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| author | Johannes Ranke <johannes.ranke@jrwb.de> | 2025-02-14 07:19:15 +0100 |
|---|---|---|
| committer | Johannes Ranke <johannes.ranke@jrwb.de> | 2025-02-14 07:19:15 +0100 |
| commit | b0f08271d1dae8ffaf57f557c27eba1314ece1d5 (patch) | |
| tree | 98da899d455d6945849d6f4b4e98adfb98dc8b2b /docs/dev/articles | |
| parent | 7dc59c522d0639f6473463340e518e2e8074e364 (diff) | |
| parent | 55d9c2331e468efd364472555dbfae84603a4f73 (diff) | |
Merge branch 'main' into dev
Diffstat (limited to 'docs/dev/articles')
165 files changed, 0 insertions, 19407 deletions
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- - <div class="container template-article"> - <header><div class="navbar navbar-default navbar-fixed-top" role="navigation"> - <div class="container"> - <div class="navbar-header"> - <button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#navbar" aria-expanded="false"> - <span class="sr-only">Toggle navigation</span> - <span class="icon-bar"></span> - <span class="icon-bar"></span> - <span class="icon-bar"></span> - </button> - <span class="navbar-brand"> - <a class="navbar-link" href="../index.html">mkin</a> - <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">1.2.2</span> - </span> - </div> - - <div id="navbar" class="navbar-collapse collapse"> - <ul class="nav navbar-nav"> -<li> - <a href="../reference/index.html">Functions and data</a> -</li> -<li class="dropdown"> - <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false"> - 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- <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/2022_wp_1.1_dmta_parent.rmd" class="external-link"><code>vignettes/2022_wp_1.1_dmta_parent.rmd</code></a></small> - <div class="hidden name"><code>2022_wp_1.1_dmta_parent.rmd</code></div> - - </div> - - - -<div class="section level2"> -<h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#introduction"></a> -</h2> -<p>The purpose of this document is to demonstrate how nonlinear -hierarchical models (NLHM) based on the parent degradation models SFO, -FOMC, DFOP and HS can be fitted with the mkin package.</p> -<p>The mkin package is used in version 1.2.2. It contains the test data -and the functions used in the evaluations. The <code>saemix</code> -package is used as a backend for fitting the NLHM, but is also loaded to -make the convergence plot function available.</p> -<p>This document is processed with the <code>knitr</code> package, which -also provides the <code>kable</code> function that is used to improve -the display of tabular data in R markdown documents. For parallel -processing, the <code>parallel</code> package is used.</p> -<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://pkgdown.jrwb.de/mkin/">mkin</a></span><span class="op">)</span></span> -<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://yihui.org/knitr/" class="external-link">knitr</a></span><span class="op">)</span></span> -<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">saemix</span><span class="op">)</span></span> -<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">parallel</span><span class="op">)</span></span> -<span><span class="va">n_cores</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/detectCores.html" class="external-link">detectCores</a></span><span class="op">(</span><span class="op">)</span></span> -<span><span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/Sys.info.html" class="external-link">Sys.info</a></span><span class="op">(</span><span class="op">)</span><span class="op">[</span><span class="st">"sysname"</span><span class="op">]</span> <span class="op">==</span> <span class="st">"Windows"</span><span class="op">)</span> <span class="op">{</span></span> -<span> <span class="va">cl</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makePSOCKcluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> -<span><span class="op">}</span> <span class="kw">else</span> <span class="op">{</span></span> -<span> <span class="va">cl</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makeForkCluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> -<span><span class="op">}</span></span></code></pre></div> -<div class="section level3"> -<h3 id="preprocessing-of-test-data">Preprocessing of test data<a class="anchor" aria-label="anchor" href="#preprocessing-of-test-data"></a> -</h3> -<p>The test data are available in the mkin package as an object of class -<code>mkindsg</code> (mkin dataset group) under the identifier -<code>dimethenamid_2018</code>. The following preprocessing steps are -still necessary:</p> -<ul> -<li>The data available for the enantiomer dimethenamid-P (DMTAP) are -renamed to have the same substance name as the data for the racemic -mixture dimethenamid (DMTA). The reason for this is that no difference -between their degradation behaviour was identified in the EU risk -assessment.</li> -<li>The data for transformation products and unnecessary columns are -discarded</li> -<li>The observation times of each dataset are multiplied with the -corresponding normalisation factor also available in the dataset, in -order to make it possible to describe all datasets with a single set of -parameters that are independent of temperature</li> -<li>Finally, datasets observed in the same soil (<code>Elliot 1</code> -and <code>Elliot 2</code>) are combined, resulting in dimethenamid -(DMTA) data from six soils.</li> -</ul> -<p>The following commented R code performs this preprocessing.</p> -<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="co"># Apply a function to each of the seven datasets in the mkindsg object to create a list</span></span> -<span><span class="va">dmta_ds</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">lapply</a></span><span class="op">(</span><span class="fl">1</span><span class="op">:</span><span class="fl">7</span>, <span class="kw">function</span><span class="op">(</span><span class="va">i</span><span class="op">)</span> <span class="op">{</span></span> -<span> <span class="va">ds_i</span> <span class="op"><-</span> <span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">ds</span><span class="op">[[</span><span class="va">i</span><span class="op">]</span><span class="op">]</span><span class="op">$</span><span class="va">data</span> <span class="co"># Get a dataset</span></span> -<span> <span class="va">ds_i</span><span class="op">[</span><span class="va">ds_i</span><span class="op">$</span><span class="va">name</span> <span class="op">==</span> <span class="st">"DMTAP"</span>, <span class="st">"name"</span><span class="op">]</span> <span class="op"><-</span> <span class="st">"DMTA"</span> <span class="co"># Rename DMTAP to DMTA</span></span> -<span> <span class="va">ds_i</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/subset.html" class="external-link">subset</a></span><span class="op">(</span><span class="va">ds_i</span>, <span class="va">name</span> <span class="op">==</span> <span class="st">"DMTA"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"name"</span>, <span class="st">"time"</span>, <span class="st">"value"</span><span class="op">)</span><span class="op">)</span> <span class="co"># Select data</span></span> -<span> <span class="va">ds_i</span><span class="op">$</span><span class="va">time</span> <span class="op"><-</span> <span class="va">ds_i</span><span class="op">$</span><span class="va">time</span> <span class="op">*</span> <span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">f_time_norm</span><span class="op">[</span><span class="va">i</span><span class="op">]</span> <span class="co"># Normalise time</span></span> -<span> <span class="va">ds_i</span> <span class="co"># Return the dataset</span></span> -<span><span class="op">}</span><span class="op">)</span></span> -<span></span> -<span><span class="co"># Use dataset titles as names for the list elements</span></span> -<span><span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">)</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</span><span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">ds</span>, <span class="kw">function</span><span class="op">(</span><span class="va">ds</span><span class="op">)</span> <span class="va">ds</span><span class="op">$</span><span class="va">title</span><span class="op">)</span></span> -<span></span> -<span><span class="co"># Combine data for Elliot soil to obtain a named list with six elements</span></span> -<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/cbind.html" class="external-link">rbind</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 1"</span><span class="op">]</span><span class="op">]</span>, <span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 2"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span> <span class="co">#</span></span> -<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 1"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="cn">NULL</span></span> -<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 2"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="cn">NULL</span></span></code></pre></div> -<p>The following tables show the 6 datasets.</p> -<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="kw">for</span> <span class="op">(</span><span class="va">ds_name</span> <span class="kw">in</span> <span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">)</span><span class="op">)</span> <span class="op">{</span></span> -<span> <span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="fu"><a href="../reference/mkin_long_to_wide.html">mkin_long_to_wide</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">[[</span><span class="va">ds_name</span><span class="op">]</span><span class="op">]</span><span class="op">)</span>,</span> -<span> caption <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste</a></span><span class="op">(</span><span class="st">"Dataset"</span>, <span class="va">ds_name</span><span class="op">)</span>,</span> -<span> label <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste0</a></span><span class="op">(</span><span class="st">"tab:"</span>, <span class="va">ds_name</span><span class="op">)</span>, booktabs <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span><span class="op">)</span></span> -<span> <span class="fu"><a href="https://rdrr.io/r/base/cat.html" class="external-link">cat</a></span><span class="op">(</span><span class="st">"\n\\clearpage\n"</span><span class="op">)</span></span> -<span><span class="op">}</span></span></code></pre></div> -<table class="table"> -<caption>Dataset Calke</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">DMTA</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0</td> -<td align="right">95.8</td> -</tr> -<tr class="even"> -<td align="right">0</td> -<td align="right">98.7</td> -</tr> -<tr class="odd"> -<td align="right">14</td> -<td align="right">60.5</td> -</tr> -<tr class="even"> -<td align="right">30</td> -<td align="right">39.1</td> -</tr> -<tr class="odd"> -<td align="right">59</td> -<td align="right">15.2</td> -</tr> -<tr class="even"> -<td align="right">120</td> -<td align="right">4.8</td> -</tr> -<tr class="odd"> -<td align="right">120</td> -<td align="right">4.6</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset Borstel</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">DMTA</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.000000</td> -<td align="right">100.5</td> -</tr> -<tr class="even"> -<td align="right">0.000000</td> -<td align="right">99.6</td> -</tr> -<tr class="odd"> -<td align="right">1.941295</td> -<td align="right">91.9</td> -</tr> -<tr class="even"> -<td align="right">1.941295</td> -<td align="right">91.3</td> -</tr> -<tr class="odd"> -<td align="right">6.794534</td> -<td align="right">81.8</td> -</tr> -<tr class="even"> -<td align="right">6.794534</td> -<td align="right">82.1</td> -</tr> -<tr class="odd"> -<td align="right">13.589067</td> -<td align="right">69.1</td> -</tr> -<tr class="even"> -<td align="right">13.589067</td> -<td align="right">68.0</td> -</tr> -<tr class="odd"> -<td align="right">27.178135</td> -<td align="right">51.4</td> -</tr> -<tr class="even"> -<td align="right">27.178135</td> -<td align="right">51.4</td> -</tr> -<tr class="odd"> -<td align="right">56.297565</td> -<td align="right">27.6</td> -</tr> -<tr class="even"> -<td align="right">56.297565</td> -<td align="right">26.8</td> -</tr> -<tr class="odd"> -<td align="right">86.387643</td> -<td align="right">15.7</td> -</tr> -<tr class="even"> -<td align="right">86.387643</td> -<td align="right">15.3</td> -</tr> -<tr class="odd"> -<td align="right">115.507073</td> -<td align="right">7.9</td> -</tr> -<tr class="even"> -<td align="right">115.507073</td> -<td align="right">8.1</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset Flaach</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">DMTA</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.0000000</td> -<td align="right">96.5</td> -</tr> -<tr class="even"> -<td align="right">0.0000000</td> -<td align="right">96.8</td> -</tr> -<tr class="odd"> -<td align="right">0.0000000</td> -<td align="right">97.0</td> -</tr> -<tr class="even"> -<td align="right">0.6233856</td> -<td align="right">82.9</td> -</tr> -<tr class="odd"> -<td align="right">0.6233856</td> -<td align="right">86.7</td> -</tr> -<tr class="even"> -<td align="right">0.6233856</td> -<td align="right">87.4</td> -</tr> -<tr class="odd"> -<td align="right">1.8701567</td> -<td align="right">72.8</td> -</tr> -<tr class="even"> -<td align="right">1.8701567</td> -<td align="right">69.9</td> -</tr> -<tr class="odd"> -<td align="right">1.8701567</td> -<td align="right">71.9</td> -</tr> -<tr class="even"> -<td align="right">4.3636989</td> -<td align="right">51.4</td> -</tr> -<tr class="odd"> -<td align="right">4.3636989</td> -<td align="right">52.9</td> -</tr> -<tr class="even"> -<td align="right">4.3636989</td> -<td align="right">48.6</td> -</tr> -<tr class="odd"> -<td align="right">8.7273979</td> -<td align="right">28.5</td> -</tr> -<tr class="even"> -<td align="right">8.7273979</td> -<td align="right">27.3</td> -</tr> -<tr class="odd"> -<td align="right">8.7273979</td> -<td align="right">27.5</td> -</tr> -<tr class="even"> -<td align="right">13.0910968</td> -<td align="right">14.8</td> -</tr> -<tr class="odd"> -<td align="right">13.0910968</td> -<td align="right">13.4</td> -</tr> -<tr class="even"> -<td align="right">13.0910968</td> -<td align="right">14.4</td> -</tr> -<tr class="odd"> -<td align="right">17.4547957</td> -<td align="right">7.7</td> -</tr> -<tr class="even"> -<td align="right">17.4547957</td> -<td align="right">7.3</td> -</tr> -<tr class="odd"> -<td align="right">17.4547957</td> -<td align="right">8.1</td> -</tr> -<tr class="even"> -<td align="right">26.1821936</td> -<td align="right">2.0</td> -</tr> -<tr class="odd"> -<td align="right">26.1821936</td> -<td align="right">1.5</td> -</tr> -<tr class="even"> -<td align="right">26.1821936</td> -<td align="right">1.9</td> -</tr> -<tr class="odd"> -<td align="right">34.9095915</td> -<td align="right">1.3</td> -</tr> -<tr class="even"> -<td align="right">34.9095915</td> -<td align="right">1.0</td> -</tr> -<tr class="odd"> -<td align="right">34.9095915</td> -<td align="right">1.1</td> -</tr> -<tr class="even"> -<td align="right">43.6369893</td> -<td align="right">0.9</td> -</tr> -<tr class="odd"> -<td align="right">43.6369893</td> -<td align="right">0.7</td> -</tr> -<tr class="even"> -<td align="right">43.6369893</td> -<td align="right">0.7</td> -</tr> -<tr