -<td align="right">82.1</td> -</tr> -<tr class="odd"> -<td align="right">13.589067</td> -<td align="right">69.1</td> -</tr> -<tr class="even"> -<td align="right">13.589067</td> -<td align="right">68.0</td> -</tr> -<tr class="odd"> -<td align="right">27.178135</td> -<td align="right">51.4</td> -</tr> -<tr class="even"> -<td align="right">27.178135</td> -<td align="right">51.4</td> -</tr> -<tr class="odd"> -<td align="right">56.297565</td> -<td align="right">27.6</td> -</tr> -<tr class="even"> -<td align="right">56.297565</td> -<td align="right">26.8</td> -</tr> -<tr class="odd"> -<td align="right">86.387643</td> -<td align="right">15.7</td> -</tr> -<tr class="even"> -<td align="right">86.387643</td> -<td align="right">15.3</td> -</tr> -<tr class="odd"> -<td align="right">115.507073</td> -<td align="right">7.9</td> -</tr> -<tr class="even"> -<td align="right">115.507073</td> -<td align="right">8.1</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset Flaach</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">DMTA</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.0000000</td> -<td align="right">96.5</td> -</tr> -<tr class="even"> -<td align="right">0.0000000</td> -<td align="right">96.8</td> -</tr> -<tr class="odd"> -<td align="right">0.0000000</td> -<td align="right">97.0</td> -</tr> -<tr class="even"> -<td align="right">0.6233856</td> -<td align="right">82.9</td> -</tr> -<tr class="odd"> -<td align="right">0.6233856</td> -<td align="right">86.7</td> -</tr> -<tr class="even"> -<td align="right">0.6233856</td> -<td align="right">87.4</td> -</tr> -<tr class="odd"> -<td align="right">1.8701567</td> -<td align="right">72.8</td> -</tr> -<tr class="even"> -<td align="right">1.8701567</td> -<td align="right">69.9</td> -</tr> -<tr class="odd"> -<td align="right">1.8701567</td> -<td align="right">71.9</td> -</tr> -<tr class="even"> -<td align="right">4.3636989</td> -<td align="right">51.4</td> -</tr> -<tr class="odd"> -<td align="right">4.3636989</td> -<td align="right">52.9</td> -</tr> -<tr class="even"> -<td align="right">4.3636989</td> -<td align="right">48.6</td> -</tr> -<tr class="odd"> -<td align="right">8.7273979</td> -<td align="right">28.5</td> -</tr> -<tr class="even"> -<td align="right">8.7273979</td> -<td align="right">27.3</td> -</tr> -<tr class="odd"> -<td align="right">8.7273979</td> -<td align="right">27.5</td> -</tr> -<tr class="even"> -<td align="right">13.0910968</td> -<td align="right">14.8</td> -</tr> -<tr class="odd"> -<td align="right">13.0910968</td> -<td align="right">13.4</td> -</tr> -<tr class="even"> -<td align="right">13.0910968</td> -<td align="right">14.4</td> -</tr> -<tr class="odd"> -<td align="right">17.4547957</td> -<td align="right">7.7</td> -</tr> -<tr class="even"> -<td align="right">17.4547957</td> -<td align="right">7.3</td> -</tr> -<tr class="odd"> -<td align="right">17.4547957</td> -<td align="right">8.1</td> -</tr> -<tr class="even"> -<td align="right">26.1821936</td> -<td align="right">2.0</td> -</tr> -<tr class="odd"> -<td align="right">26.1821936</td> -<td align="right">1.5</td> -</tr> -<tr class="even"> -<td align="right">26.1821936</td> -<td align="right">1.9</td> -</tr> -<tr class="odd"> -<td align="right">34.9095915</td> -<td align="right">1.3</td> -</tr> -<tr class="even"> -<td align="right">34.9095915</td> -<td align="right">1.0</td> -</tr> -<tr class="odd"> -<td align="right">34.9095915</td> -<td align="right">1.1</td> -</tr> -<tr class="even"> -<td align="right">43.6369893</td> -<td align="right">0.9</td> -</tr> -<tr class="odd"> -<td align="right">43.6369893</td> -<td align="right">0.7</td> -</tr> -<tr class="even"> -<td align="right">43.6369893</td> -<td align="right">0.7</td> -</tr> -<tr class="odd"> -<td align="right">52.3643872</td> -<td align="right">0.6</td> -</tr> -<tr class="even"> -<td align="right">52.3643872</td> -<td align="right">0.4</td> -</tr> -<tr class="odd"> -<td align="right">52.3643872</td> -<td align="right">0.5</td> -</tr> -<tr class="even"> -<td align="right">74.8062674</td> -<td align="right">0.4</td> -</tr> -<tr class="odd"> -<td align="right">74.8062674</td> -<td align="right">0.3</td> -</tr> -<tr class="even"> -<td align="right">74.8062674</td> -<td align="right">0.3</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset BBA 2.2</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">DMTA</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.0000000</td> -<td align="right">98.09</td> -</tr> -<tr class="even"> -<td align="right">0.0000000</td> -<td align="right">98.77</td> -</tr> -<tr class="odd"> -<td align="right">0.7678922</td> -<td align="right">93.52</td> -</tr> -<tr class="even"> -<td align="right">0.7678922</td> -<td align="right">92.03</td> -</tr> -<tr class="odd"> -<td align="right">2.3036765</td> -<td align="right">88.39</td> -</tr> -<tr class="even"> -<td align="right">2.3036765</td> -<td align="right">87.18</td> -</tr> -<tr class="odd"> -<td align="right">5.3752452</td> -<td align="right">69.38</td> -</tr> -<tr class="even"> -<td align="right">5.3752452</td> -<td align="right">71.06</td> -</tr> -<tr class="odd"> -<td align="right">10.7504904</td> -<td align="right">45.21</td> -</tr> -<tr class="even"> -<td align="right">10.7504904</td> -<td align="right">46.81</td> -</tr> -<tr class="odd"> -<td align="right">16.1257355</td> -<td align="right">30.54</td> -</tr> -<tr class="even"> -<td align="right">16.1257355</td> -<td align="right">30.07</td> -</tr> -<tr class="odd"> -<td align="right">21.5009807</td> -<td align="right">21.60</td> -</tr> -<tr class="even"> -<td align="right">21.5009807</td> -<td align="right">20.41</td> -</tr> -<tr class="odd"> -<td align="right">32.2514711</td> -<td align="right">9.10</td> -</tr> -<tr class="even"> -<td align="right">32.2514711</td> -<td align="right">9.70</td> -</tr> -<tr class="odd"> -<td align="right">43.0019614</td> -<td align="right">6.58</td> -</tr> -<tr class="even"> -<td align="right">43.0019614</td> -<td align="right">6.31</td> -</tr> -<tr class="odd"> -<td align="right">53.7524518</td> -<td align="right">3.47</td> -</tr> -<tr class="even"> -<td align="right">53.7524518</td> -<td align="right">3.52</td> -</tr> -<tr class="odd"> -<td align="right">64.5029421</td> -<td align="right">3.40</td> -</tr> -<tr class="even"> -<td align="right">64.5029421</td> -<td align="right">3.67</td> -</tr> -<tr class="odd"> -<td align="right">91.3791680</td> -<td align="right">1.62</td> -</tr> -<tr class="even"> -<td align="right">91.3791680</td> -<td align="right">1.62</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset BBA 2.3</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">DMTA</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.0000000</td> -<td align="right">99.33</td> -</tr> -<tr class="even"> -<td align="right">0.0000000</td> -<td align="right">97.44</td> -</tr> -<tr class="odd"> -<td align="right">0.6733938</td> -<td align="right">93.73</td> -</tr> -<tr class="even"> -<td align="right">0.6733938</td> -<td align="right">93.77</td> -</tr> -<tr class="odd"> -<td align="right">2.0201814</td> -<td align="right">87.84</td> -</tr> -<tr class="even"> -<td align="right">2.0201814</td> -<td align="right">89.82</td> -</tr> -<tr class="odd"> -<td align="right">4.7137565</td> -<td align="right">71.61</td> -</tr> -<tr class="even"> -<td align="right">4.7137565</td> -<td align="right">71.42</td> -</tr> -<tr class="odd"> -<td align="right">9.4275131</td> -<td align="right">45.60</td> -</tr> -<tr class="even"> -<td align="right">9.4275131</td> -<td align="right">45.42</td> -</tr> -<tr class="odd"> -<td align="right">14.1412696</td> -<td align="right">31.12</td> -</tr> -<tr class="even"> -<td align="right">14.1412696</td> -<td align="right">31.68</td> -</tr> -<tr class="odd"> -<td align="right">18.8550262</td> -<td align="right">23.20</td> -</tr> -<tr class="even"> -<td align="right">18.8550262</td> -<td align="right">24.13</td> -</tr> -<tr class="odd"> -<td align="right">28.2825393</td> -<td align="right">9.43</td> -</tr> -<tr class="even"> -<td align="right">28.2825393</td> -<td align="right">9.82</td> -</tr> -<tr class="odd"> -<td align="right">37.7100523</td> -<td align="right">7.08</td> -</tr> -<tr class="even"> -<td align="right">37.7100523</td> -<td align="right">8.64</td> -</tr> -<tr class="odd"> -<td align="right">47.1375654</td> -<td align="right">4.41</td> -</tr> -<tr class="even"> -<td align="right">47.1375654</td> -<td align="right">4.78</td> -</tr> -<tr class="odd"> -<td align="right">56.5650785</td> -<td align="right">4.92</td> -</tr> -<tr class="even"> -<td align="right">56.5650785</td> -<td align="right">5.08</td> -</tr> -<tr class="odd"> -<td align="right">80.1338612</td> -<td align="right">2.13</td> -</tr> -<tr class="even"> -<td align="right">80.1338612</td> -<td align="right">2.23</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset Elliot</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">DMTA</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.000000</td> -<td align="right">97.5</td> -</tr> -<tr class="even"> -<td align="right">0.000000</td> -<td align="right">100.7</td> -</tr> -<tr class="odd"> -<td align="right">1.228478</td> -<td align="right">86.4</td> -</tr> -<tr class="even"> -<td align="right">1.228478</td> -<td align="right">88.5</td> -</tr> -<tr class="odd"> -<td align="right">3.685435</td> -<td align="right">69.8</td> -</tr> -<tr class="even"> -<td align="right">3.685435</td> -<td align="right">77.1</td> -</tr> -<tr class="odd"> -<td align="right">8.599349</td> -<td align="right">59.0</td> -</tr> -<tr class="even"> -<td align="right">8.599349</td> -<td align="right">54.2</td> -</tr> -<tr class="odd"> -<td align="right">17.198697</td> -<td align="right">31.3</td> -</tr> -<tr class="even"> -<td align="right">17.198697</td> -<td align="right">33.5</td> -</tr> -<tr class="odd"> -<td align="right">25.798046</td> -<td align="right">19.6</td> -</tr> -<tr class="even"> -<td align="right">25.798046</td> -<td align="right">20.9</td> -</tr> -<tr class="odd"> -<td align="right">34.397395</td> -<td align="right">13.3</td> -</tr> -<tr class="even"> -<td align="right">34.397395</td> -<td align="right">15.8</td> -</tr> -<tr class="odd"> -<td align="right">51.596092</td> -<td align="right">6.7</td> -</tr> -<tr class="even"> -<td align="right">51.596092</td> -<td align="right">8.7</td> -</tr> -<tr class="odd"> -<td align="right">68.794789</td> -<td align="right">8.8</td> -</tr> -<tr class="even"> -<td align="right">68.794789</td> -<td align="right">8.7</td> -</tr> -<tr class="odd"> -<td align="right">103.192184</td> -<td align="right">6.0</td> -</tr> -<tr class="even"> -<td align="right">103.192184</td> -<td align="right">4.4</td> -</tr> -<tr class="odd"> -<td align="right">146.188928</td> -<td align="right">3.3</td> -</tr> -<tr class="even"> -<td align="right">146.188928</td> -<td align="right">2.8</td> -</tr> -<tr class="odd"> -<td align="right">223.583066</td> -<td align="right">1.4</td> -</tr> -<tr class="even"> -<td align="right">223.583066</td> -<td align="right">1.8</td> -</tr> -<tr class="odd"> -<td align="right">0.000000</td> -<td align="right">93.4</td> -</tr> -<tr class="even"> -<td align="right">0.000000</td> -<td align="right">103.2</td> -</tr> -<tr class="odd"> -<td align="right">1.228478</td> -<td align="right">89.2</td> -</tr> -<tr class="even"> -<td align="right">1.228478</td> -<td align="right">86.6</td> -</tr> -<tr class="odd"> -<td align="right">3.685435</td> -<td align="right">78.2</td> -</tr> -<tr class="even"> -<td align="right">3.685435</td> -<td align="right">78.1</td> -</tr> -<tr class="odd"> -<td align="right">8.599349</td> -<td align="right">55.6</td> -</tr> -<tr class="even"> -<td align="right">8.599349</td> -<td align="right">53.0</td> -</tr> -<tr class="odd"> -<td align="right">17.198697</td> -<td align="right">33.7</td> -</tr> -<tr class="even"> -<td align="right">17.198697</td> -<td align="right">33.2</td> -</tr> -<tr class="odd"> -<td align="right">25.798046</td> -<td align="right">20.9</td> -</tr> -<tr class="even"> -<td align="right">25.798046</td> -<td align="right">19.9</td> -</tr> -<tr class="odd"> -<td align="right">34.397395</td> -<td align="right">18.2</td> -</tr> -<tr class="even"> -<td align="right">34.397395</td> -<td align="right">12.7</td> -</tr> -<tr class="odd"> -<td align="right">51.596092</td> -<td align="right">7.8</td> -</tr> -<tr class="even"> -<td align="right">51.596092</td> -<td align="right">9.0</td> -</tr> -<tr class="odd"> -<td align="right">68.794789</td> -<td align="right">11.4</td> -</tr> -<tr class="even"> -<td align="right">68.794789</td> -<td align="right">9.0</td> -</tr> -<tr class="odd"> -<td align="right">103.192184</td> -<td align="right">3.9</td> -</tr> -<tr class="even"> -<td align="right">103.192184</td> -<td align="right">4.4</td> -</tr> -<tr class="odd"> -<td align="right">146.188928</td> -<td align="right">2.6</td> -</tr> -<tr class="even"> -<td align="right">146.188928</td> -<td align="right">3.4</td> -</tr> -<tr class="odd"> -<td align="right">223.583066</td> -<td align="right">2.0</td> -</tr> -<tr class="even"> -<td align="right">223.583066</td> -<td align="right">1.7</td> -</tr> -</tbody> -</table> -</div> -<div class="section level2"> -<h2 id="separate-evaluations">Separate evaluations<a class="anchor" aria-label="anchor" href="#separate-evaluations"></a> -</h2> -<p>In order to obtain suitable starting parameters for the NLHM fits, -separate fits of the four models to the data for each soil are generated -using the <code>mmkin</code> function from the <code>mkin</code> -package. In a first step, constant variance is assumed. Convergence is -checked with the <code>status</code> function.</p> -<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">deg_mods</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>, <span class="st">"HS"</span><span class="op">)</span></span> -<span><span class="va">f_sep_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span></span> -<span> <span class="va">deg_mods</span>,</span> -<span> <span class="va">dmta_ds</span>,</span> -<span> error_model <span class="op">=</span> <span class="st">"const"</span>,</span> -<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<span></span> -<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">Calke</th> -<th align="left">Borstel</th> -<th align="left">Flaach</th> -<th align="left">BBA 2.2</th> -<th align="left">BBA 2.3</th> -<th align="left">Elliot</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">SFO</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">FOMC</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">DFOP</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">HS</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -</tbody> -</table> -<p>In the table above, OK indicates convergence, and C indicates failure -to converge. All separate fits with constant variance converged, with -the sole exception of the HS fit to the BBA 2.2 data. To prepare for -fitting NLHM using the two-component error model, the separate fits are -updated assuming two-component error.