diff options
| author | Johannes Ranke <jranke@uni-bremen.de> | 2023-04-20 19:53:28 +0200 |
|---|---|---|
| committer | Johannes Ranke <jranke@uni-bremen.de> | 2023-04-20 20:03:32 +0200 |
| commit | 9ae42bd20bc2543a94cf1581ba9820c2f9e3afbd (patch) | |
| tree | b3539a9689f5930b8444a5fc459781b825e00fa4 /docs/articles/prebuilt/2022_cyan_pathway.html | |
| parent | ad0efc2d16a84c674307ad2df9d44153b44a9cf8 (diff) | |
Fix and rebuild documentation, see NEWS
I had to fix the two pathway vignettes, as they did not work with
the released version any more. So they and the multistart vignette
which got some small fixes as well were rebuilt.
Complete rebuild of the online docs with the released version. The
documentation of the 'hierarchial_kinetics' format had to be fixed
as well.
Diffstat (limited to 'docs/articles/prebuilt/2022_cyan_pathway.html')
| -rw-r--r-- | docs/articles/prebuilt/2022_cyan_pathway.html | 5657 |
1 files changed, 5657 insertions, 0 deletions
diff --git a/docs/articles/prebuilt/2022_cyan_pathway.html b/docs/articles/prebuilt/2022_cyan_pathway.html new file mode 100644 index 00000000..cd63fa3c --- /dev/null +++ b/docs/articles/prebuilt/2022_cyan_pathway.html @@ -0,0 +1,5657 @@ +<!DOCTYPE html> +<!-- Generated by pkgdown: do not edit by hand --><html lang="en"> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> +<meta charset="utf-8"> +<meta http-equiv="X-UA-Compatible" content="IE=edge"> +<meta name="viewport" content="width=device-width, initial-scale=1.0"> +<title>Testing hierarchical pathway kinetics with residue data on cyantraniliprole • mkin</title> +<!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" 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+</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 1.2.3 which is currently under +development. The newly introduced functionality that is used here is a +simplification of excluding random effects for a set of fits based on a +related set of fits with a reduced model, and the documentation of the +starting parameters of the fit, so that all starting parameters of +<code>saem</code> fits are now listed in the summary. The +<code>saemix</code> package is used as a backend for fitting the NLHM, +but is also loaded to make the convergence plot function available.</p> +<p>This document is processed with the <code>knitr</code> package, which +also provides the <code>kable</code> function that is used to improve +the display of tabular data in R markdown documents. For parallel +processing, the <code>parallel</code> package is used.</p> +<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://pkgdown.jrwb.de/mkin/">mkin</a></span><span class="op">)</span></span> +<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://yihui.org/knitr/" class="external-link">knitr</a></span><span class="op">)</span></span> +<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">saemix</span><span class="op">)</span></span> +<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">parallel</span><span class="op">)</span></span> +<span><span class="va">n_cores</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/detectCores.html" class="external-link">detectCores</a></span><span class="op">(</span><span class="op">)</span></span> +<span></span> +<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: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 07:44:55 2023 +Date of summary: Thu Apr 20 20:01:30 2023 + +Equations: +d_cyan/dt = - k_cyan * cyan +d_JCZ38/dt = + f_cyan_to_JCZ38 * k_cyan * cyan - k_JCZ38 * JCZ38 +d_J9Z38/dt = + f_cyan_to_J9Z38 * k_cyan * cyan - k_J9Z38 * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 431.793 s +Using 300, 100 iterations and 10 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + cyan_0 log_k_cyan log_k_JCZ38 log_k_J9Z38 log_k_JSE76 + 95.3304 -3.8459 -3.1305 -5.0678 -5.3196 + f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis + 0.8158 22.5404 10.4289 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_0 log_k_cyan log_k_JCZ38 log_k_J9Z38 log_k_JSE76 +cyan_0 4.797 0.0000 0.000 0.000 0.0000 +log_k_cyan 0.000 0.9619 0.000 0.000 0.0000 +log_k_JCZ38 0.000 0.0000 2.139 0.000 0.0000 +log_k_J9Z38 0.000 0.0000 0.000 1.639 0.0000 +log_k_JSE76 0.000 0.0000 0.000 0.000 0.7894 +f_cyan_ilr_1 0.000 0.0000 0.000 0.000 0.0000 +f_cyan_ilr_2 0.000 0.0000 0.000 0.000 0.0000 +f_JCZ38_qlogis 0.000 0.0000 0.000 0.000 0.0000 + f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis +cyan_0 0.0000 0.000 0.00 +log_k_cyan 0.0000 0.000 0.00 +log_k_JCZ38 0.0000 0.000 0.00 +log_k_J9Z38 0.0000 0.000 0.00 +log_k_JSE76 0.0000 0.000 0.00 +f_cyan_ilr_1 0.7714 0.000 0.00 +f_cyan_ilr_2 0.0000 8.684 0.00 +f_JCZ38_qlogis 0.0000 0.000 13.48 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2693 2687 -1330 + +Optimised parameters: + est. lower upper +cyan_0 95.0946 NA NA +log_k_cyan -3.8544 NA NA +log_k_JCZ38 -3.0402 NA NA +log_k_J9Z38 -5.0109 NA NA +log_k_JSE76 -5.2857 NA NA +f_cyan_ilr_1 0.8069 NA NA +f_cyan_ilr_2 16.6623 NA NA +f_JCZ38_qlogis 1.3602 NA NA +a.1 4.8326 NA NA +SD.log_k_cyan 0.5842 NA NA +SD.log_k_JCZ38 1.2680 NA NA +SD.log_k_J9Z38 0.3626 NA NA +SD.log_k_JSE76 0.5244 NA NA +SD.f_cyan_ilr_1 0.2752 NA NA +SD.f_cyan_ilr_2 2.3556 NA NA +SD.f_JCZ38_qlogis 0.2400 NA NA + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_cyan 0.5842 NA NA +SD.log_k_JCZ38 1.2680 NA NA +SD.log_k_J9Z38 0.3626 NA NA +SD.log_k_JSE76 0.5244 NA NA +SD.f_cyan_ilr_1 0.2752 NA NA +SD.f_cyan_ilr_2 2.3556 NA NA +SD.f_JCZ38_qlogis 0.2400 NA NA + +Variance model: + est. lower upper +a.1 4.833 NA NA + +Backtransformed parameters: + est. lower upper +cyan_0 95.094581 NA NA +k_cyan 0.021186 NA NA +k_JCZ38 0.047825 NA NA +k_J9Z38 0.006665 NA NA +k_JSE76 0.005063 NA NA +f_cyan_to_JCZ38 0.757885 NA NA +f_cyan_to_J9Z38 0.242115 NA NA +f_JCZ38_to_JSE76 0.795792 NA NA + +Resulting formation fractions: + ff +cyan_JCZ38 7.579e-01 +cyan_J9Z38 2.421e-01 +cyan_sink 5.877e-10 +JCZ38_JSE76 7.958e-01 +JCZ38_sink 2.042e-01 + +Estimated disappearance times: + DT50 DT90 +cyan 32.72 108.68 +JCZ38 14.49 48.15 +J9Z38 103.99 345.46 +JSE76 136.90 454.76 + +</code></pre> +<p></p> +<caption> +Hierarchical SFO path 1 fit with two-component error +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 07:44:53 2023 +Date of summary: Thu Apr 20 20:01:30 2023 + +Equations: +d_cyan/dt = - k_cyan * cyan +d_JCZ38/dt = + f_cyan_to_JCZ38 * k_cyan * cyan - k_JCZ38 * JCZ38 +d_J9Z38/dt = + f_cyan_to_J9Z38 * k_cyan * cyan - k_J9Z38 * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 429.526 s +Using 300, 100 iterations and 10 chains + +Variance model: Two-component variance function + +Starting values for degradation parameters: + cyan_0 log_k_cyan log_k_JCZ38 log_k_J9Z38 log_k_JSE76 + 96.0039 -3.8907 -3.1276 -5.0069 -4.9367 + f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis + 0.7937 20.0030 15.1336 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_0 log_k_cyan log_k_JCZ38 log_k_J9Z38 log_k_JSE76 +cyan_0 4.859 0.000 0.00 0.00 0.0000 +log_k_cyan 0.000 0.962 0.00 0.00 0.0000 +log_k_JCZ38 0.000 0.000 2.04 0.00 0.0000 +log_k_J9Z38 0.000 0.000 0.00 1.72 0.0000 +log_k_JSE76 0.000 0.000 0.00 0.00 0.9076 +f_cyan_ilr_1 0.000 0.000 0.00 0.00 0.0000 +f_cyan_ilr_2 0.000 0.000 0.00 0.00 0.0000 +f_JCZ38_qlogis 0.000 0.000 0.00 0.00 0.0000 + f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis +cyan_0 0.0000 0.000 0.00 +log_k_cyan 0.0000 0.000 0.00 +log_k_JCZ38 0.0000 0.000 0.00 +log_k_J9Z38 0.0000 0.000 0.00 +log_k_JSE76 0.0000 0.000 0.00 +f_cyan_ilr_1 0.7598 0.000 0.00 +f_cyan_ilr_2 0.0000 7.334 0.00 +f_JCZ38_qlogis 0.0000 0.000 11.78 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2658 2651 -1312 + +Optimised parameters: + est. lower upper +cyan_0 94.72923 NA NA +log_k_cyan -3.91670 NA NA +log_k_JCZ38 -3.12917 NA NA +log_k_J9Z38 -5.06070 NA NA +log_k_JSE76 -5.09254 NA NA +f_cyan_ilr_1 0.81116 NA NA +f_cyan_ilr_2 39.97850 NA NA +f_JCZ38_qlogis 3.09728 NA NA +a.1 3.95044 NA NA +b.1 0.07998 NA NA +SD.log_k_cyan 0.58855 NA NA +SD.log_k_JCZ38 1.29753 NA NA +SD.log_k_J9Z38 0.62851 NA NA +SD.log_k_JSE76 0.37235 NA NA +SD.f_cyan_ilr_1 0.37346 NA NA +SD.f_cyan_ilr_2 1.41667 NA NA +SD.f_JCZ38_qlogis 1.81467 NA NA + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_cyan 0.5886 NA NA +SD.log_k_JCZ38 1.2975 NA NA +SD.log_k_J9Z38 0.6285 NA NA +SD.log_k_JSE76 0.3724 NA NA +SD.f_cyan_ilr_1 0.3735 NA NA +SD.f_cyan_ilr_2 1.4167 NA NA +SD.f_JCZ38_qlogis 1.8147 NA NA + +Variance model: + est. lower upper +a.1 3.95044 NA NA +b.1 0.07998 NA NA + +Backtransformed parameters: + est. lower upper +cyan_0 94.729229 NA NA +k_cyan 0.019907 NA NA +k_JCZ38 0.043754 NA NA +k_J9Z38 0.006341 NA NA +k_JSE76 0.006142 NA NA +f_cyan_to_JCZ38 0.758991 NA NA +f_cyan_to_J9Z38 0.241009 NA NA +f_JCZ38_to_JSE76 0.956781 NA NA + +Resulting formation fractions: + ff +cyan_JCZ38 0.75899 +cyan_J9Z38 0.24101 +cyan_sink 0.00000 +JCZ38_JSE76 0.95678 +JCZ38_sink 0.04322 + +Estimated disappearance times: + DT50 DT90 +cyan 34.82 115.67 +JCZ38 15.84 52.63 +J9Z38 109.31 363.12 +JSE76 112.85 374.87 + +</code></pre> +<p></p> +<caption> +Hierarchical FOMC path 1 fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 07:45:50 2023 +Date of summary: Thu Apr 20 20:01:30 2023 + +Equations: +d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan +d_JCZ38/dt = + f_cyan_to_JCZ38 * (alpha/beta) * 1/((time/beta) + 1) * + cyan - k_JCZ38 * JCZ38 +d_J9Z38/dt = + f_cyan_to_J9Z38 * (alpha/beta) * 1/((time/beta) + 1) * + cyan - k_J9Z38 * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 477.996 s +Using 300, 100 iterations and 10 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 + 101.2314 -3.3680 -5.1108 -5.9416 0.7144 + f_cyan_ilr_2 f_JCZ38_qlogis log_alpha log_beta + 7.3870 15.7604 -0.1791 2.9811 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 +cyan_0 5.416 0.000 0.0 0.000 0.0000 +log_k_JCZ38 0.000 2.439 0.0 0.000 0.0000 +log_k_J9Z38 0.000 0.000 1.7 0.000 0.0000 +log_k_JSE76 0.000 0.000 0.0 1.856 0.0000 +f_cyan_ilr_1 0.000 0.000 0.0 0.000 0.7164 +f_cyan_ilr_2 0.000 0.000 0.0 0.000 0.0000 +f_JCZ38_qlogis 0.000 0.000 0.0 0.000 0.0000 +log_alpha 0.000 0.000 0.0 0.000 0.0000 +log_beta 0.000 0.000 0.0 0.000 0.0000 + f_cyan_ilr_2 f_JCZ38_qlogis log_alpha log_beta +cyan_0 0.00 0.00 0.0000 0.0000 +log_k_JCZ38 0.00 0.00 0.0000 0.0000 +log_k_J9Z38 0.00 0.00 0.0000 0.0000 +log_k_JSE76 0.00 0.00 0.0000 0.0000 +f_cyan_ilr_1 0.00 0.00 0.0000 0.0000 +f_cyan_ilr_2 12.33 0.00 0.0000 0.0000 +f_JCZ38_qlogis 0.00 20.42 0.0000 0.0000 +log_alpha 0.00 0.00 0.4144 0.0000 +log_beta 0.00 0.00 0.0000 0.5077 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2428 2421 -1196 + +Optimised parameters: + est. lower upper +cyan_0 101.0225 98.306270 103.7387 +log_k_JCZ38 -3.3786 -4.770657 -1.9866 +log_k_J9Z38 -5.2603 -5.902085 -4.6186 +log_k_JSE76 -6.1427 -7.318336 -4.9671 +f_cyan_ilr_1 0.7437 0.421215 1.0663 +f_cyan_ilr_2 0.9108 0.267977 1.5537 +f_JCZ38_qlogis 2.0487 0.524897 3.5724 +log_alpha -0.2268 -0.618049 0.1644 +log_beta 2.8986 2.700701 3.0964 +a.1 3.4058 3.169913 3.6416 +SD.cyan_0 2.5279 0.454190 4.6016 +SD.log_k_JCZ38 1.5636 0.572824 2.5543 +SD.log_k_J9Z38 0.5316 -0.004405 1.0677 +SD.log_k_JSE76 0.9903 0.106325 1.8742 +SD.f_cyan_ilr_1 0.3464 0.112066 0.5807 +SD.f_cyan_ilr_2 0.2804 -0.393900 0.9546 +SD.f_JCZ38_qlogis 0.9416 -0.152986 2.0362 +SD.log_alpha 0.4273 0.161044 0.6936 + +Correlation: + cyan_0 l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 log_lph +log_k_JCZ38 -0.0156 +log_k_J9Z38 -0.0493 0.0073 +log_k_JSE76 -0.0329 0.0018 0.0069 +f_cyan_ilr_1 -0.0086 0.0180 -0.1406 0.0012 +f_cyan_ilr_2 -0.2629 0.0779 0.2826 0.0274 0.0099 +f_JCZ38_qlogis 0.0713 -0.0747 -0.0505 0.1169 -0.1022 -0.4893 +log_alpha -0.0556 0.0120 0.0336 0.0193 0.0036 0.0840 -0.0489 +log_beta -0.2898 0.0460 0.1305 0.0768 0.0190 0.4071 -0.1981 0.2772 + +Random effects: + est. lower upper +SD.cyan_0 2.5279 0.454190 4.6016 +SD.log_k_JCZ38 1.5636 0.572824 2.5543 +SD.log_k_J9Z38 0.5316 -0.004405 1.0677 +SD.log_k_JSE76 0.9903 0.106325 1.8742 +SD.f_cyan_ilr_1 0.3464 0.112066 0.5807 +SD.f_cyan_ilr_2 0.2804 -0.393900 0.9546 +SD.f_JCZ38_qlogis 0.9416 -0.152986 2.0362 +SD.log_alpha 0.4273 0.161044 0.6936 + +Variance model: + est. lower upper +a.1 3.406 3.17 3.642 + +Backtransformed parameters: + est. lower upper +cyan_0 1.010e+02 9.831e+01 1.037e+02 +k_JCZ38 3.409e-02 8.475e-03 1.372e-01 +k_J9Z38 5.194e-03 2.734e-03 9.867e-03 +k_JSE76 2.149e-03 6.633e-04 6.963e-03 +f_cyan_to_JCZ38 6.481e-01 NA NA +f_cyan_to_J9Z38 2.264e-01 NA NA +f_JCZ38_to_JSE76 8.858e-01 6.283e-01 9.727e-01 +alpha 7.971e-01 5.390e-01 1.179e+00 +beta 1.815e+01 1.489e+01 2.212e+01 + +Resulting formation fractions: + ff +cyan_JCZ38 0.6481 +cyan_J9Z38 0.2264 +cyan_sink 0.1255 +JCZ38_JSE76 0.8858 +JCZ38_sink 0.1142 + +Estimated disappearance times: + DT50 DT90 DT50back +cyan 25.15 308.01 92.72 +JCZ38 20.33 67.54 NA +J9Z38 133.46 443.35 NA +JSE76 322.53 1071.42 NA + +</code></pre> +<p></p> +<caption> +Hierarchical FOMC path 1 fit with two-component error +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 07:45:45 2023 +Date of summary: Thu Apr 20 20:01:30 2023 + +Equations: +d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan +d_JCZ38/dt = + f_cyan_to_JCZ38 * (alpha/beta) * 1/((time/beta) + 1) * + cyan - k_JCZ38 * JCZ38 +d_J9Z38/dt = + f_cyan_to_J9Z38 * (alpha/beta) * 1/((time/beta) + 1) * + cyan - k_J9Z38 * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 480.648 s +Using 300, 100 iterations and 10 chains + +Variance model: Two-component variance function + +Starting values for degradation parameters: + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 + 101.13827 -3.32493 -5.08921 -5.93478 0.71330 + f_cyan_ilr_2 f_JCZ38_qlogis log_alpha log_beta + 10.05989 12.79248 -0.09621 3.10646 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 +cyan_0 5.643 0.000 0.000 0.00 0.0000 +log_k_JCZ38 0.000 2.319 0.000 0.00 0.0000 +log_k_J9Z38 0.000 0.000 1.731 0.00 0.0000 +log_k_JSE76 0.000 0.000 0.000 1.86 0.0000 +f_cyan_ilr_1 0.000 0.000 0.000 0.00 0.7186 +f_cyan_ilr_2 0.000 0.000 0.000 0.00 0.0000 +f_JCZ38_qlogis 0.000 0.000 0.000 0.00 0.0000 +log_alpha 0.000 0.000 0.000 0.00 0.0000 +log_beta 0.000 0.000 0.000 0.00 0.0000 + f_cyan_ilr_2 f_JCZ38_qlogis log_alpha log_beta +cyan_0 0.00 0.00 0.0000 0.0000 +log_k_JCZ38 0.00 0.00 0.0000 0.0000 +log_k_J9Z38 0.00 0.00 0.0000 0.0000 +log_k_JSE76 0.00 0.00 0.0000 0.0000 +f_cyan_ilr_1 0.00 0.00 0.0000 0.0000 +f_cyan_ilr_2 12.49 0.00 0.0000 0.0000 +f_JCZ38_qlogis 0.00 20.19 0.0000 0.0000 +log_alpha 0.00 0.00 0.3142 0.0000 +log_beta 0.00 0.00 0.0000 0.7331 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2423 2416 -1193 + +Optimised parameters: + est. lower upper +cyan_0 100.57649 NA NA +log_k_JCZ38 -3.46250 NA NA +log_k_J9Z38 -5.24442 NA NA +log_k_JSE76 -5.75229 NA NA +f_cyan_ilr_1 0.68480 NA NA +f_cyan_ilr_2 0.61670 NA NA +f_JCZ38_qlogis 87.97407 NA NA +log_alpha -0.15699 NA NA +log_beta 3.01540 NA NA +a.1 3.11518 NA NA +b.1 0.04445 NA NA +SD.log_k_JCZ38 1.40732 NA NA +SD.log_k_J9Z38 0.56510 NA NA +SD.log_k_JSE76 0.72067 NA NA +SD.f_cyan_ilr_1 0.31199 NA NA +SD.f_cyan_ilr_2 0.36894 NA NA +SD.f_JCZ38_qlogis 6.92892 NA NA +SD.log_alpha 0.25662 NA NA +SD.log_beta 0.35845 NA NA + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_JCZ38 1.4073 NA NA +SD.log_k_J9Z38 0.5651 NA NA +SD.log_k_JSE76 0.7207 NA NA +SD.f_cyan_ilr_1 0.3120 NA NA +SD.f_cyan_ilr_2 0.3689 NA NA +SD.f_JCZ38_qlogis 6.9289 NA NA +SD.log_alpha 0.2566 NA NA +SD.log_beta 0.3585 NA NA + +Variance model: + est. lower upper +a.1 3.11518 NA NA +b.1 0.04445 NA NA + +Backtransformed parameters: + est. lower upper +cyan_0 1.006e+02 NA NA +k_JCZ38 3.135e-02 NA NA +k_J9Z38 5.277e-03 NA NA +k_JSE76 3.175e-03 NA NA +f_cyan_to_JCZ38 5.991e-01 NA NA +f_cyan_to_J9Z38 2.275e-01 NA NA +f_JCZ38_to_JSE76 1.000e+00 NA NA +alpha 8.547e-01 NA NA +beta 2.040e+01 NA NA + +Resulting formation fractions: + ff +cyan_JCZ38 0.5991 +cyan_J9Z38 0.2275 +cyan_sink 0.1734 +JCZ38_JSE76 1.0000 +JCZ38_sink 0.0000 + +Estimated disappearance times: + DT50 DT90 DT50back +cyan 25.50 281.29 84.68 +JCZ38 22.11 73.44 NA +J9Z38 131.36 436.35 NA +JSE76 218.28 725.11 NA + +</code></pre> +<p></p> +<caption> +Hierarchical DFOP path 1 fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 07:46:41 2023 +Date of summary: Thu Apr 20 20:01:30 2023 + +Equations: +d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * + time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) + * cyan +d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - + g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * + exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38 +d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - + g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * + exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 528.713 s +Using 300, 100 iterations and 10 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 + 102.0644 -3.4008 -5.0024 -5.8613 0.6855 + f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 g_qlogis + 1.2365 13.7245 -1.8641 -4.5063 -0.6468 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 +cyan_0 4.466 0.000 0.000 0.000 0.0000 +log_k_JCZ38 0.000 2.382 0.000 0.000 0.0000 +log_k_J9Z38 0.000 0.000 1.595 0.000 0.0000 +log_k_JSE76 0.000 0.000 0.000 1.245 0.0000 +f_cyan_ilr_1 0.000 0.000 0.000 0.000 0.6852 +f_cyan_ilr_2 0.000 0.000 0.000 0.000 0.0000 +f_JCZ38_qlogis 0.000 0.000 0.000 0.000 0.0000 +log_k1 0.000 0.000 0.000 0.000 0.0000 +log_k2 0.000 0.000 0.000 0.000 0.0000 +g_qlogis 0.000 0.000 0.000 0.000 0.0000 + f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 g_qlogis +cyan_0 0.00 0.00 0.0000 0.0000 0.000 +log_k_JCZ38 0.00 0.00 0.0000 0.0000 0.000 +log_k_J9Z38 0.00 0.00 0.0000 0.0000 0.000 +log_k_JSE76 0.00 0.00 0.0000 0.0000 0.000 +f_cyan_ilr_1 0.00 0.00 0.0000 0.0000 0.000 +f_cyan_ilr_2 1.28 0.00 0.0000 0.0000 0.000 +f_JCZ38_qlogis 0.00 16.11 0.0000 0.0000 0.000 +log_k1 0.00 0.00 0.9866 0.0000 0.000 +log_k2 0.00 0.00 0.0000 0.5953 0.000 +g_qlogis 0.00 0.00 0.0000 0.0000 1.583 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2403 2395 -1182 + +Optimised parameters: + est. lower upper +cyan_0 102.6079 NA NA +log_k_JCZ38 -3.4855 NA NA +log_k_J9Z38 -5.1686 NA NA +log_k_JSE76 -5.6697 NA NA +f_cyan_ilr_1 0.6714 NA NA +f_cyan_ilr_2 0.4986 NA NA +f_JCZ38_qlogis 55.4760 NA NA +log_k1 -1.8409 NA NA +log_k2 -4.4915 NA NA +g_qlogis -0.6403 NA NA +a.1 3.2387 NA NA +SD.log_k_JCZ38 1.4524 NA NA +SD.log_k_J9Z38 0.5151 NA NA +SD.log_k_JSE76 0.6514 NA NA +SD.f_cyan_ilr_1 0.3023 NA NA +SD.f_cyan_ilr_2 0.2959 NA NA +SD.f_JCZ38_qlogis 1.9984 NA NA +SD.log_k1 0.5188 NA NA +SD.log_k2 0.3894 NA NA +SD.g_qlogis 0.8579 NA NA + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_JCZ38 1.4524 NA NA +SD.log_k_J9Z38 0.5151 NA NA +SD.log_k_JSE76 0.6514 NA NA +SD.f_cyan_ilr_1 0.3023 NA NA +SD.f_cyan_ilr_2 0.2959 NA NA +SD.f_JCZ38_qlogis 1.9984 NA NA +SD.log_k1 0.5188 NA NA +SD.log_k2 0.3894 NA NA +SD.g_qlogis 0.8579 NA NA + +Variance model: + est. lower upper +a.1 3.239 NA NA + +Backtransformed parameters: + est. lower upper +cyan_0 1.026e+02 NA NA +k_JCZ38 3.064e-02 NA NA +k_J9Z38 5.692e-03 NA NA +k_JSE76 3.449e-03 NA NA +f_cyan_to_JCZ38 5.798e-01 NA NA +f_cyan_to_J9Z38 2.243e-01 NA NA +f_JCZ38_to_JSE76 1.000e+00 NA NA +k1 1.587e-01 NA NA +k2 1.120e-02 NA NA +g 3.452e-01 NA NA + +Resulting formation fractions: + ff +cyan_JCZ38 0.5798 +cyan_J9Z38 0.2243 +cyan_sink 0.1958 +JCZ38_JSE76 1.0000 +JCZ38_sink 0.0000 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +cyan 25.21 167.73 50.49 4.368 61.87 +JCZ38 22.62 75.15 NA NA NA +J9Z38 121.77 404.50 NA NA NA +JSE76 200.98 667.64 NA NA NA + +</code></pre> +<p></p> +<caption> +Hierarchical DFOP path 1 fit with two-component error +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 07:49:05 2023 +Date of summary: Thu Apr 20 20:01:30 2023 + +Equations: +d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * + time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) + * cyan +d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - + g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * + exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38 +d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - + g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * + exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 673.139 s +Using 300, 100 iterations and 10 chains + +Variance model: Two-component variance function + +Starting values for degradation parameters: + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 + 101.3964 -3.3626 -4.9792 -5.8727 0.6814 + f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 g_qlogis + 6.7799 13.7245 -1.9222 -4.5035 -0.7172 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 +cyan_0 5.317 0.000 0.000 0.000 0.0000 +log_k_JCZ38 0.000 2.272 0.000 0.000 0.0000 +log_k_J9Z38 0.000 0.000 1.633 0.000 0.0000 +log_k_JSE76 0.000 0.000 0.000 1.271 0.0000 +f_cyan_ilr_1 0.000 0.000 0.000 0.000 0.6838 +f_cyan_ilr_2 0.000 0.000 0.000 0.000 0.0000 +f_JCZ38_qlogis 0.000 0.000 0.000 0.000 0.0000 +log_k1 0.000 0.000 0.000 0.000 0.0000 +log_k2 0.000 0.000 0.000 0.000 0.0000 +g_qlogis 0.000 0.000 0.000 0.000 0.0000 + f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 g_qlogis +cyan_0 0.00 0.00 0.0000 0.0000 0.000 +log_k_JCZ38 0.00 0.00 0.0000 0.0000 0.000 +log_k_J9Z38 0.00 0.00 0.0000 0.0000 0.000 +log_k_JSE76 0.00 0.00 0.0000 0.0000 0.000 +f_cyan_ilr_1 0.00 0.00 0.0000 0.0000 0.000 +f_cyan_ilr_2 11.77 0.00 0.0000 0.0000 0.000 +f_JCZ38_qlogis 0.00 16.11 0.0000 0.0000 0.000 +log_k1 0.00 0.00 0.9496 0.0000 0.000 +log_k2 0.00 0.00 0.0000 0.5846 0.000 +g_qlogis 0.00 0.00 0.0000 0.0000 1.719 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2398 2390 -1179 + +Optimised parameters: + est. lower upper +cyan_0 100.8076 NA NA +log_k_JCZ38 -3.4684 NA NA +log_k_J9Z38 -5.0844 NA NA +log_k_JSE76 -5.5743 NA NA +f_cyan_ilr_1 0.6669 NA NA +f_cyan_ilr_2 0.7912 NA NA +f_JCZ38_qlogis 84.1825 NA NA +log_k1 -2.1671 NA NA +log_k2 -4.5447 NA NA +g_qlogis -0.5631 NA NA +a.1 2.9627 NA NA +b.1 0.0444 NA NA +SD.log_k_JCZ38 1.4044 NA NA +SD.log_k_J9Z38 0.6410 NA NA +SD.log_k_JSE76 0.5391 NA NA +SD.f_cyan_ilr_1 0.3203 NA NA +SD.f_cyan_ilr_2 0.5038 NA NA +SD.f_JCZ38_qlogis 3.5865 NA NA +SD.log_k2 0.3119 NA NA +SD.g_qlogis 0.8276 NA NA + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_JCZ38 1.4044 NA NA +SD.log_k_J9Z38 0.6410 NA NA +SD.log_k_JSE76 0.5391 NA NA +SD.f_cyan_ilr_1 0.3203 NA NA +SD.f_cyan_ilr_2 0.5038 NA NA +SD.f_JCZ38_qlogis 3.5865 NA NA +SD.log_k2 0.3119 NA NA +SD.g_qlogis 0.8276 NA NA + +Variance model: + est. lower upper +a.1 2.9627 NA NA +b.1 0.0444 NA NA + +Backtransformed parameters: + est. lower upper +cyan_0 1.008e+02 NA NA +k_JCZ38 3.117e-02 NA NA +k_J9Z38 6.193e-03 NA NA +k_JSE76 3.794e-03 NA NA +f_cyan_to_JCZ38 6.149e-01 NA NA +f_cyan_to_J9Z38 2.395e-01 NA NA +f_JCZ38_to_JSE76 1.000e+00 NA NA +k1 1.145e-01 NA NA +k2 1.062e-02 NA NA +g 3.628e-01 NA NA + +Resulting formation fractions: + ff +cyan_JCZ38 0.6149 +cyan_J9Z38 0.2395 +cyan_sink 0.1456 +JCZ38_JSE76 1.0000 +JCZ38_sink 0.0000 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +cyan 26.26 