class="odd"> -<td align="right">52.3643872</td> -<td align="right">0.6</td> -</tr> -<tr class="even"> -<td align="right">52.3643872</td> -<td align="right">0.4</td> -</tr> -<tr class="odd"> -<td align="right">52.3643872</td> -<td align="right">0.5</td> -</tr> -<tr class="even"> -<td align="right">74.8062674</td> -<td align="right">0.4</td> -</tr> -<tr class="odd"> -<td align="right">74.8062674</td> -<td align="right">0.3</td> -</tr> -<tr class="even"> -<td align="right">74.8062674</td> -<td align="right">0.3</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset BBA 2.2</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">DMTA</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.0000000</td> -<td align="right">98.09</td> -</tr> -<tr class="even"> -<td align="right">0.0000000</td> -<td align="right">98.77</td> -</tr> -<tr class="odd"> -<td align="right">0.7678922</td> -<td align="right">93.52</td> -</tr> -<tr class="even"> -<td align="right">0.7678922</td> -<td align="right">92.03</td> -</tr> -<tr class="odd"> -<td align="right">2.3036765</td> -<td align="right">88.39</td> -</tr> -<tr class="even"> -<td align="right">2.3036765</td> -<td align="right">87.18</td> -</tr> -<tr class="odd"> -<td align="right">5.3752452</td> -<td align="right">69.38</td> -</tr> -<tr class="even"> -<td align="right">5.3752452</td> -<td align="right">71.06</td> -</tr> -<tr class="odd"> -<td align="right">10.7504904</td> -<td align="right">45.21</td> -</tr> -<tr class="even"> -<td align="right">10.7504904</td> -<td align="right">46.81</td> -</tr> -<tr class="odd"> -<td align="right">16.1257355</td> -<td align="right">30.54</td> -</tr> -<tr class="even"> -<td align="right">16.1257355</td> -<td align="right">30.07</td> -</tr> -<tr class="odd"> -<td align="right">21.5009807</td> -<td align="right">21.60</td> -</tr> -<tr class="even"> -<td align="right">21.5009807</td> -<td align="right">20.41</td> -</tr> -<tr class="odd"> -<td align="right">32.2514711</td> -<td align="right">9.10</td> -</tr> -<tr class="even"> -<td align="right">32.2514711</td> -<td align="right">9.70</td> -</tr> -<tr class="odd"> -<td align="right">43.0019614</td> -<td align="right">6.58</td> -</tr> -<tr class="even"> -<td align="right">43.0019614</td> -<td align="right">6.31</td> -</tr> -<tr class="odd"> -<td align="right">53.7524518</td> -<td align="right">3.47</td> -</tr> -<tr class="even"> -<td align="right">53.7524518</td> -<td align="right">3.52</td> -</tr> -<tr class="odd"> -<td align="right">64.5029421</td> -<td align="right">3.40</td> -</tr> -<tr class="even"> -<td align="right">64.5029421</td> -<td align="right">3.67</td> -</tr> -<tr class="odd"> -<td align="right">91.3791680</td> -<td align="right">1.62</td> -</tr> -<tr class="even"> -<td align="right">91.3791680</td> -<td align="right">1.62</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset BBA 2.3</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">DMTA</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.0000000</td> -<td align="right">99.33</td> -</tr> -<tr class="even"> -<td align="right">0.0000000</td> -<td align="right">97.44</td> -</tr> -<tr class="odd"> -<td align="right">0.6733938</td> -<td align="right">93.73</td> -</tr> -<tr class="even"> -<td align="right">0.6733938</td> -<td align="right">93.77</td> -</tr> -<tr class="odd"> -<td align="right">2.0201814</td> -<td align="right">87.84</td> -</tr> -<tr class="even"> -<td align="right">2.0201814</td> -<td align="right">89.82</td> -</tr> -<tr class="odd"> -<td align="right">4.7137565</td> -<td align="right">71.61</td> -</tr> -<tr class="even"> -<td align="right">4.7137565</td> -<td align="right">71.42</td> -</tr> -<tr class="odd"> -<td align="right">9.4275131</td> -<td align="right">45.60</td> -</tr> -<tr class="even"> -<td align="right">9.4275131</td> -<td align="right">45.42</td> -</tr> -<tr class="odd"> -<td align="right">14.1412696</td> -<td align="right">31.12</td> -</tr> -<tr class="even"> -<td align="right">14.1412696</td> -<td align="right">31.68</td> -</tr> -<tr class="odd"> -<td align="right">18.8550262</td> -<td align="right">23.20</td> -</tr> -<tr class="even"> -<td align="right">18.8550262</td> -<td align="right">24.13</td> -</tr> -<tr class="odd"> -<td align="right">28.2825393</td> -<td align="right">9.43</td> -</tr> -<tr class="even"> -<td align="right">28.2825393</td> -<td align="right">9.82</td> -</tr> -<tr class="odd"> -<td align="right">37.7100523</td> -<td align="right">7.08</td> -</tr> -<tr class="even"> -<td align="right">37.7100523</td> -<td align="right">8.64</td> -</tr> -<tr class="odd"> -<td align="right">47.1375654</td> -<td align="right">4.41</td> -</tr> -<tr class="even"> -<td align="right">47.1375654</td> -<td align="right">4.78</td> -</tr> -<tr class="odd"> -<td align="right">56.5650785</td> -<td align="right">4.92</td> -</tr> -<tr class="even"> -<td align="right">56.5650785</td> -<td align="right">5.08</td> -</tr> -<tr class="odd"> -<td align="right">80.1338612</td> -<td align="right">2.13</td> -</tr> -<tr class="even"> -<td align="right">80.1338612</td> -<td align="right">2.23</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset Elliot</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">DMTA</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.000000</td> -<td align="right">97.5</td> -</tr> -<tr class="even"> -<td align="right">0.000000</td> -<td align="right">100.7</td> -</tr> -<tr class="odd"> -<td align="right">1.228478</td> -<td align="right">86.4</td> -</tr> -<tr class="even"> -<td align="right">1.228478</td> -<td align="right">88.5</td> -</tr> -<tr class="odd"> -<td align="right">3.685435</td> -<td align="right">69.8</td> -</tr> -<tr class="even"> -<td align="right">3.685435</td> -<td align="right">77.1</td> -</tr> -<tr class="odd"> -<td align="right">8.599349</td> -<td align="right">59.0</td> -</tr> -<tr class="even"> -<td align="right">8.599349</td> -<td align="right">54.2</td> -</tr> -<tr class="odd"> -<td align="right">17.198697</td> -<td align="right">31.3</td> -</tr> -<tr class="even"> -<td align="right">17.198697</td> -<td align="right">33.5</td> -</tr> -<tr class="odd"> -<td align="right">25.798046</td> -<td align="right">19.6</td> -</tr> -<tr class="even"> -<td align="right">25.798046</td> -<td align="right">20.9</td> -</tr> -<tr class="odd"> -<td align="right">34.397395</td> -<td align="right">13.3</td> -</tr> -<tr class="even"> -<td align="right">34.397395</td> -<td align="right">15.8</td> -</tr> -<tr class="odd"> -<td align="right">51.596092</td> -<td align="right">6.7</td> -</tr> -<tr class="even"> -<td align="right">51.596092</td> -<td align="right">8.7</td> -</tr> -<tr class="odd"> -<td align="right">68.794789</td> -<td align="right">8.8</td> -</tr> -<tr class="even"> -<td align="right">68.794789</td> -<td align="right">8.7</td> -</tr> -<tr class="odd"> -<td align="right">103.192184</td> -<td align="right">6.0</td> -</tr> -<tr class="even"> -<td align="right">103.192184</td> -<td align="right">4.4</td> -</tr> -<tr class="odd"> -<td align="right">146.188928</td> -<td align="right">3.3</td> -</tr> -<tr class="even"> -<td align="right">146.188928</td> -<td align="right">2.8</td> -</tr> -<tr class="odd"> -<td align="right">223.583066</td> -<td align="right">1.4</td> -</tr> -<tr class="even"> -<td align="right">223.583066</td> -<td align="right">1.8</td> -</tr> -<tr class="odd"> -<td align="right">0.000000</td> -<td align="right">93.4</td> -</tr> -<tr class="even"> -<td align="right">0.000000</td> -<td align="right">103.2</td> -</tr> -<tr class="odd"> -<td align="right">1.228478</td> -<td align="right">89.2</td> -</tr> -<tr class="even"> -<td align="right">1.228478</td> -<td align="right">86.6</td> -</tr> -<tr class="odd"> -<td align="right">3.685435</td> -<td align="right">78.2</td> -</tr> -<tr class="even"> -<td align="right">3.685435</td> -<td align="right">78.1</td> -</tr> -<tr class="odd"> -<td align="right">8.599349</td> -<td align="right">55.6</td> -</tr> -<tr class="even"> -<td align="right">8.599349</td> -<td align="right">53.0</td> -</tr> -<tr class="odd"> -<td align="right">17.198697</td> -<td align="right">33.7</td> -</tr> -<tr class="even"> -<td align="right">17.198697</td> -<td align="right">33.2</td> -</tr> -<tr class="odd"> -<td align="right">25.798046</td> -<td align="right">20.9</td> -</tr> -<tr class="even"> -<td align="right">25.798046</td> -<td align="right">19.9</td> -</tr> -<tr class="odd"> -<td align="right">34.397395</td> -<td align="right">18.2</td> -</tr> -<tr class="even"> -<td align="right">34.397395</td> -<td align="right">12.7</td> -</tr> -<tr class="odd"> -<td align="right">51.596092</td> -<td align="right">7.8</td> -</tr> -<tr class="even"> -<td align="right">51.596092</td> -<td align="right">9.0</td> -</tr> -<tr class="odd"> -<td align="right">68.794789</td> -<td align="right">11.4</td> -</tr> -<tr class="even"> -<td align="right">68.794789</td> -<td align="right">9.0</td> -</tr> -<tr class="odd"> -<td align="right">103.192184</td> -<td align="right">3.9</td> -</tr> -<tr class="even"> -<td align="right">103.192184</td> -<td align="right">4.4</td> -</tr> -<tr class="odd"> -<td align="right">146.188928</td> -<td align="right">2.6</td> -</tr> -<tr class="even"> -<td align="right">146.188928</td> -<td align="right">3.4</td> -</tr> -<tr class="odd"> -<td align="right">223.583066</td> -<td align="right">2.0</td> -</tr> -<tr class="even"> -<td align="right">223.583066</td> -<td align="right">1.7</td> -</tr> -</tbody> -</table> -</div> -</div> -<div class="section level2"> -<h2 id="separate-evaluations">Separate evaluations<a class="anchor" aria-label="anchor" href="#separate-evaluations"></a> -</h2> -<p>In order to obtain suitable starting parameters for the NLHM fits, -separate fits of the four models to the data for each soil are generated -using the <code>mmkin</code> function from the <code>mkin</code> -package. In a first step, constant variance is assumed. Convergence is -checked with the <code>status</code> function.</p> -<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">deg_mods</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>, <span class="st">"HS"</span><span class="op">)</span></span> -<span><span class="va">f_sep_const</span> <span class="op"><-</span> <span class="fu"><a href="../reference/mmkin.html">mmkin</a></span><span class="op">(</span></span> -<span> <span class="va">deg_mods</span>,</span> -<span> <span class="va">dmta_ds</span>,</span> -<span> error_model <span class="op">=</span> <span class="st">"const"</span>,</span> -<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<span></span> -<span><span class="fu"><a href="../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">Calke</th> -<th align="left">Borstel</th> -<th align="left">Flaach</th> -<th align="left">BBA 2.2</th> -<th align="left">BBA 2.3</th> -<th align="left">Elliot</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">SFO</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">FOMC</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">DFOP</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">HS</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -</tbody> -</table> -<p>In the table above, OK indicates convergence, and C indicates failure -to converge. All separate fits with constant variance converged, with -the sole exception of the HS fit to the BBA 2.2 data. To prepare for -fitting NLHM using the two-component error model, the separate fits are -updated assuming two-component error.</p> -<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_sep_tc</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_sep_const</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span> -<span><span class="fu"><a href="../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_tc</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">Calke</th> -<th align="left">Borstel</th> -<th align="left">Flaach</th> -<th align="left">BBA 2.2</th> -<th align="left">BBA 2.3</th> -<th align="left">Elliot</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">SFO</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">FOMC</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">DFOP</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">HS</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -</tbody> -</table> -<p>Using the two-component error model, the one fit that did not -converge with constant variance did converge, but other non-SFO fits -failed to converge.</p> -</div> -<div class="section level2"> -<h2 id="hierarchichal-model-fits">Hierarchichal model fits<a class="anchor" aria-label="anchor" href="#hierarchichal-model-fits"></a> -</h2> -<p>The following code fits eight versions of hierarchical models to the -data, using SFO, FOMC, DFOP and HS for the parent compound, and using -either constant variance or two-component error for the error model. The -default parameter distribution model in mkin allows for variation of all -degradation parameters across the assumed population of soils. In other -words, each degradation parameter is associated with a random effect as -a first step. The <code>mhmkin</code> function makes it possible to fit -all eight versions in parallel (given a sufficient number of computing -cores being available) to save execution time.</p> -<p>Convergence plots and summaries for these fits are shown in the -appendix.</p> -<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_saem</span> <span class="op"><-</span> <span class="fu"><a href="../reference/mhmkin.html">mhmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">f_sep_const</span>, <span class="va">f_sep_tc</span><span class="op">)</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span></span></code></pre></div> -<p>The output of the <code>status</code> function shows that all fits -terminated successfully.</p> -<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_saem</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">const</th> -<th align="left">tc</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">SFO</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">FOMC</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">DFOP</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">HS</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -</tbody> -</table> -<p>The AIC and BIC values show that the biphasic models DFOP and HS give -the best fits.</p> -<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="right">npar</th> -<th align="right">AIC</th> -<th align="right">BIC</th> -<th align="right">Lik</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">SFO const</td> -<td align="right">5</td> -<td align="right">796.3</td> -<td align="right">795.3</td> -<td align="right">-393.2</td> -</tr> -<tr class="even"> -<td align="left">SFO tc</td> -<td align="right">6</td> -<td align="right">798.3</td> -<td align="right">797.1</td> -<td align="right">-393.2</td> -</tr> -<tr class="odd"> -<td align="left">FOMC const</td> -<td align="right">7</td> -<td align="right">734.2</td> -<td align="right">732.7</td> -<td align="right">-360.1</td> -</tr> -<tr class="even"> -<td align="left">FOMC tc</td> -<td align="right">8</td> -<td align="right">720.4</td> -<td align="right">718.8</td> -<td align="right">-352.2</td> -</tr> -<tr class="odd"> -<td align="left">DFOP const</td> -<td align="right">9</td> -<td align="right">711.8</td> -<td align="right">710.0</td> -<td align="right">-346.9</td> -</tr> -<tr class="even"> -<td align="left">HS const</td> -<td align="right">9</td> -<td align="right">714.0</td> -<td align="right">712.1</td> -<td align="right">-348.0</td> -</tr> -<tr class="odd"> -<td align="left">DFOP tc</td> -<td align="right">10</td> -<td align="right">665.5</td> -<td align="right">663.4</td> -<td align="right">-322.8</td> -</tr> -<tr class="even"> -<td align="left">HS tc</td> -<td align="right">10</td> -<td align="right">667.1</td> -<td align="right">665.0</td> -<td align="right">-323.6</td> -</tr> -</tbody> -</table> -<p>The DFOP model is preferred here, as it has a better mechanistic -basis for batch experiments with constant incubation conditions. Also, -it shows the lowest AIC and BIC values in the first set of fits when -combined with the two-component error model. Therefore, the DFOP model -was selected for further refinements of the fits with the aim to make -the model fully identifiable.