</p> -<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_sep_tc</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_sep_const</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span> -<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_tc</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">Calke</th> -<th align="left">Borstel</th> -<th align="left">Flaach</th> -<th align="left">BBA 2.2</th> -<th align="left">BBA 2.3</th> -<th align="left">Elliot</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">SFO</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">FOMC</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">DFOP</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">HS</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -</tbody> -</table> -<p>Using the two-component error model, the one fit that did not -converge with constant variance did converge, but other non-SFO fits -failed to converge.</p> -</div> -<div class="section level2"> -<h2 id="hierarchichal-model-fits">Hierarchichal model fits<a class="anchor" aria-label="anchor" href="#hierarchichal-model-fits"></a> -</h2> -<p>The following code fits eight versions of hierarchical models to the -data, using SFO, FOMC, DFOP and HS for the parent compound, and using -either constant variance or two-component error for the error model. The -default parameter distribution model in mkin allows for variation of all -degradation parameters across the assumed population of soils. In other -words, each degradation parameter is associated with a random effect as -a first step. The <code>mhmkin</code> function makes it possible to fit -all eight versions in parallel (given a sufficient number of computing -cores being available) to save execution time.</p> -<p>Convergence plots and summaries for these fits are shown in the -appendix.</p> -<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_saem</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mhmkin.html">mhmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">f_sep_const</span>, <span class="va">f_sep_tc</span><span class="op">)</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span></span></code></pre></div> -<p>The output of the <code>status</code> function shows that all fits -terminated successfully.</p> -<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_saem</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">const</th> -<th align="left">tc</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">SFO</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">FOMC</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">DFOP</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">HS</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -</tbody> -</table> -<p>The AIC and BIC values show that the biphasic models DFOP and HS give -the best fits.</p> -<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="right">npar</th> -<th align="right">AIC</th> -<th align="right">BIC</th> -<th align="right">Lik</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">SFO const</td> -<td align="right">5</td> -<td align="right">796.3</td> -<td align="right">795.3</td> -<td align="right">-393.2</td> -</tr> -<tr class="even"> -<td align="left">SFO tc</td> -<td align="right">6</td> -<td align="right">798.3</td> -<td align="right">797.1</td> -<td align="right">-393.2</td> -</tr> -<tr class="odd"> -<td align="left">FOMC const</td> -<td align="right">7</td> -<td align="right">734.2</td> -<td align="right">732.7</td> -<td align="right">-360.1</td> -</tr> -<tr class="even"> -<td align="left">FOMC tc</td> -<td align="right">8</td> -<td align="right">720.4</td> -<td align="right">718.8</td> -<td align="right">-352.2</td> -</tr> -<tr class="odd"> -<td align="left">DFOP const</td> -<td align="right">9</td> -<td align="right">711.8</td> -<td align="right">710.0</td> -<td align="right">-346.9</td> -</tr> -<tr class="even"> -<td align="left">HS const</td> -<td align="right">9</td> -<td align="right">714.0</td> -<td align="right">712.1</td> -<td align="right">-348.0</td> -</tr> -<tr class="odd"> -<td align="left">DFOP tc</td> -<td align="right">10</td> -<td align="right">665.5</td> -<td align="right">663.4</td> -<td align="right">-322.8</td> -</tr> -<tr class="even"> -<td align="left">HS tc</td> -<td align="right">10</td> -<td align="right">667.1</td> -<td align="right">665.0</td> -<td align="right">-323.6</td> -</tr> -</tbody> -</table> -<p>The DFOP model is preferred here, as it has a better mechanistic -basis for batch experiments with constant incubation conditions. Also, -it shows the lowest AIC and BIC values in the first set of fits when -combined with the two-component error model. Therefore, the DFOP model -was selected for further refinements of the fits with the aim to make -the model fully identifiable.</p> -<div class="section level3"> -<h3 id="parameter-identifiability-based-on-the-fisher-information-matrix">Parameter identifiability based on the Fisher Information -Matrix<a class="anchor" aria-label="anchor" href="#parameter-identifiability-based-on-the-fisher-information-matrix"></a> -</h3> -<p>Using the <code>illparms</code> function, ill-defined statistical -model parameters such as standard deviations of the degradation -parameters in the population and error model parameters can be -found.</p> -<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">const</th> -<th align="left">tc</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">SFO</td> -<td align="left"></td> -<td align="left">b.1</td> -</tr> -<tr class="even"> -<td align="left">FOMC</td> -<td align="left"></td> -<td align="left">sd(DMTA_0)</td> -</tr> -<tr class="odd"> -<td align="left">DFOP</td> -<td align="left">sd(k2)</td> -<td align="left">sd(k2)</td> -</tr> -<tr class="even"> -<td align="left">HS</td> -<td align="left"></td> -<td align="left">sd(tb)</td> -</tr> -</tbody> -</table> -<p>According to the <code>illparms</code> function, the fitted standard -deviation of the second kinetic rate constant <code>k2</code> is -ill-defined in both DFOP fits. This suggests that different values would -be obtained for this standard deviation when using different starting -values.</p> -<p>The thus identified overparameterisation is addressed by removing the -random effect for <code>k2</code> from the parameter model.</p> -<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_saem_dfop_tc_no_ranef_k2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_saem</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span>,</span> -<span> no_random_effect <span class="op">=</span> <span class="st">"k2"</span><span class="op">)</span></span></code></pre></div> -<p>For the resulting fit, it is checked whether there are still -ill-defined parameters,</p> -<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_dfop_tc_no_ranef_k2</span><span class="op">)</span></span></code></pre></div> -<p>which is not the case. Below, the refined model is compared with the -previous best model. The model without random effect for <code>k2</code> -is a reduced version of the previous model. Therefore, the models are -nested and can be compared using the likelihood ratio test. This is -achieved with the argument <code>test = TRUE</code> to the -<code>anova</code> function.</p> -<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span>, <span class="va">f_saem_dfop_tc_no_ranef_k2</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|></span></span> -<span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>format.args <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">4</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<colgroup> -<col width="37%"> -<col width="6%"> -<col width="8%"> -<col width="8%"> -<col width="9%"> -<col width="9%"> -<col width="4%"> -<col width="15%"> -</colgroup> -<thead><tr class="header"> -<th align="left"></th> -<th align="right">npar</th> -<th align="right">AIC</th> -<th align="right">BIC</th> -<th align="right">Lik</th> -<th align="right">Chisq</th> -<th align="right">Df</th> -<th align="right">Pr(>Chisq)</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">f_saem_dfop_tc_no_ranef_k2</td> -<td align="right">9</td> -<td align="right">663.8</td> -<td align="right">661.9</td> -<td align="right">-322.9</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="left">f_saem[[“DFOP”, “tc”]]</td> -<td align="right">10</td> -<td align="right">665.5</td> -<td align="right">663.4</td> -<td align="right">-322.8</td> -<td align="right">0.2809</td> -<td align="right">1</td> -<td align="right">0.5961</td> -</tr> -</tbody> -</table> -<p>The AIC and BIC criteria are lower after removal of the ill-defined -random effect for <code>k2</code>. The p value of the likelihood ratio -test is much greater than 0.05, indicating that the model with the -higher likelihood (here the model with random effects for all -degradation parameters <code>f_saem[["DFOP", "tc"]]</code>) does not fit -significantly better than the model with the lower likelihood (the -reduced model <code>f_saem_dfop_tc_no_ranef_k2</code>).</p> -<p>Therefore, AIC, BIC and likelihood ratio test suggest the use of the -reduced model.</p> -<p>The convergence of the fit is checked visually.</p> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_parent_files/figure-html/convergence-saem-dfop-tc-no-ranef-k2-1.png" alt="Convergence plot for the NLHM DFOP fit with two-component error and without a random effect on 'k2'" width="864"><p class="caption"> -Convergence plot for the NLHM DFOP fit with two-component error and -without a random effect on ‘k2’ -</p> -</div> -<p>All parameters appear to have converged to a satisfactory degree. The -final fit is plotted using the plot method from the mkin package.</p> -<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_dfop_tc_no_ranef_k2</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_parent_files/figure-html/plot-saem-dfop-tc-no-ranef-k2-1.png" alt="Plot of the final NLHM DFOP fit" width="864"><p class="caption"> -Plot of the final NLHM DFOP fit -</p> -</div> -<p>Finally, a summary report of the fit is produced.</p> -<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">f_saem_dfop_tc_no_ranef_k2</span><span class="op">)</span></span></code></pre></div> -<pre><code>saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.2 -R version used for fitting: 4.2.2 -Date of fit: Sat Jan 28 11:22:51 2023 -Date of summary: Sat Jan 28 11:22:52 2023 - -Equations: -d_DMTA/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * - time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) - * DMTA - -Data: -155 observations of 1 variable(s) grouped in 6 datasets - -Model predictions using solution type analytical - -Fitted in 3.74 s -Using 300, 100 iterations and 9 chains - -Variance model: Two-component variance function - -Starting values for degradation parameters: - DMTA_0 k1 k2 g -98.759266 0.087034 0.009933 0.930827 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - DMTA_0 k1 k2 g -DMTA_0 98.76 0 0 0 -k1 0.00 1 0 0 -k2 0.00 0 1 0 -g 0.00 0 0 1 - -Starting values for error model parameters: -a.1 b.1 - 1 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 663.8 661.9 -322.9 - -Optimised parameters: - est. lower upper -DMTA_0 98.228939 96.285869 100.17201 -k1 0.064063 0.033477 0.09465 -k2 0.008297 0.005824 0.01077 -g 0.953821 0.914328 0.99331 -a.1 1.068479 0.869538 1.26742 -b.1 0.029424 0.022406 0.03644 -SD.DMTA_0 2.030437 0.404824 3.65605 -SD.k1 0.594692 0.256660 0.93272 -SD.g 1.006754 0.361327 1.65218 - -Correlation: - DMTA_0 k1 k2 -k1 0.0218 -k2 0.0556 0.0355 -g -0.0516 -0.0284 -0.2800 - -Random effects: - est. lower upper -SD.DMTA_0 2.0304 0.4048 3.6560 -SD.k1 0.5947 0.2567 0.9327 -SD.g 1.0068 0.3613 1.6522 - -Variance model: - est. lower upper -a.1 1.06848 0.86954 1.26742 -b.1 0.02942 0.02241 0.03644 - -Estimated disappearance times: - DT50 DT90 DT50back DT50_k1 DT50_k2 -DMTA 11.45 41.4 12.46 10.82 83.54</code></pre> -</div> -<div class="section level3"> -<h3 id="alternative-check-of-parameter-identifiability">Alternative check of parameter identifiability<a class="anchor" aria-label="anchor" href="#alternative-check-of-parameter-identifiability"></a> -</h3> -<p>The parameter check used in the <code>illparms</code> function is -based on a quadratic approximation of the likelihood surface near its -optimum, which is calculated using the Fisher Information Matrix (FIM). -An alternative way to check parameter identifiability <span class="citation">(Duchesne et al. 2021)</span> based on a multistart -approach has recently been implemented in mkin.</p> -<p>The graph below shows boxplots of the parameters obtained in 50 runs -of the saem algorithm with different parameter combinations, sampled -from the range of the parameters obtained for the individual datasets -fitted separately using nonlinear regression.</p> -<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_saem_dfop_tc_multi</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/multistart.html">multistart</a></span><span class="op">(</span><span class="va">f_saem</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span>, n <span class="op">=</span> <span class="fl">50</span>, cores <span class="op">=</span> <span class="fl">15</span><span class="op">)</span></span></code></pre></div> -<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/par.html" class="external-link">par</a></span><span class="op">(</span>mar <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">6.1</span>, <span class="fl">4.1</span>, <span class="fl">2.1</span>, <span class="fl">2.1</span><span class="op">)</span><span class="op">)</span></span> -<span><span class="fu"><a href="../../reference/parplot.html">parplot</a></span><span class="op">(</span><span class="va">f_saem_dfop_tc_multi</span>, lpos <span class="op">=</span> <span class="st">"bottomright"</span>, ylim <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.3</span>, <span class="fl">10</span><span class="op">)</span>, las <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_parent_files/figure-html/multistart-full-par-1.png" alt="Scaled parameters from the multistart runs, full model" width="960"><p class="caption"> -Scaled parameters from the multistart runs, full model -</p> -</div> -<p>The graph clearly confirms the lack of identifiability of the -variance of <code>k2</code> in the full model. The overparameterisation -of the model also indicates a lack of identifiability of the variance of -parameter <code>g</code>.