174.32 52.47 6.053 65.25 +JCZ38 22.24 73.88 NA NA NA +J9Z38 111.93 371.82 NA NA NA +JSE76 182.69 606.88 NA NA NA + +</code></pre> +<p></p> +<caption> +Hierarchical SFORB path 1 fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 07:46:35 2023 +Date of summary: Thu Apr 20 20:01:30 2023 + +Equations: +d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound * + cyan_free + k_cyan_bound_free * cyan_bound +d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free * + cyan_bound +d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38 + * JCZ38 +d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38 + * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 531.17 s +Using 300, 100 iterations and 10 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + cyan_free_0 log_k_cyan_free log_k_cyan_free_bound + 102.0643 -2.8987 -2.7077 +log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 + -3.4717 -3.4008 -5.0024 + log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 + -5.8613 0.6855 1.2366 + f_JCZ38_qlogis + 13.7418 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_free_0 log_k_cyan_free log_k_cyan_free_bound +cyan_free_0 4.466 0.0000 0.000 +log_k_cyan_free 0.000 0.6158 0.000 +log_k_cyan_free_bound 0.000 0.0000 1.463 +log_k_cyan_bound_free 0.000 0.0000 0.000 +log_k_JCZ38 0.000 0.0000 0.000 +log_k_J9Z38 0.000 0.0000 0.000 +log_k_JSE76 0.000 0.0000 0.000 +f_cyan_ilr_1 0.000 0.0000 0.000 +f_cyan_ilr_2 0.000 0.0000 0.000 +f_JCZ38_qlogis 0.000 0.0000 0.000 + log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 +cyan_free_0 0.000 0.000 0.000 0.000 +log_k_cyan_free 0.000 0.000 0.000 0.000 +log_k_cyan_free_bound 0.000 0.000 0.000 0.000 +log_k_cyan_bound_free 1.058 0.000 0.000 0.000 +log_k_JCZ38 0.000 2.382 0.000 0.000 +log_k_J9Z38 0.000 0.000 1.595 0.000 +log_k_JSE76 0.000 0.000 0.000 1.245 +f_cyan_ilr_1 0.000 0.000 0.000 0.000 +f_cyan_ilr_2 0.000 0.000 0.000 0.000 +f_JCZ38_qlogis 0.000 0.000 0.000 0.000 + f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis +cyan_free_0 0.0000 0.00 0.00 +log_k_cyan_free 0.0000 0.00 0.00 +log_k_cyan_free_bound 0.0000 0.00 0.00 +log_k_cyan_bound_free 0.0000 0.00 0.00 +log_k_JCZ38 0.0000 0.00 0.00 +log_k_J9Z38 0.0000 0.00 0.00 +log_k_JSE76 0.0000 0.00 0.00 +f_cyan_ilr_1 0.6852 0.00 0.00 +f_cyan_ilr_2 0.0000 1.28 0.00 +f_JCZ38_qlogis 0.0000 0.00 16.14 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2401 2394 -1181 + +Optimised parameters: + est. lower upper +cyan_free_0 102.7803 NA NA +log_k_cyan_free -2.8068 NA NA +log_k_cyan_free_bound -2.5714 NA NA +log_k_cyan_bound_free -3.4426 NA NA +log_k_JCZ38 -3.4994 NA NA +log_k_J9Z38 -5.1148 NA NA +log_k_JSE76 -5.6335 NA NA +f_cyan_ilr_1 0.6597 NA NA +f_cyan_ilr_2 0.5132 NA NA +f_JCZ38_qlogis 37.2090 NA NA +a.1 3.2367 NA NA +SD.log_k_cyan_free 0.3161 NA NA +SD.log_k_cyan_free_bound 0.8103 NA NA +SD.log_k_cyan_bound_free 0.5554 NA NA +SD.log_k_JCZ38 1.4858 NA NA +SD.log_k_J9Z38 0.5859 NA NA +SD.log_k_JSE76 0.6195 NA NA +SD.f_cyan_ilr_1 0.3118 NA NA +SD.f_cyan_ilr_2 0.3344 NA NA +SD.f_JCZ38_qlogis 0.5518 NA NA + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_cyan_free 0.3161 NA NA +SD.log_k_cyan_free_bound 0.8103 NA NA +SD.log_k_cyan_bound_free 0.5554 NA NA +SD.log_k_JCZ38 1.4858 NA NA +SD.log_k_J9Z38 0.5859 NA NA +SD.log_k_JSE76 0.6195 NA NA +SD.f_cyan_ilr_1 0.3118 NA NA +SD.f_cyan_ilr_2 0.3344 NA NA +SD.f_JCZ38_qlogis 0.5518 NA NA + +Variance model: + est. lower upper +a.1 3.237 NA NA + +Backtransformed parameters: + est. lower upper +cyan_free_0 1.028e+02 NA NA +k_cyan_free 6.040e-02 NA NA +k_cyan_free_bound 7.643e-02 NA NA +k_cyan_bound_free 3.198e-02 NA NA +k_JCZ38 3.022e-02 NA NA +k_J9Z38 6.007e-03 NA NA +k_JSE76 3.576e-03 NA NA +f_cyan_free_to_JCZ38 5.787e-01 NA NA +f_cyan_free_to_J9Z38 2.277e-01 NA NA +f_JCZ38_to_JSE76 1.000e+00 NA NA + +Estimated Eigenvalues of SFORB model(s): +cyan_b1 cyan_b2 cyan_g +0.15646 0.01235 0.33341 + +Resulting formation fractions: + ff +cyan_free_JCZ38 0.5787 +cyan_free_J9Z38 0.2277 +cyan_free_sink 0.1936 +cyan_free 1.0000 +JCZ38_JSE76 1.0000 +JCZ38_sink 0.0000 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 +cyan 24.48 153.7 46.26 4.43 56.15 +JCZ38 22.94 76.2 NA NA NA +J9Z38 115.39 383.3 NA NA NA +JSE76 193.84 643.9 NA NA NA + +</code></pre> +<p></p> +<caption> +Hierarchical SFORB path 1 fit with two-component error +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 07:49:08 2023 +Date of summary: Thu Apr 20 20:01:30 2023 + +Equations: +d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound * + cyan_free + k_cyan_bound_free * cyan_bound +d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free * + cyan_bound +d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38 + * JCZ38 +d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38 + * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 675.659 s +Using 300, 100 iterations and 10 chains + +Variance model: Two-component variance function + +Starting values for degradation parameters: + cyan_free_0 log_k_cyan_free log_k_cyan_free_bound + 101.3964 -2.9881 -2.7949 +log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 + -3.4376 -3.3626 -4.9792 + log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 + -5.8727 0.6814 6.8139 + f_JCZ38_qlogis + 13.7419 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_free_0 log_k_cyan_free log_k_cyan_free_bound +cyan_free_0 5.317 0.0000 0.000 +log_k_cyan_free 0.000 0.7301 0.000 +log_k_cyan_free_bound 0.000 0.0000 1.384 +log_k_cyan_bound_free 0.000 0.0000 0.000 +log_k_JCZ38 0.000 0.0000 0.000 +log_k_J9Z38 0.000 0.0000 0.000 +log_k_JSE76 0.000 0.0000 0.000 +f_cyan_ilr_1 0.000 0.0000 0.000 +f_cyan_ilr_2 0.000 0.0000 0.000 +f_JCZ38_qlogis 0.000 0.0000 0.000 + log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 +cyan_free_0 0.000 0.000 0.000 0.000 +log_k_cyan_free 0.000 0.000 0.000 0.000 +log_k_cyan_free_bound 0.000 0.000 0.000 0.000 +log_k_cyan_bound_free 1.109 0.000 0.000 0.000 +log_k_JCZ38 0.000 2.272 0.000 0.000 +log_k_J9Z38 0.000 0.000 1.633 0.000 +log_k_JSE76 0.000 0.000 0.000 1.271 +f_cyan_ilr_1 0.000 0.000 0.000 0.000 +f_cyan_ilr_2 0.000 0.000 0.000 0.000 +f_JCZ38_qlogis 0.000 0.000 0.000 0.000 + f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis +cyan_free_0 0.0000 0.00 0.00 +log_k_cyan_free 0.0000 0.00 0.00 +log_k_cyan_free_bound 0.0000 0.00 0.00 +log_k_cyan_bound_free 0.0000 0.00 0.00 +log_k_JCZ38 0.0000 0.00 0.00 +log_k_J9Z38 0.0000 0.00 0.00 +log_k_JSE76 0.0000 0.00 0.00 +f_cyan_ilr_1 0.6838 0.00 0.00 +f_cyan_ilr_2 0.0000 11.84 0.00 +f_JCZ38_qlogis 0.0000 0.00 16.14 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2400 2392 -1180 + +Optimised parameters: + est. lower upper +cyan_free_0 100.69983 NA NA +log_k_cyan_free -3.11584 NA NA +log_k_cyan_free_bound -3.15216 NA NA +log_k_cyan_bound_free -3.65986 NA NA +log_k_JCZ38 -3.47811 NA NA +log_k_J9Z38 -5.08835 NA NA +log_k_JSE76 -5.55514 NA NA +f_cyan_ilr_1 0.66764 NA NA +f_cyan_ilr_2 0.78329 NA NA +f_JCZ38_qlogis 25.35245 NA NA +a.1 2.99088 NA NA +b.1 0.04346 NA NA +SD.log_k_cyan_free 0.48797 NA NA +SD.log_k_cyan_bound_free 0.27243 NA NA +SD.log_k_JCZ38 1.42450 NA NA +SD.log_k_J9Z38 0.63496 NA NA +SD.log_k_JSE76 0.55951 NA NA +SD.f_cyan_ilr_1 0.32687 NA NA +SD.f_cyan_ilr_2 0.48056 NA NA +SD.f_JCZ38_qlogis 0.43818 NA NA + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_cyan_free 0.4880 NA NA +SD.log_k_cyan_bound_free 0.2724 NA NA +SD.log_k_JCZ38 1.4245 NA NA +SD.log_k_J9Z38 0.6350 NA NA +SD.log_k_JSE76 0.5595 NA NA +SD.f_cyan_ilr_1 0.3269 NA NA +SD.f_cyan_ilr_2 0.4806 NA NA +SD.f_JCZ38_qlogis 0.4382 NA NA + +Variance model: + est. lower upper +a.1 2.99088 NA NA +b.1 0.04346 NA NA + +Backtransformed parameters: + est. lower upper +cyan_free_0 1.007e+02 NA NA +k_cyan_free 4.434e-02 NA NA +k_cyan_free_bound 4.276e-02 NA NA +k_cyan_bound_free 2.574e-02 NA NA +k_JCZ38 3.087e-02 NA NA +k_J9Z38 6.168e-03 NA NA +k_JSE76 3.868e-03 NA NA +f_cyan_free_to_JCZ38 6.143e-01 NA NA +f_cyan_free_to_J9Z38 2.389e-01 NA NA +f_JCZ38_to_JSE76 1.000e+00 NA NA + +Estimated Eigenvalues of SFORB model(s): +cyan_b1 cyan_b2 cyan_g +0.10161 0.01123 0.36636 + +Resulting formation fractions: + ff +cyan_free_JCZ38 6.143e-01 +cyan_free_J9Z38 2.389e-01 +cyan_free_sink 1.468e-01 +cyan_free 1.000e+00 +JCZ38_JSE76 1.000e+00 +JCZ38_sink 9.763e-12 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 +cyan 25.91 164.4 49.49 6.822 61.72 +JCZ38 22.46 74.6 NA NA NA +J9Z38 112.37 373.3 NA NA NA +JSE76 179.22 595.4 NA NA NA + +</code></pre> +<p></p> +<caption> +Hierarchical HS path 1 fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 07:46:30 2023 +Date of summary: Thu Apr 20 20:01:30 2023 + +Equations: +d_cyan/dt = - ifelse(time <= 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 525.846 s +Using 300, 100 iterations and 10 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 + 102.8738 -3.4490 -4.9348 -5.5989 0.6469 + f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 log_tb + 1.2854 9.7193 -2.9084 -4.1810 1.7813 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 +cyan_0 5.409 0.00 0.00 0.000 0.0000 +log_k_JCZ38 0.000 2.33 0.00 0.000 0.0000 +log_k_J9Z38 0.000 0.00 1.59 0.000 0.0000 +log_k_JSE76 0.000 0.00 0.00 1.006 0.0000 +f_cyan_ilr_1 0.000 0.00 0.00 0.000 0.6371 +f_cyan_ilr_2 0.000 0.00 0.00 0.000 0.0000 +f_JCZ38_qlogis 0.000 0.00 0.00 0.000 0.0000 +log_k1 0.000 0.00 0.00 0.000 0.0000 +log_k2 0.000 0.00 0.00 0.000 0.0000 +log_tb 0.000 0.00 0.00 0.000 0.0000 + f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 log_tb +cyan_0 0.000 0.00 0.0000 0.0000 0.0000 +log_k_JCZ38 0.000 0.00 0.0000 0.0000 0.0000 +log_k_J9Z38 0.000 0.00 0.0000 0.0000 0.0000 +log_k_JSE76 0.000 0.00 0.0000 0.0000 0.0000 +f_cyan_ilr_1 0.000 0.00 0.0000 0.0000 0.0000 +f_cyan_ilr_2 2.167 0.00 0.0000 0.0000 0.0000 +f_JCZ38_qlogis 0.000 10.22 0.0000 0.0000 0.0000 +log_k1 0.000 0.00 0.7003 0.0000 0.0000 +log_k2 0.000 0.00 0.0000 0.8928 0.0000 +log_tb 0.000 0.00 0.0000 0.0000 0.6774 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2427 2420 -1194 + +Optimised parameters: + est. lower upper +cyan_0 101.84849 NA NA +log_k_JCZ38 -3.47365 NA NA +log_k_J9Z38 -5.10562 NA NA +log_k_JSE76 -5.60318 NA NA +f_cyan_ilr_1 0.66127 NA NA +f_cyan_ilr_2 0.60283 NA NA +f_JCZ38_qlogis 45.06408 NA NA +log_k1 -3.10124 NA NA +log_k2 -4.39028 NA NA +log_tb 2.32256 NA NA +a.1 3.32683 NA NA +SD.log_k_JCZ38 1.41427 NA NA +SD.log_k_J9Z38 0.54767 NA NA +SD.log_k_JSE76 0.62147 NA NA +SD.f_cyan_ilr_1 0.30189 NA NA +SD.f_cyan_ilr_2 0.34960 NA NA +SD.f_JCZ38_qlogis 0.04644 NA NA +SD.log_k1 0.39534 NA NA +SD.log_k2 0.43468 NA NA +SD.log_tb 0.60781 NA NA + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_JCZ38 1.41427 NA NA +SD.log_k_J9Z38 0.54767 NA NA +SD.log_k_JSE76 0.62147 NA NA +SD.f_cyan_ilr_1 0.30189 NA NA +SD.f_cyan_ilr_2 0.34960 NA NA +SD.f_JCZ38_qlogis 0.04644 NA NA +SD.log_k1 0.39534 NA NA +SD.log_k2 0.43468 NA NA +SD.log_tb 0.60781 NA NA + +Variance model: + est. lower upper +a.1 3.327 NA NA + +Backtransformed parameters: + est. lower upper +cyan_0 1.018e+02 NA NA +k_JCZ38 3.100e-02 NA NA +k_J9Z38 6.063e-03 NA NA +k_JSE76 3.686e-03 NA NA +f_cyan_to_JCZ38 5.910e-01 NA NA +f_cyan_to_J9Z38 2.320e-01 NA NA +f_JCZ38_to_JSE76 1.000e+00 NA NA +k1 4.499e-02 NA NA +k2 1.240e-02 NA NA +tb 1.020e+01 NA NA + +Resulting formation fractions: + ff +cyan_JCZ38 0.591 +cyan_J9Z38 0.232 +cyan_sink 0.177 +JCZ38_JSE76 1.000 +JCZ38_sink 0.000 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +cyan 29.09 158.91 47.84 15.41 55.91 +JCZ38 22.36 74.27 NA NA NA +J9Z38 114.33 379.80 NA NA NA +JSE76 188.04 624.66 NA NA NA + +</code></pre> +<p></p> +<caption> +Hierarchical HS path 1 fit with two-component error +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 07:46:19 2023 +Date of summary: Thu Apr 20 20:01:30 2023 + +Equations: +d_cyan/dt = - ifelse(time <= 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 514.968 s +Using 300, 100 iterations and 10 chains + +Variance model: Two-component variance function + +Starting values for degradation parameters: + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 + 101.168 -3.358 -4.941 -5.794 0.676 + f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 log_tb + 5.740 13.863 -3.147 -4.262 2.173 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 +cyan_0 5.79 0.000 0.000 0.000 0.0000 +log_k_JCZ38 0.00 2.271 0.000 0.000 0.0000 +log_k_J9Z38 0.00 0.000 1.614 0.000 0.0000 +log_k_JSE76 0.00 0.000 0.000 1.264 0.0000 +f_cyan_ilr_1 0.00 0.000 0.000 0.000 0.6761 +f_cyan_ilr_2 0.00 0.000 0.000 0.000 0.0000 +f_JCZ38_qlogis 0.00 0.000 0.000 0.000 0.0000 +log_k1 0.00 0.000 0.000 0.000 0.0000 +log_k2 0.00 0.000 0.000 0.000 0.0000 +log_tb 0.00 0.000 0.000 0.000 0.0000 + f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 log_tb +cyan_0 0.000 0.00 0.0000 0.0000 0.000 +log_k_JCZ38 0.000 0.00 0.0000 0.0000 0.000 +log_k_J9Z38 0.000 0.00 0.0000 0.0000 0.000 +log_k_JSE76 0.000 0.00 0.0000 0.0000 0.000 +f_cyan_ilr_1 0.000 0.00 0.0000 0.0000 0.000 +f_cyan_ilr_2 9.572 0.00 0.0000 0.0000 0.000 +f_JCZ38_qlogis 0.000 19.19 0.0000 0.0000 0.000 +log_k1 0.000 0.00 0.8705 0.0000 0.000 +log_k2 0.000 0.00 0.0000 0.9288 0.000 +log_tb 0.000 0.00 0.0000 0.0000 1.065 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2422 2414 -1190 + +Optimised parameters: + est. lower upper +cyan_0 100.9521 NA NA +log_k_JCZ38 -3.4629 NA NA +log_k_J9Z38 -5.0346 NA NA +log_k_JSE76 -5.5722 NA NA +f_cyan_ilr_1 0.6560 NA NA +f_cyan_ilr_2 0.7983 NA NA +f_JCZ38_qlogis 42.7949 NA NA +log_k1 -3.1721 NA NA +log_k2 -4.4039 NA NA +log_tb 2.3994 NA NA +a.1 3.0586 NA NA +b.1 0.0380 NA NA +SD.log_k_JCZ38 1.3754 NA NA +SD.log_k_J9Z38 0.6703 NA NA +SD.log_k_JSE76 0.5876 NA NA +SD.f_cyan_ilr_1 0.3272 NA NA +SD.f_cyan_ilr_2 0.5300 NA NA +SD.f_JCZ38_qlogis 6.4465 NA NA +SD.log_k1 0.4135 NA NA +SD.log_k2 0.4182 NA NA +SD.log_tb 0.6035 NA NA + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_JCZ38 1.3754 NA NA +SD.log_k_J9Z38 0.6703 NA NA +SD.log_k_JSE76 0.5876 NA NA +SD.f_cyan_ilr_1 0.3272 NA NA +SD.f_cyan_ilr_2 0.5300 NA NA +SD.f_JCZ38_qlogis 6.4465 NA NA +SD.log_k1 0.4135 NA NA +SD.log_k2 0.4182 NA NA +SD.log_tb 0.6035 NA NA + +Variance model: + est. lower upper +a.1 3.059 NA NA +b.1 0.038 NA NA + +Backtransformed parameters: + est. lower upper +cyan_0 1.010e+02 NA NA +k_JCZ38 3.134e-02 NA NA +k_J9Z38 6.509e-03 NA NA +k_JSE76 3.802e-03 NA NA +f_cyan_to_JCZ38 6.127e-01 NA NA +f_cyan_to_J9Z38 2.423e-01 NA NA +f_JCZ38_to_JSE76 1.000e+00 NA NA +k1 4.191e-02 NA NA +k2 1.223e-02 NA NA +tb 1.102e+01 NA NA + +Resulting formation fractions: + ff +cyan_JCZ38 0.6127 +cyan_J9Z38 0.2423 +cyan_sink 0.1449 +JCZ38_JSE76 1.0000 +JCZ38_sink 0.0000 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +cyan 29.94 161.54 48.63 16.54 56.68 +JCZ38 22.12 73.47 NA NA NA +J9Z38 106.50 353.77 NA NA NA +JSE76 182.30 605.60 NA NA NA + +</code></pre> +<p></p> +</div> +<div class="section level4"> +<h4 id="pathway-2">Pathway 2<a class="anchor" aria-label="anchor" href="#pathway-2"></a> +</h4> +<caption> +Hierarchical FOMC path 2 fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 07:58:00 2023 +Date of summary: Thu Apr 20 20:01:30 2023 + +Equations: +d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan +d_JCZ38/dt = + f_cyan_to_JCZ38 * (alpha/beta) * 1/((time/beta) + 1) * + cyan - k_JCZ38 * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76 +d_J9Z38/dt = + f_cyan_to_J9Z38 * (alpha/beta) * 1/((time/beta) + 1) * + cyan - k_J9Z38 * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 522.351 s +Using 300, 100 iterations and 10 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 + 101.8173 -1.8998 -5.1449 -2.5415 0.6705 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta + 4.4669 16.1281 13.3327 -0.2314 2.8738 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 +cyan_0 5.742 0.000 0.000 0.00 0.0000 +log_k_JCZ38 0.000 1.402 0.000 0.00 0.0000 +log_k_J9Z38 0.000 0.000 1.718 0.00 0.0000 +log_k_JSE76 0.000 0.000 0.000 3.57 0.0000 +f_cyan_ilr_1 0.000 0.000 0.000 0.00 0.5926 +f_cyan_ilr_2 0.000 0.000 0.000 0.00 0.0000 +f_JCZ38_qlogis 0.000 0.000 0.000 0.00 0.0000 +f_JSE76_qlogis 0.000 0.000 0.000 0.00 0.0000 +log_alpha 0.000 0.000 0.000 0.00 0.0000 +log_beta 0.000 0.000 0.000 0.00 0.0000 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta +cyan_0 0.00 0.00 0.00 0.0000 0.0000 +log_k_JCZ38 0.00 0.00 0.00 0.0000 0.0000 +log_k_J9Z38 0.00 0.00 0.00 0.0000 0.0000 +log_k_JSE76 0.00 0.00 0.00 0.0000 0.0000 +f_cyan_ilr_1 0.00 0.00 0.00 0.0000 0.0000 +f_cyan_ilr_2 10.56 0.00 0.00 0.0000 0.0000 +f_JCZ38_qlogis 0.00 12.04 0.00 0.0000 0.0000 +f_JSE76_qlogis 0.00 0.00 15.26 0.0000 0.0000 +log_alpha 0.00 0.00 0.00 0.4708 0.0000 +log_beta 0.00 0.00 0.00 0.0000 0.4432 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2308 2301 -1134 + +Optimised parameters: + est. lower upper +cyan_0 101.9586 99.22024 104.69700 +log_k_JCZ38 -2.4861 -3.17661 -1.79560 +log_k_J9Z38 -5.3926 -6.08842 -4.69684 +log_k_JSE76 -3.1193 -4.12904 -2.10962 +f_cyan_ilr_1 0.7368 0.42085 1.05276 +f_cyan_ilr_2 0.6196 0.06052 1.17861 +f_JCZ38_qlogis 4.8970 -4.68003 14.47398 +f_JSE76_qlogis 4.4066 -1.02087 9.83398 +log_alpha -0.3021 -0.68264 0.07838 +log_beta 2.7438 2.57970 2.90786 +a.1 2.9008 2.69920 3.10245 +SD.cyan_0 2.7081 0.64216 4.77401 +SD.log_k_JCZ38 0.7043 0.19951 1.20907 +SD.log_k_J9Z38 0.6248 0.05790 1.19180 +SD.log_k_JSE76 1.0750 0.33157 1.81839 +SD.f_cyan_ilr_1 0.3429 0.11688 0.56892 +SD.f_cyan_ilr_2 0.4774 0.09381 0.86097 +SD.f_JCZ38_qlogis 1.5565 -7.83970 10.95279 +SD.f_JSE76_qlogis 1.6871 -1.25577 4.63000 +SD.log_alpha 0.4216 0.15913 0.68405 + +Correlation: + cyan_0 l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76 +log_k_JCZ38 -0.0167 +log_k_J9Z38 -0.0307 0.0057 +log_k_JSE76 -0.0032 0.1358 0.0009 +f_cyan_ilr_1 -0.0087 0.0206 -0.1158 -0.0009 +f_cyan_ilr_2 -0.1598 0.0690 0.1770 0.0002 -0.0007 +f_JCZ38_qlogis 0.0966 -0.1132 -0.0440 0.0182 -0.1385 -0.4583 +f_JSE76_qlogis -0.0647 0.1157 0.0333 -0.0026 0.1110 0.3620 -0.8586 +log_alpha -0.0389 0.0113 0.0209 0.0021 0.0041 0.0451 -0.0605 0.0412 +log_beta -0.2508 0.0533 0.0977 0.0098 0.0220 0.2741 -0.2934 0.1999 + log_lph +log_k_JCZ38 +log_k_J9Z38 +log_k_JSE76 +f_cyan_ilr_1 +f_cyan_ilr_2 +f_JCZ38_qlogis +f_JSE76_qlogis +log_alpha +log_beta 0.2281 + +Random effects: + est. lower upper +SD.cyan_0 2.7081 0.64216 4.7740 +SD.log_k_JCZ38 0.7043 0.19951 1.2091 +SD.log_k_J9Z38 0.6248 0.05790 1.1918 +SD.log_k_JSE76 1.0750 0.33157 1.8184 +SD.f_cyan_ilr_1 0.3429 0.11688 0.5689 +SD.f_cyan_ilr_2 0.4774 0.09381 0.8610 +SD.f_JCZ38_qlogis 1.5565 -7.83970 10.9528 +SD.f_JSE76_qlogis 1.6871 -1.25577 4.6300 +SD.log_alpha 0.4216 0.15913 0.6840 + +Variance model: + est. lower upper +a.1 2.901 2.699 3.102 + +Backtransformed parameters: + est. lower upper +cyan_0 101.95862 99.220240 1.047e+02 +k_JCZ38 0.08323 0.041727 1.660e-01 +k_J9Z38 0.00455 0.002269 9.124e-03 +k_JSE76 0.04419 0.016098 1.213e-01 +f_cyan_to_JCZ38 0.61318 NA NA +f_cyan_to_J9Z38 0.21630 NA NA +f_JCZ38_to_JSE76 0.99259 0.009193 1.000e+00 +f_JSE76_to_JCZ38 0.98795 0.264857 9.999e-01 +alpha 0.73924 0.505281 1.082e+00 +beta 15.54568 13.193194 1.832e+01 + +Resulting formation fractions: + ff +cyan_JCZ38 0.613182 +cyan_J9Z38 0.216298 +cyan_sink 0.170519 +JCZ38_JSE76 0.992586 +JCZ38_sink 0.007414 +JSE76_JCZ38 0.987950 +JSE76_sink 0.012050 + +Estimated disappearance times: + DT50 DT90 DT50back +cyan 24.157 334.68 100.7 +JCZ38 8.328 27.66 NA +J9Z38 152.341 506.06 NA +JSE76 15.687 52.11 NA + +</code></pre> +<p></p> +<caption> +Hierarchical FOMC path 2 fit with two-component error +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 07:57:52 2023 +Date of summary: Thu Apr 20 20:01:30 2023 + +Equations: +d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan +d_JCZ38/dt = + f_cyan_to_JCZ38 * (alpha/beta) * 1/((time/beta) + 1) * + cyan - k_JCZ38 * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76 +d_J9Z38/dt = + f_cyan_to_J9Z38 * (alpha/beta) * 1/((time/beta) + 1) * + cyan - k_J9Z38 * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 514.301 s +Using 300, 100 iterations and 10 chains + +Variance model: Two-component variance function + +Starting values for degradation parameters: + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 + 101.9028 -1.9055 -5.0249 -2.5646 0.6807 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta + 4.8883 16.0676 9.3923 -0.1346 3.0364 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 +cyan_0 6.321 0.000 0.000 0.000 0.0000 +log_k_JCZ38 0.000 1.392 0.000 0.000 0.0000 +log_k_J9Z38 0.000 0.000 1.561 0.000 0.0000 +log_k_JSE76 0.000 0.000 0.000 3.614 0.0000 +f_cyan_ilr_1 0.000 0.000 0.000 0.000 0.6339 +f_cyan_ilr_2 0.000 0.000 0.000 0.000 0.0000 +f_JCZ38_qlogis 0.000 0.000 0.000 0.000 0.0000 +f_JSE76_qlogis 0.000 0.000 0.000 0.000 0.0000 +log_alpha 0.000 0.000 0.000 0.000 0.0000 +log_beta 0.000 0.000 0.000 0.000 0.0000 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta +cyan_0 0.00 0.00 0.00 0.0000 0.0000 +log_k_JCZ38 0.00 0.00 0.00 0.0000 0.0000 +log_k_J9Z38 0.00 0.00 0.00 0.0000 0.0000 +log_k_JSE76 0.00 0.00 0.00 0.0000 0.0000 +f_cyan_ilr_1 0.00 0.00 0.00 0.0000 0.0000 +f_cyan_ilr_2 10.41 0.00 0.00 0.0000 0.0000 +f_JCZ38_qlogis 0.00 12.24 0.00 0.0000 0.0000 +f_JSE76_qlogis 0.00 0.00 15.13 0.0000 0.0000 +log_alpha 0.00 0.00 0.00 0.3701 0.0000 +log_beta 0.00 0.00 0.00 0.0000 0.5662 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2248 2240 -1103 + +Optimised parameters: + est. lower upper +cyan_0 101.55545 9.920e+01 1.039e+02 +log_k_JCZ38 -2.37354 -2.928e+00 -1.819e+00 +log_k_J9Z38 -5.14736 -5.960e+00 -4.335e+00 +log_k_JSE76 -3.07802 -4.243e+00 -1.913e+00 +f_cyan_ilr_1 0.71263 3.655e-01 1.060e+00 +f_cyan_ilr_2 0.95202 2.701e-01 1.634e+00 +f_JCZ38_qlogis 3.58473 1.251e+00 5.919e+00 +f_JSE76_qlogis 19.03623 -1.037e+07 1.037e+07 +log_alpha -0.15297 -4.490e-01 1.431e-01 +log_beta 2.99230 2.706e+00 3.278e+00 +a.1 2.04816 NA NA +b.1 0.06886 NA NA +SD.log_k_JCZ38 0.56174 NA NA +SD.log_k_J9Z38 0.86509 NA NA +SD.log_k_JSE76 1.28450 NA NA +SD.f_cyan_ilr_1 0.38705 NA NA +SD.f_cyan_ilr_2 0.54153 NA NA +SD.f_JCZ38_qlogis 1.65311 NA NA +SD.f_JSE76_qlogis 7.51468 NA NA +SD.log_alpha 0.31586 NA NA +SD.log_beta 0.24696 NA NA + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_JCZ38 0.5617 NA NA +SD.log_k_J9Z38 0.8651 NA NA +SD.log_k_JSE76 1.2845 NA NA +SD.f_cyan_ilr_1 0.3870 NA NA +SD.f_cyan_ilr_2 0.5415 NA NA +SD.f_JCZ38_qlogis 1.6531 NA NA +SD.f_JSE76_qlogis 7.5147 NA NA +SD.log_alpha 0.3159 NA NA +SD.log_beta 0.2470 NA NA + +Variance model: + est. lower upper +a.1 2.04816 NA NA +b.1 0.06886 NA NA + +Backtransformed parameters: + est. lower upper +cyan_0 1.016e+02 99.20301 103.9079 +k_JCZ38 9.315e-02 0.05349 0.1622 +k_J9Z38 5.815e-03 0.00258 0.0131 +k_JSE76 4.605e-02 0.01436 0.1477 +f_cyan_to_JCZ38 6.438e-01 NA NA +f_cyan_to_J9Z38 2.350e-01 NA NA +f_JCZ38_to_JSE76 9.730e-01 0.77745 0.9973 +f_JSE76_to_JCZ38 1.000e+00 0.00000 1.0000 +alpha 8.582e-01 0.63824 1.1538 +beta 1.993e+01 14.97621 26.5262 + +Resulting formation fractions: + ff +cyan_JCZ38 6.438e-01 +cyan_J9Z38 2.350e-01 +cyan_sink 1.212e-01 +JCZ38_JSE76 9.730e-01 +JCZ38_sink 2.700e-02 +JSE76_JCZ38 1.000e+00 +JSE76_sink 5.403e-09 + +Estimated