</p> -<div class="section level3"> -<h3 id="parameter-identifiability-based-on-the-fisher-information-matrix">Parameter identifiability based on the Fisher Information -Matrix<a class="anchor" aria-label="anchor" href="#parameter-identifiability-based-on-the-fisher-information-matrix"></a> -</h3> -<p>Using the <code>illparms</code> function, ill-defined statistical -model parameters such as standard deviations of the degradation -parameters in the population and error model parameters can be -found.</p> -<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">const</th> -<th align="left">tc</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">SFO</td> -<td align="left"></td> -<td align="left">b.1</td> -</tr> -<tr class="even"> -<td align="left">FOMC</td> -<td align="left"></td> -<td align="left">sd(DMTA_0)</td> -</tr> -<tr class="odd"> -<td align="left">DFOP</td> -<td align="left">sd(k2)</td> -<td align="left">sd(k2)</td> -</tr> -<tr class="even"> -<td align="left">HS</td> -<td align="left"></td> -<td align="left">sd(tb)</td> -</tr> -</tbody> -</table> -<p>According to the <code>illparms</code> function, the fitted standard -deviation of the second kinetic rate constant <code>k2</code> is -ill-defined in both DFOP fits. This suggests that different values would -be obtained for this standard deviation when using different starting -values.</p> -<p>The thus identified overparameterisation is addressed by removing the -random effect for <code>k2</code> from the parameter model.</p> -<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_saem_dfop_tc_no_ranef_k2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_saem</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span>,</span> -<span> no_random_effect <span class="op">=</span> <span class="st">"k2"</span><span class="op">)</span></span></code></pre></div> -<p>For the resulting fit, it is checked whether there are still -ill-defined parameters,</p> -<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_dfop_tc_no_ranef_k2</span><span class="op">)</span></span></code></pre></div> -<p>which is not the case. Below, the refined model is compared with the -previous best model. The model without random effect for <code>k2</code> -is a reduced version of the previous model. Therefore, the models are -nested and can be compared using the likelihood ratio test. This is -achieved with the argument <code>test = TRUE</code> to the -<code>anova</code> function.</p> -<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span>, <span class="va">f_saem_dfop_tc_no_ranef_k2</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|></span></span> -<span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>format.args <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">4</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<colgroup> -<col width="37%"> -<col width="6%"> -<col width="8%"> -<col width="8%"> -<col width="9%"> -<col width="9%"> -<col width="4%"> -<col width="15%"> -</colgroup> -<thead><tr class="header"> -<th align="left"></th> -<th align="right">npar</th> -<th align="right">AIC</th> -<th align="right">BIC</th> -<th align="right">Lik</th> -<th align="right">Chisq</th> -<th align="right">Df</th> -<th align="right">Pr(>Chisq)</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">f_saem_dfop_tc_no_ranef_k2</td> -<td align="right">9</td> -<td align="right">663.8</td> -<td align="right">661.9</td> -<td align="right">-322.9</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="left">f_saem[[“DFOP”, “tc”]]</td> -<td align="right">10</td> -<td align="right">665.5</td> -<td align="right">663.4</td> -<td align="right">-322.8</td> -<td align="right">0.2809</td> -<td align="right">1</td> -<td align="right">0.5961</td> -</tr> -</tbody> -</table> -<p>The AIC and BIC criteria are lower after removal of the ill-defined -random effect for <code>k2</code>. The p value of the likelihood ratio -test is much greater than 0.05, indicating that the model with the -higher likelihood (here the model with random effects for all -degradation parameters <code>f_saem[["DFOP", "tc"]]</code>) does not fit -significantly better than the model with the lower likelihood (the -reduced model <code>f_saem_dfop_tc_no_ranef_k2</code>).</p> -<p>Therefore, AIC, BIC and likelihood ratio test suggest the use of the -reduced model.</p> -<p>The convergence of the fit is checked visually.</p> -<div class="figure" style="text-align: center"> -<img src="2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-dfop-tc-no-ranef-k2-1.png" alt="Convergence plot for the NLHM DFOP fit with two-component error and without a random effect on 'k2'" width="864"><p class="caption"> -Convergence plot for the NLHM DFOP fit with two-component error and -without a random effect on ‘k2’ -</p> -</div> -<p>All parameters appear to have converged to a satisfactory degree. The -final fit is plotted using the plot method from the mkin package.</p> -<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_dfop_tc_no_ranef_k2</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_wp_1.1_dmta_parent_files/figure-html/plot-saem-dfop-tc-no-ranef-k2-1.png" alt="Plot of the final NLHM DFOP fit" width="864"><p class="caption"> -Plot of the final NLHM DFOP fit -</p> -</div> -<p>Finally, a summary report of the fit is produced.</p> -<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">f_saem_dfop_tc_no_ranef_k2</span><span class="op">)</span></span></code></pre></div> -<pre><code>saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.2 -R version used for fitting: 4.2.2 -Date of fit: Thu Jan 5 08:19:13 2023 -Date of summary: Thu Jan 5 08:19:13 2023 - -Equations: -d_DMTA/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * - time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) - * DMTA - -Data: -155 observations of 1 variable(s) grouped in 6 datasets - -Model predictions using solution type analytical - -Fitted in 4.075 s -Using 300, 100 iterations and 9 chains - -Variance model: Two-component variance function - -Starting values for degradation parameters: - DMTA_0 k1 k2 g -98.759266 0.087034 0.009933 0.930827 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - DMTA_0 k1 k2 g -DMTA_0 98.76 0 0 0 -k1 0.00 1 0 0 -k2 0.00 0 1 0 -g 0.00 0 0 1 - -Starting values for error model parameters: -a.1 b.1 - 1 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 663.8 661.9 -322.9 - -Optimised parameters: - est. lower upper -DMTA_0 98.228939 96.285869 100.17201 -k1 0.064063 0.033477 0.09465 -k2 0.008297 0.005824 0.01077 -g 0.953821 0.914328 0.99331 -a.1 1.068479 0.869538 1.26742 -b.1 0.029424 0.022406 0.03644 -SD.DMTA_0 2.030437 0.404824 3.65605 -SD.k1 0.594692 0.256660 0.93272 -SD.g 1.006754 0.361327 1.65218 - -Correlation: - DMTA_0 k1 k2 -k1 0.0218 -k2 0.0556 0.0355 -g -0.0516 -0.0284 -0.2800 - -Random effects: - est. lower upper -SD.DMTA_0 2.0304 0.4048 3.6560 -SD.k1 0.5947 0.2567 0.9327 -SD.g 1.0068 0.3613 1.6522 - -Variance model: - est. lower upper -a.1 1.06848 0.86954 1.26742 -b.1 0.02942 0.02241 0.03644 - -Estimated disappearance times: - DT50 DT90 DT50back DT50_k1 DT50_k2 -DMTA 11.45 41.4 12.46 10.82 83.54</code></pre> -</div> -<div class="section level3"> -<h3 id="alternative-check-of-parameter-identifiability">Alternative check of parameter identifiability<a class="anchor" aria-label="anchor" href="#alternative-check-of-parameter-identifiability"></a> -</h3> -<p>The parameter check used in the <code>illparms</code> function is -based on a quadratic approximation of the likelihood surface near its -optimum, which is calculated using the Fisher Information Matrix (FIM). -An alternative way to check parameter identifiability based on a -multistart approach has recently been implemented in mkin.</p> -<p>The graph below shows boxplots of the parameters obtained in 50 runs -of the saem algorithm with different parameter combinations, sampled -from the range of the parameters obtained for the individual datasets -fitted separately using nonlinear regression.</p> -<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_saem_dfop_tc_multi</span> <span class="op"><-</span> <span class="fu"><a href="../reference/multistart.html">multistart</a></span><span class="op">(</span><span class="va">f_saem</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span>, n <span class="op">=</span> <span class="fl">50</span>, cores <span class="op">=</span> <span class="fl">15</span><span class="op">)</span></span></code></pre></div> -<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/par.html" class="external-link">par</a></span><span class="op">(</span>mar <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">6.1</span>, <span class="fl">4.1</span>, <span class="fl">2.1</span>, <span class="fl">2.1</span><span class="op">)</span><span class="op">)</span></span> -<span><span class="fu"><a href="../reference/parplot.html">parplot</a></span><span class="op">(</span><span class="va">f_saem_dfop_tc_multi</span>, lpos <span class="op">=</span> <span class="st">"bottomright"</span>, ylim <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.3</span>, <span class="fl">10</span><span class="op">)</span>, las <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_wp_1.1_dmta_parent_files/figure-html/multistart-full-par-1.png" alt="Scaled parameters from the multistart runs, full model" width="960"><p class="caption"> -Scaled parameters from the multistart runs, full model -</p> -</div> -<p>The graph clearly confirms the lack of identifiability of the -variance of <code>k2</code> in the full model. The overparameterisation -of the model also indicates a lack of identifiability of the variance of -parameter <code>g</code>.</p> -<p>The parameter boxplots of the multistart runs with the reduced model -shown below indicate that all runs give similar results, regardless of -the starting parameters.</p> -<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_saem_dfop_tc_no_ranef_k2_multi</span> <span class="op"><-</span> <span class="fu"><a href="../reference/multistart.html">multistart</a></span><span class="op">(</span><span class="va">f_saem_dfop_tc_no_ranef_k2</span>,</span> -<span> n <span class="op">=</span> <span class="fl">50</span>, cores <span class="op">=</span> <span class="fl">15</span><span class="op">)</span></span></code></pre></div> -<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/par.html" class="external-link">par</a></span><span class="op">(</span>mar <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">6.1</span>, <span class="fl">4.1</span>, <span class="fl">2.1</span>, <span class="fl">2.1</span><span class="op">)</span><span class="op">)</span></span> -<span><span class="fu"><a href="../reference/parplot.html">parplot</a></span><span class="op">(</span><span class="va">f_saem_dfop_tc_no_ranef_k2_multi</span>, ylim <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.5</span>, <span class="fl">2</span><span class="op">)</span>, las <span class="op">=</span> <span class="fl">2</span>,</span> -<span> lpos <span class="op">=</span> <span class="st">"bottomright"</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_wp_1.1_dmta_parent_files/figure-html/multistart-reduced-par-1.png" alt="Scaled parameters from the multistart runs, reduced model" width="960"><p class="caption"> -Scaled parameters from the multistart runs, reduced model -</p> -</div> -<p>When only the parameters of the top 25% of the fits are shown (based -on a feature introduced in mkin 1.2.2 currently under development), the -scatter is even less as shown below.</p> -<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/par.html" class="external-link">par</a></span><span class="op">(</span>mar <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">6.1</span>, <span class="fl">4.1</span>, <span class="fl">2.1</span>, <span class="fl">2.1</span><span class="op">)</span><span class="op">)</span></span> -<span><span class="fu"><a href="../reference/parplot.html">parplot</a></span><span class="op">(</span><span class="va">f_saem_dfop_tc_no_ranef_k2_multi</span>, ylim <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.5</span>, <span class="fl">2</span><span class="op">)</span>, las <span class="op">=</span> <span class="fl">2</span>, llquant <span class="op">=</span> <span class="fl">0.25</span>,</span> -<span> lpos <span class="op">=</span> <span class="st">"bottomright"</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_wp_1.1_dmta_parent_files/figure-html/multistart-reduced-par-llquant-1.png" alt="Scaled parameters from the multistart runs, reduced model, fits with the top 25\% likelihood values" width="960"><p class="caption"> -Scaled parameters from the multistart runs, reduced model, fits with the -top 25% likelihood values -</p> -</div> -</div> -</div> -<div class="section level2"> -<h2 id="conclusions">Conclusions<a class="anchor" aria-label="anchor" href="#conclusions"></a> -</h2> -<p>Fitting the four parent degradation models SFO, FOMC, DFOP and HS as -part of hierarchical model fits with two different error models and -normal distributions of the transformed degradation parameters works -without technical problems. The biphasic models DFOP and HS gave the -best fit to the data, but the default parameter distribution model was -not fully identifiable. Removing the random effect for the second -kinetic rate constant of the DFOP model resulted in a reduced model that -was fully identifiable and showed the lowest values for the model -selection criteria AIC and BIC. The reliability of the identification of -all model parameters was confirmed using multiple starting values.