</p> -<p>The parameter boxplots of the multistart runs with the reduced model -shown below indicate that all runs give similar results, regardless of -the starting parameters.</p> -<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_saem_dfop_tc_no_ranef_k2_multi</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/multistart.html">multistart</a></span><span class="op">(</span><span class="va">f_saem_dfop_tc_no_ranef_k2</span>,</span> -<span> n <span class="op">=</span> <span class="fl">50</span>, cores <span class="op">=</span> <span class="fl">15</span><span class="op">)</span></span></code></pre></div> -<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/par.html" class="external-link">par</a></span><span class="op">(</span>mar <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">6.1</span>, <span class="fl">4.1</span>, <span class="fl">2.1</span>, <span class="fl">2.1</span><span class="op">)</span><span class="op">)</span></span> -<span><span class="fu"><a href="../../reference/parplot.html">parplot</a></span><span class="op">(</span><span class="va">f_saem_dfop_tc_no_ranef_k2_multi</span>, ylim <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.5</span>, <span class="fl">2</span><span class="op">)</span>, las <span class="op">=</span> <span class="fl">2</span>,</span> -<span> lpos <span class="op">=</span> <span class="st">"bottomright"</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_parent_files/figure-html/multistart-reduced-par-1.png" alt="Scaled parameters from the multistart runs, reduced model" width="960"><p class="caption"> -Scaled parameters from the multistart runs, reduced model -</p> -</div> -<p>When only the parameters of the top 25% of the fits are shown (based -on a feature introduced in mkin 1.2.2 currently under development), the -scatter is even less as shown below.</p> -<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/par.html" class="external-link">par</a></span><span class="op">(</span>mar <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">6.1</span>, <span class="fl">4.1</span>, <span class="fl">2.1</span>, <span class="fl">2.1</span><span class="op">)</span><span class="op">)</span></span> -<span><span class="fu"><a href="../../reference/parplot.html">parplot</a></span><span class="op">(</span><span class="va">f_saem_dfop_tc_no_ranef_k2_multi</span>, ylim <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.5</span>, <span class="fl">2</span><span class="op">)</span>, las <span class="op">=</span> <span class="fl">2</span>, llquant <span class="op">=</span> <span class="fl">0.25</span>,</span> -<span> lpos <span class="op">=</span> <span class="st">"bottomright"</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_parent_files/figure-html/multistart-reduced-par-llquant-1.png" alt="Scaled parameters from the multistart runs, reduced model, fits with the top 25\% likelihood values" width="960"><p class="caption"> -Scaled parameters from the multistart runs, reduced model, fits with the -top 25% likelihood values -</p> -</div> -</div> -</div> -<div class="section level2"> -<h2 id="conclusions">Conclusions<a class="anchor" aria-label="anchor" href="#conclusions"></a> -</h2> -<p>Fitting the four parent degradation models SFO, FOMC, DFOP and HS as -part of hierarchical model fits with two different error models and -normal distributions of the transformed degradation parameters works -without technical problems. The biphasic models DFOP and HS gave the -best fit to the data, but the default parameter distribution model was -not fully identifiable. Removing the random effect for the second -kinetic rate constant of the DFOP model resulted in a reduced model that -was fully identifiable and showed the lowest values for the model -selection criteria AIC and BIC. The reliability of the identification of -all model parameters was confirmed using multiple starting values.</p> -</div> -<div class="section level2"> -<h2 id="acknowledgements">Acknowledgements<a class="anchor" aria-label="anchor" href="#acknowledgements"></a> -</h2> -<p>The helpful comments by Janina Wöltjen of the German Environment -Agency are gratefully acknowledged.</p> -</div> -<div class="section level2"> -<h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a> -</h2> -<div id="refs" class="references csl-bib-body hanging-indent"> -<div id="ref-duchesne_2021" class="csl-entry"> -Duchesne, Ronan, Anissa Guillemin, Olivier Gandrillon, and Fabien -Crauste. 2021. <span>“Practical Identifiability in the Frame of -Nonlinear Mixed Effects Models: The Example of the in Vitro -Erythropoiesis.”</span> <em>BMC Bioinformatics</em> 22 (478). <a href="https://doi.org/10.1186/s12859-021-04373-4" class="external-link">https://doi.org/10.1186/s12859-021-04373-4</a>. -</div> -</div> -</div> -<div class="section level2"> -<h2 id="appendix">Appendix<a class="anchor" aria-label="anchor" href="#appendix"></a> -</h2> -<div class="section level3"> -<h3 id="hierarchical-model-fit-listings">Hierarchical model fit listings<a class="anchor" aria-label="anchor" href="#hierarchical-model-fit-listings"></a> -</h3> -<caption> -Hierarchical mkin fit of the SFO model with error model const -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.2 -R version used for fitting: 4.2.2 -Date of fit: Sat Jan 28 11:22:44 2023 -Date of summary: Sat Jan 28 11:23:57 2023 - -Equations: -d_DMTA/dt = - k_DMTA * DMTA - -Data: -155 observations of 1 variable(s) grouped in 6 datasets - -Model predictions using solution type analytical - -Fitted in 0.982 s -Using 300, 100 iterations and 9 chains - -Variance model: Constant variance - -Starting values for degradation parameters: - DMTA_0 k_DMTA -97.2953 0.0566 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - DMTA_0 k_DMTA -DMTA_0 97.3 0 -k_DMTA 0.0 1 - -Starting values for error model parameters: -a.1 - 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 796.3 795.3 -393.2 - -Optimised parameters: - est. lower upper -DMTA_0 97.28130 95.71113 98.8515 -k_DMTA 0.05665 0.02909 0.0842 -a.1 2.66442 2.35579 2.9731 -SD.DMTA_0 1.54776 0.15447 2.9411 -SD.k_DMTA 0.60690 0.26248 0.9513 - -Correlation: - DMTA_0 -k_DMTA 0.0168 - -Random effects: - est. lower upper -SD.DMTA_0 1.5478 0.1545 2.9411 -SD.k_DMTA 0.6069 0.2625 0.9513 - -Variance model: - est. lower upper -a.1 2.664 2.356 2.973 - -Estimated disappearance times: - DT50 DT90 -DMTA 12.24 40.65 - -</code></pre> -<p></p> -<caption> -Hierarchical mkin fit of the SFO model with error model tc -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.2 -R version used for fitting: 4.2.2 -Date of fit: Sat Jan 28 11:22:46 2023 -Date of summary: Sat Jan 28 11:23:57 2023 - -Equations: -d_DMTA/dt = - k_DMTA * DMTA - -Data: -155 observations of 1 variable(s) grouped in 6 datasets - -Model predictions using solution type analytical - -Fitted in 2.39 s -Using 300, 100 iterations and 9 chains - -Variance model: Two-component variance function - -Starting values for degradation parameters: - DMTA_0 k_DMTA -96.99175 0.05603 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - DMTA_0 k_DMTA -DMTA_0 96.99 0 -k_DMTA 0.00 1 - -Starting values for error model parameters: -a.1 b.1 - 1 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 798.3 797.1 -393.2 - -Optimised parameters: - est. lower upper -DMTA_0 97.271822 95.703157 98.84049 -k_DMTA 0.056638 0.029110 0.08417 -a.1 2.660081 2.230398 3.08976 -b.1 0.001665 -0.006911 0.01024 -SD.DMTA_0 1.545520 0.145035 2.94601 -SD.k_DMTA 0.606422 0.262274 0.95057 - -Correlation: - DMTA_0 -k_DMTA 0.0169 - -Random effects: - est. lower upper -SD.DMTA_0 1.5455 0.1450 2.9460 -SD.k_DMTA 0.6064 0.2623 0.9506 - -Variance model: - est. lower upper -a.1 2.660081 2.230398 3.08976 -b.1 0.001665 -0.006911 0.01024 - -Estimated disappearance times: - DT50 DT90 -DMTA 12.24 40.65 - -</code></pre> -<p></p> -<caption> -Hierarchical mkin fit of the FOMC model with error model const -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.2 -R version used for fitting: 4.2.2 -Date of fit: Sat Jan 28 11:22:45 2023 -Date of summary: Sat Jan 28 11:23:57 2023 - -Equations: -d_DMTA/dt = - (alpha/beta) * 1/((time/beta) + 1) * DMTA - -Data: -155 observations of 1 variable(s) grouped in 6 datasets - -Model predictions using solution type analytical - -Fitted in 1.552 s -Using 300, 100 iterations and 9 chains - -Variance model: Constant variance - -Starting values for degradation parameters: - DMTA_0 alpha beta - 98.292 9.909 156.341 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - DMTA_0 alpha beta -DMTA_0 98.29 0 0 -alpha 0.00 1 0 -beta 0.00 0 1 - -Starting values for error model parameters: -a.1 - 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 734.2 732.7 -360.1 - -Optimised parameters: - est. lower upper -DMTA_0 98.3435 96.9033 99.784 -alpha 7.2007 2.5889 11.812 -beta 112.8746 34.8816 190.868 -a.1 2.0459 1.8054 2.286 -SD.DMTA_0 1.4795 0.2717 2.687 -SD.alpha 0.6396 0.1509 1.128 -SD.beta 0.6874 0.1587 1.216 - -Correlation: - DMTA_0 alpha -alpha -0.1125 -beta -0.1227 0.3632 - -Random effects: - est. lower upper -SD.DMTA_0 1.4795 0.2717 2.687 -SD.alpha 0.6396 0.1509 1.128 -SD.beta 0.6874 0.1587 1.216 - -Variance model: - est. lower upper -a.1 2.046 1.805 2.286 - -Estimated disappearance times: - DT50 DT90 DT50back -DMTA 11.41 42.53 12.8 - -</code></pre> -<p></p> -<caption> -Hierarchical mkin fit of the FOMC model with error model tc -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.2 -R version used for fitting: 4.2.2 -Date of fit: Sat Jan 28 11:22:46 2023 -Date of summary: Sat Jan 28 11:23:57 2023 - -Equations: -d_DMTA/dt = - (alpha/beta) * 1/((time/beta) + 1) * DMTA - -Data: -155 observations of 1 variable(s) grouped in 6 datasets - -Model predictions using solution type analytical - -Fitted in 2.764 s -Using 300, 100 iterations and 9 chains - -Variance model: Two-component variance function - -Starting values for degradation parameters: -DMTA_0 alpha beta -98.772 4.663 92.597 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - DMTA_0 alpha beta -DMTA_0 98.77 0 0 -alpha 0.00 1 0 -beta 0.00 0 1 - -Starting values for error model parameters: -a.1 b.1 - 1 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 720.4 718.8 -352.2 - -Optimised parameters: - est. lower upper -DMTA_0 98.99136 97.26011 100.72261 -alpha 5.86312 2.57485 9.15138 -beta 88.55571 29.20889 147.90254 -a.1 1.51063 1.24384 1.77741 -b.1 0.02824 0.02040 0.03609 -SD.DMTA_0 1.57436 -0.04867 3.19739 -SD.alpha 0.59871 0.17132 1.02611 -SD.beta 0.72994 0.22849 1.23139 - -Correlation: - DMTA_0 alpha -alpha -0.1363 -beta -0.1414 0.2542 - -Random effects: - est. lower upper -SD.DMTA_0 1.5744 -0.04867 3.197 -SD.alpha 0.5987 0.17132 1.026 -SD.beta 0.7299 0.22849 1.231 - -Variance model: - est. lower upper -a.1 1.51063 1.2438 1.77741 -b.1 0.02824 0.0204 0.03609 - -Estimated disappearance times: - DT50 DT90 DT50back -DMTA 11.11 42.6 12.82 - -</code></pre> -<p></p> -<caption> -Hierarchical mkin fit of the DFOP model with error model const -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.2 -R version used for fitting: 4.2.2 -Date of fit: Sat Jan 28 11:22:45 2023 -Date of summary: Sat Jan 28 11:23:57 2023 - -Equations: -d_DMTA/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * - time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) - * DMTA - -Data: -155 observations of 1 variable(s) grouped in 6 datasets - -Model predictions using solution type analytical - -Fitted in 1.649 s -Using 300, 100 iterations and 9 chains - -Variance model: Constant variance - -Starting values for degradation parameters: - DMTA_0 k1 k2 g -98.64383 0.09211 0.02999 0.76814 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - DMTA_0 k1 k2 g -DMTA_0 98.64 0 0 0 -k1 0.00 1 0 0 -k2 0.00 0 1 0 -g 0.00 0 0 1 - -Starting values for error model parameters: -a.1 - 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 711.8 710 -346.9 - -Optimised parameters: - est. lower upper -DMTA_0 98.092481 96.573898 99.61106 -k1 0.062499 0.030336 0.09466 -k2 0.009065 -0.005133 0.02326 -g 0.948967 0.862079 1.03586 -a.1 1.821671 1.604774 2.03857 -SD.DMTA_0 1.677785 0.472066 2.88350 -SD.k1 0.634962 0.270788 0.99914 -SD.k2 1.033498 -0.205994 2.27299 -SD.g 1.710046 0.428642 2.99145 - -Correlation: - DMTA_0 k1 k2 -k1 0.0246 -k2 0.0491 0.0953 -g -0.0552 -0.0889 -0.4795 - -Random effects: - est. lower upper -SD.DMTA_0 1.678 0.4721 2.8835 -SD.k1 0.635 0.2708 0.9991 -SD.k2 1.033 -0.2060 2.2730 -SD.g 1.710 0.4286 2.9914 - -Variance model: - est. lower upper -a.1 1.822 1.605 2.039 - -Estimated disappearance times: - DT50 DT90 DT50back DT50_k1 DT50_k2 -DMTA 11.79 42.8 12.88 11.09 76.46 - -</code></pre> -<p></p> -<caption> -Hierarchical mkin fit of the DFOP model with error model tc -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.2 -R version used for fitting: 4.2.2 -Date of fit: Sat Jan 28 11:22:46 2023 -Date of summary: Sat Jan 28 11:23:57 2023 - -Equations: -d_DMTA/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * - time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) - * DMTA - -Data: -155 observations of 1 variable(s) grouped in 6 datasets - -Model predictions using solution type analytical - -Fitted in 3.288 s -Using 300, 100 iterations and 9 chains - -Variance model: Two-component variance function - -Starting values for degradation parameters: - DMTA_0 k1 k2 g -98.759266 0.087034 0.009933 0.930827 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - DMTA_0 k1 k2 g -DMTA_0 98.76 0 0 0 -k1 0.00 1 0 0 -k2 0.00 0 1 0 -g 0.00 0 0 1 - -Starting values for error model parameters: -a.1 b.1 - 1 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 665.5 663.4 -322.8 - -Optimised parameters: - est. lower upper -DMTA_0 98.377019 96.447952 100.30609 -k1 0.064843 0.034607 0.09508 -k2 0.008895 0.006368 0.01142 -g 0.949696 0.903815 0.99558 -a.1 1.065241 0.865754 1.26473 -b.1 0.029340 0.022336 0.03634 -SD.DMTA_0 2.007754 0.387982 3.62753 -SD.k1 0.580473 0.250286 0.91066 -SD.k2 0.006105 -4.920337 4.93255 -SD.g 1.097149 0.412779 1.78152 - -Correlation: - DMTA_0 k1 k2 -k1 0.0235 -k2 0.0595 0.0424 -g -0.0470 -0.0278 -0.2731 - -Random effects: - est. lower upper -SD.DMTA_0 2.007754 0.3880 3.6275 -SD.k1 0.580473 0.2503 0.9107 -SD.k2 0.006105 -4.9203 4.9325 -SD.g 1.097149 0.4128 1.7815 - -Variance model: - est. lower upper -a.1 1.06524 0.86575 1.26473 -b.1 0.02934 0.02234 0.03634 - -Estimated disappearance times: - DT50 DT90 DT50back DT50_k1 DT50_k2 -DMTA 11.36 41.32 12.44 10.69 77.92 - -</code></pre> -<p></p> -<caption> -Hierarchical mkin fit of the HS model with error model const -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.2 -R version used for fitting: 4.2.2 -Date of fit: Sat Jan 28 11:22:45 2023 -Date of summary: Sat Jan 28 11:23:57 2023 - -Equations: -d_DMTA/dt = - ifelse(time <= tb, k1, k2) * DMTA - -Data: -155 observations of 1 variable(s) grouped in 6 datasets - -Model predictions using solution type analytical - -Fitted in 2.006 s -Using 300, 100 iterations and 9 chains - -Variance model: Constant variance - -Starting values for degradation parameters: - DMTA_0 k1 k2 tb -97.82176 0.06931 0.02997 11.13945 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - DMTA_0 k1 k2 tb -DMTA_0 97.82 0 0 0 -k1 0.00 1 0 0 -k2 0.00 0 1 0 -tb 0.00 0 0 1 - -Starting values for error model parameters: -a.1 - 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 714 712.1 -348 - -Optimised parameters: - est. lower upper -DMTA_0 98.16102 96.47747 99.84456 -k1 0.07876 0.05261 0.10491 -k2 0.02227 0.01706 0.02747 -tb 13.99089 -7.40049 35.38228 -a.1 1.82305 1.60700 2.03910 -SD.DMTA_0 1.88413 0.56204 3.20622 -SD.k1 0.34292 0.10482 0.58102 -SD.k2 0.19851 0.01718 0.37985 -SD.tb 1.68168 0.58064 2.78272 - -Correlation: - DMTA_0 k1 k2 -k1 0.0142 -k2 0.0001 -0.0025 -tb 0.0165 -0.1256 -0.0301 - -Random effects: - est. lower upper -SD.DMTA_0 1.8841 0.56204 3.2062 -SD.k1 0.3429 0.10482 0.5810 -SD.k2 0.1985 0.01718 0.3798 -SD.tb 1.6817 0.58064 2.7827 - -Variance model: - est. lower upper -a.1 1.823 1.607 2.039 - -Estimated disappearance times: - DT50 DT90 DT50back DT50_k1 DT50_k2 -DMTA 8.801 67.91 20.44 8.801 31.13 - -</code></pre> -<p></p> -<caption> -Hierarchical mkin fit of the HS model with error model tc -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.2 -R version used for fitting: 4.2.2 -Date of fit: Sat Jan 28 11:22:46 2023 -Date of summary: Sat Jan 28 11:23:57 2023 - -Equations: -d_DMTA/dt = - ifelse(time <= tb, k1, k2) * DMTA - -Data: -155 observations of 1 variable(s) grouped in 6 datasets - -Model predictions using solution type analytical - -Fitted in 3.267 s -Using 300, 100 iterations and 9 chains - -Variance model: Two-component variance function - -Starting values for degradation parameters: - DMTA_0 k1 k2 tb -98.45190 0.07525 0.02576 19.19375 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - DMTA_0 k1 k2 tb -DMTA_0 98.45 0 0 0 -k1 0.00 1 0 0 -k2 0.00 0 1 0 -tb 0.00 0 0 1 - -Starting values for error model parameters: -a.1 b.1 - 1 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 667.1 665 -323.6 - -Optimised parameters: - est. lower upper -DMTA_0 97.76570 95.81350 99.71791 -k1 0.05855 0.03080 0.08630 -k2 0.02337 0.01664 0.03010 -tb 31.09638 29.38289 32.80987 -a.1 1.08835 0.88590 1.29080 -b.1 0.02964 0.02257 0.03671 -SD.DMTA_0 2.04877 0.42607 3.67147 -SD.k1 0.59166 0.25621 0.92711 -SD.k2 0.30698 0.09561 0.51835 -SD.tb 0.01274 -0.10914 0.13462 - -Correlation: - DMTA_0 k1 k2 -k1 0.0160 -k2 -0.0070 -0.0024 -tb -0.0668 -0.0103 -0.2013 - -Random effects: - est. lower upper -SD.DMTA_0 2.04877 0.42607 3.6715 -SD.k1 0.59166 0.25621 0.9271 -SD.k2 0.30698 0.09561 0.5183 -SD.tb 0.01274 -0.10914 0.1346 - -Variance model: - est. lower upper -a.1 1.08835 0.88590 1.29080 -b.1 0.02964 0.02257 0.03671 - -Estimated disappearance times: - DT50 DT90 DT50back DT50_k1 DT50_k2 -DMTA 11.84 51.71 15.57 11.84 29.66 - -</code></pre> -<p></p> -</div> -<div class="section level3"> -<h3 id="hierarchical-model-convergence-plots">Hierarchical model convergence plots<a class="anchor" aria-label="anchor" href="#hierarchical-model-convergence-plots"></a> -</h3> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_parent_files/figure-html/convergence-saem-sfo-const-1.png" alt="Convergence plot for the NLHM SFO fit with constant variance" width="864"><p class="caption"> -Convergence plot for the NLHM SFO fit with constant variance -</p> -</div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_parent_files/figure-html/convergence-saem-sfo-tc-1.png" alt="Convergence plot for the NLHM SFO fit with two-component error" width="864"><p class="caption"> -Convergence plot for the NLHM SFO fit with two-component error -</p> -</div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_parent_files/figure-html/convergence-saem-fomc-const-1.png" alt="Convergence plot for the NLHM FOMC fit with constant variance" width="864"><p class="caption"> -Convergence plot for the NLHM FOMC fit with constant variance -</p> -</div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_parent_files/figure-html/convergence-saem-fomc-tc-1.png" alt="Convergence plot for the NLHM FOMC fit with two-component error" width="864"><p class="caption"> -Convergence plot for the NLHM FOMC fit with two-component error -</p> -</div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_parent_files/figure-html/convergence-saem-dfop-const-1.png" alt="Convergence plot for the NLHM DFOP fit with constant variance" width="864"><p class="caption"> -Convergence plot for the NLHM DFOP fit with constant variance -</p> -</div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_parent_files/figure-html/convergence-saem-dfop-tc-1.png" alt="Convergence plot for the NLHM DFOP fit with two-component error" width="864"><p class="caption"> -Convergence plot for the NLHM DFOP fit with two-component error -</p> -</div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_parent_files/figure-html/convergence-saem-hs-const-1.png" alt="Convergence plot for the NLHM HS fit with constant variance" width="864"><p class="caption"> -Convergence plot for the NLHM HS fit with constant variance -</p> -</div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_parent_files/figure-html/convergence-saem-hs-tc-1.png" alt="Convergence plot for the NLHM HS fit with two-component error" width="864"><p class="caption"> -Convergence plot for the NLHM HS fit with two-component error -</p> -</div> -</div> -<div class="section level3"> -<h3 id="session-info">Session info<a class="anchor" aria-label="anchor" href="#session-info"></a> -</h3> -<pre><code>R version 4.2.2 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_1.2.2 - -loaded via a namespace (and not attached): - [1] deSolve_1.34 zoo_1.8-11 tidyselect_1.2.0 xfun_0.35 - [5] bslib_0.4.2 purrr_1.0.0 lattice_0.20-45 colorspace_2.0-3 - [9] vctrs_0.5.1 generics_0.1.3 htmltools_0.5.4 yaml_2.3.6 -[13] utf8_1.2.2 rlang_1.0.6 pkgdown_2.0.7 jquerylib_0.1.4 -[17] pillar_1.8.1 glue_1.6.2 DBI_1.1.3 lifecycle_1.0.3 -[21] stringr_1.5.0 munsell_0.5.0 gtable_0.3.1 ragg_1.2.4 -[25] codetools_0.2-18 memoise_2.0.1 evaluate_0.19 fastmap_1.1.0 -[29] lmtest_0.9-40 fansi_1.0.3 highr_0.9 scales_1.2.1 -[33] cachem_1.0.6 desc_1.4.2 jsonlite_1.8.4 systemfonts_1.0.4 -[37] fs_1.5.2 textshaping_0.3.6 gridExtra_2.3 ggplot2_3.4.0 -[41] digest_0.6.31 stringi_1.7.8 dplyr_1.0.10 grid_4.2.2 -[45] rprojroot_2.0.3 cli_3.5.0 tools_4.2.2 magrittr_2.0.3 -[49] sass_0.4.4 tibble_3.1.8 pkgconfig_2.0.3 assertthat_0.2.1 -[53] rmarkdown_2.19 R6_2.5.1 mclust_6.0.0 nlme_3.1-161 -[57] compiler_4.2.2 </code></pre> -</div> -<div class="section level3"> -<h3 id="hardware-info">Hardware info<a class="anchor" aria-label="anchor" href="#hardware-info"></a> -</h3> -<pre><code>CPU model: AMD Ryzen 9 7950X 16-Core Processor</code></pre> -<pre><code>MemTotal: 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 href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p> -</div> - - </footer> -</div> - - - - - - - </body> -</html> diff --git a/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-dfop-const-1.png b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-dfop-const-1.png Binary files differdeleted file mode 100644 index 3f145074..00000000 --- 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fa-lg"></span> - - </a> -</li> - </ul> -</div> -<!--/.nav-collapse --> - </div> -<!--/.container --> -</div> -<!--/.navbar --> - - - - </header><div class="row"> - <div class="col-md-9 contents"> - <div class="page-header toc-ignore"> - <h1 data-toc-skip>Testing hierarchical pathway kinetics with -residue data on dimethenamid and dimethenamid-P</h1> - <h4 data-toc-skip class="author">Johannes -Ranke</h4> - - <h4 data-toc-skip class="date">Last change on 20 April 2023, -last compiled on 20 April 2023</h4> - - <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/prebuilt/2022_dmta_pathway.rmd" class="external-link"><code>vignettes/prebuilt/2022_dmta_pathway.rmd</code></a></small> - <div class="hidden name"><code>2022_dmta_pathway.rmd</code></div> - - </div> - - - -<div class="section level2"> -<h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#introduction"></a> -</h2> -<p>The purpose of this document is to test demonstrate how nonlinear -hierarchical models (NLHM) based on the parent degradation models SFO, -FOMC, DFOP and HS, with parallel formation of two or more metabolites -can be fitted with the mkin package.</p> -<p>It was assembled in the course of work package 1.2 of Project Number -173340 (Application of nonlinear hierarchical models to the kinetic -evaluation of chemical degradation data) of the German Environment -Agency carried out in 2022 and 2023.</p> -<p>The mkin package is used in version 1.2.4, which is currently under -development. It contains the test data, and the functions used in the -evaluations. The <code>saemix</code> package is used as a backend for -fitting the NLHM, but is also loaded to make the convergence plot -function available.</p> -<p>This document is processed with the <code>knitr</code> package, which -also provides the <code>kable</code> function that is used to improve -the display of tabular data in R markdown documents. For parallel -processing, the <code>parallel</code> package is used.</p> -<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://pkgdown.jrwb.de/mkin/">mkin</a></span><span class="op">)</span></span> -<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://yihui.org/knitr/" class="external-link">knitr</a></span><span class="op">)</span></span> -<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">saemix</span><span class="op">)</span></span> -<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">parallel</span><span class="op">)</span></span> -<span><span class="va">n_cores</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/detectCores.html" class="external-link">detectCores</a></span><span class="op">(</span><span class="op">)</span></span> -<span></span> -<span><span class="co"># We need to start a new cluster after defining a compiled model that is</span></span> -<span><span class="co"># saved as a DLL to the user directory, therefore we define a function</span></span> -<span><span class="co"># This is used again after defining the pathway model</span></span> -<span><span class="va">start_cluster</span> <span class="op"><-</span> <span class="kw">function</span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span> <span class="op">{</span></span> -<span> <span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/Sys.info.html" class="external-link">Sys.info</a></span><span class="op">(</span><span class="op">)</span><span class="op">[</span><span class="st">"sysname"</span><span class="op">]</span> <span class="op">==</span> <span class="st">"Windows"</span><span class="op">)</span> <span class="op">{</span></span> -<span> <span class="va">ret</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makePSOCKcluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> -<span> <span class="op">}</span> <span class="kw">else</span> <span class="op">{</span></span> -<span> <span class="va">ret</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makeForkCluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> -<span> <span class="op">}</span></span> -<span> <span class="kw"><a href="https://rdrr.io/r/base/function.html" class="external-link">return</a></span><span class="op">(</span><span class="va">ret</span><span class="op">)</span></span> -<span><span class="op">}</span></span></code></pre></div> -</div> -<div class="section level2"> -<h2 id="data">Data<a class="anchor" aria-label="anchor" href="#data"></a> -</h2> -<p>The test data are available in the mkin package as an object of class -<code>mkindsg</code> (mkin dataset group) under the identifier -<code>dimethenamid_2018</code>. The following preprocessing steps are -done in this document.</p> -<ul> -<li>The data available for the enantiomer dimethenamid-P (DMTAP) are -renamed to have the same substance name as the data for the racemic -mixture dimethenamid (DMTA). The reason for this is that no difference -between their degradation behaviour was identified in the EU risk -assessment.</li> -<li>Unnecessary columns are discarded</li> -<li>The observation times of each dataset are multiplied with the -corresponding normalisation factor also available in the dataset, in -order to make it possible to describe all datasets with a single set of -parameters that are independent of temperature</li> -<li>Finally, datasets observed in the same soil (<code>Elliot 1</code> -and <code>Elliot 2</code>) are combined, resulting in dimethenamid -(DMTA) data from six soils.</li> -</ul> -<p>The following commented R code performs this preprocessing.