disappearance times: + DT50 DT90 DT50back +cyan 24.771 271.70 81.79 +JCZ38 7.441 24.72 NA +J9Z38 119.205 395.99 NA +JSE76 15.052 50.00 NA + +</code></pre> +<p></p> +<caption> +Hierarchical DFOP path 2 fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 07:58:43 2023 +Date of summary: Thu Apr 20 20:01:30 2023 + +Equations: +d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * + time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) + * cyan +d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - + g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * + exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38 + + f_JSE76_to_JCZ38 * k_JSE76 * JSE76 +d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - + g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * + exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 565.562 s +Using 300, 100 iterations and 10 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 + 102.4358 -2.3107 -5.3123 -3.7120 0.6753 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 + 1.1462 12.4095 12.3630 -1.9317 -4.4557 + g_qlogis + -0.5648 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 +cyan_0 4.594 0.0000 0.000 0.0 0.0000 +log_k_JCZ38 0.000 0.7966 0.000 0.0 0.0000 +log_k_J9Z38 0.000 0.0000 1.561 0.0 0.0000 +log_k_JSE76 0.000 0.0000 0.000 0.8 0.0000 +f_cyan_ilr_1 0.000 0.0000 0.000 0.0 0.6349 +f_cyan_ilr_2 0.000 0.0000 0.000 0.0 0.0000 +f_JCZ38_qlogis 0.000 0.0000 0.000 0.0 0.0000 +f_JSE76_qlogis 0.000 0.0000 0.000 0.0 0.0000 +log_k1 0.000 0.0000 0.000 0.0 0.0000 +log_k2 0.000 0.0000 0.000 0.0 0.0000 +g_qlogis 0.000 0.0000 0.000 0.0 0.0000 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 +cyan_0 0.000 0.00 0.0 0.000 0.0000 +log_k_JCZ38 0.000 0.00 0.0 0.000 0.0000 +log_k_J9Z38 0.000 0.00 0.0 0.000 0.0000 +log_k_JSE76 0.000 0.00 0.0 0.000 0.0000 +f_cyan_ilr_1 0.000 0.00 0.0 0.000 0.0000 +f_cyan_ilr_2 1.797 0.00 0.0 0.000 0.0000 +f_JCZ38_qlogis 0.000 13.85 0.0 0.000 0.0000 +f_JSE76_qlogis 0.000 0.00 14.1 0.000 0.0000 +log_k1 0.000 0.00 0.0 1.106 0.0000 +log_k2 0.000 0.00 0.0 0.000 0.6141 +g_qlogis 0.000 0.00 0.0 0.000 0.0000 + g_qlogis +cyan_0 0.000 +log_k_JCZ38 0.000 +log_k_J9Z38 0.000 +log_k_JSE76 0.000 +f_cyan_ilr_1 0.000 +f_cyan_ilr_2 0.000 +f_JCZ38_qlogis 0.000 +f_JSE76_qlogis 0.000 +log_k1 0.000 +log_k2 0.000 +g_qlogis 1.595 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2290 2281 -1123 + +Optimised parameters: + est. lower upper +cyan_0 102.6903 101.44420 103.9365 +log_k_JCZ38 -2.4018 -2.98058 -1.8230 +log_k_J9Z38 -5.1865 -5.92931 -4.4437 +log_k_JSE76 -3.0784 -4.25226 -1.9045 +f_cyan_ilr_1 0.7157 0.37625 1.0551 +f_cyan_ilr_2 0.7073 0.20136 1.2132 +f_JCZ38_qlogis 4.6797 0.43240 8.9269 +f_JSE76_qlogis 5.0080 -1.01380 11.0299 +log_k1 -1.9620 -2.62909 -1.2949 +log_k2 -4.4894 -4.94958 -4.0292 +g_qlogis -0.4658 -1.34443 0.4129 +a.1 2.7158 2.52576 2.9059 +SD.log_k_JCZ38 0.5818 0.15679 1.0067 +SD.log_k_J9Z38 0.7421 0.16751 1.3167 +SD.log_k_JSE76 1.2841 0.43247 2.1356 +SD.f_cyan_ilr_1 0.3748 0.13040 0.6192 +SD.f_cyan_ilr_2 0.4550 0.08396 0.8261 +SD.f_JCZ38_qlogis 2.0862 -0.73390 4.9062 +SD.f_JSE76_qlogis 1.9585 -3.14773 7.0647 +SD.log_k1 0.7389 0.25761 1.2201 +SD.log_k2 0.5132 0.18143 0.8450 +SD.g_qlogis 0.9870 0.35773 1.6164 + +Correlation: + cyan_0 l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76 +log_k_JCZ38 -0.0170 +log_k_J9Z38 -0.0457 0.0016 +log_k_JSE76 -0.0046 0.1183 0.0005 +f_cyan_ilr_1 0.0079 0.0072 -0.0909 0.0003 +f_cyan_ilr_2 -0.3114 0.0343 0.1542 0.0023 -0.0519 +f_JCZ38_qlogis 0.0777 -0.0601 -0.0152 0.0080 -0.0520 -0.2524 +f_JSE76_qlogis -0.0356 0.0817 0.0073 0.0051 0.0388 0.1959 -0.6236 +log_k1 0.0848 -0.0028 0.0010 -0.0010 -0.0014 -0.0245 0.0121 -0.0177 +log_k2 0.0274 -0.0001 0.0075 0.0000 -0.0023 -0.0060 0.0000 -0.0130 +g_qlogis 0.0159 0.0002 -0.0095 0.0002 0.0029 -0.0140 -0.0001 0.0149 + log_k1 log_k2 +log_k_JCZ38 +log_k_J9Z38 +log_k_JSE76 +f_cyan_ilr_1 +f_cyan_ilr_2 +f_JCZ38_qlogis +f_JSE76_qlogis +log_k1 +log_k2 0.0280 +g_qlogis -0.0278 -0.0310 + +Random effects: + est. lower upper +SD.log_k_JCZ38 0.5818 0.15679 1.0067 +SD.log_k_J9Z38 0.7421 0.16751 1.3167 +SD.log_k_JSE76 1.2841 0.43247 2.1356 +SD.f_cyan_ilr_1 0.3748 0.13040 0.6192 +SD.f_cyan_ilr_2 0.4550 0.08396 0.8261 +SD.f_JCZ38_qlogis 2.0862 -0.73390 4.9062 +SD.f_JSE76_qlogis 1.9585 -3.14773 7.0647 +SD.log_k1 0.7389 0.25761 1.2201 +SD.log_k2 0.5132 0.18143 0.8450 +SD.g_qlogis 0.9870 0.35773 1.6164 + +Variance model: + est. lower upper +a.1 2.716 2.526 2.906 + +Backtransformed parameters: + est. lower upper +cyan_0 1.027e+02 1.014e+02 103.93649 +k_JCZ38 9.056e-02 5.076e-02 0.16154 +k_J9Z38 5.591e-03 2.660e-03 0.01175 +k_JSE76 4.603e-02 1.423e-02 0.14890 +f_cyan_to_JCZ38 6.184e-01 NA NA +f_cyan_to_J9Z38 2.248e-01 NA NA +f_JCZ38_to_JSE76 9.908e-01 6.064e-01 0.99987 +f_JSE76_to_JCZ38 9.934e-01 2.662e-01 0.99998 +k1 1.406e-01 7.214e-02 0.27393 +k2 1.123e-02 7.086e-03 0.01779 +g 3.856e-01 2.068e-01 0.60177 + +Resulting formation fractions: + ff +cyan_JCZ38 0.618443 +cyan_J9Z38 0.224770 +cyan_sink 0.156787 +JCZ38_JSE76 0.990803 +JCZ38_sink 0.009197 +JSE76_JCZ38 0.993360 +JSE76_sink 0.006640 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +cyan 21.674 161.70 48.68 4.931 61.74 +JCZ38 7.654 25.43 NA NA NA +J9Z38 123.966 411.81 NA NA NA +JSE76 15.057 50.02 NA NA NA + +</code></pre> +<p></p> +<caption> +Hierarchical DFOP path 2 fit with two-component error +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 08:01:24 2023 +Date of summary: Thu Apr 20 20:01:30 2023 + +Equations: +d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * + time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) + * cyan +d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - + g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * + exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38 + + f_JSE76_to_JCZ38 * k_JSE76 * JSE76 +d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - + g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * + exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 726.501 s +Using 300, 100 iterations and 10 chains + +Variance model: Two-component variance function + +Starting values for degradation parameters: + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 + 101.7523 -1.5948 -5.0119 -2.2723 0.6719 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 + 5.1681 12.8238 12.4130 -2.0057 -4.5526 + g_qlogis + -0.5805 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 +cyan_0 5.627 0.000 0.000 0.000 0.0000 +log_k_JCZ38 0.000 2.327 0.000 0.000 0.0000 +log_k_J9Z38 0.000 0.000 1.664 0.000 0.0000 +log_k_JSE76 0.000 0.000 0.000 4.566 0.0000 +f_cyan_ilr_1 0.000 0.000 0.000 0.000 0.6519 +f_cyan_ilr_2 0.000 0.000 0.000 0.000 0.0000 +f_JCZ38_qlogis 0.000 0.000 0.000 0.000 0.0000 +f_JSE76_qlogis 0.000 0.000 0.000 0.000 0.0000 +log_k1 0.000 0.000 0.000 0.000 0.0000 +log_k2 0.000 0.000 0.000 0.000 0.0000 +g_qlogis 0.000 0.000 0.000 0.000 0.0000 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 +cyan_0 0.0 0.00 0.00 0.0000 0.0000 +log_k_JCZ38 0.0 0.00 0.00 0.0000 0.0000 +log_k_J9Z38 0.0 0.00 0.00 0.0000 0.0000 +log_k_JSE76 0.0 0.00 0.00 0.0000 0.0000 +f_cyan_ilr_1 0.0 0.00 0.00 0.0000 0.0000 +f_cyan_ilr_2 10.1 0.00 0.00 0.0000 0.0000 +f_JCZ38_qlogis 0.0 13.99 0.00 0.0000 0.0000 +f_JSE76_qlogis 0.0 0.00 14.15 0.0000 0.0000 +log_k1 0.0 0.00 0.00 0.8452 0.0000 +log_k2 0.0 0.00 0.00 0.0000 0.5968 +g_qlogis 0.0 0.00 0.00 0.0000 0.0000 + g_qlogis +cyan_0 0.000 +log_k_JCZ38 0.000 +log_k_J9Z38 0.000 +log_k_JSE76 0.000 +f_cyan_ilr_1 0.000 +f_cyan_ilr_2 0.000 +f_JCZ38_qlogis 0.000 +f_JSE76_qlogis 0.000 +log_k1 0.000 +log_k2 0.000 +g_qlogis 1.691 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2234 2226 -1095 + +Optimised parameters: + est. lower upper +cyan_0 101.10667 9.903e+01 103.18265 +log_k_JCZ38 -2.49437 -3.297e+00 -1.69221 +log_k_J9Z38 -5.08171 -5.875e+00 -4.28846 +log_k_JSE76 -3.20072 -4.180e+00 -2.22163 +f_cyan_ilr_1 0.71059 3.639e-01 1.05727 +f_cyan_ilr_2 1.15398 2.981e-01 2.00984 +f_JCZ38_qlogis 3.18027 1.056e+00 5.30452 +f_JSE76_qlogis 5.61578 -2.505e+01 36.28077 +log_k1 -2.38875 -2.517e+00 -2.26045 +log_k2 -4.67246 -4.928e+00 -4.41715 +g_qlogis -0.28231 -1.135e+00 0.57058 +a.1 2.08190 1.856e+00 2.30785 +b.1 0.06114 5.015e-02 0.07214 +SD.log_k_JCZ38 0.84622 2.637e-01 1.42873 +SD.log_k_J9Z38 0.84564 2.566e-01 1.43464 +SD.log_k_JSE76 1.04385 3.242e-01 1.76351 +SD.f_cyan_ilr_1 0.38568 1.362e-01 0.63514 +SD.f_cyan_ilr_2 0.68046 7.166e-02 1.28925 +SD.f_JCZ38_qlogis 1.25244 -4.213e-02 2.54700 +SD.f_JSE76_qlogis 0.28202 -1.515e+03 1515.87968 +SD.log_k2 0.25749 7.655e-02 0.43843 +SD.g_qlogis 0.94535 3.490e-01 1.54174 + +Correlation: + cyan_0 l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76 +log_k_JCZ38 -0.0086 +log_k_J9Z38 -0.0363 -0.0007 +log_k_JSE76 0.0015 0.1210 -0.0017 +f_cyan_ilr_1 -0.0048 0.0095 -0.0572 0.0030 +f_cyan_ilr_2 -0.4788 0.0328 0.1143 0.0027 -0.0316 +f_JCZ38_qlogis 0.0736 -0.0664 -0.0137 0.0145 -0.0444 -0.2175 +f_JSE76_qlogis -0.0137 0.0971 0.0035 0.0009 0.0293 0.1333 -0.6767 +log_k1 0.2345 -0.0350 -0.0099 -0.0113 -0.0126 -0.1652 0.1756 -0.2161 +log_k2 0.0440 -0.0133 0.0199 -0.0040 -0.0097 -0.0119 0.0604 -0.1306 +g_qlogis 0.0438 0.0078 -0.0123 0.0029 0.0046 -0.0363 -0.0318 0.0736 + log_k1 log_k2 +log_k_JCZ38 +log_k_J9Z38 +log_k_JSE76 +f_cyan_ilr_1 +f_cyan_ilr_2 +f_JCZ38_qlogis +f_JSE76_qlogis +log_k1 +log_k2 0.3198 +g_qlogis -0.1666 -0.0954 + +Random effects: + est. lower upper +SD.log_k_JCZ38 0.8462 2.637e-01 1.4287 +SD.log_k_J9Z38 0.8456 2.566e-01 1.4346 +SD.log_k_JSE76 1.0439 3.242e-01 1.7635 +SD.f_cyan_ilr_1 0.3857 1.362e-01 0.6351 +SD.f_cyan_ilr_2 0.6805 7.166e-02 1.2893 +SD.f_JCZ38_qlogis 1.2524 -4.213e-02 2.5470 +SD.f_JSE76_qlogis 0.2820 -1.515e+03 1515.8797 +SD.log_k2 0.2575 7.655e-02 0.4384 +SD.g_qlogis 0.9453 3.490e-01 1.5417 + +Variance model: + est. lower upper +a.1 2.08190 1.85595 2.30785 +b.1 0.06114 0.05015 0.07214 + +Backtransformed parameters: + est. lower upper +cyan_0 1.011e+02 9.903e+01 103.18265 +k_JCZ38 8.255e-02 3.701e-02 0.18411 +k_J9Z38 6.209e-03 2.809e-03 0.01373 +k_JSE76 4.073e-02 1.530e-02 0.10843 +f_cyan_to_JCZ38 6.608e-01 NA NA +f_cyan_to_J9Z38 2.419e-01 NA NA +f_JCZ38_to_JSE76 9.601e-01 7.419e-01 0.99506 +f_JSE76_to_JCZ38 9.964e-01 1.322e-11 1.00000 +k1 9.174e-02 8.070e-02 0.10430 +k2 9.349e-03 7.243e-03 0.01207 +g 4.299e-01 2.432e-01 0.63890 + +Resulting formation fractions: + ff +cyan_JCZ38 0.660808 +cyan_J9Z38 0.241904 +cyan_sink 0.097288 +JCZ38_JSE76 0.960085 +JCZ38_sink 0.039915 +JSE76_JCZ38 0.996373 +JSE76_sink 0.003627 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +cyan 24.359 186.18 56.05 7.555 74.14 +JCZ38 8.397 27.89 NA NA NA +J9Z38 111.631 370.83 NA NA NA +JSE76 17.017 56.53 NA NA NA + +</code></pre> +<p></p> +<caption> +Hierarchical SFORB path 2 fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 07:58:46 2023 +Date of summary: Thu Apr 20 20:01:30 2023 + +Equations: +d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound * + cyan_free + k_cyan_bound_free * cyan_bound +d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free * + cyan_bound +d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38 + * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76 +d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38 + * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 568.562 s +Using 300, 100 iterations and 10 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + cyan_free_0 log_k_cyan_free log_k_cyan_free_bound + 102.4394 -2.7673 -2.8942 +log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 + -3.6201 -2.3107 -5.3123 + log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 + -3.7120 0.6754 1.1448 + f_JCZ38_qlogis f_JSE76_qlogis + 13.2672 13.3538 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_free_0 log_k_cyan_free log_k_cyan_free_bound +cyan_free_0 4.589 0.0000 0.00 +log_k_cyan_free 0.000 0.4849 0.00 +log_k_cyan_free_bound 0.000 0.0000 1.62 +log_k_cyan_bound_free 0.000 0.0000 0.00 +log_k_JCZ38 0.000 0.0000 0.00 +log_k_J9Z38 0.000 0.0000 0.00 +log_k_JSE76 0.000 0.0000 0.00 +f_cyan_ilr_1 0.000 0.0000 0.00 +f_cyan_ilr_2 0.000 0.0000 0.00 +f_JCZ38_qlogis 0.000 0.0000 0.00 +f_JSE76_qlogis 0.000 0.0000 0.00 + log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 +cyan_free_0 0.000 0.0000 0.000 0.0 +log_k_cyan_free 0.000 0.0000 0.000 0.0 +log_k_cyan_free_bound 0.000 0.0000 0.000 0.0 +log_k_cyan_bound_free 1.197 0.0000 0.000 0.0 +log_k_JCZ38 0.000 0.7966 0.000 0.0 +log_k_J9Z38 0.000 0.0000 1.561 0.0 +log_k_JSE76 0.000 0.0000 0.000 0.8 +f_cyan_ilr_1 0.000 0.0000 0.000 0.0 +f_cyan_ilr_2 0.000 0.0000 0.000 0.0 +f_JCZ38_qlogis 0.000 0.0000 0.000 0.0 +f_JSE76_qlogis 0.000 0.0000 0.000 0.0 + f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis +cyan_free_0 0.0000 0.000 0.00 0.00 +log_k_cyan_free 0.0000 0.000 0.00 0.00 +log_k_cyan_free_bound 0.0000 0.000 0.00 0.00 +log_k_cyan_bound_free 0.0000 0.000 0.00 0.00 +log_k_JCZ38 0.0000 0.000 0.00 0.00 +log_k_J9Z38 0.0000 0.000 0.00 0.00 +log_k_JSE76 0.0000 0.000 0.00 0.00 +f_cyan_ilr_1 0.6349 0.000 0.00 0.00 +f_cyan_ilr_2 0.0000 1.797 0.00 0.00 +f_JCZ38_qlogis 0.0000 0.000 13.84 0.00 +f_JSE76_qlogis 0.0000 0.000 0.00 14.66 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2284 2275 -1120 + +Optimised parameters: + est. lower upper +cyan_free_0 102.7730 1.015e+02 1.041e+02 +log_k_cyan_free -2.8530 -3.167e+00 -2.539e+00 +log_k_cyan_free_bound -2.7326 -3.543e+00 -1.922e+00 +log_k_cyan_bound_free -3.5582 -4.126e+00 -2.990e+00 +log_k_JCZ38 -2.3810 -2.921e+00 -1.841e+00 +log_k_J9Z38 -5.2301 -5.963e+00 -4.497e+00 +log_k_JSE76 -3.0286 -4.286e+00 -1.771e+00 +f_cyan_ilr_1 0.7081 3.733e-01 1.043e+00 +f_cyan_ilr_2 0.5847 7.846e-03 1.162e+00 +f_JCZ38_qlogis 9.5676 -1.323e+03 1.342e+03 +f_JSE76_qlogis 3.7042 7.254e-02 7.336e+00 +a.1 2.7222 2.532e+00 2.913e+00 +SD.log_k_cyan_free 0.3338 1.086e-01 5.589e-01 +SD.log_k_cyan_free_bound 0.8888 3.023e-01 1.475e+00 +SD.log_k_cyan_bound_free 0.6220 2.063e-01 1.038e+00 +SD.log_k_JCZ38 0.5221 1.334e-01 9.108e-01 +SD.log_k_J9Z38 0.7104 1.371e-01 1.284e+00 +SD.log_k_JSE76 1.3837 4.753e-01 2.292e+00 +SD.f_cyan_ilr_1 0.3620 1.248e-01 5.992e-01 +SD.f_cyan_ilr_2 0.4259 8.145e-02 7.704e-01 +SD.f_JCZ38_qlogis 3.5332 -1.037e+05 1.037e+05 +SD.f_JSE76_qlogis 1.6990 -2.771e-01 3.675e+00 + +Correlation: + cyn_f_0 lg_k_c_ lg_k_cyn_f_ lg_k_cyn_b_ l__JCZ3 l__J9Z3 +log_k_cyan_free 0.2126 +log_k_cyan_free_bound 0.0894 0.0871 +log_k_cyan_bound_free 0.0033 0.0410 0.0583 +log_k_JCZ38 -0.0708 -0.0280 -0.0147 0.0019 +log_k_J9Z38 -0.0535 -0.0138 0.0012 0.0148 0.0085 +log_k_JSE76 -0.0066 -0.0030 -0.0021 -0.0005 0.1090 0.0010 +f_cyan_ilr_1 -0.0364 -0.0157 -0.0095 -0.0015 0.0458 -0.0960 +f_cyan_ilr_2 -0.3814 -0.1104 -0.0423 0.0146 0.1540 0.1526 +f_JCZ38_qlogis 0.2507 0.0969 0.0482 -0.0097 -0.2282 -0.0363 +f_JSE76_qlogis -0.1648 -0.0710 -0.0443 -0.0087 0.2002 0.0226 + l__JSE7 f_cy__1 f_cy__2 f_JCZ38 +log_k_cyan_free +log_k_cyan_free_bound +log_k_cyan_bound_free +log_k_JCZ38 +log_k_J9Z38 +log_k_JSE76 +f_cyan_ilr_1 0.0001 +f_cyan_ilr_2 0.0031 0.0586 +f_JCZ38_qlogis 0.0023 -0.1867 -0.6255 +f_JSE76_qlogis 0.0082 0.1356 0.4519 -0.7951 + +Random effects: + est. lower upper +SD.log_k_cyan_free 0.3338 1.086e-01 5.589e-01 +SD.log_k_cyan_free_bound 0.8888 3.023e-01 1.475e+00 +SD.log_k_cyan_bound_free 0.6220 2.063e-01 1.038e+00 +SD.log_k_JCZ38 0.5221 1.334e-01 9.108e-01 +SD.log_k_J9Z38 0.7104 1.371e-01 1.284e+00 +SD.log_k_JSE76 1.3837 4.753e-01 2.292e+00 +SD.f_cyan_ilr_1 0.3620 1.248e-01 5.992e-01 +SD.f_cyan_ilr_2 0.4259 8.145e-02 7.704e-01 +SD.f_JCZ38_qlogis 3.5332 -1.037e+05 1.037e+05 +SD.f_JSE76_qlogis 1.6990 -2.771e-01 3.675e+00 + +Variance model: + est. lower upper +a.1 2.722 2.532 2.913 + +Backtransformed parameters: + est. lower upper +cyan_free_0 1.028e+02 1.015e+02 104.06475 +k_cyan_free 5.767e-02 4.213e-02 0.07894 +k_cyan_free_bound 6.505e-02 2.892e-02 0.14633 +k_cyan_bound_free 2.849e-02 1.614e-02 0.05028 +k_JCZ38 9.246e-02 5.390e-02 0.15859 +k_J9Z38 5.353e-03 2.572e-03 0.01114 +k_JSE76 4.838e-02 1.376e-02 0.17009 +f_cyan_free_to_JCZ38 6.011e-01 5.028e-01 0.83792 +f_cyan_free_to_J9Z38 2.208e-01 5.028e-01 0.83792 +f_JCZ38_to_JSE76 9.999e-01 0.000e+00 1.00000 +f_JSE76_to_JCZ38 9.760e-01 5.181e-01 0.99935 + +Estimated Eigenvalues of SFORB model(s): +cyan_b1 cyan_b2 cyan_g +0.13942 0.01178 0.35948 + +Resulting formation fractions: + ff +cyan_free_JCZ38 6.011e-01 +cyan_free_J9Z38 2.208e-01 +cyan_free_sink 1.780e-01 +cyan_free 1.000e+00 +JCZ38_JSE76 9.999e-01 +JCZ38_sink 6.996e-05 +JSE76_JCZ38 9.760e-01 +JSE76_sink 2.403e-02 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 +cyan 23.390 157.60 47.44 4.971 58.82 +JCZ38 7.497 24.90 NA NA NA +J9Z38 129.482 430.13 NA NA NA +JSE76 14.326 47.59 NA NA NA + +</code></pre> +<p></p> +<caption> +Hierarchical SFORB path 2 fit with two-component error +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 08:01:30 2023 +Date of summary: Thu Apr 20 20:01:30 2023 + +Equations: +d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound * + cyan_free + k_cyan_bound_free * cyan_bound +d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free * + cyan_bound +d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38 + * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76 +d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38 + * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 732.212 s +Using 300, 100 iterations and 10 chains + +Variance model: Two-component variance function + +Starting values for degradation parameters: + cyan_free_0 log_k_cyan_free log_k_cyan_free_bound + 101.751 -2.837 -3.016 +log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 + -3.660 -2.299 -5.313 + log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 + -3.699 0.672 5.873 + f_JCZ38_qlogis f_JSE76_qlogis + 13.216 13.338 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_free_0 log_k_cyan_free log_k_cyan_free_bound +cyan_free_0 5.629 0.000 0.000 +log_k_cyan_free 0.000 0.446 0.000 +log_k_cyan_free_bound 0.000 0.000 1.449 +log_k_cyan_bound_free 0.000 0.000 0.000 +log_k_JCZ38 0.000 0.000 0.000 +log_k_J9Z38 0.000 0.000 0.000 +log_k_JSE76 0.000 0.000 0.000 +f_cyan_ilr_1 0.000 0.000 0.000 +f_cyan_ilr_2 0.000 0.000 0.000 +f_JCZ38_qlogis 0.000 0.000 0.000 +f_JSE76_qlogis 0.000 0.000 0.000 + log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 +cyan_free_0 0.000 0.0000 0.000 0.0000 +log_k_cyan_free 0.000 0.0000 0.000 0.0000 +log_k_cyan_free_bound 0.000 0.0000 0.000 0.0000 +log_k_cyan_bound_free 1.213 0.0000 0.000 0.0000 +log_k_JCZ38 0.000 0.7801 0.000 0.0000 +log_k_J9Z38 0.000 0.0000 1.575 0.0000 +log_k_JSE76 0.000 0.0000 0.000 0.8078 +f_cyan_ilr_1 0.000 0.0000 0.000 0.0000 +f_cyan_ilr_2 0.000 0.0000 0.000 0.0000 +f_JCZ38_qlogis 0.000 0.0000 0.000 0.0000 +f_JSE76_qlogis 0.000 0.0000 0.000 0.0000 + f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis +cyan_free_0 0.0000 0.00 0.00 0.00 +log_k_cyan_free 0.0000 0.00 0.00 0.00 +log_k_cyan_free_bound 0.0000 0.00 0.00 0.00 +log_k_cyan_bound_free 0.0000 0.00 0.00 0.00 +log_k_JCZ38 0.0000 0.00 0.00 0.00 +log_k_J9Z38 0.0000 0.00 0.00 0.00 +log_k_JSE76 0.0000 0.00 0.00 0.00 +f_cyan_ilr_1 0.6519 0.00 0.00 0.00 +f_cyan_ilr_2 0.0000 10.78 0.00 0.00 +f_JCZ38_qlogis 0.0000 0.00 13.96 0.00 +f_JSE76_qlogis 0.0000 0.00 0.00 14.69 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2240 2232 -1098 + +Optimised parameters: + est. lower upper +cyan_free_0 101.10205 98.99221 103.2119 +log_k_cyan_free -3.16929 -3.61395 -2.7246 +log_k_cyan_free_bound -3.38259 -3.63022 -3.1350 +log_k_cyan_bound_free -3.81075 -4.13888 -3.4826 +log_k_JCZ38 -2.42057 -3.00756 -1.8336 +log_k_J9Z38 -5.07501 -5.85138 -4.2986 +log_k_JSE76 -3.12442 -4.21277 -2.0361 +f_cyan_ilr_1 0.70577 0.35788 1.0537 +f_cyan_ilr_2 1.14824 0.15810 2.1384 +f_JCZ38_qlogis 3.52245 0.43257 6.6123 +f_JSE76_qlogis 5.65140 -21.22295 32.5257 +a.1 2.07062 1.84329 2.2980 +b.1 0.06227 0.05124 0.0733 +SD.log_k_cyan_free 0.49468 0.18566 0.8037 +SD.log_k_cyan_bound_free 0.28972 0.07188 0.5076 +SD.log_k_JCZ38 0.58852 0.16800 1.0090 +SD.log_k_J9Z38 0.82500 0.24730 1.4027 +SD.log_k_JSE76 1.19201 0.40313 1.9809 +SD.f_cyan_ilr_1 0.38534 0.13640 0.6343 +SD.f_cyan_ilr_2 0.72463 0.10076 1.3485 +SD.f_JCZ38_qlogis 1.38223 -0.20997 2.9744 +SD.f_JSE76_qlogis 2.07989 -72.53027 76.6901 + +Correlation: + cyn_f_0 lg_k_c_ lg_k_cyn_f_ lg_k_cyn_b_ l__JCZ3 l__J9Z3 +log_k_cyan_free 0.1117 +log_k_cyan_free_bound 0.1763 0.1828 +log_k_cyan_bound_free 0.0120 0.0593 0.5030 +log_k_JCZ38 -0.0459 -0.0230 -0.0931 -0.0337 +log_k_J9Z38 -0.0381 -0.0123 -0.0139 0.0237 0.0063 +log_k_JSE76 -0.0044 -0.0038 -0.0175 -0.0072 0.1120 0.0003 +f_cyan_ilr_1 -0.0199 -0.0087 -0.0407 -0.0233 0.0268 -0.0552 +f_cyan_ilr_2 -0.4806 -0.1015 -0.2291 -0.0269 0.1156 0.1113 +f_JCZ38_qlogis 0.1805 0.0825 0.3085 0.0963 -0.1674 -0.0314 +f_JSE76_qlogis -0.1586 -0.0810 -0.3560 -0.1563 0.2025 0.0278 + l__JSE7 f_cy__1 f_cy__2 f_JCZ38 +log_k_cyan_free +log_k_cyan_free_bound +log_k_cyan_bound_free +log_k_JCZ38 +log_k_J9Z38 +log_k_JSE76 +f_cyan_ilr_1 0.0024 +f_cyan_ilr_2 0.0087 0.0172 +f_JCZ38_qlogis -0.0016 -0.1047 -0.4656 +f_JSE76_qlogis 0.0119 0.1034 0.4584 -0.8137 + +Random effects: + est. lower upper +SD.log_k_cyan_free 0.4947 0.18566 0.8037 +SD.log_k_cyan_bound_free 0.2897 0.07188 0.5076 +SD.log_k_JCZ38 0.5885 0.16800 1.0090 +SD.log_k_J9Z38 0.8250 0.24730 1.4027 +SD.log_k_JSE76 1.1920 0.40313 1.9809 +SD.f_cyan_ilr_1 0.3853 0.13640 0.6343 +SD.f_cyan_ilr_2 0.7246 0.10076 1.3485 +SD.f_JCZ38_qlogis 1.3822 -0.20997 2.9744 +SD.f_JSE76_qlogis 2.0799 -72.53027 76.6901 + +Variance model: + est. lower upper +a.1 2.07062 1.84329 2.2980 +b.1 0.06227 0.05124 0.0733 + +Backtransformed parameters: + est. lower upper +cyan_free_0 1.011e+02 9.899e+01 103.21190 +k_cyan_free 4.203e-02 2.695e-02 0.06557 +k_cyan_free_bound 3.396e-02 2.651e-02 0.04350 +k_cyan_bound_free 2.213e-02 1.594e-02 0.03073 +k_JCZ38 8.887e-02 4.941e-02 0.15984 +k_J9Z38 6.251e-03 2.876e-03 0.01359 +k_JSE76 4.396e-02 1.481e-02 0.13054 +f_cyan_free_to_JCZ38 6.590e-01 5.557e-01 0.95365 +f_cyan_free_to_J9Z38 2.429e-01 5.557e-01 0.95365 +f_JCZ38_to_JSE76 9.713e-01 6.065e-01 0.99866 +f_JSE76_to_JCZ38 9.965e-01 6.067e-10 1.00000 + +Estimated Eigenvalues of SFORB model(s): +cyan_b1 cyan_b2 cyan_g +0.08749 0.01063 0.40855 + +Resulting formation fractions: + ff +cyan_free_JCZ38 0.65905 +cyan_free_J9Z38 0.24291 +cyan_free_sink 0.09805 +cyan_free 1.00000 +JCZ38_JSE76 0.97132 +JCZ38_sink 0.02868 +JSE76_JCZ38 0.99650 +JSE76_sink 0.00350 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 +cyan 24.91 167.16 50.32 7.922 65.19 +JCZ38 7.80 25.91 NA NA NA +J9Z38 110.89 368.36 NA NA NA +JSE76 15.77 52.38 NA NA NA + +</code></pre> +<p></p> +</div> +<div class="section level4"> +<h4 id="pathway-2-refined-fits">Pathway 2, refined fits<a class="anchor" aria-label="anchor" href="#pathway-2-refined-fits"></a> +</h4> +<caption> +Hierarchical FOMC path 2 fit with reduced random effects, two-component +error +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 08:15:01 2023 +Date of summary: Thu Apr 20 20:01:31 2023 + +Equations: +d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan +d_JCZ38/dt = + f_cyan_to_JCZ38 * (alpha/beta) * 1/((time/beta) + 