</p> -</div> -<div class="section level2"> -<h2 id="appendix">Appendix<a class="anchor" aria-label="anchor" href="#appendix"></a> -</h2> -<div class="section level3"> -<h3 id="hierarchical-model-fit-listings">Hierarchical model fit listings<a class="anchor" aria-label="anchor" href="#hierarchical-model-fit-listings"></a> -</h3> -<caption> -Hierarchical mkin fit of the SFO model with error model const -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.2 -R version used for fitting: 4.2.2 -Date of fit: Thu Jan 5 08:19:06 2023 -Date of summary: Thu Jan 5 08:20:11 2023 - -Equations: -d_DMTA/dt = - k_DMTA * DMTA - -Data: -155 observations of 1 variable(s) grouped in 6 datasets - -Model predictions using solution type analytical - -Fitted in 1.09 s -Using 300, 100 iterations and 9 chains - -Variance model: Constant variance - -Starting values for degradation parameters: - DMTA_0 k_DMTA -97.2953 0.0566 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - DMTA_0 k_DMTA -DMTA_0 97.3 0 -k_DMTA 0.0 1 - -Starting values for error model parameters: -a.1 - 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 796.3 795.3 -393.2 - -Optimised parameters: - est. lower upper -DMTA_0 97.28130 95.71113 98.8515 -k_DMTA 0.05665 0.02909 0.0842 -a.1 2.66442 2.35579 2.9731 -SD.DMTA_0 1.54776 0.15447 2.9411 -SD.k_DMTA 0.60690 0.26248 0.9513 - -Correlation: - DMTA_0 -k_DMTA 0.0168 - -Random effects: - est. lower upper -SD.DMTA_0 1.5478 0.1545 2.9411 -SD.k_DMTA 0.6069 0.2625 0.9513 - -Variance model: - est. lower upper -a.1 2.664 2.356 2.973 - -Estimated disappearance times: - DT50 DT90 -DMTA 12.24 40.65 - -</code></pre> -<p></p> -<caption> -Hierarchical mkin fit of the SFO model with error model tc -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.2 -R version used for fitting: 4.2.2 -Date of fit: Thu Jan 5 08:19:07 2023 -Date of summary: Thu Jan 5 08:20:11 2023 - -Equations: -d_DMTA/dt = - k_DMTA * DMTA - -Data: -155 observations of 1 variable(s) grouped in 6 datasets - -Model predictions using solution type analytical - -Fitted in 2.441 s -Using 300, 100 iterations and 9 chains - -Variance model: Two-component variance function - -Starting values for degradation parameters: - DMTA_0 k_DMTA -96.99175 0.05603 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - DMTA_0 k_DMTA -DMTA_0 96.99 0 -k_DMTA 0.00 1 - -Starting values for error model parameters: -a.1 b.1 - 1 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 798.3 797.1 -393.2 - -Optimised parameters: - est. lower upper -DMTA_0 97.271822 95.703157 98.84049 -k_DMTA 0.056638 0.029110 0.08417 -a.1 2.660081 2.230398 3.08976 -b.1 0.001665 -0.006911 0.01024 -SD.DMTA_0 1.545520 0.145035 2.94601 -SD.k_DMTA 0.606422 0.262274 0.95057 - -Correlation: - DMTA_0 -k_DMTA 0.0169 - -Random effects: - est. lower upper -SD.DMTA_0 1.5455 0.1450 2.9460 -SD.k_DMTA 0.6064 0.2623 0.9506 - -Variance model: - est. lower upper -a.1 2.660081 2.230398 3.08976 -b.1 0.001665 -0.006911 0.01024 - -Estimated disappearance times: - DT50 DT90 -DMTA 12.24 40.65 - -</code></pre> -<p></p> -<caption> -Hierarchical mkin fit of the FOMC model with error model const -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.2 -R version used for fitting: 4.2.2 -Date of fit: Thu Jan 5 08:19:06 2023 -Date of summary: Thu Jan 5 08:20:11 2023 - -Equations: -d_DMTA/dt = - (alpha/beta) * 1/((time/beta) + 1) * DMTA - -Data: -155 observations of 1 variable(s) grouped in 6 datasets - -Model predictions using solution type analytical - -Fitted in 1.156 s -Using 300, 100 iterations and 9 chains - -Variance model: Constant variance - -Starting values for degradation parameters: - DMTA_0 alpha beta - 98.292 9.909 156.341 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - DMTA_0 alpha beta -DMTA_0 98.29 0 0 -alpha 0.00 1 0 -beta 0.00 0 1 - -Starting values for error model parameters: -a.1 - 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 734.2 732.7 -360.1 - -Optimised parameters: - est. lower upper -DMTA_0 98.3435 96.9033 99.784 -alpha 7.2007 2.5889 11.812 -beta 112.8746 34.8816 190.868 -a.1 2.0459 1.8054 2.286 -SD.DMTA_0 1.4795 0.2717 2.687 -SD.alpha 0.6396 0.1509 1.128 -SD.beta 0.6874 0.1587 1.216 - -Correlation: - DMTA_0 alpha -alpha -0.1125 -beta -0.1227 0.3632 - -Random effects: - est. lower upper -SD.DMTA_0 1.4795 0.2717 2.687 -SD.alpha 0.6396 0.1509 1.128 -SD.beta 0.6874 0.1587 1.216 - -Variance model: - est. lower upper -a.1 2.046 1.805 2.286 - -Estimated disappearance times: - DT50 DT90 DT50back -DMTA 11.41 42.53 12.8 - -</code></pre> -<p></p> -<caption> -Hierarchical mkin fit of the FOMC model with error model tc -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.2 -R version used for fitting: 4.2.2 -Date of fit: Thu Jan 5 08:19:07 2023 -Date of summary: Thu Jan 5 08:20:11 2023 - -Equations: -d_DMTA/dt = - (alpha/beta) * 1/((time/beta) + 1) * DMTA - -Data: -155 observations of 1 variable(s) grouped in 6 datasets - -Model predictions using solution type analytical - -Fitted in 2.729 s -Using 300, 100 iterations and 9 chains - -Variance model: Two-component variance function - -Starting values for degradation parameters: -DMTA_0 alpha beta -98.772 4.663 92.597 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - DMTA_0 alpha beta -DMTA_0 98.77 0 0 -alpha 0.00 1 0 -beta 0.00 0 1 - -Starting values for error model parameters: -a.1 b.1 - 1 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 720.4 718.8 -352.2 - -Optimised parameters: - est. lower upper -DMTA_0 98.99136 97.26011 100.72261 -alpha 5.86312 2.57485 9.15138 -beta 88.55571 29.20889 147.90254 -a.1 1.51063 1.24384 1.77741 -b.1 0.02824 0.02040 0.03609 -SD.DMTA_0 1.57436 -0.04867 3.19739 -SD.alpha 0.59871 0.17132 1.02611 -SD.beta 0.72994 0.22849 1.23139 - -Correlation: - DMTA_0 alpha -alpha -0.1363 -beta -0.1414 0.2542 - -Random effects: - est. lower upper -SD.DMTA_0 1.5744 -0.04867 3.197 -SD.alpha 0.5987 0.17132 1.026 -SD.beta 0.7299 0.22849 1.231 - -Variance model: - est. lower upper -a.1 1.51063 1.2438 1.77741 -b.1 0.02824 0.0204 0.03609 - -Estimated disappearance times: - DT50 DT90 DT50back -DMTA 11.11 42.6 12.82 - -</code></pre> -<p></p> -<caption> -Hierarchical mkin fit of the DFOP model with error model const -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.2 -R version used for fitting: 4.2.2 -Date of fit: Thu Jan 5 08:19:07 2023 -Date of summary: Thu Jan 5 08:20:11 2023 - -Equations: -d_DMTA/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * - time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) - * DMTA - -Data: -155 observations of 1 variable(s) grouped in 6 datasets - -Model predictions using solution type analytical - -Fitted in 2.007 s -Using 300, 100 iterations and 9 chains - -Variance model: Constant variance - -Starting values for degradation parameters: - DMTA_0 k1 k2 g -98.64383 0.09211 0.02999 0.76814 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - DMTA_0 k1 k2 g -DMTA_0 98.64 0 0 0 -k1 0.00 1 0 0 -k2 0.00 0 1 0 -g 0.00 0 0 1 - -Starting values for error model parameters: -a.1 - 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 711.8 710 -346.9 - -Optimised parameters: - est. lower upper -DMTA_0 98.092481 96.573898 99.61106 -k1 0.062499 0.030336 0.09466 -k2 0.009065 -0.005133 0.02326 -g 0.948967 0.862079 1.03586 -a.1 1.821671 1.604774 2.03857 -SD.DMTA_0 1.677785 0.472066 2.88350 -SD.k1 0.634962 0.270788 0.99914 -SD.k2 1.033498 -0.205994 2.27299 -SD.g 1.710046 0.428642 2.99145 - -Correlation: - DMTA_0 k1 k2 -k1 0.0246 -k2 0.0491 0.0953 -g -0.0552 -0.0889 -0.4795 - -Random effects: - est. lower upper -SD.DMTA_0 1.678 0.4721 2.8835 -SD.k1 0.635 0.2708 0.9991 -SD.k2 1.033 -0.2060 2.2730 -SD.g 1.710 0.4286 2.9914 - -Variance model: - est. lower upper -a.1 1.822 1.605 2.039 - -Estimated disappearance times: - DT50 DT90 DT50back DT50_k1 DT50_k2 -DMTA 11.79 42.8 12.88 11.09 76.46 - -</code></pre> -<p></p> -<caption> -Hierarchical mkin fit of the DFOP model with error model tc -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.2 -R version used for fitting: 4.2.2 -Date of fit: Thu Jan 5 08:19:08 2023 -Date of summary: Thu Jan 5 08:20:11 2023 - -Equations: -d_DMTA/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * - time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) - * DMTA - -Data: -155 observations of 1 variable(s) grouped in 6 datasets - -Model predictions using solution type analytical - -Fitted in 3.033 s -Using 300, 100 iterations and 9 chains - -Variance model: Two-component variance function - -Starting values for degradation parameters: - DMTA_0 k1 k2 g -98.759266 0.087034 0.009933 0.930827 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - DMTA_0 k1 k2 g -DMTA_0 98.76 0 0 0 -k1 0.00 1 0 0 -k2 0.00 0 1 0 -g 0.00 0 0 1 - -Starting values for error model parameters: -a.1 b.1 - 1 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 665.5 663.4 -322.8 - -Optimised parameters: - est. lower upper -DMTA_0 98.377019 96.447952 100.30609 -k1 0.064843 0.034607 0.09508 -k2 0.008895 0.006368 0.01142 -g 0.949696 0.903815 0.99558 -a.1 1.065241 0.865754 1.26473 -b.1 0.029340 0.022336 0.03634 -SD.DMTA_0 2.007754 0.387982 3.62753 -SD.k1 0.580473 0.250286 0.91066 -SD.k2 0.006105 -4.920337 4.93255 -SD.g 1.097149 0.412779 1.78152 - -Correlation: - DMTA_0 k1 k2 -k1 0.0235 -k2 0.0595 0.0424 -g -0.0470 -0.0278 -0.2731 - -Random effects: - est. lower upper -SD.DMTA_0 2.007754 0.3880 3.6275 -SD.k1 0.580473 0.2503 0.9107 -SD.k2 0.006105 -4.9203 4.9325 -SD.g 1.097149 0.4128 1.7815 - -Variance model: - est. lower upper -a.1 1.06524 0.86575 1.26473 -b.1 0.02934 0.02234 0.03634 - -Estimated disappearance times: - DT50 DT90 DT50back DT50_k1 DT50_k2 -DMTA 11.36 41.32 12.44 10.69 77.92 - -</code></pre> -<p></p> -<caption> -Hierarchical mkin fit of the HS model with error model const -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.2 -R version used for fitting: 4.2.2 -Date of fit: Thu Jan 5 08:19:07 2023 -Date of summary: Thu Jan 5 08:20:11 2023 - -Equations: -d_DMTA/dt = - ifelse(time <= tb, k1, k2) * DMTA - -Data: -155 observations of 1 variable(s) grouped in 6 datasets - -Model predictions using solution type analytical - -Fitted in 2.004 s -Using 300, 100 iterations and 9 chains - -Variance model: Constant variance - -Starting values for degradation parameters: - DMTA_0 k1 k2 tb -97.82176 0.06931 0.02997 11.13945 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - DMTA_0 k1 k2 tb -DMTA_0 97.82 0 0 0 -k1 0.00 1 0 0 -k2 0.00 0 1 0 -tb 0.00 0 0 1 - -Starting values for error model parameters: -a.1 - 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 714 712.1 -348 - -Optimised parameters: - est. lower upper -DMTA_0 98.16102 96.47747 99.84456 -k1 0.07876 0.05261 0.10491 -k2 0.02227 0.01706 0.02747 -tb 13.99089 -7.40049 35.38228 -a.1 1.82305 1.60700 2.03910 -SD.DMTA_0 1.88413 0.56204 3.20622 -SD.k1 0.34292 0.10482 0.58102 -SD.k2 0.19851 0.01718 0.37985 -SD.tb 1.68168 0.58064 2.78272 - -Correlation: - DMTA_0 k1 k2 -k1 0.0142 -k2 0.0001 -0.0025 -tb 0.0165 -0.1256 -0.0301 - -Random effects: - est. lower upper -SD.DMTA_0 1.8841 0.56204 3.2062 -SD.k1 0.3429 0.10482 0.5810 -SD.k2 0.1985 0.01718 0.3798 -SD.tb 1.6817 0.58064 2.7827 - -Variance model: - est. lower upper -a.1 1.823 1.607 2.039 - -Estimated disappearance times: - DT50 DT90 DT50back DT50_k1 DT50_k2 -DMTA 8.801 67.91 20.44 8.801 31.13 - -</code></pre> -<p></p> -<caption> -Hierarchical mkin fit of the HS model with error model tc -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.2 -R version used for fitting: 4.2.2 -Date of fit: Thu Jan 5 08:19:08 2023 -Date of summary: Thu Jan 5 08:20:11 2023 - -Equations: -d_DMTA/dt = - ifelse(time <= tb, k1, k2) * DMTA - -Data: -155 observations of 1 variable(s) grouped in 6 datasets - -Model predictions using solution type analytical - -Fitted in 3.287 s -Using 300, 100 iterations and 9 chains - -Variance model: Two-component variance function - -Starting values for degradation parameters: - DMTA_0 k1 k2 tb -98.45190 0.07525 0.02576 19.19375 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - DMTA_0 k1 k2 tb -DMTA_0 98.45 0 0 0 -k1 0.00 1 0 0 -k2 0.00 0 1 0 -tb 0.00 0 0 1 - -Starting values for error model parameters: -a.1 b.1 - 1 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 667.1 665 -323.6 - -Optimised parameters: - est. lower upper -DMTA_0 97.76570 95.81350 99.71791 -k1 0.05855 0.03080 0.08630 -k2 0.02337 0.01664 0.03010 -tb 31.09638 29.38289 32.80987 -a.1 1.08835 0.88590 1.29080 -b.1 0.02964 0.02257 0.03671 -SD.DMTA_0 2.04877 0.42607 3.67147 -SD.k1 0.59166 0.25621 0.92711 -SD.k2 0.30698 0.09561 0.51835 -SD.tb 0.01274 -0.10914 0.13462 - -Correlation: - DMTA_0 k1 k2 -k1 0.0160 -k2 -0.0070 -0.0024 -tb -0.0668 -0.0103 -0.2013 - -Random effects: - est. lower upper -SD.DMTA_0 2.04877 0.42607 3.6715 -SD.k1 0.59166 0.25621 0.9271 -SD.k2 0.30698 0.09561 0.5183 -SD.tb 0.01274 -0.10914 0.1346 - -Variance model: - est. lower upper -a.1 1.08835 0.88590 1.29080 -b.1 0.02964 0.02257 0.03671 - -Estimated disappearance times: - DT50 DT90 DT50back DT50_k1 DT50_k2 -DMTA 11.84 51.71 15.57 11.84 29.66 - -</code></pre> -<p></p> -</div> -<div class="section level3"> -<h3 id="hierarchical-model-convergence-plots">Hierarchical model convergence plots<a class="anchor" aria-label="anchor" href="#hierarchical-model-convergence-plots"></a> -</h3> -<div class="figure" style="text-align: center"> -<img src="2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-sfo-const-1.png" alt="Convergence plot for the NLHM SFO fit with constant variance" width="864"><p class="caption"> -Convergence plot for the NLHM SFO fit with constant variance -</p> -</div> -<div class="figure" style="text-align: center"> -<img src="2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-sfo-tc-1.png" alt="Convergence plot for the NLHM SFO fit with two-component error" width="864"><p class="caption"> -Convergence plot for the NLHM SFO fit with two-component error -</p> -</div> -<div class="figure" style="text-align: center"> -<img src="2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-fomc-const-1.png" alt="Convergence plot for the NLHM FOMC fit with constant variance" width="864"><p class="caption"> -Convergence plot for the NLHM FOMC fit with constant variance -</p> -</div> -<div class="figure" style="text-align: center"> -<img src="2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-fomc-tc-1.png" alt="Convergence plot for the NLHM FOMC fit with two-component error" width="864"><p class="caption"> -Convergence plot for the NLHM FOMC fit with two-component error -</p> -</div> -<div class="figure" style="text-align: center"> -<img src="2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-dfop-const-1.png" alt="Convergence plot for the NLHM DFOP fit with constant variance" width="864"><p class="caption"> -Convergence plot for the NLHM DFOP fit with constant variance -</p> -</div> -<div class="figure" style="text-align: center"> -<img src="2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-dfop-tc-1.png" alt="Convergence plot for the NLHM DFOP fit with two-component error" width="864"><p class="caption"> -Convergence plot for the NLHM DFOP fit with two-component error -</p> -</div> -<div class="figure" style="text-align: center"> -<img src="2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-hs-const-1.png" alt="Convergence plot for the NLHM HS fit with constant variance" width="864"><p class="caption"> -Convergence plot for the NLHM HS fit with constant variance -</p> -</div> -<div class="figure" style="text-align: center"> -<img src="2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-hs-tc-1.png" alt="Convergence plot for the NLHM HS fit with two-component error" width="864"><p class="caption"> -Convergence plot for the NLHM HS fit with two-component error -</p> -</div> -</div> -<div class="section level3"> -<h3 id="session-info">Session info<a class="anchor" aria-label="anchor" href="#session-info"></a> -</h3> -<pre><code>R version 4.2.2 Patched (2022-11-10 r83330) -Platform: x86_64-pc-linux-gnu (64-bit) -Running under: Debian GNU/Linux bookworm/sid - -Matrix products: default -BLAS: /usr/lib/x86_64-linux-gnu/openblas-serial/libblas.so.3 -LAPACK: /usr/lib/x86_64-linux-gnu/openblas-serial/libopenblas-r0.3.21.so - -locale: - [1] LC_CTYPE=de_DE.UTF-8 LC_NUMERIC=C - [3] LC_TIME=de_DE.UTF-8 LC_COLLATE=de_DE.UTF-8 - [5] LC_MONETARY=de_DE.UTF-8 LC_MESSAGES=de_DE.UTF-8 - [7] LC_PAPER=de_DE.UTF-8 LC_NAME=C - [9] LC_ADDRESS=C LC_TELEPHONE=C -[11] LC_MEASUREMENT=de_DE.UTF-8 LC_IDENTIFICATION=C - -attached base packages: -[1] parallel stats graphics grDevices utils datasets methods -[8] base - -other attached packages: -[1] saemix_3.2 npde_3.3 knitr_1.41 mkin_1.2.2 - -loaded via a namespace (and not attached): - [1] deSolve_1.34 zoo_1.8-11 tidyselect_1.2.0 xfun_0.35 - [5] bslib_0.4.2 purrr_1.0.0 lattice_0.20-45 colorspace_2.0-3 - [9] vctrs_0.5.1 generics_0.1.3 htmltools_0.5.4 yaml_2.3.6 -[13] utf8_1.2.2 rlang_1.0.6 pkgdown_2.0.7 jquerylib_0.1.4 -[17] pillar_1.8.1 glue_1.6.2 DBI_1.1.3 lifecycle_1.0.3 -[21] stringr_1.5.0 munsell_0.5.0 gtable_0.3.1 ragg_1.2.4 -[25] codetools_0.2-18 memoise_2.0.1 evaluate_0.19 fastmap_1.1.0 -[29] lmtest_0.9-40 fansi_1.0.3 highr_0.9 scales_1.2.1 -[33] cachem_1.0.6 desc_1.4.2 jsonlite_1.8.4 systemfonts_1.0.4 -[37] fs_1.5.2 textshaping_0.3.6 gridExtra_2.3 ggplot2_3.4.0 -[41] digest_0.6.31 stringi_1.7.8 dplyr_1.0.10 grid_4.2.2 -[45] rprojroot_2.0.3 cli_3.5.0 tools_4.2.2 magrittr_2.0.3 -[49] sass_0.4.4 tibble_3.1.8 pkgconfig_2.0.3 assertthat_0.2.1 -[53] rmarkdown_2.19 R6_2.5.1 mclust_6.0.0 nlme_3.1-161 -[57] compiler_4.2.2 </code></pre> -</div> -</div> - </div> - - <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar"> - - <nav id="toc" data-toggle="toc"><h2 data-toc-skip>Contents</h2> - </nav> -</div> - -</div> - - - - <footer><div class="copyright"> - <p></p> -<p>Developed by Johannes Ranke.