</p> -<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="co"># Apply a function to each of the seven datasets in the mkindsg object to create a list</span></span> -<span><span class="va">dmta_ds</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">lapply</a></span><span class="op">(</span><span class="fl">1</span><span class="op">:</span><span class="fl">7</span>, <span class="kw">function</span><span class="op">(</span><span class="va">i</span><span class="op">)</span> <span class="op">{</span></span> -<span> <span class="va">ds_i</span> <span class="op"><-</span> <span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">ds</span><span class="op">[[</span><span class="va">i</span><span class="op">]</span><span class="op">]</span><span class="op">$</span><span class="va">data</span> <span class="co"># Get a dataset</span></span> -<span> <span class="va">ds_i</span><span class="op">[</span><span class="va">ds_i</span><span class="op">$</span><span class="va">name</span> <span class="op">==</span> <span class="st">"DMTAP"</span>, <span class="st">"name"</span><span class="op">]</span> <span class="op"><-</span> <span class="st">"DMTA"</span> <span class="co"># Rename DMTAP to DMTA</span></span> -<span> <span class="va">ds_i</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/subset.html" class="external-link">subset</a></span><span class="op">(</span><span class="va">ds_i</span>, select <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"name"</span>, <span class="st">"time"</span>, <span class="st">"value"</span><span class="op">)</span><span class="op">)</span> <span class="co"># Select data</span></span> -<span> <span class="va">ds_i</span><span class="op">$</span><span class="va">time</span> <span class="op"><-</span> <span class="va">ds_i</span><span class="op">$</span><span class="va">time</span> <span class="op">*</span> <span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">f_time_norm</span><span class="op">[</span><span class="va">i</span><span class="op">]</span> <span class="co"># Normalise time</span></span> -<span> <span class="va">ds_i</span> <span class="co"># Return the dataset</span></span> -<span><span class="op">}</span><span class="op">)</span></span> -<span></span> -<span><span class="co"># Use dataset titles as names for the list elements</span></span> -<span><span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">)</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</span><span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">ds</span>, <span class="kw">function</span><span class="op">(</span><span class="va">ds</span><span class="op">)</span> <span class="va">ds</span><span class="op">$</span><span class="va">title</span><span class="op">)</span></span> -<span></span> -<span><span class="co"># Combine data for Elliot soil to obtain a named list with six elements</span></span> -<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/cbind.html" class="external-link">rbind</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 1"</span><span class="op">]</span><span class="op">]</span>, <span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 2"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span> <span class="co">#</span></span> -<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 1"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="cn">NULL</span></span> -<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 2"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="cn">NULL</span></span></code></pre></div> -<p>The following tables show the 6 datasets.</p> -<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="kw">for</span> <span class="op">(</span><span class="va">ds_name</span> <span class="kw">in</span> <span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">)</span><span class="op">)</span> <span class="op">{</span></span> -<span> <span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span></span> -<span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="fu"><a href="../../reference/mkin_long_to_wide.html">mkin_long_to_wide</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">[[</span><span class="va">ds_name</span><span class="op">]</span><span class="op">]</span><span class="op">)</span>,</span> -<span> caption <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste</a></span><span class="op">(</span><span class="st">"Dataset"</span>, <span class="va">ds_name</span><span class="op">)</span>,</span> -<span> booktabs <span class="op">=</span> <span class="cn">TRUE</span>, row.names <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">)</span></span> -<span> <span class="fu"><a href="https://rdrr.io/r/base/cat.html" class="external-link">cat</a></span><span class="op">(</span><span class="st">"\n\\clearpage\n"</span><span class="op">)</span></span> -<span><span class="op">}</span></span></code></pre></div> -<table class="table"> -<caption>Dataset Calke</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">DMTA</th> -<th align="right">M23</th> -<th align="right">M27</th> -<th align="right">M31</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0</td> -<td align="right">95.8</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">0</td> -<td align="right">98.7</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">14</td> -<td align="right">60.5</td> -<td align="right">4.1</td> -<td align="right">1.5</td> -<td align="right">2.0</td> -</tr> -<tr class="even"> -<td align="right">30</td> -<td align="right">39.1</td> -<td align="right">5.3</td> -<td align="right">2.4</td> -<td align="right">2.1</td> -</tr> -<tr class="odd"> -<td align="right">59</td> -<td align="right">15.2</td> -<td align="right">6.0</td> -<td align="right">3.2</td> -<td align="right">2.2</td> -</tr> -<tr class="even"> -<td align="right">120</td> -<td align="right">4.8</td> -<td align="right">4.3</td> -<td align="right">3.8</td> -<td align="right">1.8</td> -</tr> -<tr class="odd"> -<td align="right">120</td> -<td align="right">4.6</td> -<td align="right">4.1</td> -<td align="right">3.7</td> -<td align="right">2.1</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset Borstel</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">DMTA</th> -<th align="right">M23</th> -<th align="right">M27</th> -<th align="right">M31</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.000000</td> -<td align="right">100.5</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">0.000000</td> -<td align="right">99.6</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">1.941295</td> -<td align="right">91.9</td> -<td align="right">0.4</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">1.941295</td> -<td align="right">91.3</td> -<td align="right">0.5</td> -<td align="right">0.3</td> -<td align="right">0.1</td> -</tr> -<tr class="odd"> -<td align="right">6.794534</td> -<td align="right">81.8</td> -<td align="right">1.2</td> -<td align="right">0.8</td> -<td align="right">1.0</td> -</tr> -<tr class="even"> -<td align="right">6.794534</td> -<td align="right">82.1</td> -<td align="right">1.3</td> -<td align="right">0.9</td> -<td align="right">0.9</td> -</tr> -<tr class="odd"> -<td align="right">13.589067</td> -<td align="right">69.1</td> -<td align="right">2.8</td> -<td align="right">1.4</td> -<td align="right">2.0</td> -</tr> -<tr class="even"> -<td align="right">13.589067</td> -<td align="right">68.0</td> -<td align="right">2.0</td> -<td align="right">1.4</td> -<td align="right">2.5</td> -</tr> -<tr class="odd"> -<td align="right">27.178135</td> -<td align="right">51.4</td> -<td align="right">2.9</td> -<td align="right">2.7</td> -<td align="right">4.3</td> -</tr> -<tr class="even"> -<td align="right">27.178135</td> -<td align="right">51.4</td> -<td align="right">4.9</td> -<td align="right">2.6</td> -<td align="right">3.2</td> -</tr> -<tr class="odd"> -<td align="right">56.297565</td> -<td align="right">27.6</td> -<td align="right">12.2</td> -<td align="right">4.4</td> -<td align="right">4.3</td> -</tr> -<tr class="even"> -<td align="right">56.297565</td> -<td align="right">26.8</td> -<td align="right">12.2</td> -<td align="right">4.7</td> -<td align="right">4.8</td> -</tr> -<tr class="odd"> -<td align="right">86.387643</td> -<td align="right">15.7</td> -<td align="right">12.2</td> -<td align="right">5.4</td> -<td align="right">5.0</td> -</tr> -<tr class="even"> -<td align="right">86.387643</td> -<td align="right">15.3</td> -<td align="right">12.0</td> -<td align="right">5.2</td> -<td align="right">5.1</td> -</tr> -<tr class="odd"> -<td align="right">115.507073</td> -<td align="right">7.9</td> -<td align="right">10.4</td> -<td align="right">5.4</td> -<td align="right">4.3</td> -</tr> -<tr class="even"> -<td align="right">115.507073</td> -<td align="right">8.1</td> -<td align="right">11.6</td> -<td align="right">5.4</td> -<td align="right">4.4</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset Flaach</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">DMTA</th> -<th align="right">M23</th> -<th align="right">M27</th> -<th align="right">M31</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.0000000</td> -<td align="right">96.5</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">0.0000000</td> -<td align="right">96.8</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">0.0000000</td> -<td align="right">97.0</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">0.6233856</td> -<td align="right">82.9</td> -<td align="right">0.7</td> -<td align="right">1.1</td> -<td align="right">0.3</td> -</tr> -<tr class="odd"> -<td align="right">0.6233856</td> -<td align="right">86.7</td> -<td align="right">0.7</td> -<td align="right">1.1</td> -<td align="right">0.3</td> -</tr> -<tr class="even"> -<td align="right">0.6233856</td> -<td align="right">87.4</td> -<td align="right">0.2</td> -<td align="right">0.3</td> -<td align="right">0.1</td> -</tr> -<tr class="odd"> -<td align="right">1.8701567</td> -<td align="right">72.8</td> -<td align="right">2.2</td> -<td align="right">2.6</td> -<td align="right">0.7</td> -</tr> -<tr class="even"> -<td align="right">1.8701567</td> -<td align="right">69.9</td> -<td align="right">1.8</td> -<td align="right">2.4</td> -<td align="right">0.6</td> -</tr> -<tr class="odd"> -<td align="right">1.8701567</td> -<td align="right">71.9</td> -<td align="right">1.6</td> -<td align="right">2.3</td> -<td align="right">0.7</td> -</tr> -<tr class="even"> -<td align="right">4.3636989</td> -<td align="right">51.4</td> -<td align="right">4.1</td> -<td align="right">5.0</td> -<td align="right">1.3</td> -</tr> -<tr class="odd"> -<td align="right">4.3636989</td> -<td align="right">52.9</td> -<td align="right">4.2</td> -<td align="right">5.9</td> -<td align="right">1.2</td> -</tr> -<tr class="even"> -<td align="right">4.3636989</td> -<td align="right">48.6</td> -<td align="right">4.2</td> -<td align="right">4.8</td> -<td align="right">1.4</td> -</tr> -<tr class="odd"> -<td align="right">8.7273979</td> -<td align="right">28.5</td> -<td align="right">7.5</td> -<td align="right">8.5</td> -<td align="right">2.4</td> -</tr> -<tr class="even"> -<td align="right">8.7273979</td> -<td align="right">27.3</td> -<td align="right">7.1</td> -<td align="right">8.5</td> -<td align="right">2.1</td> -</tr> -<tr class="odd"> -<td align="right">8.7273979</td> -<td align="right">27.5</td> -<td align="right">7.5</td> -<td align="right">8.3</td> -<td align="right">2.3</td> -</tr> -<tr class="even"> -<td align="right">13.0910968</td> -<td align="right">14.8</td> -<td align="right">8.4</td> -<td align="right">9.3</td> -<td align="right">3.3</td> -</tr> -<tr class="odd"> -<td align="right">13.0910968</td> -<td align="right">13.4</td> -<td align="right">6.8</td> -<td align="right">8.7</td> -<td align="right">2.4</td> -</tr> -<tr class="even"> -<td align="right">13.0910968</td> -<td align="right">14.4</td> -<td align="right">8.0</td> -<td align="right">9.1</td> -<td align="right">2.6</td> -</tr> -<tr class="odd"> -<td align="right">17.4547957</td> -<td align="right">7.7</td> -<td align="right">7.2</td> -<td align="right">8.6</td> -<td align="right">4.0</td> -</tr> -<tr class="even"> -<td align="right">17.4547957</td> -<td align="right">7.3</td> -<td align="right">7.2</td> -<td align="right">8.5</td> -<td align="right">3.6</td> -</tr> -<tr class="odd"> -<td align="right">17.4547957</td> -<td align="right">8.1</td> -<td align="right">6.9</td> -<td align="right">8.9</td> -<td align="right">3.3</td> -</tr> -<tr class="even"> -<td align="right">26.1821936</td> -<td align="right">2.0</td> -<td align="right">4.9</td> -<td align="right">8.1</td> -<td align="right">2.1</td> -</tr> -<tr class="odd"> -<td align="right">26.1821936</td> -<td align="right">1.5</td> -<td align="right">4.3</td> -<td align="right">7.7</td> -<td align="right">1.7</td> -</tr> -<tr class="even"> -<td align="right">26.1821936</td> -<td align="right">1.9</td> -<td align="right">4.5</td> -<td align="right">7.4</td> -<td align="right">1.8</td> -</tr> -<tr class="odd"> -<td align="right">34.9095915</td> -<td align="right">1.3</td> -<td align="right">3.8</td> -<td align="right">5.9</td> -<td align="right">1.6</td> -</tr> -<tr class="even"> -<td align="right">34.9095915</td> -<td align="right">1.0</td> -<td align="right">3.1</td> -<td align="right">6.0</td> -<td align="right">1.6</td> -</tr> -<tr class="odd"> -<td align="right">34.9095915</td> -<td align="right">1.1</td> -<td align="right">3.1</td> -<td align="right">5.9</td> -<td align="right">1.4</td> -</tr> -<tr class="even"> -<td align="right">43.6369893</td> -<td align="right">0.9</td> -<td align="right">2.7</td> -<td align="right">5.6</td> -<td align="right">1.8</td> -</tr> -<tr class="odd"> -<td align="right">43.6369893</td> -<td align="right">0.7</td> -<td align="right">2.3</td> -<td align="right">5.2</td> -<td align="right">1.5</td> -</tr> -<tr class="even"> -<td align="right">43.6369893</td> -<td align="right">0.7</td> -<td align="right">2.1</td> -<td align="right">5.6</td> -<td align="right">1.3</td> -</tr> -<tr class="odd"> -<td align="right">52.3643872</td> -<td align="right">0.6</td> -<td align="right">1.6</td> -<td align="right">4.3</td> -<td align="right">1.2</td> -</tr> -<tr class="even"> -<td align="right">52.3643872</td> -<td align="right">0.4</td> -<td align="right">1.1</td> -<td align="right">3.7</td> -<td align="right">0.9</td> -</tr> -<tr class="odd"> -<td align="right">52.3643872</td> -<td align="right">0.5</td> -<td align="right">1.3</td> -<td align="right">3.9</td> -<td align="right">1.1</td> -</tr> -<tr class="even"> -<td align="right">74.8062674</td> -<td align="right">0.4</td> -<td align="right">0.4</td> -<td align="right">2.5</td> -<td align="right">0.5</td> -</tr> -<tr class="odd"> -<td align="right">74.8062674</td> -<td align="right">0.3</td> -<td align="right">0.4</td> -<td align="right">2.4</td> -<td align="right">0.5</td> -</tr> -<tr class="even"> -<td align="right">74.8062674</td> -<td align="right">0.3</td> -<td align="right">0.3</td> -<td align="right">2.2</td> -<td align="right">0.3</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset BBA 2.2</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">DMTA</th> -<th align="right">M23</th> -<th align="right">M27</th> -<th align="right">M31</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.0000000</td> -<td align="right">98.09</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">0.0000000</td> -<td align="right">98.77</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">0.7678922</td> -<td align="right">93.52</td> -<td align="right">0.36</td> -<td align="right">0.42</td> -<td align="right">0.36</td> -</tr> -<tr class="even"> -<td align="right">0.7678922</td> -<td align="right">92.03</td> -<td align="right">0.40</td> -<td align="right">0.47</td> -<td align="right">0.33</td> -</tr> -<tr class="odd"> -<td align="right">2.3036765</td> -<td align="right">88.39</td> -<td align="right">1.03</td> -<td align="right">0.71</td> -<td align="right">0.55</td> -</tr> -<tr class="even"> -<td align="right">2.3036765</td> -<td align="right">87.18</td> -<td align="right">1.07</td> -<td align="right">0.82</td> -<td align="right">0.64</td> -</tr> -<tr class="odd"> -<td align="right">5.3752452</td> -<td align="right">69.38</td> -<td align="right">3.60</td> -<td align="right">2.19</td> -<td align="right">1.94</td> -</tr> -<tr