1) * + cyan - k_JCZ38 * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76 +d_J9Z38/dt = + f_cyan_to_J9Z38 * (alpha/beta) * 1/((time/beta) + 1) * + cyan - k_J9Z38 * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 808.728 s +Using 300, 100 iterations and 10 chains + +Variance model: Two-component variance function + +Starting values for degradation parameters: + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 + 101.9028 -1.9055 -5.0249 -2.5646 0.6807 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta + 4.8883 16.0676 9.3923 -0.1346 3.0364 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 +cyan_0 6.321 0.000 0.000 0.000 0.0000 +log_k_JCZ38 0.000 1.392 0.000 0.000 0.0000 +log_k_J9Z38 0.000 0.000 1.561 0.000 0.0000 +log_k_JSE76 0.000 0.000 0.000 3.614 0.0000 +f_cyan_ilr_1 0.000 0.000 0.000 0.000 0.6339 +f_cyan_ilr_2 0.000 0.000 0.000 0.000 0.0000 +f_JCZ38_qlogis 0.000 0.000 0.000 0.000 0.0000 +f_JSE76_qlogis 0.000 0.000 0.000 0.000 0.0000 +log_alpha 0.000 0.000 0.000 0.000 0.0000 +log_beta 0.000 0.000 0.000 0.000 0.0000 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta +cyan_0 0.00 0.00 0.00 0.0000 0.0000 +log_k_JCZ38 0.00 0.00 0.00 0.0000 0.0000 +log_k_J9Z38 0.00 0.00 0.00 0.0000 0.0000 +log_k_JSE76 0.00 0.00 0.00 0.0000 0.0000 +f_cyan_ilr_1 0.00 0.00 0.00 0.0000 0.0000 +f_cyan_ilr_2 10.41 0.00 0.00 0.0000 0.0000 +f_JCZ38_qlogis 0.00 12.24 0.00 0.0000 0.0000 +f_JSE76_qlogis 0.00 0.00 15.13 0.0000 0.0000 +log_alpha 0.00 0.00 0.00 0.3701 0.0000 +log_beta 0.00 0.00 0.00 0.0000 0.5662 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2251 2244 -1106 + +Optimised parameters: + est. lower upper +cyan_0 101.05768 NA NA +log_k_JCZ38 -2.73252 NA NA +log_k_J9Z38 -5.07399 NA NA +log_k_JSE76 -3.52863 NA NA +f_cyan_ilr_1 0.72176 NA NA +f_cyan_ilr_2 1.34610 NA NA +f_JCZ38_qlogis 2.08337 NA NA +f_JSE76_qlogis 1590.31880 NA NA +log_alpha -0.09336 NA NA +log_beta 3.10191 NA NA +a.1 2.08557 1.85439 2.31675 +b.1 0.06998 0.05800 0.08197 +SD.log_k_JCZ38 1.20053 0.43329 1.96777 +SD.log_k_J9Z38 0.85854 0.26708 1.45000 +SD.log_k_JSE76 0.62528 0.16061 1.08995 +SD.f_cyan_ilr_1 0.35190 0.12340 0.58039 +SD.f_cyan_ilr_2 0.85385 0.15391 1.55378 +SD.log_alpha 0.28971 0.08718 0.49225 +SD.log_beta 0.31614 0.05938 0.57290 + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_JCZ38 1.2005 0.43329 1.9678 +SD.log_k_J9Z38 0.8585 0.26708 1.4500 +SD.log_k_JSE76 0.6253 0.16061 1.0900 +SD.f_cyan_ilr_1 0.3519 0.12340 0.5804 +SD.f_cyan_ilr_2 0.8538 0.15391 1.5538 +SD.log_alpha 0.2897 0.08718 0.4923 +SD.log_beta 0.3161 0.05938 0.5729 + +Variance model: + est. lower upper +a.1 2.08557 1.854 2.31675 +b.1 0.06998 0.058 0.08197 + +Backtransformed parameters: + est. lower upper +cyan_0 1.011e+02 NA NA +k_JCZ38 6.506e-02 NA NA +k_J9Z38 6.257e-03 NA NA +k_JSE76 2.935e-02 NA NA +f_cyan_to_JCZ38 6.776e-01 NA NA +f_cyan_to_J9Z38 2.442e-01 NA NA +f_JCZ38_to_JSE76 8.893e-01 NA NA +f_JSE76_to_JCZ38 1.000e+00 NA NA +alpha 9.109e-01 NA NA +beta 2.224e+01 NA NA + +Resulting formation fractions: + ff +cyan_JCZ38 0.67761 +cyan_J9Z38 0.24417 +cyan_sink 0.07822 +JCZ38_JSE76 0.88928 +JCZ38_sink 0.11072 +JSE76_JCZ38 1.00000 +JSE76_sink 0.00000 + +Estimated disappearance times: + DT50 DT90 DT50back +cyan 25.36 256.37 77.18 +JCZ38 10.65 35.39 NA +J9Z38 110.77 367.98 NA +JSE76 23.62 78.47 NA + +</code></pre> +<p></p> +<caption> +Hierarchical DFOP path 2 fit with reduced random effects, constant +variance +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 08:16:32 2023 +Date of summary: Thu Apr 20 20:01:31 2023 + +Equations: +d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * + time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) + * cyan +d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - + g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * + exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38 + + f_JSE76_to_JCZ38 * k_JSE76 * JSE76 +d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - + g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * + exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 900.061 s +Using 300, 100 iterations and 10 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 + 102.4358 -2.3107 -5.3123 -3.7120 0.6753 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 + 1.1462 12.4095 12.3630 -1.9317 -4.4557 + g_qlogis + -0.5648 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 +cyan_0 4.594 0.0000 0.000 0.0 0.0000 +log_k_JCZ38 0.000 0.7966 0.000 0.0 0.0000 +log_k_J9Z38 0.000 0.0000 1.561 0.0 0.0000 +log_k_JSE76 0.000 0.0000 0.000 0.8 0.0000 +f_cyan_ilr_1 0.000 0.0000 0.000 0.0 0.6349 +f_cyan_ilr_2 0.000 0.0000 0.000 0.0 0.0000 +f_JCZ38_qlogis 0.000 0.0000 0.000 0.0 0.0000 +f_JSE76_qlogis 0.000 0.0000 0.000 0.0 0.0000 +log_k1 0.000 0.0000 0.000 0.0 0.0000 +log_k2 0.000 0.0000 0.000 0.0 0.0000 +g_qlogis 0.000 0.0000 0.000 0.0 0.0000 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 +cyan_0 0.000 0.00 0.0 0.000 0.0000 +log_k_JCZ38 0.000 0.00 0.0 0.000 0.0000 +log_k_J9Z38 0.000 0.00 0.0 0.000 0.0000 +log_k_JSE76 0.000 0.00 0.0 0.000 0.0000 +f_cyan_ilr_1 0.000 0.00 0.0 0.000 0.0000 +f_cyan_ilr_2 1.797 0.00 0.0 0.000 0.0000 +f_JCZ38_qlogis 0.000 13.85 0.0 0.000 0.0000 +f_JSE76_qlogis 0.000 0.00 14.1 0.000 0.0000 +log_k1 0.000 0.00 0.0 1.106 0.0000 +log_k2 0.000 0.00 0.0 0.000 0.6141 +g_qlogis 0.000 0.00 0.0 0.000 0.0000 + g_qlogis +cyan_0 0.000 +log_k_JCZ38 0.000 +log_k_J9Z38 0.000 +log_k_JSE76 0.000 +f_cyan_ilr_1 0.000 +f_cyan_ilr_2 0.000 +f_JCZ38_qlogis 0.000 +f_JSE76_qlogis 0.000 +log_k1 0.000 +log_k2 0.000 +g_qlogis 1.595 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2282 2274 -1121 + +Optimised parameters: + est. lower upper +cyan_0 102.5254 NA NA +log_k_JCZ38 -2.9358 NA NA +log_k_J9Z38 -5.1424 NA NA +log_k_JSE76 -3.6458 NA NA +f_cyan_ilr_1 0.6957 NA NA +f_cyan_ilr_2 0.6635 NA NA +f_JCZ38_qlogis 4984.8163 NA NA +f_JSE76_qlogis 1.9415 NA NA +log_k1 -1.9456 NA NA +log_k2 -4.4705 NA NA +g_qlogis -0.5117 NA NA +a.1 2.7455 2.55392 2.9370 +SD.log_k_JCZ38 1.3163 0.47635 2.1563 +SD.log_k_J9Z38 0.7162 0.16133 1.2711 +SD.log_k_JSE76 0.6457 0.15249 1.1390 +SD.f_cyan_ilr_1 0.3424 0.11714 0.5677 +SD.f_cyan_ilr_2 0.4524 0.09709 0.8077 +SD.log_k1 0.7353 0.25445 1.2161 +SD.log_k2 0.5137 0.18206 0.8453 +SD.g_qlogis 0.9857 0.35651 1.6148 + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_JCZ38 1.3163 0.47635 2.1563 +SD.log_k_J9Z38 0.7162 0.16133 1.2711 +SD.log_k_JSE76 0.6457 0.15249 1.1390 +SD.f_cyan_ilr_1 0.3424 0.11714 0.5677 +SD.f_cyan_ilr_2 0.4524 0.09709 0.8077 +SD.log_k1 0.7353 0.25445 1.2161 +SD.log_k2 0.5137 0.18206 0.8453 +SD.g_qlogis 0.9857 0.35651 1.6148 + +Variance model: + est. lower upper +a.1 2.745 2.554 2.937 + +Backtransformed parameters: + est. lower upper +cyan_0 1.025e+02 NA NA +k_JCZ38 5.309e-02 NA NA +k_J9Z38 5.844e-03 NA NA +k_JSE76 2.610e-02 NA NA +f_cyan_to_JCZ38 6.079e-01 NA NA +f_cyan_to_J9Z38 2.272e-01 NA NA +f_JCZ38_to_JSE76 1.000e+00 NA NA +f_JSE76_to_JCZ38 8.745e-01 NA NA +k1 1.429e-01 NA NA +k2 1.144e-02 NA NA +g 3.748e-01 NA NA + +Resulting formation fractions: + ff +cyan_JCZ38 0.6079 +cyan_J9Z38 0.2272 +cyan_sink 0.1649 +JCZ38_JSE76 1.0000 +JCZ38_sink 0.0000 +JSE76_JCZ38 0.8745 +JSE76_sink 0.1255 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +cyan 22.29 160.20 48.22 4.85 60.58 +JCZ38 13.06 43.37 NA NA NA +J9Z38 118.61 394.02 NA NA NA +JSE76 26.56 88.22 NA NA NA + +</code></pre> +<p></p> +<caption> +Hierarchical DFOP path 2 fit with reduced random effects, two-component +error +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 08:16:47 2023 +Date of summary: Thu Apr 20 20:01:31 2023 + +Equations: +d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * + time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) + * cyan +d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - + g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * + exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38 + + f_JSE76_to_JCZ38 * k_JSE76 * JSE76 +d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - + g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * + exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 914.763 s +Using 300, 100 iterations and 10 chains + +Variance model: Two-component variance function + +Starting values for degradation parameters: + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 + 101.7523 -1.5948 -5.0119 -2.2723 0.6719 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 + 5.1681 12.8238 12.4130 -2.0057 -4.5526 + g_qlogis + -0.5805 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 +cyan_0 5.627 0.000 0.000 0.000 0.0000 +log_k_JCZ38 0.000 2.327 0.000 0.000 0.0000 +log_k_J9Z38 0.000 0.000 1.664 0.000 0.0000 +log_k_JSE76 0.000 0.000 0.000 4.566 0.0000 +f_cyan_ilr_1 0.000 0.000 0.000 0.000 0.6519 +f_cyan_ilr_2 0.000 0.000 0.000 0.000 0.0000 +f_JCZ38_qlogis 0.000 0.000 0.000 0.000 0.0000 +f_JSE76_qlogis 0.000 0.000 0.000 0.000 0.0000 +log_k1 0.000 0.000 0.000 0.000 0.0000 +log_k2 0.000 0.000 0.000 0.000 0.0000 +g_qlogis 0.000 0.000 0.000 0.000 0.0000 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 +cyan_0 0.0 0.00 0.00 0.0000 0.0000 +log_k_JCZ38 0.0 0.00 0.00 0.0000 0.0000 +log_k_J9Z38 0.0 0.00 0.00 0.0000 0.0000 +log_k_JSE76 0.0 0.00 0.00 0.0000 0.0000 +f_cyan_ilr_1 0.0 0.00 0.00 0.0000 0.0000 +f_cyan_ilr_2 10.1 0.00 0.00 0.0000 0.0000 +f_JCZ38_qlogis 0.0 13.99 0.00 0.0000 0.0000 +f_JSE76_qlogis 0.0 0.00 14.15 0.0000 0.0000 +log_k1 0.0 0.00 0.00 0.8452 0.0000 +log_k2 0.0 0.00 0.00 0.0000 0.5968 +g_qlogis 0.0 0.00 0.00 0.0000 0.0000 + g_qlogis +cyan_0 0.000 +log_k_JCZ38 0.000 +log_k_J9Z38 0.000 +log_k_JSE76 0.000 +f_cyan_ilr_1 0.000 +f_cyan_ilr_2 0.000 +f_JCZ38_qlogis 0.000 +f_JSE76_qlogis 0.000 +log_k1 0.000 +log_k2 0.000 +g_qlogis 1.691 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2232 2224 -1096 + +Optimised parameters: + est. lower upper +cyan_0 101.20051 NA NA +log_k_JCZ38 -2.93542 NA NA +log_k_J9Z38 -5.03151 NA NA +log_k_JSE76 -3.67679 NA NA +f_cyan_ilr_1 0.67290 NA NA +f_cyan_ilr_2 0.99787 NA NA +f_JCZ38_qlogis 348.32484 NA NA +f_JSE76_qlogis 1.87846 NA NA +log_k1 -2.32738 NA NA +log_k2 -4.61295 NA NA +g_qlogis -0.38342 NA NA +a.1 2.06184 1.83746 2.28622 +b.1 0.06329 0.05211 0.07447 +SD.log_k_JCZ38 1.29042 0.47468 2.10617 +SD.log_k_J9Z38 0.84235 0.25903 1.42566 +SD.log_k_JSE76 0.56930 0.13934 0.99926 +SD.f_cyan_ilr_1 0.35183 0.12298 0.58068 +SD.f_cyan_ilr_2 0.77269 0.17908 1.36631 +SD.log_k2 0.28549 0.09210 0.47888 +SD.g_qlogis 0.93830 0.34568 1.53093 + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_JCZ38 1.2904 0.4747 2.1062 +SD.log_k_J9Z38 0.8423 0.2590 1.4257 +SD.log_k_JSE76 0.5693 0.1393 0.9993 +SD.f_cyan_ilr_1 0.3518 0.1230 0.5807 +SD.f_cyan_ilr_2 0.7727 0.1791 1.3663 +SD.log_k2 0.2855 0.0921 0.4789 +SD.g_qlogis 0.9383 0.3457 1.5309 + +Variance model: + est. lower upper +a.1 2.06184 1.83746 2.28622 +b.1 0.06329 0.05211 0.07447 + +Backtransformed parameters: + est. lower upper +cyan_0 1.012e+02 NA NA +k_JCZ38 5.311e-02 NA NA +k_J9Z38 6.529e-03 NA NA +k_JSE76 2.530e-02 NA NA +f_cyan_to_JCZ38 6.373e-01 NA NA +f_cyan_to_J9Z38 2.461e-01 NA NA +f_JCZ38_to_JSE76 1.000e+00 NA NA +f_JSE76_to_JCZ38 8.674e-01 NA NA +k1 9.755e-02 NA NA +k2 9.922e-03 NA NA +g 4.053e-01 NA NA + +Resulting formation fractions: + ff +cyan_JCZ38 0.6373 +cyan_J9Z38 0.2461 +cyan_sink 0.1167 +JCZ38_JSE76 1.0000 +JCZ38_sink 0.0000 +JSE76_JCZ38 0.8674 +JSE76_sink 0.1326 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +cyan 24.93 179.68 54.09 7.105 69.86 +JCZ38 13.05 43.36 NA NA NA +J9Z38 106.16 352.67 NA NA NA +JSE76 27.39 91.00 NA NA NA + +</code></pre> +<p></p> +<caption> +Hierarchical SFORB path 2 fit with reduced random effects, constant +variance +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 08:16:33 2023 +Date of summary: Thu Apr 20 20:01:31 2023 + +Equations: +d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound * + cyan_free + k_cyan_bound_free * cyan_bound +d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free * + cyan_bound +d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38 + * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76 +d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38 + * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 901.179 s +Using 300, 100 iterations and 10 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + cyan_free_0 log_k_cyan_free log_k_cyan_free_bound + 102.4394 -2.7673 -2.8942 +log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 + -3.6201 -2.3107 -5.3123 + log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 + -3.7120 0.6754 1.1448 + f_JCZ38_qlogis f_JSE76_qlogis + 13.2672 13.3538 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_free_0 log_k_cyan_free log_k_cyan_free_bound +cyan_free_0 4.589 0.0000 0.00 +log_k_cyan_free 0.000 0.4849 0.00 +log_k_cyan_free_bound 0.000 0.0000 1.62 +log_k_cyan_bound_free 0.000 0.0000 0.00 +log_k_JCZ38 0.000 0.0000 0.00 +log_k_J9Z38 0.000 0.0000 0.00 +log_k_JSE76 0.000 0.0000 0.00 +f_cyan_ilr_1 0.000 0.0000 0.00 +f_cyan_ilr_2 0.000 0.0000 0.00 +f_JCZ38_qlogis 0.000 0.0000 0.00 +f_JSE76_qlogis 0.000 0.0000 0.00 + log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 +cyan_free_0 0.000 0.0000 0.000 0.0 +log_k_cyan_free 0.000 0.0000 0.000 0.0 +log_k_cyan_free_bound 0.000 0.0000 0.000 0.0 +log_k_cyan_bound_free 1.197 0.0000 0.000 0.0 +log_k_JCZ38 0.000 0.7966 0.000 0.0 +log_k_J9Z38 0.000 0.0000 1.561 0.0 +log_k_JSE76 0.000 0.0000 0.000 0.8 +f_cyan_ilr_1 0.000 0.0000 0.000 0.0 +f_cyan_ilr_2 0.000 0.0000 0.000 0.0 +f_JCZ38_qlogis 0.000 0.0000 0.000 0.0 +f_JSE76_qlogis 0.000 0.0000 0.000 0.0 + f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis +cyan_free_0 0.0000 0.000 0.00 0.00 +log_k_cyan_free 0.0000 0.000 0.00 0.00 +log_k_cyan_free_bound 0.0000 0.000 0.00 0.00 +log_k_cyan_bound_free 0.0000 0.000 0.00 0.00 +log_k_JCZ38 0.0000 0.000 0.00 0.00 +log_k_J9Z38 0.0000 0.000 0.00 0.00 +log_k_JSE76 0.0000 0.000 0.00 0.00 +f_cyan_ilr_1 0.6349 0.000 0.00 0.00 +f_cyan_ilr_2 0.0000 1.797 0.00 0.00 +f_JCZ38_qlogis 0.0000 0.000 13.84 0.00 +f_JSE76_qlogis 0.0000 0.000 0.00 14.66 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2279 2272 -1120 + +Optimised parameters: + est. lower upper +cyan_free_0 102.5621 NA NA +log_k_cyan_free -2.8531 NA NA +log_k_cyan_free_bound -2.6916 NA NA +log_k_cyan_bound_free -3.5032 NA NA +log_k_JCZ38 -2.9436 NA NA +log_k_J9Z38 -5.1140 NA NA +log_k_JSE76 -3.6472 NA NA +f_cyan_ilr_1 0.6887 NA NA +f_cyan_ilr_2 0.6874 NA NA +f_JCZ38_qlogis 4063.6389 NA NA +f_JSE76_qlogis 1.9556 NA NA +a.1 2.7460 2.55451 2.9376 +SD.log_k_cyan_free 0.3131 0.09841 0.5277 +SD.log_k_cyan_free_bound 0.8850 0.29909 1.4710 +SD.log_k_cyan_bound_free 0.6167 0.20391 1.0295 +SD.log_k_JCZ38 1.3555 0.49101 2.2200 +SD.log_k_J9Z38 0.7200 0.16166 1.2783 +SD.log_k_JSE76 0.6252 0.14619 1.1042 +SD.f_cyan_ilr_1 0.3386 0.11447 0.5627 +SD.f_cyan_ilr_2 0.4699 0.09810 0.8417 + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_cyan_free 0.3131 0.09841 0.5277 +SD.log_k_cyan_free_bound 0.8850 0.29909 1.4710 +SD.log_k_cyan_bound_free 0.6167 0.20391 1.0295 +SD.log_k_JCZ38 1.3555 0.49101 2.2200 +SD.log_k_J9Z38 0.7200 0.16166 1.2783 +SD.log_k_JSE76 0.6252 0.14619 1.1042 +SD.f_cyan_ilr_1 0.3386 0.11447 0.5627 +SD.f_cyan_ilr_2 0.4699 0.09810 0.8417 + +Variance model: + est. lower upper +a.1 2.746 2.555 2.938 + +Backtransformed parameters: + est. lower upper +cyan_free_0 1.026e+02 NA NA +k_cyan_free 5.767e-02 NA NA +k_cyan_free_bound 6.777e-02 NA NA +k_cyan_bound_free 3.010e-02 NA NA +k_JCZ38 5.267e-02 NA NA +k_J9Z38 6.012e-03 NA NA +k_JSE76 2.606e-02 NA NA +f_cyan_free_to_JCZ38 6.089e-01 NA NA +f_cyan_free_to_J9Z38 2.299e-01 NA NA +f_JCZ38_to_JSE76 1.000e+00 NA NA +f_JSE76_to_JCZ38 8.761e-01 NA NA + +Estimated Eigenvalues of SFORB model(s): +cyan_b1 cyan_b2 cyan_g + 0.1434 0.0121 0.3469 + +Resulting formation fractions: + ff +cyan_free_JCZ38 0.6089 +cyan_free_J9Z38 0.2299 +cyan_free_sink 0.1612 +cyan_free 1.0000 +JCZ38_JSE76 1.0000 +JCZ38_sink 0.0000 +JSE76_JCZ38 0.8761 +JSE76_sink 0.1239 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 +cyan 23.94 155.06 46.68 4.832 57.28 +JCZ38 13.16 43.71 NA NA NA +J9Z38 115.30 383.02 NA NA NA +JSE76 26.59 88.35 NA NA NA + +</code></pre> +<p></p> +<caption> +Hierarchical SFORB path 2 fit with reduced random effects, two-component +error +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 08:16:19 2023 +Date of summary: Thu Apr 20 20:01:31 2023 + +Equations: +d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound * + cyan_free + k_cyan_bound_free * cyan_bound +d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free * + cyan_bound +d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38 + * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76 +d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38 + * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 887.343 s +Using 300, 100 iterations and 10 chains + +Variance model: Two-component variance function + +Starting values for degradation parameters: + cyan_free_0 log_k_cyan_free log_k_cyan_free_bound + 101.751 -2.837 -3.016 +log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 + -3.660 -2.299 -5.313 + log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 + -3.699 0.672 5.873 + f_JCZ38_qlogis f_JSE76_qlogis + 13.216 13.338 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_free_0 log_k_cyan_free log_k_cyan_free_bound +cyan_free_0 5.629 0.000 0.000 +log_k_cyan_free 0.000 0.446 0.000 +log_k_cyan_free_bound 0.000 0.000 1.449 +log_k_cyan_bound_free 0.000 0.000 0.000 +log_k_JCZ38 0.000 0.000 0.000 +log_k_J9Z38 0.000 0.000 0.000 +log_k_JSE76 0.000 0.000 0.000 +f_cyan_ilr_1 0.000 0.000 0.000 +f_cyan_ilr_2 0.000 0.000 0.000 +f_JCZ38_qlogis 0.000 0.000 0.000 +f_JSE76_qlogis 0.000 0.000 0.000 + log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 +cyan_free_0 0.000 0.0000 0.000 0.0000 +log_k_cyan_free 0.000 0.0000 0.000 0.0000 +log_k_cyan_free_bound 0.000 0.0000 0.000 0.0000 +log_k_cyan_bound_free 1.213 0.0000 0.000 0.0000 +log_k_JCZ38 0.000 0.7801 0.000 0.0000 +log_k_J9Z38 0.000 0.0000 1.575 0.0000 +log_k_JSE76 0.000 0.0000 0.000 0.8078 +f_cyan_ilr_1 0.000 0.0000 0.000 0.0000 +f_cyan_ilr_2 0.000 0.0000 0.000 0.0000 +f_JCZ38_qlogis 0.000 0.0000 0.000 0.0000 +f_JSE76_qlogis 0.000 0.0000 0.000 0.0000 + f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis +cyan_free_0 0.0000 0.00 0.00 0.00 +log_k_cyan_free 0.0000 0.00 0.00 0.00 +log_k_cyan_free_bound 0.0000 0.00 0.00 0.00 +log_k_cyan_bound_free 0.0000 0.00 0.00 0.00 +log_k_JCZ38 0.0000 0.00 0.00 0.00 +log_k_J9Z38 0.0000 0.00 0.00 0.00 +log_k_JSE76 0.0000 0.00 0.00 0.00 +f_cyan_ilr_1 0.6519 0.00 0.00 0.00 +f_cyan_ilr_2 0.0000 10.78 0.00 0.00 +f_JCZ38_qlogis 0.0000 0.00 13.96 0.00 +f_JSE76_qlogis 0.0000 0.00 0.00 14.69 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2236 2228 -1098 + +Optimised parameters: + est. lower upper +cyan_free_0 100.72760 NA NA +log_k_cyan_free -3.18281 NA NA +log_k_cyan_free_bound -3.37924 NA NA +log_k_cyan_bound_free -3.77107 NA NA +log_k_JCZ38 -2.92811 NA NA +log_k_J9Z38 -5.02759 NA NA +log_k_JSE76 -3.65835 NA NA +f_cyan_ilr_1 0.67390 NA NA +f_cyan_ilr_2 1.15106 NA NA +f_JCZ38_qlogis 827.82299 NA NA +f_JSE76_qlogis 1.83064 NA NA +a.1 2.06921 1.84443 2.29399 +b.1 0.06391 0.05267 0.07515 +SD.log_k_cyan_free 0.50518 0.18962 0.82075 +SD.log_k_cyan_bound_free 0.30991 0.08170 0.53813 +SD.log_k_JCZ38 1.26661 0.46578 2.06744 +SD.log_k_J9Z38 0.88272 0.27813 1.48730 +SD.log_k_JSE76 0.53050 0.12561 0.93538 +SD.f_cyan_ilr_1 0.35547 0.12461 0.58633 +SD.f_cyan_ilr_2 0.91446 0.20131 1.62761 + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_cyan_free 0.5052 0.1896 0.8207 +SD.log_k_cyan_bound_free 0.3099 0.0817 0.5381 +SD.log_k_JCZ38 1.2666 0.4658 2.0674 +SD.log_k_J9Z38 0.8827 0.2781 1.4873 +SD.log_k_JSE76 0.5305 0.1256 0.9354 +SD.f_cyan_ilr_1 0.3555 0.1246 0.5863 +SD.f_cyan_ilr_2 0.9145 0.2013 1.6276 + +Variance model: + est. lower upper +a.1 2.06921 1.84443 2.29399 +b.1 0.06391 0.05267 0.07515 + +Backtransformed parameters: + est. lower upper +cyan_free_0 1.007e+02 NA NA +k_cyan_free 4.147e-02 NA NA +k_cyan_free_bound 3.407e-02 NA NA +k_cyan_bound_free 2.303e-02 NA NA +k_JCZ38 5.350e-02 NA NA +k_J9Z38 6.555e-03 NA NA +k_JSE76 2.578e-02 NA NA +f_cyan_free_to_JCZ38 6.505e-01 NA NA +f_cyan_free_to_J9Z38 2.508e-01 NA NA +f_JCZ38_to_JSE76 1.000e+00 NA NA +f_JSE76_to_JCZ38 8.618e-01 NA NA + +Estimated Eigenvalues of SFORB model(s): +cyan_b1 cyan_b2 cyan_g +0.08768 0.01089 0.39821 + +Resulting formation fractions: + ff +cyan_free_JCZ38 0.65053 +cyan_free_J9Z38 0.25082 +cyan_free_sink 0.09864 +cyan_free 1.00000 +JCZ38_JSE76 1.00000 +JCZ38_sink 0.00000 +JSE76_JCZ38 0.86184 +JSE76_sink 0.13816 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 +cyan 25.32 164.79 49.61 7.906 63.64 +JCZ38 12.96 43.04 NA NA NA +J9Z38 105.75 351.29 NA NA NA +JSE76 26.89 89.33 NA NA NA + +</code></pre> +<p></p> +</div> +</div> +<div class="section level3"> +<h3 id="session-info">Session info<a class="anchor" aria-label="anchor" href="#session-info"></a> +</h3> +<pre><code>R version 4.2.3 (2023-03-15) +Platform: x86_64-pc-linux-gnu (64-bit) +Running under: Debian GNU/Linux 12 (bookworm) + +Matrix products: default +BLAS: /usr/lib/x86_64-linux-gnu/openblas-serial/libblas.so.3 +LAPACK: /usr/lib/x86_64-linux-gnu/openblas-serial/libopenblas-r0.3.21.so + +locale: + [1] LC_CTYPE=de_DE.UTF-8 LC_NUMERIC=C + [3] LC_TIME=de_DE.UTF-8 LC_COLLATE=de_DE.UTF-8 + [5] LC_MONETARY=de_DE.UTF-8 LC_MESSAGES=de_DE.UTF-8 + [7] LC_PAPER=de_DE.UTF-8 LC_NAME=C + [9] LC_ADDRESS=C LC_TELEPHONE=C +[11] LC_MEASUREMENT=de_DE.UTF-8 LC_IDENTIFICATION=C + +attached base packages: +[1] parallel stats graphics grDevices utils datasets methods +[8] base + +other attached packages: +[1] saemix_3.2 npde_3.3 knitr_1.42 mkin_1.2.3 + +loaded via a namespace (and not attached): + [1] pillar_1.9.0 bslib_0.4.2 compiler_4.2.3 jquerylib_0.1.4 + [5] tools_4.2.3 mclust_6.0.0 digest_0.6.31 tibble_3.2.1 + [9] jsonlite_1.8.4 evaluate_0.20 memoise_2.0.1 lifecycle_1.0.3 +[13] nlme_3.1-162 gtable_0.3.3 lattice_0.21-8 pkgconfig_2.0.3 +[17] rlang_1.1.0 DBI_1.1.3 cli_3.6.1 yaml_2.3.7 +[21] pkgdown_2.0.7 xfun_0.38 fastmap_1.1.1 gridExtra_2.3 +[25] dplyr_1.1.1 stringr_1.5.0 generics_0.1.3 desc_1.4.2 +[29] fs_1.6.1 vctrs_0.6.1 sass_0.4.5 systemfonts_1.0.4 +[33] tidyselect_1.2.0 rprojroot_2.0.3 lmtest_0.9-40 grid_4.2.3 +[37] inline_0.3.19 glue_1.6.2 R6_2.5.1 textshaping_0.3.6 +[41] fansi_1.0.4 rmarkdown_2.21 purrr_1.0.1 ggplot2_3.4.2 +[45] magrittr_2.0.3 scales_1.2.1 htmltools_0.5.5 colorspace_2.1-0 +[49] ragg_1.2.5 utf8_1.2.3 stringi_1.7.12 munsell_0.5.0 +[53] cachem_1.0.7 zoo_1.8-12 </code></pre> +</div> +<div class="section level3"> +<h3 id="hardware-info">Hardware info<a class="anchor" aria-label="anchor" href="#hardware-info"></a> +</h3> +<pre><code>CPU model: AMD Ryzen 9 7950X 16-Core Processor</code></pre> +<pre><code>MemTotal: 64936316 kB</code></pre> +</div> +</div> + </div> + + <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar"> + + <nav id="toc" data-toggle="toc"><h2 data-toc-skip>Contents</h2> + </nav> +</div> + +</div> + + + + <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> |