</p> -</div> - -<div class="pkgdown"> - <p></p> -<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p> -</div> - - </footer> -</div> - - - - - - - </body> -</html> diff --git a/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-dfop-const-1.png b/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-dfop-const-1.png Binary files differdeleted file mode 100644 index 4f87b956..00000000 --- a/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-dfop-const-1.png +++ /dev/null diff --git 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weighted average concentrations with mkin</a> - </li> - <li> - <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> - </li> - </ul> -</li> -<li> - <a href="../news/index.html">News</a> -</li> - </ul> -<ul class="nav navbar-nav navbar-right"> -<li> - <a href="https://github.com/jranke/mkin/" class="external-link"> - <span class="fab fa-github fa-lg"></span> - - </a> -</li> - </ul> -</div> -<!--/.nav-collapse --> - </div> -<!--/.container --> -</div> -<!--/.navbar --> - - - - </header><div class="row"> - <div class="col-md-9 contents"> - <div class="page-header toc-ignore"> - <h1 data-toc-skip>Example evaluation of FOCUS Example Dataset -D</h1> - <h4 data-toc-skip class="author">Johannes -Ranke</h4> - - <h4 data-toc-skip class="date">Last change 31 January 2019 -(rebuilt 2023-04-16)</h4> - - <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/FOCUS_D.rmd" class="external-link"><code>vignettes/FOCUS_D.rmd</code></a></small> - <div class="hidden name"><code>FOCUS_D.rmd</code></div> - - </div> - - - -<p>This is just a very simple vignette showing how to fit a degradation -model for a parent compound with one transformation product using -<code>mkin</code>. After loading the library we look at the data. We -have observed concentrations in the column named <code>value</code> at -the times specified in column <code>time</code> for the two observed -variables named <code>parent</code> and <code>m1</code>.</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>, quietly <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">FOCUS_2006_D</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## name time value</span></span> -<span><span class="co">## 1 parent 0 99.46</span></span> -<span><span class="co">## 2 parent 0 102.04</span></span> -<span><span class="co">## 3 parent 1 93.50</span></span> -<span><span class="co">## 4 parent 1 92.50</span></span> -<span><span class="co">## 5 parent 3 63.23</span></span> -<span><span class="co">## 6 parent 3 68.99</span></span> -<span><span class="co">## 7 parent 7 52.32</span></span> -<span><span class="co">## 8 parent 7 55.13</span></span> -<span><span class="co">## 9 parent 14 27.27</span></span> -<span><span class="co">## 10 parent 14 26.64</span></span> -<span><span class="co">## 11 parent 21 11.50</span></span> -<span><span class="co">## 12 parent 21 11.64</span></span> -<span><span class="co">## 13 parent 35 2.85</span></span> -<span><span class="co">## 14 parent 35 2.91</span></span> -<span><span class="co">## 15 parent 50 0.69</span></span> -<span><span class="co">## 16 parent 50 0.63</span></span> -<span><span class="co">## 17 parent 75 0.05</span></span> -<span><span class="co">## 18 parent 75 0.06</span></span> -<span><span class="co">## 19 parent 100 NA</span></span> -<span><span class="co">## 20 parent 100 NA</span></span> -<span><span class="co">## 21 parent 120 NA</span></span> -<span><span class="co">## 22 parent 120 NA</span></span> -<span><span class="co">## 23 m1 0 0.00</span></span> -<span><span class="co">## 24 m1 0 0.00</span></span> -<span><span class="co">## 25 m1 1 4.84</span></span> -<span><span class="co">## 26 m1 1 5.64</span></span> -<span><span class="co">## 27 m1 3 12.91</span></span> -<span><span class="co">## 28 m1 3 12.96</span></span> -<span><span class="co">## 29 m1 7 22.97</span></span> -<span><span class="co">## 30 m1 7 24.47</span></span> -<span><span class="co">## 31 m1 14 41.69</span></span> -<span><span class="co">## 32 m1 14 33.21</span></span> -<span><span class="co">## 33 m1 21 44.37</span></span> -<span><span class="co">## 34 m1 21 46.44</span></span> -<span><span class="co">## 35 m1 35 41.22</span></span> -<span><span class="co">## 36 m1 35 37.95</span></span> -<span><span class="co">## 37 m1 50 41.19</span></span> -<span><span class="co">## 38 m1 50 40.01</span></span> -<span><span class="co">## 39 m1 75 40.09</span></span> -<span><span class="co">## 40 m1 75 33.85</span></span> -<span><span class="co">## 41 m1 100 31.04</span></span> -<span><span class="co">## 42 m1 100 33.13</span></span> -<span><span class="co">## 43 m1 120 25.15</span></span> -<span><span class="co">## 44 m1 120 33.31</span></span></code></pre> -<p>Next we specify the degradation model: The parent compound degrades -with simple first-order kinetics (SFO) to one metabolite named m1, which -also degrades with SFO kinetics.</p> -<p>The call to mkinmod returns a degradation model. The differential -equations represented in R code can be found in the character vector -<code>$diffs</code> of the <code>mkinmod</code> object. If a C compiler -(gcc) is installed and functional, the differential equation model will -be compiled from auto-generated C code.</p> -<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">SFO_SFO</span> <span class="op"><-</span> <span class="fu"><a href="../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>parent <span class="op">=</span> <span class="fu"><a href="../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"m1"</span><span class="op">)</span>, m1 <span class="op">=</span> <span class="fu"><a href="../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre> -<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">SFO_SFO</span><span class="op">$</span><span class="va">diffs</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## parent </span></span> -<span><span class="co">## "d_parent = - k_parent * parent" </span></span> -<span><span class="co">## m1 </span></span> -<span><span class="co">## "d_m1 = + f_parent_to_m1 * k_parent * parent - k_m1 * m1"</span></span></code></pre> -<p>We do the fitting without progress report -(<code>quiet = TRUE</code>).</p> -<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">fit</span> <span class="op"><-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOCUS_2006_D</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, quiet = TRUE): Observations with</span></span> -<span><span class="co">## value of zero were removed from the data</span></span></code></pre> -<p>A plot of the fit including a residual plot for both observed -variables is obtained using the <code>plot_sep</code> method for -<code>mkinfit</code> objects, which shows separate graphs for all -compounds and their residuals.</p> -<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">fit</span>, lpos <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">"topright"</span>, <span class="st">"bottomright"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_D_files/figure-html/plot-1.png" width="768"></p> -<p>Confidence intervals for the parameter estimates are obtained using -the <code>mkinparplot</code> function.</p> -<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../reference/mkinparplot.html">mkinparplot</a></span><span class="op">(</span><span class="va">fit</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_D_files/figure-html/plot_2-1.png" width="768"></p> -<p>A comprehensive report of the results is obtained using the -<code>summary</code> method for <code>mkinfit</code> objects.</p> -<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">fit</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## mkin version used for fitting: 1.2.3 </span></span> -<span><span class="co">## R version used for fitting: 4.2.3 </span></span> -<span><span class="co">## Date of fit: Sun Apr 16 08:35:12 2023 </span></span> -<span><span class="co">## Date of summary: Sun Apr 16 08:35:12 2023 </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Equations:</span></span> -<span><span class="co">## d_parent/dt = - k_parent * parent</span></span> -<span><span class="co">## d_m1/dt = + f_parent_to_m1 * k_parent * parent - k_m1 * m1</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Model predictions using solution type analytical </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Fitted using 401 model solutions performed in 0.05 s</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Error model: Constant variance </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Error model algorithm: OLS </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Starting values for parameters to be optimised:</span></span> -<span><span class="co">## value type</span></span> -<span><span class="co">## parent_0 100.7500 state</span></span> -<span><span class="co">## k_parent 0.1000 deparm</span></span> -<span><span class="co">## k_m1 0.1001 deparm</span></span> -<span><span class="co">## f_parent_to_m1 0.5000 deparm</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Starting values for the transformed parameters actually optimised:</span></span> -<span><span class="co">## value lower upper</span></span> -<span><span class="co">## parent_0 100.750000 -Inf Inf</span></span> -<span><span class="co">## log_k_parent -2.302585 -Inf Inf</span></span> -<span><span class="co">## log_k_m1 -2.301586 -Inf Inf</span></span> -<span><span class="co">## f_parent_qlogis 0.000000 -Inf Inf</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Fixed parameter values:</span></span> -<span><span class="co">## value type</span></span> -<span><span class="co">## m1_0 0 state</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Warning(s): </span></span> -<span><span class="co">## Observations with value of zero were removed from the data</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Results:</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## AIC BIC logLik</span></span> -<span><span class="co">## 204.4486 212.6365 -97.22429</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Optimised, transformed parameters with symmetric confidence intervals:</span></span> -<span><span class="co">## Estimate Std. Error Lower Upper</span></span> -<span><span class="co">## parent_0 99.60000 1.57000 96.4000 102.8000</span></span> -<span><span class="co">## log_k_parent -2.31600 0.04087 -2.3990 -2.2330</span></span> -<span><span class="co">## log_k_m1 -5.24700 0.13320 -5.5180 -4.9770</span></span> -<span><span class="co">## f_parent_qlogis 0.05792 0.08926 -0.1237 0.2395</span></span> -<span><span class="co">## sigma 3.12600 0.35850 2.3960 3.8550</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Parameter correlation:</span></span> -<span><span class="co">## parent_0 log_k_parent log_k_m1 f_parent_qlogis sigma</span></span> -<span><span class="co">## parent_0 1.000e+00 5.174e-01 -1.688e-01 -5.471e-01 -1.172e-06</span></span> -<span><span class="co">## log_k_parent 5.174e-01 1.000e+00 -3.263e-01 -5.426e-01 -8.483e-07</span></span> -<span><span class="co">## log_k_m1 -1.688e-01 -3.263e-01 1.000e+00 7.478e-01 8.205e-07</span></span> -<span><span class="co">## f_parent_qlogis -5.471e-01 -5.426e-01 7.478e-01 1.000e+00 1.305e-06</span></span> -<span><span class="co">## sigma -1.172e-06 -8.483e-07 8.205e-07 1.305e-06 1.000e+00</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Backtransformed parameters:</span></span> -<span><span class="co">## Confidence intervals for internally transformed parameters are asymmetric.</span></span> -<span><span class="co">## t-test (unrealistically) based on the assumption of normal distribution</span></span> -<span><span class="co">## for estimators of untransformed parameters.</span></span> -<span><span class="co">## Estimate t value Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 99.600000 63.430 2.298e-36 96.400000 1.028e+02</span></span> -<span><span class="co">## k_parent 0.098700 24.470 4.955e-23 0.090820 1.073e-01</span></span> -<span><span class="co">## k_m1 0.005261 7.510 6.165e-09 0.004012 6.898e-03</span></span> -<span><span class="co">## f_parent_to_m1 0.514500 23.070 3.104e-22 0.469100 5.596e-01</span></span> -<span><span class="co">## sigma 3.126000 8.718 2.235e-10 2.396000 3.855e+00</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## FOCUS Chi2 error levels in percent:</span></span> -<span><span class="co">## err.min n.optim df</span></span> -<span><span class="co">## All data 6.398 4 15</span></span> -<span><span class="co">## parent 6.459 2 7</span></span> -<span><span class="co">## m1 4.690 2 8</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Resulting formation fractions:</span></span> -<span><span class="co">## ff</span></span> -<span><span class="co">## parent_m1 0.5145</span></span> -<span><span class="co">## parent_sink 0.4855</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Estimated disappearance times:</span></span> -<span><span class="co">## DT50 DT90</span></span> -<span><span class="co">## parent 7.023 23.33</span></span> -<span><span class="co">## m1 131.761 437.70</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Data:</span></span> -<span><span class="co">## time variable observed predicted residual</span></span> -<span><span class="co">## 0 parent 99.46 99.59848 -1.385e-01</span></span> -<span><span class="co">## 0 parent 102.04 99.59848 2.442e+00</span></span> -<span><span class="co">## 1 parent 93.50 90.23787 3.262e+00</span></span> -<span><span class="co">## 1 parent 92.50 90.23787 2.262e+00</span></span> -<span><span class="co">## 3 parent 63.23 74.07319 -1.084e+01</span></span> -<span><span class="co">## 3 parent 68.99 74.07319 -5.083e+00</span></span> -<span><span class="co">## 7 parent 52.32 49.91207 2.408e+00</span></span> -<span><span class="co">## 7 parent 55.13 49.91207 5.218e+00</span></span> -<span><span class="co">## 14 parent 27.27 25.01258 2.257e+00</span></span> -<span><span class="co">## 14 parent 26.64 25.01258 1.627e+00</span></span> -<span><span class="co">## 21 parent 11.50 12.53462 -1.035e+00</span></span> -<span><span class="co">## 21 parent 11.64 12.53462 -8.946e-01</span></span> -<span><span class="co">## 35 parent 2.85 3.14787 -2.979e-01</span></span> -<span><span class="co">## 35 parent 2.91 3.14787 -2.379e-01</span></span> -<span><span class="co">## 50 parent 0.69 0.71624 -2.624e-02</span></span> -<span><span class="co">## 50 parent 0.63 0.71624 -8.624e-02</span></span> -<span><span class="co">## 75 parent 0.05 0.06074 -1.074e-02</span></span> -<span><span class="co">## 75 parent 0.06 0.06074 -7.382e-04</span></span> -<span><span class="co">## 1 m1 4.84 4.80296 3.704e-02</span></span> -<span><span class="co">## 1 m1 5.64 4.80296 8.370e-01</span></span> -<span><span class="co">## 3 m1 12.91 13.02400 -1.140e-01</span></span> -<span><span class="co">## 3 m1 12.96 13.02400 -6.400e-02</span></span> -<span><span class="co">## 7 m1 22.97 25.04476 -2.075e+00</span></span> -<span><span class="co">## 7 m1 24.47 25.04476 -5.748e-01</span></span> -<span><span class="co">## 14 m1 41.69 36.69003 5.000e+00</span></span> -<span><span class="co">## 14 m1 33.21 36.69003 -3.480e+00</span></span> -<span><span class="co">## 21 m1 44.37 41.65310 2.717e+00</span></span> -<span><span class="co">## 21 m1 46.44 41.65310 4.787e+00</span></span> -<span><span class="co">## 35 m1 41.22 43.31313 -2.093e+00</span></span> -<span><span class="co">## 35 m1 37.95 43.31313 -5.363e+00</span></span> -<span><span class="co">## 50 m1 41.19 41.21832 -2.832e-02</span></span> -<span><span class="co">## 50 m1 40.01 41.21832 -1.208e+00</span></span> -<span><span class="co">## 75 m1 40.09 36.44704 3.643e+00</span></span> -<span><span class="co">## 75 m1 33.85 36.44704 -2.597e+00</span></span> -<span><span class="co">## 100 m1 31.04 31.98162 -9.416e-01</span></span> -<span><span class="co">## 100 m1 33.13 31.98162 1.148e+00</span></span> -<span><span class="co">## 120 m1 25.15 28.78984 -3.640e+00</span></span> -<span><span class="co">## 120 m1 33.31 28.78984 4.520e+00</span></span></code></pre> - </div> - - <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar"> - - </div> - -</div> - - - - <footer><div class="copyright"> - <p></p> -<p>Developed by Johannes Ranke.