class="even"> -<td align="right">5.3752452</td> -<td align="right">71.06</td> -<td align="right">3.66</td> -<td align="right">2.28</td> -<td align="right">1.62</td> -</tr> -<tr class="odd"> -<td align="right">10.7504904</td> -<td align="right">45.21</td> -<td align="right">6.97</td> -<td align="right">5.45</td> -<td align="right">4.22</td> -</tr> -<tr class="even"> -<td align="right">10.7504904</td> -<td align="right">46.81</td> -<td align="right">7.22</td> -<td align="right">5.19</td> -<td align="right">4.37</td> -</tr> -<tr class="odd"> -<td align="right">16.1257355</td> -<td align="right">30.54</td> -<td align="right">8.65</td> -<td align="right">8.81</td> -<td align="right">6.31</td> -</tr> -<tr class="even"> -<td align="right">16.1257355</td> -<td align="right">30.07</td> -<td align="right">8.38</td> -<td align="right">7.93</td> -<td align="right">6.85</td> -</tr> -<tr class="odd"> -<td align="right">21.5009807</td> -<td align="right">21.60</td> -<td align="right">9.10</td> -<td align="right">10.25</td> -<td align="right">7.05</td> -</tr> -<tr class="even"> -<td align="right">21.5009807</td> -<td align="right">20.41</td> -<td align="right">8.63</td> -<td align="right">10.77</td> -<td align="right">6.84</td> -</tr> -<tr class="odd"> -<td align="right">32.2514711</td> -<td align="right">9.10</td> -<td align="right">7.63</td> -<td align="right">10.89</td> -<td align="right">6.53</td> -</tr> -<tr class="even"> -<td align="right">32.2514711</td> -<td align="right">9.70</td> -<td align="right">8.01</td> -<td align="right">10.85</td> -<td align="right">7.11</td> -</tr> -<tr class="odd"> -<td align="right">43.0019614</td> -<td align="right">6.58</td> -<td align="right">6.40</td> -<td align="right">10.41</td> -<td align="right">6.06</td> -</tr> -<tr class="even"> -<td align="right">43.0019614</td> -<td align="right">6.31</td> -<td align="right">6.35</td> -<td align="right">10.35</td> -<td align="right">6.05</td> -</tr> -<tr class="odd"> -<td align="right">53.7524518</td> -<td align="right">3.47</td> -<td align="right">5.35</td> -<td align="right">9.92</td> -<td align="right">5.50</td> -</tr> -<tr class="even"> -<td align="right">53.7524518</td> -<td align="right">3.52</td> -<td align="right">5.06</td> -<td align="right">9.42</td> -<td align="right">5.07</td> -</tr> -<tr class="odd"> -<td align="right">64.5029421</td> -<td align="right">3.40</td> -<td align="right">5.14</td> -<td align="right">9.15</td> -<td align="right">4.94</td> -</tr> -<tr class="even"> -<td align="right">64.5029421</td> -<td align="right">3.67</td> -<td align="right">5.91</td> -<td align="right">9.25</td> -<td align="right">4.39</td> -</tr> -<tr class="odd"> -<td align="right">91.3791680</td> -<td align="right">1.62</td> -<td align="right">3.35</td> -<td align="right">7.14</td> -<td align="right">3.64</td> -</tr> -<tr class="even"> -<td align="right">91.3791680</td> -<td align="right">1.62</td> -<td align="right">2.87</td> -<td align="right">7.13</td> -<td align="right">3.55</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset BBA 2.3</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">DMTA</th> -<th align="right">M23</th> -<th align="right">M27</th> -<th align="right">M31</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.0000000</td> -<td align="right">99.33</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">0.0000000</td> -<td align="right">97.44</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">0.6733938</td> -<td align="right">93.73</td> -<td align="right">0.18</td> -<td align="right">0.50</td> -<td align="right">0.47</td> -</tr> -<tr class="even"> -<td align="right">0.6733938</td> -<td align="right">93.77</td> -<td align="right">0.18</td> -<td align="right">0.83</td> -<td align="right">0.34</td> -</tr> -<tr class="odd"> -<td align="right">2.0201814</td> -<td align="right">87.84</td> -<td align="right">0.52</td> -<td align="right">1.25</td> -<td align="right">1.00</td> -</tr> -<tr class="even"> -<td align="right">2.0201814</td> -<td align="right">89.82</td> -<td align="right">0.43</td> -<td align="right">1.09</td> -<td align="right">0.89</td> -</tr> -<tr class="odd"> -<td align="right">4.7137565</td> -<td align="right">71.61</td> -<td align="right">1.19</td> -<td align="right">3.28</td> -<td align="right">3.58</td> -</tr> -<tr class="even"> -<td align="right">4.7137565</td> -<td align="right">71.42</td> -<td align="right">1.11</td> -<td align="right">3.24</td> -<td align="right">3.41</td> -</tr> -<tr class="odd"> -<td align="right">9.4275131</td> -<td align="right">45.60</td> -<td align="right">2.26</td> -<td align="right">7.17</td> -<td align="right">8.74</td> -</tr> -<tr class="even"> -<td align="right">9.4275131</td> -<td align="right">45.42</td> -<td align="right">1.99</td> -<td align="right">7.91</td> -<td align="right">8.28</td> -</tr> -<tr class="odd"> -<td align="right">14.1412696</td> -<td align="right">31.12</td> -<td align="right">2.81</td> -<td align="right">10.15</td> -<td align="right">9.67</td> -</tr> -<tr class="even"> -<td align="right">14.1412696</td> -<td align="right">31.68</td> -<td align="right">2.83</td> -<td align="right">9.55</td> -<td align="right">8.95</td> -</tr> -<tr class="odd"> -<td align="right">18.8550262</td> -<td align="right">23.20</td> -<td align="right">3.39</td> -<td align="right">12.09</td> -<td align="right">10.34</td> -</tr> -<tr class="even"> -<td align="right">18.8550262</td> -<td align="right">24.13</td> -<td align="right">3.56</td> -<td align="right">11.89</td> -<td align="right">10.00</td> -</tr> -<tr class="odd"> -<td align="right">28.2825393</td> -<td align="right">9.43</td> -<td align="right">3.49</td> -<td align="right">13.32</td> -<td align="right">7.89</td> -</tr> -<tr class="even"> -<td align="right">28.2825393</td> -<td align="right">9.82</td> -<td align="right">3.28</td> -<td align="right">12.05</td> -<td align="right">8.13</td> -</tr> -<tr class="odd"> -<td align="right">37.7100523</td> -<td align="right">7.08</td> -<td align="right">2.80</td> -<td align="right">10.04</td> -<td align="right">5.06</td> -</tr> -<tr class="even"> -<td align="right">37.7100523</td> -<td align="right">8.64</td> -<td align="right">2.97</td> -<td align="right">10.78</td> -<td align="right">5.54</td> -</tr> -<tr class="odd"> -<td align="right">47.1375654</td> -<td align="right">4.41</td> -<td align="right">2.42</td> -<td align="right">9.32</td> -<td align="right">3.79</td> -</tr> -<tr class="even"> -<td align="right">47.1375654</td> -<td align="right">4.78</td> -<td align="right">2.51</td> -<td align="right">9.62</td> -<td align="right">4.11</td> -</tr> -<tr class="odd"> -<td align="right">56.5650785</td> -<td align="right">4.92</td> -<td align="right">2.22</td> -<td align="right">8.00</td> -<td align="right">3.11</td> -</tr> -<tr class="even"> -<td align="right">56.5650785</td> -<td align="right">5.08</td> -<td align="right">1.95</td> -<td align="right">8.45</td> -<td align="right">2.98</td> -</tr> -<tr class="odd"> -<td align="right">80.1338612</td> -<td align="right">2.13</td> -<td align="right">1.28</td> -<td align="right">5.71</td> -<td align="right">1.78</td> -</tr> -<tr class="even"> -<td align="right">80.1338612</td> -<td align="right">2.23</td> -<td align="right">0.99</td> -<td align="right">3.33</td> -<td align="right">1.55</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset Elliot</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">DMTA</th> -<th align="right">M23</th> -<th align="right">M27</th> -<th align="right">M31</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.000000</td> -<td align="right">97.5</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">0.000000</td> -<td align="right">100.7</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">1.228478</td> -<td align="right">86.4</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">1.228478</td> -<td align="right">88.5</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">1.5</td> -</tr> -<tr class="odd"> -<td align="right">3.685435</td> -<td align="right">69.8</td> -<td align="right">2.8</td> -<td align="right">2.3</td> -<td align="right">5.0</td> -</tr> -<tr class="even"> -<td align="right">3.685435</td> -<td align="right">77.1</td> -<td align="right">1.7</td> -<td align="right">2.1</td> -<td align="right">2.4</td> -</tr> -<tr class="odd"> -<td align="right">8.599349</td> -<td align="right">59.0</td> -<td align="right">4.3</td> -<td align="right">4.0</td> -<td align="right">4.3</td> -</tr> -<tr class="even"> -<td align="right">8.599349</td> -<td align="right">54.2</td> -<td align="right">5.8</td> -<td align="right">3.4</td> -<td align="right">5.0</td> -</tr> -<tr class="odd"> -<td align="right">17.198697</td> -<td align="right">31.3</td> -<td align="right">8.2</td> -<td align="right">6.6</td> -<td align="right">8.0</td> -</tr> -<tr class="even"> -<td align="right">17.198697</td> -<td align="right">33.5</td> -<td align="right">5.2</td> -<td align="right">6.9</td> -<td align="right">7.7</td> -</tr> -<tr class="odd"> -<td align="right">25.798046</td> -<td align="right">19.6</td> -<td align="right">5.1</td> -<td align="right">8.2</td> -<td align="right">7.8</td> -</tr> -<tr class="even"> -<td align="right">25.798046</td> -<td align="right">20.9</td> -<td align="right">6.1</td> -<td align="right">8.8</td> -<td align="right">6.5</td> -</tr> -<tr class="odd"> -<td align="right">34.397395</td> -<td align="right">13.3</td> -<td align="right">6.0</td> -<td align="right">9.7</td> -<td align="right">8.0</td> -</tr> -<tr class="even"> -<td align="right">34.397395</td> -<td align="right">15.8</td> -<td align="right">6.0</td> -<td align="right">8.8</td> -<td align="right">7.4</td> -</tr> -<tr class="odd"> -<td align="right">51.596092</td> -<td align="right">6.7</td> -<td align="right">5.0</td> -<td align="right">8.3</td> -<td align="right">6.9</td> -</tr> -<tr class="even"> -<td align="right">51.596092</td> -<td align="right">8.7</td> -<td align="right">4.2</td> -<td align="right">9.2</td> -<td align="right">9.0</td> -</tr> -<tr class="odd"> -<td align="right">68.794789</td> -<td align="right">8.8</td> -<td align="right">3.9</td> -<td align="right">9.3</td> -<td align="right">5.5</td> -</tr> -<tr class="even"> -<td align="right">68.794789</td> -<td align="right">8.7</td> -<td align="right">2.9</td> -<td align="right">8.5</td> -<td align="right">6.1</td> -</tr> -<tr class="odd"> -<td align="right">103.192184</td> -<td align="right">6.0</td> -<td align="right">1.9</td> -<td align="right">8.6</td> -<td align="right">6.1</td> -</tr> -<tr class="even"> -<td align="right">103.192184</td> -<td align="right">4.4</td> -<td align="right">1.5</td> -<td align="right">6.0</td> -<td align="right">4.0</td> -</tr> -<tr class="odd"> -<td align="right">146.188928</td> -<td align="right">3.3</td> -<td align="right">2.0</td> -<td align="right">5.6</td> -<td align="right">3.1</td> -</tr> -<tr class="even"> -<td align="right">146.188928</td> -<td align="right">2.8</td> -<td align="right">2.3</td> -<td align="right">4.5</td> -<td align="right">2.9</td> -</tr> -<tr class="odd"> -<td align="right">223.583066</td> -<td align="right">1.4</td> -<td align="right">1.2</td> -<td align="right">4.1</td> -<td align="right">1.8</td> -</tr> -<tr class="even"> -<td align="right">223.583066</td> -<td align="right">1.8</td> -<td align="right">1.9</td> -<td align="right">3.9</td> -<td align="right">2.6</td> -</tr> -<tr class="odd"> -<td align="right">0.000000</td> -<td align="right">93.4</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">0.000000</td> -<td align="right">103.2</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">1.228478</td> -<td align="right">89.2</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">1.3</td> -</tr> -<tr class="even"> -<td align="right">1.228478</td> -<td align="right">86.6</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">3.685435</td> -<td align="right">78.2</td> -<td align="right">2.6</td> -<td align="right">1.0</td> -<td align="right">3.1</td> -</tr> -<tr class="even"> -<td align="right">3.685435</td> -<td align="right">78.1</td> -<td align="right">2.4</td> -<td align="right">2.6</td> -<td align="right">2.3</td> -</tr> -<tr class="odd"> -<td align="right">8.599349</td> -<td align="right">55.6</td> -<td align="right">5.5</td> -<td align="right">4.5</td> -<td align="right">3.4</td> -</tr> -<tr class="even"> -<td align="right">8.599349</td> -<td align="right">53.0</td> -<td align="right">5.6</td> -<td align="right">4.6</td> -<td align="right">4.3</td> -</tr> -<tr class="odd"> -<td align="right">17.198697</td> -<td align="right">33.7</td> -<td align="right">7.3</td> -<td align="right">7.6</td> -<td align="right">7.8</td> -</tr> -<tr class="even"> -<td align="right">17.198697</td> -<td align="right">33.2</td> -<td align="right">6.5</td> -<td align="right">6.7</td> -<td align="right">8.7</td> -</tr> -<tr class="odd"> -<td align="right">25.798046</td> -<td align="right">20.9</td> -<td align="right">5.8</td> -<td align="right">8.7</td> -<td align="right">7.7</td> -</tr> -<tr class="even"> -<td align="right">25.798046</td> -<td align="right">19.9</td> -<td align="right">7.7</td> -<td align="right">7.6</td> -<td align="right">6.5</td> -</tr> -<tr class="odd"> -<td align="right">34.397395</td> -<td align="right">18.2</td> -<td align="right">7.8</td> -<td align="right">8.0</td> -<td align="right">6.3</td> -</tr> -<tr class="even"> -<td align="right">34.397395</td> -<td align="right">12.7</td> -<td align="right">7.3</td> -<td align="right">8.6</td> -<td align="right">8.7</td> -</tr> -<tr class="odd"> -<td align="right">51.596092</td> -<td align="right">7.8</td> -<td align="right">7.0</td> -<td align="right">7.4</td> -<td align="right">5.7</td> -</tr> -<tr class="even"> -<td align="right">51.596092</td> -<td align="right">9.0</td> -<td align="right">6.3</td> -<td align="right">7.2</td> -<td align="right">4.2</td> -</tr> -<tr class="odd"> -<td align="right">68.794789</td> -<td align="right">11.4</td> -<td align="right">4.3</td> -<td align="right">10.3</td> -<td align="right">3.2</td> -</tr> -<tr class="even"> -<td align="right">68.794789</td> -<td align="right">9.0</td> -<td align="right">3.8</td> -<td align="right">9.4</td> -<td align="right">4.2</td> -</tr> -<tr class="odd"> -<td align="right">103.192184</td> -<td align="right">3.9</td> -<td align="right">2.6</td> -<td align="right">6.5</td> -<td align="right">3.8</td> -</tr> -<tr class="even"> -<td align="right">103.192184</td> -<td align="right">4.4</td> -<td align="right">2.8</td> -<td align="right">6.9</td> -<td align="right">4.0</td> -</tr> -<tr class="odd"> -<td align="right">146.188928</td> -<td align="right">2.6</td> -<td align="right">1.6</td> -<td align="right">4.6</td> -<td align="right">4.5</td> -</tr> -<tr class="even"> -<td align="right">146.188928</td> -<td align="right">3.4</td> -<td align="right">1.1</td> -<td align="right">4.5</td> -<td align="right">4.5</td> -</tr> -<tr class="odd"> -<td align="right">223.583066</td> -<td align="right">2.0</td> -<td align="right">1.4</td> -<td align="right">4.3</td> -<td align="right">3.8</td> -</tr> -<tr class="even"> -<td align="right">223.583066</td> -<td align="right">1.7</td> -<td align="right">1.3</td> -<td align="right">4.2</td> -<td align="right">2.3</td> -</tr> -</tbody> -</table> -</div> -<div class="section level2"> -<h2 id="separate-evaluations">Separate evaluations<a class="anchor" aria-label="anchor" href="#separate-evaluations"></a> -</h2> -<p>As a first step to obtain suitable starting parameters for the NLHM -fits, we do separate fits of several variants of the pathway model used -previously <span class="citation">(Ranke et al. 2021)</span>, varying -the kinetic model for the parent compound. Because the SFORB model often -provides faster convergence than the DFOP model, and can sometimes be -fitted where the DFOP model results in errors, it is included in the set -of parent models tested here.