</p> -</div> - -<div class="pkgdown"> - <p></p> -<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p> -</div> - - </footer> -</div> - - - - - - - </body> -</html> diff --git a/docs/dev/articles/FOCUS_D_files/accessible-code-block-0.0.1/empty-anchor.js b/docs/dev/articles/FOCUS_D_files/accessible-code-block-0.0.1/empty-anchor.js deleted file mode 100644 index ca349fd6..00000000 --- a/docs/dev/articles/FOCUS_D_files/accessible-code-block-0.0.1/empty-anchor.js +++ /dev/null @@ -1,15 +0,0 @@ -// Hide empty <a> tag within highlighted CodeBlock for screen reader accessibility (see https://github.com/jgm/pandoc/issues/6352#issuecomment-626106786) --> -// 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- </div> - - - -<div class="section level2"> -<h2 id="laboratory-data-l1">Laboratory Data L1<a class="anchor" aria-label="anchor" href="#laboratory-data-l1"></a> -</h2> -<p>The following code defines example dataset L1 from the FOCUS kinetics -report, p. 284:</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="st"><a href="https://pkgdown.jrwb.de/mkin/">"mkin"</a></span>, quietly <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<span><span class="va">FOCUS_2006_L1</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span></span> -<span> t <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/rep.html" class="external-link">rep</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="fl">0</span>, <span class="fl">1</span>, <span class="fl">2</span>, <span class="fl">3</span>, <span class="fl">5</span>, <span class="fl">7</span>, <span class="fl">14</span>, <span class="fl">21</span>, <span class="fl">30</span><span class="op">)</span>, each <span class="op">=</span> <span class="fl">2</span><span class="op">)</span>,</span> -<span> parent <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">88.3</span>, <span class="fl">91.4</span>, <span class="fl">85.6</span>, <span class="fl">84.5</span>, <span class="fl">78.9</span>, <span class="fl">77.6</span>,</span> -<span> <span class="fl">72.0</span>, <span class="fl">71.9</span>, <span class="fl">50.3</span>, <span class="fl">59.4</span>, <span class="fl">47.0</span>, <span class="fl">45.1</span>,</span> -<span> <span class="fl">27.7</span>, <span class="fl">27.3</span>, <span class="fl">10.0</span>, <span class="fl">10.4</span>, <span class="fl">2.9</span>, <span class="fl">4.0</span><span class="op">)</span><span class="op">)</span></span> -<span><span class="va">FOCUS_2006_L1_mkin</span> <span class="op"><-</span> <span class="fu"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span><span class="op">(</span><span class="va">FOCUS_2006_L1</span><span class="op">)</span></span></code></pre></div> -<p>Here we use the assumptions of simple first order (SFO), the case of -declining rate constant over time (FOMC) and the case of two different -phases of the kinetics (DFOP). For a more detailed discussion of the -models, please see the FOCUS kinetics report.</p> -<p>Since mkin version 0.9-32 (July 2014), we can use shorthand notation -like <code>"SFO"</code> for parent only degradation models. The -following two lines fit the model and produce the summary report of the -model fit. This covers the numerical analysis given in the FOCUS -report.</p> -<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">m.L1.SFO</span> <span class="op"><-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="va">FOCUS_2006_L1_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.L1.SFO</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## mkin version used for fitting: 1.2.3 </span></span> -<span><span class="co">## R version used for fitting: 4.2.3 </span></span> -<span><span class="co">## Date of fit: Sun Apr 16 08:35:14 2023 </span></span> -<span><span class="co">## Date of summary: Sun Apr 16 08:35:14 2023 </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Equations:</span></span> -<span><span class="co">## d_parent/dt = - k_parent * parent</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Model predictions using solution type analytical </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Fitted using 133 model solutions performed in 0.011 s</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Error model: Constant variance </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Error model algorithm: OLS </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Starting values for parameters to be optimised:</span></span> -<span><span class="co">## value type</span></span> -<span><span class="co">## parent_0 89.85 state</span></span> -<span><span class="co">## k_parent 0.10 deparm</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Starting values for the transformed parameters actually optimised:</span></span> -<span><span class="co">## value lower upper</span></span> -<span><span class="co">## parent_0 89.850000 -Inf Inf</span></span> -<span><span class="co">## log_k_parent -2.302585 -Inf Inf</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Fixed parameter values:</span></span> -<span><span class="co">## None</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Results:</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## AIC BIC logLik</span></span> -<span><span class="co">## 93.88778 96.5589 -43.94389</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Optimised, transformed parameters with symmetric confidence intervals:</span></span> -<span><span class="co">## Estimate Std. Error Lower Upper</span></span> -<span><span class="co">## parent_0 92.470 1.28200 89.740 95.200</span></span> -<span><span class="co">## log_k_parent -2.347 0.03763 -2.428 -2.267</span></span> -<span><span class="co">## sigma 2.780 0.46330 1.792 3.767</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Parameter correlation:</span></span> -<span><span class="co">## parent_0 log_k_parent sigma</span></span> -<span><span class="co">## parent_0 1.000e+00 6.186e-01 -1.516e-09</span></span> -<span><span class="co">## log_k_parent 6.186e-01 1.000e+00 -3.124e-09</span></span> -<span><span class="co">## sigma -1.516e-09 -3.124e-09 1.000e+00</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Backtransformed parameters:</span></span> -<span><span class="co">## Confidence intervals for internally transformed parameters are asymmetric.</span></span> -<span><span class="co">## t-test (unrealistically) based on the assumption of normal distribution</span></span> -<span><span class="co">## for estimators of untransformed parameters.</span></span> -<span><span class="co">## Estimate t value Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 92.47000 72.13 8.824e-21 89.74000 95.2000</span></span> -<span><span class="co">## k_parent 0.09561 26.57 2.487e-14 0.08824 0.1036</span></span> -<span><span class="co">## sigma 2.78000 6.00 1.216e-05 1.79200 3.7670</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## FOCUS Chi2 error levels in percent:</span></span> -<span><span class="co">## err.min n.optim df</span></span> -<span><span class="co">## All data 3.424 2 7</span></span> -<span><span class="co">## parent 3.424 2 7</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Estimated disappearance times:</span></span> -<span><span class="co">## DT50 DT90</span></span> -<span><span class="co">## parent 7.249 24.08</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Data:</span></span> -<span><span class="co">## time variable observed predicted residual</span></span> -<span><span class="co">## 0 parent 88.3 92.471 -4.1710</span></span> -<span><span class="co">## 0 parent 91.4 92.471 -1.0710</span></span> -<span><span class="co">## 1 parent 85.6 84.039 1.5610</span></span> -<span><span class="co">## 1 parent 84.5 84.039 0.4610</span></span> -<span><span class="co">## 2 parent 78.9 76.376 2.5241</span></span> -<span><span class="co">## 2 parent 77.6 76.376 1.2241</span></span> -<span><span class="co">## 3 parent 72.0 69.412 2.5884</span></span> -<span><span class="co">## 3 parent 71.9 69.412 2.4884</span></span> -<span><span class="co">## 5 parent 50.3 57.330 -7.0301</span></span> -<span><span class="co">## 5 parent 59.4 57.330 2.0699</span></span> -<span><span class="co">## 7 parent 47.0 47.352 -0.3515</span></span> -<span><span class="co">## 7 parent 45.1 47.352 -2.2515</span></span> -<span><span class="co">## 14 parent 27.7 24.247 3.4528</span></span> -<span><span class="co">## 14 parent 27.3 24.247 3.0528</span></span> -<span><span class="co">## 21 parent 10.0 12.416 -2.4163</span></span> -<span><span class="co">## 21 parent 10.4 12.416 -2.0163</span></span> -<span><span class="co">## 30 parent 2.9 5.251 -2.3513</span></span> -<span><span class="co">## 30 parent 4.0 5.251 -1.2513</span></span></code></pre> -<p>A plot of the fit is obtained with the plot function for mkinfit -objects.</p> -<div class="sourceCode" id="cb4"><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">m.L1.SFO</span>, show_errmin <span class="op">=</span> <span class="cn">TRUE</span>, main <span class="op">=</span> <span class="st">"FOCUS L1 - SFO"</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_L_files/figure-html/unnamed-chunk-4-1.png" width="576"></p> -<p>The residual plot can be easily obtained by</p> -<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../reference/mkinresplot.html">mkinresplot</a></span><span class="op">(</span><span class="va">m.L1.SFO</span>, ylab <span class="op">=</span> <span class="st">"Observed"</span>, xlab <span class="op">=</span> <span class="st">"Time"</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_L_files/figure-html/unnamed-chunk-5-1.png" width="576"></p> -<p>For comparison, the FOMC model is fitted as well, and the <span class="math inline">\(\chi^2\)</span> error level is checked.</p> -<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">m.L1.FOMC</span> <span class="op"><-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"FOMC"</span>, <span class="va">FOCUS_2006_L1_mkin</span>, quiet<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Warning in mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet = TRUE): Optimisation did not converge:</span></span> -<span><span class="co">## false convergence (8)</span></span></code></pre> -<div class="sourceCode" id="cb8"><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">m.L1.FOMC</span>, show_errmin <span class="op">=</span> <span class="cn">TRUE</span>, main <span class="op">=</span> <span class="st">"FOCUS L1 - FOMC"</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_L_files/figure-html/unnamed-chunk-6-1.png" width="576"></p> -<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.L1.FOMC</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Warning in sqrt(diag(covar)): NaNs produced</span></span></code></pre> -<pre><code><span><span class="co">## Warning in sqrt(1/diag(V)): NaNs produced</span></span></code></pre> -<pre><code><span><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result</span></span> -<span><span class="co">## is doubtful</span></span></code></pre> -<pre><code><span><span class="co">## mkin version used for fitting: 1.2.3 </span></span> -<span><span class="co">## R version used for fitting: 4.2.3 </span></span> -<span><span class="co">## Date of fit: Sun Apr 16 08:35:14 2023 </span></span> -<span><span class="co">## Date of summary: Sun Apr 16 08:35:14 2023 </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Equations:</span></span> -<span><span class="co">## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Model predictions using solution type analytical </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Fitted using 369 model solutions performed in 0.025 s</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Error model: Constant variance </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Error model algorithm: OLS </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Starting values for parameters to be optimised:</span></span> -<span><span class="co">## value type</span></span> -<span><span class="co">## parent_0 89.85 state</span></span> -<span><span class="co">## alpha 1.00 deparm</span></span> -<span><span class="co">## beta 10.00 deparm</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Starting values for the transformed parameters actually optimised:</span></span> -<span><span class="co">## value lower upper</span></span> -<span><span class="co">## parent_0 89.850000 -Inf Inf</span></span> -<span><span class="co">## log_alpha 0.000000 -Inf Inf</span></span> -<span><span class="co">## log_beta 2.302585 -Inf Inf</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Fixed parameter values:</span></span> -<span><span class="co">## None</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Warning(s): </span></span> -<span><span class="co">## Optimisation did not converge:</span></span> -<span><span class="co">## false convergence (8)</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Results:</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## AIC BIC logLik</span></span> -<span><span class="co">## 95.88781 99.44929 -43.9439</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Optimised, transformed parameters with symmetric confidence intervals:</span></span> -<span><span class="co">## Estimate Std. Error Lower Upper</span></span> -<span><span class="co">## parent_0 92.47 1.2820 89.720 95.220</span></span> -<span><span class="co">## log_alpha 13.78 NaN NaN NaN</span></span> -<span><span class="co">## log_beta 16.13 NaN NaN NaN</span></span> -<span><span class="co">## sigma 2.78 0.4598 1.794 3.766</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Parameter correlation:</span></span> -<span><span class="co">## parent_0 log_alpha log_beta sigma</span></span> -<span><span class="co">## parent_0 1.0000000 NaN NaN 0.0001671</span></span> -<span><span class="co">## log_alpha NaN 1 NaN NaN</span></span> -<span><span class="co">## log_beta NaN NaN 1 NaN</span></span> -<span><span class="co">## sigma 0.0001671 NaN NaN 1.0000000</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Backtransformed parameters:</span></span> -<span><span class="co">## Confidence intervals for internally transformed parameters are asymmetric.</span></span> -<span><span class="co">## t-test (unrealistically) based on the assumption of normal distribution</span></span> -<span><span class="co">## for estimators of untransformed parameters.</span></span> -<span><span class="co">## Estimate t value Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 9.247e+01 NA NA 89.720 95.220</span></span> -<span><span class="co">## alpha 9.658e+05 NA NA NA NA</span></span> -<span><span class="co">## beta 1.010e+07 NA NA NA NA</span></span> -<span><span class="co">## sigma 2.780e+00 NA NA 1.794 3.766</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## FOCUS Chi2 error levels in percent:</span></span> -<span><span class="co">## err.min n.optim df</span></span> -<span><span class="co">## All data 3.619 3 6</span></span> -<span><span class="co">## parent 3.619 3 6</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Estimated disappearance times:</span></span> -<span><span class="co">## DT50 DT90 DT50back</span></span> -<span><span class="co">## parent 7.25 24.08 7.25</span></span></code></pre> -<p>We get a warning that the default optimisation algorithm -<code>Port</code> did not converge, which is an indication that the -model is overparameterised, <em>i.e.</em> contains too many parameters -that are ill-defined as a consequence.</p> -<p>And in fact, due to the higher number of parameters, and the lower -number of degrees of freedom of the fit, the <span class="math inline">\(\chi^2\)</span> error level is actually higher for -the FOMC model (3.6%) than for the SFO model (3.4%). Additionally, the -parameters <code>log_alpha</code> and <code>log_beta</code> internally -fitted in the model have excessive confidence intervals, that span more -than 25 orders of magnitude (!) when backtransformed to the scale of -<code>alpha</code> and <code>beta</code>. Also, the t-test for -significant difference from zero does not indicate such a significant -difference, with p-values greater than 0.1, and finally, the parameter -correlation of <code>log_alpha</code> and <code>log_beta</code> is -1.000, clearly indicating that the model is overparameterised.</p> -<p>The <span class="math inline">\(\chi^2\)</span> error levels reported -in Appendix 3 and Appendix 7 to the FOCUS kinetics report are rounded to -integer percentages and partly deviate by one percentage point from the -results calculated by mkin. The reason for this is not known. However, -mkin gives the same <span class="math inline">\(\chi^2\)</span> error -levels as the kinfit package and the calculation routines of the kinfit -package have been extensively compared to the results obtained by the -KinGUI software, as documented in the kinfit package vignette. KinGUI -was the first widely used standard package in this field. Also, the -calculation of <span class="math inline">\(\chi^2\)</span> error levels -was compared with KinGUII, CAKE and DegKin manager in a project -sponsored by the German Umweltbundesamt <span class="citation">(Ranke -2014)</span>.</p> -</div> -<div class="section level2"> -<h2 id="laboratory-data-l2">Laboratory Data L2<a class="anchor" aria-label="anchor" href="#laboratory-data-l2"></a> -</h2> -<p>The following code defines example dataset L2 from the FOCUS kinetics -report, p. 287:</p> -<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">FOCUS_2006_L2</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span></span> -<span> t <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/rep.html" class="external-link">rep</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="fl">0</span>, <span class="fl">1</span>, <span class="fl">3</span>, <span class="fl">7</span>, <span class="fl">14</span>, <span class="fl">28</span><span class="op">)</span>, each <span class="op">=</span> <span class="fl">2</span><span class="op">)</span>,</span> -<span> parent <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">96.1</span>, <span class="fl">91.8</span>, <span class="fl">41.4</span>, <span class="fl">38.7</span>,</span> -<span> <span class="fl">19.3</span>, <span class="fl">22.3</span>, <span class="fl">4.6</span>, <span class="fl">4.6</span>,</span> -<span> <span class="fl">2.6</span>, <span class="fl">1.2</span>, <span class="fl">0.3</span>, <span class="fl">0.6</span><span class="op">)</span><span class="op">)</span></span> -<span><span class="va">FOCUS_2006_L2_mkin</span> <span class="op"><-</span> <span class="fu"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span><span class="op">(</span><span class="va">FOCUS_2006_L2</span><span class="op">)</span></span></code></pre></div> -<div class="section level3"> -<h3 id="sfo-fit-for-l2">SFO fit for L2<a class="anchor" aria-label="anchor" href="#sfo-fit-for-l2"></a> -</h3> -<p>Again, the SFO model is fitted and the result is plotted. The -residual plot can be obtained simply by adding the argument -<code>show_residuals</code> to the plot command.</p> -<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">m.L2.SFO</span> <span class="op"><-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="va">FOCUS_2006_L2_mkin</span>, quiet<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span></span> -<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">m.L2.SFO</span>, show_residuals <span class="op">=</span> <span class="cn">TRUE</span>, show_errmin <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> main <span class="op">=</span> <span class="st">"FOCUS L2 - SFO"</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_L_files/figure-html/unnamed-chunk-8-1.png" width="672"></p> -<p>The <span class="math inline">\(\chi^2\)</span> error level of 14% -suggests that the model does not fit very well. This is also obvious -from the plots of the fit, in which we have included the residual -plot.</p> -<p>In the FOCUS kinetics report, it is stated that there is no apparent -systematic error observed from the residual plot up to the measured DT90 -(approximately at day 5), and there is an underestimation beyond that -point.</p> -<p>We may add that it is difficult to judge the random nature of the -residuals just from the three samplings at days 0, 1 and 3. Also, it is -not clear <em>a priori</em> why a consistent underestimation after the -approximate DT90 should be irrelevant. However, this can be rationalised -by the fact that the FOCUS fate models generally only implement SFO -kinetics.</p> -</div> -<div class="section level3"> -<h3 id="fomc-fit-for-l2">FOMC fit for L2<a class="anchor" aria-label="anchor" href="#fomc-fit-for-l2"></a> -</h3> -<p>For comparison, the FOMC model is fitted as well, and the <span class="math inline">\(\chi^2\)</span> error level is checked.</p> -<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">m.L2.FOMC</span> <span class="op"><-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"FOMC"</span>, <span class="va">FOCUS_2006_L2_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<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">m.L2.FOMC</span>, show_residuals <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> main <span class="op">=</span> <span class="st">"FOCUS L2 - FOMC"</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_L_files/figure-html/unnamed-chunk-9-1.png" width="672"></p> -<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.L2.FOMC</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## mkin version used for fitting: 1.2.3 </span></span> -<span><span class="co">## R version used for fitting: 4.2.3 </span></span> -<span><span class="co">## Date of fit: Sun Apr 16 08:35:14 2023 </span></span> -<span><span class="co">## Date of summary: Sun Apr 16 08:35:14 2023 </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Equations:</span></span> -<span><span class="co">## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Model predictions using solution type analytical </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Fitted using 239 model solutions performed in 0.015 s</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Error model: Constant variance </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Error model algorithm: OLS </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Starting values for parameters to be optimised:</span></span> -<span><span class="co">## value type</span></span> -<span><span class="co">## parent_0 93.95 state</span></span> -<span><span class="co">## alpha 1.00 deparm</span></span> -<span><span class="co">## beta 10.00 deparm</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Starting values for the transformed parameters actually optimised:</span></span> -<span><span class="co">## value lower upper</span></span> -<span><span class="co">## parent_0 93.950000 -Inf Inf</span></span> -<span><span class="co">## log_alpha 0.000000 -Inf Inf</span></span> -<span><span class="co">## log_beta 2.302585 -Inf Inf</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Fixed parameter values:</span></span> -<span><span class="co">## None</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Results:</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## AIC BIC logLik</span></span> -<span><span class="co">## 61.78966 63.72928 -26.89483</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Optimised, transformed parameters with symmetric confidence intervals:</span></span> -<span><span class="co">## Estimate Std. Error Lower Upper</span></span> -<span><span class="co">## parent_0 93.7700 1.6130 90.05000 97.4900</span></span> -<span><span class="co">## log_alpha 0.3180 0.1559 -0.04149 0.6776</span></span> -<span><span class="co">## log_beta 0.2102 0.2493 -0.36460 0.7850</span></span> -<span><span class="co">## sigma 2.2760 0.4645 1.20500 3.3470</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Parameter correlation:</span></span> -<span><span class="co">## parent_0 log_alpha log_beta sigma</span></span> -<span><span class="co">## parent_0 1.000e+00 -1.151e-01 -2.085e-01 -7.828e-09</span></span> -<span><span class="co">## log_alpha -1.151e-01 1.000e+00 9.741e-01 -1.602e-07</span></span> -<span><span class="co">## log_beta -2.085e-01 9.741e-01 1.000e+00 -1.372e-07</span></span> -<span><span class="co">## sigma -7.828e-09 -1.602e-07 -1.372e-07 1.000e+00</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Backtransformed parameters:</span></span> -<span><span class="co">## Confidence intervals for internally transformed parameters are asymmetric.</span></span> -<span><span class="co">## t-test (unrealistically) based on the assumption of normal distribution</span></span> -<span><span class="co">## for estimators of untransformed parameters.</span></span> -<span><span class="co">## Estimate t value Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 93.770 58.120 4.267e-12 90.0500 97.490</span></span> -<span><span class="co">## alpha 1.374 6.414 1.030e-04 0.9594 1.969</span></span> -<span><span class="co">## beta 1.234 4.012 1.942e-03 0.6945 2.192</span></span> -<span><span class="co">## sigma 2.276 4.899 5.977e-04 1.2050 3.347</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## FOCUS Chi2 error levels in percent:</span></span> -<span><span class="co">## err.min n.optim df</span></span> -<span><span class="co">## All data 6.205 3 3</span></span> -<span><span class="co">## parent 6.205 3 3</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Estimated disappearance times:</span></span> -<span><span class="co">## DT50 DT90 DT50back</span></span> -<span><span class="co">## parent 0.8092 5.356 1.612</span></span></code></pre> -<p>The error level at which the <span class="math inline">\(\chi^2\)</span> test passes is much lower in this -case. Therefore, the FOMC model provides a better description of the -data, as less experimental error has to be assumed in order to explain -the data.</p> -</div> -<div class="section level3"> -<h3 id="dfop-fit-for-l2">DFOP fit for L2<a class="anchor" aria-label="anchor" href="#dfop-fit-for-l2"></a> -</h3> -<p>Fitting the four parameter DFOP model further reduces the <span class="math inline">\(\chi^2\)</span> error level.</p> -<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">m.L2.DFOP</span> <span class="op"><-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"DFOP"</span>, <span class="va">FOCUS_2006_L2_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<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">m.L2.DFOP</span>, show_residuals <span class="op">=</span> <span class="cn">TRUE</span>, show_errmin <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> main <span class="op">=</span> <span class="st">"FOCUS L2 - DFOP"</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_L_files/figure-html/unnamed-chunk-10-1.png" width="672"></p> -<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.L2.DFOP</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## mkin version used for fitting: 1.2.3 </span></span> -<span><span class="co">## R version used for fitting: 4.2.3 </span></span> -<span><span class="co">## Date of fit: Sun Apr 16 08:35:15 2023 </span></span> -<span><span class="co">## Date of summary: Sun Apr 16 08:35:15 2023 </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Equations:</span></span> -<span><span class="co">## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *</span></span> -<span><span class="co">## time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))</span></span> -<span><span class="co">## * parent</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Model predictions using solution type analytical </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Fitted using 581 model solutions performed in 0.04 s</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Error model: Constant variance </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Error model algorithm: OLS </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Starting values for parameters to be optimised:</span></span> -<span><span class="co">## value type</span></span> -<span><span class="co">## parent_0 93.95 state</span></span> -<span><span class="co">## k1 0.10 deparm</span></span> -<span><span class="co">## k2 0.01 deparm</span></span> -<span><span class="co">## g 0.50 deparm</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Starting values for the transformed parameters actually optimised:</span></span> -<span><span class="co">## value lower upper</span></span> -<span><span class="co">## parent_0 93.950000 -Inf Inf</span></span> -<span><span class="co">## log_k1 -2.302585 -Inf Inf</span></span> -<span><span class="co">## log_k2 -4.605170 -Inf Inf</span></span> -<span><span class="co">## g_qlogis 0.000000 -Inf Inf</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Fixed parameter values:</span></span> -<span><span class="co">## None</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Results:</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## AIC BIC logLik</span></span> -<span><span class="co">## 52.36695 54.79148 -21.18347</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Optimised, transformed parameters with symmetric confidence intervals:</span></span> -<span><span class="co">## Estimate Std. Error Lower Upper</span></span> -<span><span class="co">## parent_0 93.950 9.998e-01 91.5900 96.3100</span></span> -<span><span class="co">## log_k1 3.112 1.842e+03 -4353.0000 4359.0000</span></span> -<span><span class="co">## log_k2 -1.088 6.285e-02 -1.2370 -0.9394</span></span> -<span><span class="co">## g_qlogis -0.399 9.946e-02 -0.6342 -0.1638</span></span> -<span><span class="co">## sigma 1.414 2.886e-01 0.7314 2.0960</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Parameter correlation:</span></span> -<span><span class="co">## parent_0 log_k1 log_k2 g_qlogis sigma</span></span> -<span><span class="co">## parent_0 1.000e+00 6.783e-07 -3.390e-10 2.665e-01 -2.967e-10</span></span> -<span><span class="co">## log_k1 6.783e-07 1.000e+00 1.116e-04 -2.196e-04 -1.031e-05</span></span> -<span><span class="co">## log_k2 -3.390e-10 1.116e-04 1.000e+00 -7.903e-01 2.917e-09</span></span> -<span><span class="co">## g_qlogis 2.665e-01 -2.196e-04 -7.903e-01 1.000e+00 -4.408e-09</span></span> -<span><span class="co">## sigma -2.967e-10 -1.031e-05 2.917e-09 -4.408e-09 1.000e+00</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Backtransformed parameters:</span></span> -<span><span class="co">## Confidence intervals for internally transformed parameters are asymmetric.