</p> -<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="kw">if</span> <span class="op">(</span><span class="op">!</span><span class="fu"><a href="https://rdrr.io/r/base/files2.html" class="external-link">dir.exists</a></span><span class="op">(</span><span class="st">"dmta_dlls"</span><span class="op">)</span><span class="op">)</span> <span class="fu"><a href="https://rdrr.io/r/base/files2.html" class="external-link">dir.create</a></span><span class="op">(</span><span class="st">"dmta_dlls"</span><span class="op">)</span></span> -<span><span class="va">m_sfo_path_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> DMTA <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"M23"</span>, <span class="st">"M27"</span>, <span class="st">"M31"</span><span class="op">)</span><span class="op">)</span>,</span> -<span> M23 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> M27 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> M31 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M27"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> name <span class="op">=</span> <span class="st">"m_sfo_path"</span>, dll_dir <span class="op">=</span> <span class="st">"dmta_dlls"</span>,</span> -<span> unload <span class="op">=</span> <span class="cn">TRUE</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> quiet <span class="op">=</span> <span class="cn">TRUE</span></span> -<span><span class="op">)</span></span> -<span><span class="va">m_fomc_path_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> DMTA <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"FOMC"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"M23"</span>, <span class="st">"M27"</span>, <span class="st">"M31"</span><span class="op">)</span><span class="op">)</span>,</span> -<span> M23 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> M27 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> M31 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M27"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> name <span class="op">=</span> <span class="st">"m_fomc_path"</span>, dll_dir <span class="op">=</span> <span class="st">"dmta_dlls"</span>,</span> -<span> unload <span class="op">=</span> <span class="cn">TRUE</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> quiet <span class="op">=</span> <span class="cn">TRUE</span></span> -<span><span class="op">)</span></span> -<span><span class="va">m_dfop_path_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> DMTA <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"DFOP"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"M23"</span>, <span class="st">"M27"</span>, <span class="st">"M31"</span><span class="op">)</span><span class="op">)</span>,</span> -<span> M23 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> M27 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> M31 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M27"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> name <span class="op">=</span> <span class="st">"m_dfop_path"</span>, dll_dir <span class="op">=</span> <span class="st">"dmta_dlls"</span>,</span> -<span> unload <span class="op">=</span> <span class="cn">TRUE</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> quiet <span class="op">=</span> <span class="cn">TRUE</span></span> -<span><span class="op">)</span></span> -<span><span class="va">m_sforb_path_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> DMTA <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"M23"</span>, <span class="st">"M27"</span>, <span class="st">"M31"</span><span class="op">)</span><span class="op">)</span>,</span> -<span> M23 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> M27 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> M31 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M27"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> name <span class="op">=</span> <span class="st">"m_sforb_path"</span>, dll_dir <span class="op">=</span> <span class="st">"dmta_dlls"</span>,</span> -<span> unload <span class="op">=</span> <span class="cn">TRUE</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> quiet <span class="op">=</span> <span class="cn">TRUE</span></span> -<span><span class="op">)</span></span> -<span><span class="va">m_hs_path_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> DMTA <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"HS"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"M23"</span>, <span class="st">"M27"</span>, <span class="st">"M31"</span><span class="op">)</span><span class="op">)</span>,</span> -<span> M23 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> M27 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> M31 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M27"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> name <span class="op">=</span> <span class="st">"m_hs_path"</span>, dll_dir <span class="op">=</span> <span class="st">"dmta_dlls"</span>,</span> -<span> unload <span class="op">=</span> <span class="cn">TRUE</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> quiet <span class="op">=</span> <span class="cn">TRUE</span></span> -<span><span class="op">)</span></span> -<span><span class="va">cl</span> <span class="op"><-</span> <span class="fu">start_cluster</span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> -<span></span> -<span><span class="va">deg_mods_1</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span></span> -<span> sfo_path_1 <span class="op">=</span> <span class="va">m_sfo_path_1</span>,</span> -<span> fomc_path_1 <span class="op">=</span> <span class="va">m_fomc_path_1</span>,</span> -<span> dfop_path_1 <span class="op">=</span> <span class="va">m_dfop_path_1</span>,</span> -<span> sforb_path_1 <span class="op">=</span> <span class="va">m_sforb_path_1</span>,</span> -<span> hs_path_1 <span class="op">=</span> <span class="va">m_hs_path_1</span><span class="op">)</span></span> -<span></span> -<span><span class="va">sep_1_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span></span> -<span> <span class="va">deg_mods_1</span>,</span> -<span> <span class="va">dmta_ds</span>,</span> -<span> error_model <span class="op">=</span> <span class="st">"const"</span>,</span> -<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<span></span> -<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">sep_1_const</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">Calke</th> -<th align="left">Borstel</th> -<th align="left">Flaach</th> -<th align="left">BBA 2.2</th> -<th align="left">BBA 2.3</th> -<th align="left">Elliot</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">sfo_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">fomc_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">dfop_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">sforb_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">hs_path_1</td> -<td align="left">C</td> -<td align="left">C</td> -<td align="left">C</td> -<td align="left">C</td> -<td align="left">C</td> -<td align="left">C</td> -</tr> -</tbody> -</table> -<p>All separate pathway fits with SFO or FOMC for the parent and -constant variance converged (status OK). Most fits with DFOP or SFORB -for the parent converged as well. The fits with HS for the parent did -not converge with default settings.</p> -<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">sep_1_tc</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">sep_1_const</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span> -<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">sep_1_tc</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">Calke</th> -<th align="left">Borstel</th> -<th align="left">Flaach</th> -<th align="left">BBA 2.2</th> -<th align="left">BBA 2.3</th> -<th align="left">Elliot</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">sfo_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">fomc_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">C</td> -</tr> -<tr class="odd"> -<td align="left">dfop_path_1</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">sforb_path_1</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">hs_path_1</td> -<td align="left">C</td> -<td align="left">C</td> -<td align="left">C</td> -<td align="left">C</td> -<td align="left">C</td> -<td align="left">OK</td> -</tr> -</tbody> -</table> -<p>With the two-component error model, the set of fits with convergence -problems is slightly different, with convergence problems appearing for -different data sets when applying the DFOP and SFORB model and some -additional convergence problems when using the FOMC model for the -parent.</p> -</div> -<div class="section level2"> -<h2 id="hierarchichal-model-fits">Hierarchichal model fits<a class="anchor" aria-label="anchor" href="#hierarchichal-model-fits"></a> -</h2> -<p>The following code fits two sets of the corresponding hierarchical -models to the data, one assuming constant variance, and one assuming -two-component error.</p> -<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">saem_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mhmkin.html">mhmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">sep_1_const</span>, <span class="va">sep_1_tc</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> -<p>The run time for these fits was around two hours on five year old -hardware. After a recent hardware upgrade these fits complete in less -than twenty minutes.</p> -<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">const</th> -<th align="left">tc</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">sfo_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">fomc_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">dfop_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">sforb_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">hs_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -</tbody> -</table> -<p>According to the <code>status</code> function, all fits terminated -successfully.</p> -<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> -<pre><code>Warning in FUN(X[[i]], ...): Could not obtain log likelihood with 'is' method -for sforb_path_1 const</code></pre> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="right">npar</th> -<th align="right">AIC</th> -<th align="right">BIC</th> -<th align="right">Lik</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">sfo_path_1 const</td> -<td align="right">17</td> -<td align="right">2291.8</td> -<td align="right">2288.3</td> -<td align="right">-1128.9</td> -</tr> -<tr class="even"> -<td align="left">sfo_path_1 tc</td> -<td align="right">18</td> -<td align="right">2276.3</td> -<td align="right">2272.5</td> -<td align="right">-1120.1</td> -</tr> -<tr class="odd"> -<td align="left">fomc_path_1 const</td> -<td align="right">19</td> -<td align="right">2099.0</td> -<td align="right">2095.0</td> -<td align="right">-1030.5</td> -</tr> -<tr class="even"> -<td align="left">fomc_path_1 tc</td> -<td align="right">20</td> -<td align="right">1939.6</td> -<td align="right">1935.5</td> -<td align="right">-949.8</td> -</tr> -<tr class="odd"> -<td align="left">dfop_path_1 const</td> -<td align="right">21</td> -<td align="right">2038.8</td> -<td align="right">2034.4</td> -<td align="right">-998.4</td> -</tr> -<tr class="even"> -<td align="left">hs_path_1 const</td> -<td align="right">21</td> -<td align="right">2024.2</td> -<td align="right">2019.8</td> -<td align="right">-991.1</td> -</tr> -<tr class="odd"> -<td align="left">dfop_path_1 tc</td> -<td align="right">22</td> -<td align="right">1879.8</td> -<td align="right">1875.2</td> -<td align="right">-917.9</td> -</tr> -<tr class="even"> -<td align="left">sforb_path_1 tc</td> -<td align="right">22</td> -<td align="right">1832.9</td> -<td align="right">1828.3</td> -<td align="right">-894.4</td> -</tr> -<tr class="odd"> -<td align="left">hs_path_1 tc</td> -<td align="right">22</td> -<td align="right">1831.4</td> -<td align="right">1826.8</td> -<td align="right">-893.7</td> -</tr> -</tbody> -</table> -<p>When the goodness-of-fit of the models is compared, a warning is -obtained, indicating that the likelihood of the pathway fit with SFORB -for the parent compound and constant variance could not be calculated -with importance sampling (method ‘is’). As this is the default method on -which all AIC and BIC comparisons are based, this variant is not -included in the model comparison table. Comparing the goodness-of-fit of -the remaining models, HS model model with two-component error provides -the best fit. However, for batch experiments performed with constant -conditions such as the experiments evaluated here, there is no reason to -assume a discontinuity, so the SFORB model is preferable from a -mechanistic viewpoint. In addition, the information criteria AIC and BIC -are very similar for HS and SFORB. Therefore, the SFORB model is -selected here for further refinements.</p> -<div class="section level3"> -<h3 id="parameter-identifiability-based-on-the-fisher-information-matrix">Parameter identifiability based on the Fisher Information -Matrix<a class="anchor" aria-label="anchor" href="#parameter-identifiability-based-on-the-fisher-information-matrix"></a> -</h3> -<p>Using the <code>illparms</code> function, ill-defined statistical -model parameters such as standard deviations of the degradation -parameters in the population and error model parameters can be -found.</p> -<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">const</th> -<th align="left">tc</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">sfo_path_1</td> -<td align="left"></td> -<td align="left">sd(DMTA_0)</td> -</tr> -<tr class="even"> -<td align="left">fomc_path_1</td> -<td align="left"></td> -<td align="left">sd(DMTA_0)</td> -</tr> -<tr class="odd"> -<td align="left">dfop_path_1</td> -<td align="left"></td> -<td align="left"></td> -</tr> -<tr class="even"> -<td align="left">sforb_path_1</td> -<td align="left"></td> -<td align="left">sd(log_k_DMTA_bound_free)</td> -</tr> -<tr class="odd"> -<td align="left">hs_path_1</td> -<td align="left"></td> -<td align="left">sd(log_tb)</td> -</tr> -</tbody> -</table> -<p>When using constant variance, no ill-defined variance parameters are -identified with the <code>illparms</code> function in any of the -degradation models. When using the two-component error model, there is -one ill-defined variance parameter in all variants except for the -variant using DFOP for the parent compound.</p> -<p>For the selected combination of the SFORB pathway model with -two-component error, the random effect for the rate constant from -reversibly bound DMTA to the free DMTA (<code>k_DMTA_bound_free</code>) -is not well-defined. Therefore, the fit is updated without assuming a -random effect for this parameter.</p> -<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">saem_sforb_path_1_tc_reduced</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">[[</span><span class="st">"sforb_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span>,</span> -<span> no_random_effect <span class="op">=</span> <span class="st">"log_k_DMTA_bound_free"</span><span class="op">)</span></span> -<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">saem_sforb_path_1_tc_reduced</span><span class="op">)</span></span></code></pre></div> -<p>As expected, no ill-defined parameters remain. The model comparison -below shows that the reduced model is preferable.</p> -<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">[[</span><span class="st">"sforb_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span>, <span class="va">saem_sforb_path_1_tc_reduced</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="right">npar</th> -<th align="right">AIC</th> -<th align="right">BIC</th> -<th align="right">Lik</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">saem_sforb_path_1_tc_reduced</td> -<td align="right">21</td> -<td align="right">1830.3</td> -<td align="right">1825.9</td> -<td align="right">-894.2</td> -</tr> -<tr class="even"> -<td align="left">saem_1[[“sforb_path_1”, “tc”]]</td> -<td align="right">22</td> -<td align="right">1832.9</td> -<td align="right">1828.3</td> -<td align="right">-894.4</td> -</tr> -</tbody> -</table> -<p>The convergence plot of the refined fit is shown below.</p> -<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">saem_sforb_path_1_tc_reduced</span><span class="op">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></span></code></pre></div> -<p><img src="2022_dmta_pathway_files/figure-html/saem-sforb-path-1-tc-reduced-convergence-1.png" width="700" style="display: block; margin: auto;"></p> -<p>For some parameters, for example for <code>f_DMTA_ilr_1</code> and -<code>f_DMTA_ilr_2</code>, i.e. for two of the parameters determining -the formation fractions of the parallel formation of the three -metabolites, some movement of the parameters is still visible in the -second phase of the algorithm. However, the amplitude of this movement -is in the range of the amplitude towards the end of the first phase. -Therefore, it is likely that an increase in iterations would not improve -the parameter estimates very much, and it is proposed that the fit is -acceptable. No numeric convergence criterion is implemented in -saemix.</p> -</div> -<div class="section level3"> -<h3 id="alternative-check-of-parameter-identifiability">Alternative check of parameter identifiability<a class="anchor" aria-label="anchor" href="#alternative-check-of-parameter-identifiability"></a> -</h3> -<p>As an alternative check of parameter identifiability <span class="citation">(Duchesne et al. 2021)</span>, multistart runs were -performed on the basis of the refined fit shown above.</p> -<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">saem_sforb_path_1_tc_reduced_multi</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/multistart.html">multistart</a></span><span class="op">(</span><span class="va">saem_sforb_path_1_tc_reduced</span>,</span> -<span> n <span class="op">=</span> <span class="fl">32</span>, cores <span class="op">=</span> <span class="fl">10</span><span class="op">)</span></span></code></pre></div> -<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">saem_sforb_path_1_tc_reduced_multi</span><span class="op">)</span></span></code></pre></div> -<pre><code><multistart> object with 32 fits: - E OK -15 17 -OK: Fit terminated successfully -E: Error</code></pre> -<p>Out of the 32 fits that were initiated, only 17 terminated without an -error. The reason for this is that the wide variation of starting -parameters in combination with the parameter variation that is used in -the SAEM algorithm leads to parameter combinations for the degradation -model that the numerical integration routine cannot cope with. Because -of this variation of initial parameters, some of the model fits take up -to two times more time than the original fit.</p> -<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/par.html" class="external-link">par</a></span><span class="op">(</span>mar <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">12.1</span>, <span class="fl">4.1</span>, <span class="fl">2.1</span>, <span class="fl">2.1</span><span class="op">)</span><span class="op">)</span></span> -<span><span class="fu"><a href="../../reference/parplot.html">parplot</a></span><span class="op">(</span><span class="va">saem_sforb_path_1_tc_reduced_multi</span>, ylim <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.5</span>, <span class="fl">2</span><span class="op">)</span>, las <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_pathway_files/figure-html/unnamed-chunk-2-1.png" alt="Parameter boxplots for the multistart runs that succeeded" width="960"><p class="caption"> -Parameter boxplots for the multistart runs that succeeded -</p> -</div> -<p>However, visual analysis of the boxplot of the parameters obtained in -the successful fits confirms that the results are sufficiently -independent of the starting parameters, and there are no remaining -ill-defined parameters.</p> -</div> -</div> -<div class="section level2"> -<h2 id="plots-of-selected-fits">Plots of selected fits<a class="anchor" aria-label="anchor" href="#plots-of-selected-fits"></a> -</h2> -<p>The SFORB pathway fits with full and reduced parameter distribution -model are shown below.</p> -<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">[[</span><span class="st">"sforb_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_pathway_files/figure-html/unnamed-chunk-3-1.png" alt="SFORB pathway fit with two-component error" width="700"><p class="caption"> -SFORB pathway fit with two-component error -</p> -</div> -<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">saem_sforb_path_1_tc_reduced</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_pathway_files/figure-html/unnamed-chunk-4-1.png" alt="SFORB pathway fit with two-component error, reduced parameter model" width="700"><p class="caption"> -SFORB pathway fit with two-component error, reduced parameter model -</p> -</div> -<p>Plots of the remaining fits and listings for all successful fits are -shown in the Appendix.</p> -<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">stopCluster</a></span><span class="op">(</span><span class="va">cl</span><span class="op">)</span></span></code></pre></div> -</div> -<div class="section level2"> -<h2 id="conclusions">Conclusions<a class="anchor" aria-label="anchor" href="#conclusions"></a> -</h2> -<p>Pathway fits with SFO, FOMC, DFOP, SFORB and HS models for the parent -compound could be successfully performed.</p> -</div> -<div class="section level2"> -<h2 id="acknowledgements">Acknowledgements<a class="anchor" aria-label="anchor" href="#acknowledgements"></a> -</h2> -<p>The helpful comments by Janina Wöltjen of the German Environment -Agency on earlier versions of this document are gratefully -acknowledged.</p> -</div> -<div class="section level2"> -<h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a> -</h2> -<div id="refs" class="references csl-bib-body hanging-indent"> -<div id="ref-duchesne_2021" class="csl-entry"> -Duchesne, Ronan, Anissa Guillemin, Olivier Gandrillon, and Fabien -Crauste. 2021. <span>“Practical Identifiability in the Frame of -Nonlinear Mixed Effects Models: The Example of the in Vitro -Erythropoiesis.”</span> <em>BMC Bioinformatics</em> 22 (478). <a href="https://doi.org/10.1186/s12859-021-04373-4" class="external-link">https://doi.org/10.1186/s12859-021-04373-4</a>. -</div> -<div id="ref-ranke2021" class="csl-entry"> -Ranke, Johannes, Janina Wöltjen, Jana Schmidt, and Emmanuelle Comets. -2021. <span>“Taking Kinetic Evaluations of Degradation Data to the Next -Level with Nonlinear Mixed-Effects Models.”</span> <em>Environments</em> -8 (8). <a href="https://doi.org/10.3390/environments8080071" class="external-link">https://doi.org/10.3390/environments8080071</a>. -</div> -</div> -</div> -<div class="section level2"> -<h2 id="appendix">Appendix<a class="anchor" aria-label="anchor" href="#appendix"></a> -</h2> -<div class="section level3"> -<h3 id="plots-of-hierarchical-fits-not-selected-for-refinement">Plots of hierarchical fits not selected for refinement<a class="anchor" aria-label="anchor" href="#plots-of-hierarchical-fits-not-selected-for-refinement"></a> -</h3> -<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">[[</span><span class="st">"sfo_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_pathway_files/figure-html/unnamed-chunk-6-1.png" alt="SFO pathway fit with two-component error" width="700"><p class="caption"> -SFO pathway fit with two-component error -</p> -</div> -<div class="sourceCode" id="cb22"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">[[</span><span class="st">"fomc_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_pathway_files/figure-html/unnamed-chunk-7-1.png" alt="FOMC pathway fit with two-component error" width="700"><p class="caption"> -FOMC pathway fit with two-component error -</p> -</div> -<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">[[</span><span class="st">"sforb_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_pathway_files/figure-html/unnamed-chunk-8-1.png" alt="HS pathway fit with two-component error" width="700"><p class="caption"> -HS pathway fit with two-component error -</p> -</div> -</div> -<div class="section level3"> -<h3 id="hierarchical-model-fit-listings">Hierarchical model fit listings<a class="anchor" aria-label="anchor" href="#hierarchical-model-fit-listings"></a> -</h3> -<div class="section level4"> -<h4 id="fits-with-random-effects-for-all-degradation-parameters">Fits with random effects for all degradation parameters<a class="anchor" aria-label="anchor" href="#fits-with-random-effects-for-all-degradation-parameters"></a> -</h4> - -</div> -<div class="section level4"> -<h4 id="improved-fit-of-the-sforb-pathway-model-with-two-component-error">Improved fit of the SFORB pathway model with two-component -error<a class="anchor" aria-label="anchor" href="#improved-fit-of-the-sforb-pathway-model-with-two-component-error"></a> -</h4> - -</div> -</div> -<div class="section level3"> -<h3 id="session-info">Session info<a class="anchor" aria-label="anchor" href="#session-info"></a> -</h3> -<pre><code>R version 4.2.3 (2023-03-15) -Platform: x86_64-pc-linux-gnu (64-bit) -Running under: Debian GNU/Linux 12 (bookworm) - -Matrix products: default -BLAS: /usr/lib/x86_64-linux-gnu/openblas-serial/libblas.so.3 -LAPACK: /usr/lib/x86_64-linux-gnu/openblas-serial/libopenblas-r0.3.21.so - -locale: - [1] LC_CTYPE=de_DE.UTF-8 LC_NUMERIC=C - [3] LC_TIME=de_DE.UTF-8 LC_COLLATE=de_DE.UTF-8 - [5] LC_MONETARY=de_DE.UTF-8 LC_MESSAGES=de_DE.UTF-8 - [7] LC_PAPER=de_DE.UTF-8 LC_NAME=C - [9] LC_ADDRESS=C LC_TELEPHONE=C -[11] LC_MEASUREMENT=de_DE.UTF-8 LC_IDENTIFICATION=C - -attached base packages: -[1] parallel stats graphics grDevices utils datasets methods -[8] base - -other attached packages: -[1] saemix_3.2 npde_3.3 knitr_1.42 mkin_1.2.4 - -loaded via a namespace (and not attached): - [1] deSolve_1.35 zoo_1.8-12 tidyselect_1.2.0 xfun_0.38 - [5] bslib_0.4.2 purrr_1.0.1 lattice_0.21-8 colorspace_2.1-0 - [9] vctrs_0.6.1 generics_0.1.3 htmltools_0.5.5 yaml_2.3.7 -[13] utf8_1.2.3 rlang_1.1.0 pkgbuild_1.4.0 pkgdown_2.0.7 -[17] jquerylib_0.1.4 pillar_1.9.0 glue_1.6.2 DBI_1.1.3 -[21] lifecycle_1.0.3 stringr_1.5.0 munsell_0.5.0 gtable_0.3.3 -[25] ragg_1.2.5 codetools_0.2-19 memoise_2.0.1 evaluate_0.20 -[29] inline_0.3.19 callr_3.7.3 fastmap_1.1.1 ps_1.7.4 -[33] lmtest_0.9-40 fansi_1.0.4 highr_0.10 scales_1.2.1 -[37] cachem_1.0.7 desc_1.4.2 jsonlite_1.8.4 systemfonts_1.0.4 -[41] fs_1.6.1 textshaping_0.3.6 gridExtra_2.3 ggplot2_3.4.2 -[45] digest_0.6.31 stringi_1.7.12 processx_3.8.0 dplyr_1.1.1 -[49] grid_4.2.3 rprojroot_2.0.3 cli_3.6.1 tools_4.2.3 -[53] magrittr_2.0.3 sass_0.4.5 tibble_3.2.1 crayon_1.5.2 -[57] pkgconfig_2.0.3 prettyunits_1.1.1 rmarkdown_2.21 R6_2.5.1 -[61] mclust_6.0.0 nlme_3.1-162 compiler_4.2.3 </code></pre> -</div> -<div class="section level3"> -<h3 id="hardware-info">Hardware info<a class="anchor" aria-label="anchor" href="#hardware-info"></a> -</h3> -<pre><code>CPU model: AMD Ryzen 9 7950X 16-Core Processor</code></pre> -<pre><code>MemTotal: 64936316 kB</code></pre> -</div> -</div> - </div> - - <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar"> - - <nav id="toc" data-toggle="toc"><h2 data-toc-skip>Contents</h2> - </nav> -</div> - -</div> - - - - <footer><div class="copyright"> - <p></p> -<p>Developed by Johannes Ranke.</p> -</div> - -<div class="pkgdown"> - <p></p> -<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p> -</div> - - </footer> -</div> - - - - - - - </body> -</html> diff --git a/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/saem-sforb-path-1-tc-reduced-convergence-1.png b/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/saem-sforb-path-1-tc-reduced-convergence-1.png Binary files differdeleted file mode 100644 index 206c424d..00000000 --- a/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/saem-sforb-path-1-tc-reduced-convergence-1.png +++ /dev/null diff --git a/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-2-1.png 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