</span></span> -<span><span class="co">## t-test (unrealistically) based on the assumption of normal distribution</span></span> -<span><span class="co">## for estimators of untransformed parameters.</span></span> -<span><span class="co">## Estimate t value Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 93.9500 9.397e+01 2.036e-12 91.5900 96.3100</span></span> -<span><span class="co">## k1 22.4800 5.553e-04 4.998e-01 0.0000 Inf</span></span> -<span><span class="co">## k2 0.3369 1.591e+01 4.697e-07 0.2904 0.3909</span></span> -<span><span class="co">## g 0.4016 1.680e+01 3.238e-07 0.3466 0.4591</span></span> -<span><span class="co">## sigma 1.4140 4.899e+00 8.776e-04 0.7314 2.0960</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## FOCUS Chi2 error levels in percent:</span></span> -<span><span class="co">## err.min n.optim df</span></span> -<span><span class="co">## All data 2.53 4 2</span></span> -<span><span class="co">## parent 2.53 4 2</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Estimated disappearance times:</span></span> -<span><span class="co">## DT50 DT90 DT50back DT50_k1 DT50_k2</span></span> -<span><span class="co">## parent 0.5335 5.311 1.599 0.03084 2.058</span></span></code></pre> -<p>Here, the DFOP model is clearly the best-fit model for dataset L2 -based on the chi^2 error level criterion.</p> -</div> -</div> -<div class="section level2"> -<h2 id="laboratory-data-l3">Laboratory Data L3<a class="anchor" aria-label="anchor" href="#laboratory-data-l3"></a> -</h2> -<p>The following code defines example dataset L3 from the FOCUS kinetics -report, p. 290.</p> -<div class="sourceCode" id="cb22"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">FOCUS_2006_L3</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span></span> -<span> t <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">3</span>, <span class="fl">7</span>, <span class="fl">14</span>, <span class="fl">30</span>, <span class="fl">60</span>, <span class="fl">91</span>, <span class="fl">120</span><span class="op">)</span>,</span> -<span> parent <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">97.8</span>, <span class="fl">60</span>, <span class="fl">51</span>, <span class="fl">43</span>, <span class="fl">35</span>, <span class="fl">22</span>, <span class="fl">15</span>, <span class="fl">12</span><span class="op">)</span><span class="op">)</span></span> -<span><span class="va">FOCUS_2006_L3_mkin</span> <span class="op"><-</span> <span class="fu"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span><span class="op">(</span><span class="va">FOCUS_2006_L3</span><span class="op">)</span></span></code></pre></div> -<div class="section level3"> -<h3 id="fit-multiple-models">Fit multiple models<a class="anchor" aria-label="anchor" href="#fit-multiple-models"></a> -</h3> -<p>As of mkin version 0.9-39 (June 2015), we can fit several models to -one or more datasets in one call to the function <code>mmkin</code>. The -datasets have to be passed in a list, in this case a named list holding -only the L3 dataset prepared above.</p> -<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="co"># Only use one core here, not to offend the CRAN checks</span></span> -<span><span class="va">mm.L3</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="op">)</span>, cores <span class="op">=</span> <span class="fl">1</span>,</span> -<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="st">"FOCUS L3"</span> <span class="op">=</span> <span class="va">FOCUS_2006_L3_mkin</span><span class="op">)</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<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">mm.L3</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_L_files/figure-html/unnamed-chunk-12-1.png" width="700"></p> -<p>The <span class="math inline">\(\chi^2\)</span> error level of 21% as -well as the plot suggest that the SFO model does not fit very well. The -FOMC model performs better, with an error level at which the <span class="math inline">\(\chi^2\)</span> test passes of 7%. Fitting the -four parameter DFOP model further reduces the <span class="math inline">\(\chi^2\)</span> error level considerably.</p> -</div> -<div class="section level3"> -<h3 id="accessing-mmkin-objects">Accessing mmkin objects<a class="anchor" aria-label="anchor" href="#accessing-mmkin-objects"></a> -</h3> -<p>The objects returned by mmkin are arranged like a matrix, with models -as a row index and datasets as a column index.</p> -<p>We can extract the summary and plot for <em>e.g.</em> the DFOP fit, -using square brackets for indexing which will result in the use of the -summary and plot functions working on mkinfit objects.</p> -<div class="sourceCode" id="cb24"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">mm.L3</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="fl">1</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## mkin version used for fitting: 1.2.3 </span></span> -<span><span class="co">## R version used for fitting: 4.2.3 </span></span> -<span><span class="co">## Date of fit: Sun Apr 16 08:35:15 2023 </span></span> -<span><span class="co">## Date of summary: Sun Apr 16 08:35:15 2023 </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Equations:</span></span> -<span><span class="co">## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *</span></span> -<span><span class="co">## time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))</span></span> -<span><span class="co">## * parent</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Model predictions using solution type analytical </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Fitted using 376 model solutions performed in 0.024 s</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Error model: Constant variance </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Error model algorithm: OLS </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Starting values for parameters to be optimised:</span></span> -<span><span class="co">## value type</span></span> -<span><span class="co">## parent_0 97.80 state</span></span> -<span><span class="co">## k1 0.10 deparm</span></span> -<span><span class="co">## k2 0.01 deparm</span></span> -<span><span class="co">## g 0.50 deparm</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Starting values for the transformed parameters actually optimised:</span></span> -<span><span class="co">## value lower upper</span></span> -<span><span class="co">## parent_0 97.800000 -Inf Inf</span></span> -<span><span class="co">## log_k1 -2.302585 -Inf Inf</span></span> -<span><span class="co">## log_k2 -4.605170 -Inf Inf</span></span> -<span><span class="co">## g_qlogis 0.000000 -Inf Inf</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Fixed parameter values:</span></span> -<span><span class="co">## None</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Results:</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## AIC BIC logLik</span></span> -<span><span class="co">## 32.97732 33.37453 -11.48866</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Optimised, transformed parameters with symmetric confidence intervals:</span></span> -<span><span class="co">## Estimate Std. Error Lower Upper</span></span> -<span><span class="co">## parent_0 97.7500 1.01900 94.5000 101.000000</span></span> -<span><span class="co">## log_k1 -0.6612 0.10050 -0.9812 -0.341300</span></span> -<span><span class="co">## log_k2 -4.2860 0.04322 -4.4230 -4.148000</span></span> -<span><span class="co">## g_qlogis -0.1739 0.05270 -0.3416 -0.006142</span></span> -<span><span class="co">## sigma 1.0170 0.25430 0.2079 1.827000</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Parameter correlation:</span></span> -<span><span class="co">## parent_0 log_k1 log_k2 g_qlogis sigma</span></span> -<span><span class="co">## parent_0 1.000e+00 1.732e-01 2.282e-02 4.009e-01 -9.664e-08</span></span> -<span><span class="co">## log_k1 1.732e-01 1.000e+00 4.945e-01 -5.809e-01 7.147e-07</span></span> -<span><span class="co">## log_k2 2.282e-02 4.945e-01 1.000e+00 -6.812e-01 1.022e-06</span></span> -<span><span class="co">## g_qlogis 4.009e-01 -5.809e-01 -6.812e-01 1.000e+00 -7.926e-07</span></span> -<span><span class="co">## sigma -9.664e-08 7.147e-07 1.022e-06 -7.926e-07 1.000e+00</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Backtransformed parameters:</span></span> -<span><span class="co">## Confidence intervals for internally transformed parameters are asymmetric.</span></span> -<span><span class="co">## t-test (unrealistically) based on the assumption of normal distribution</span></span> -<span><span class="co">## for estimators of untransformed parameters.</span></span> -<span><span class="co">## Estimate t value Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 97.75000 95.960 1.248e-06 94.50000 101.00000</span></span> -<span><span class="co">## k1 0.51620 9.947 1.081e-03 0.37490 0.71090</span></span> -<span><span class="co">## k2 0.01376 23.140 8.840e-05 0.01199 0.01579</span></span> -<span><span class="co">## g 0.45660 34.920 2.581e-05 0.41540 0.49850</span></span> -<span><span class="co">## sigma 1.01700 4.000 1.400e-02 0.20790 1.82700</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## FOCUS Chi2 error levels in percent:</span></span> -<span><span class="co">## err.min n.optim df</span></span> -<span><span class="co">## All data 2.225 4 4</span></span> -<span><span class="co">## parent 2.225 4 4</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Estimated disappearance times:</span></span> -<span><span class="co">## DT50 DT90 DT50back DT50_k1 DT50_k2</span></span> -<span><span class="co">## parent 7.464 123 37.03 1.343 50.37</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Data:</span></span> -<span><span class="co">## time variable observed predicted residual</span></span> -<span><span class="co">## 0 parent 97.8 97.75 0.05396</span></span> -<span><span class="co">## 3 parent 60.0 60.45 -0.44933</span></span> -<span><span class="co">## 7 parent 51.0 49.44 1.56338</span></span> -<span><span class="co">## 14 parent 43.0 43.84 -0.83632</span></span> -<span><span class="co">## 30 parent 35.0 35.15 -0.14707</span></span> -<span><span class="co">## 60 parent 22.0 23.26 -1.25919</span></span> -<span><span class="co">## 91 parent 15.0 15.18 -0.18181</span></span> -<span><span class="co">## 120 parent 12.0 10.19 1.81395</span></span></code></pre> -<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">mm.L3</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="fl">1</span><span class="op">]</span><span class="op">]</span>, show_errmin <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_L_files/figure-html/unnamed-chunk-13-1.png" width="700"></p> -<p>Here, a look to the model plot, the confidence intervals of the -parameters and the correlation matrix suggest that the parameter -estimates are reliable, and the DFOP model can be used as the best-fit -model based on the <span class="math inline">\(\chi^2\)</span> error -level criterion for laboratory data L3.</p> -<p>This is also an example where the standard t-test for the parameter -<code>g_ilr</code> is misleading, as it tests for a significant -difference from zero. In this case, zero appears to be the correct value -for this parameter, and the confidence interval for the backtransformed -parameter <code>g</code> is quite narrow.</p> -</div> -</div> -<div class="section level2"> -<h2 id="laboratory-data-l4">Laboratory Data L4<a class="anchor" aria-label="anchor" href="#laboratory-data-l4"></a> -</h2> -<p>The following code defines example dataset L4 from the FOCUS kinetics -report, p. 293:</p> -<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">FOCUS_2006_L4</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span></span> -<span> t <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">3</span>, <span class="fl">7</span>, <span class="fl">14</span>, <span class="fl">30</span>, <span class="fl">60</span>, <span class="fl">91</span>, <span class="fl">120</span><span class="op">)</span>,</span> -<span> parent <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">96.6</span>, <span class="fl">96.3</span>, <span class="fl">94.3</span>, <span class="fl">88.8</span>, <span class="fl">74.9</span>, <span class="fl">59.9</span>, <span class="fl">53.5</span>, <span class="fl">49.0</span><span class="op">)</span><span class="op">)</span></span> -<span><span class="va">FOCUS_2006_L4_mkin</span> <span class="op"><-</span> <span class="fu"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span><span class="op">(</span><span class="va">FOCUS_2006_L4</span><span class="op">)</span></span></code></pre></div> -<p>Fits of the SFO and FOMC models, plots and summaries are produced -below:</p> -<div class="sourceCode" id="cb28"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="co"># Only use one core here, not to offend the CRAN checks</span></span> -<span><span class="va">mm.L4</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="op">)</span>, cores <span class="op">=</span> <span class="fl">1</span>,</span> -<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="st">"FOCUS L4"</span> <span class="op">=</span> <span class="va">FOCUS_2006_L4_mkin</span><span class="op">)</span>,</span> -<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<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">mm.L4</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_L_files/figure-html/unnamed-chunk-15-1.png" width="700"></p> -<p>The <span class="math inline">\(\chi^2\)</span> error level of 3.3% -as well as the plot suggest that the SFO model fits very well. The error -level at which the <span class="math inline">\(\chi^2\)</span> test -passes is slightly lower for the FOMC model. However, the difference -appears negligible.</p> -<div class="sourceCode" id="cb29"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">mm.L4</span><span class="op">[[</span><span class="st">"SFO"</span>, <span class="fl">1</span><span class="op">]</span><span class="op">]</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## mkin version used for fitting: 1.2.3 </span></span> -<span><span class="co">## R version used for fitting: 4.2.3 </span></span> -<span><span class="co">## Date of fit: Sun Apr 16 08:35:15 2023 </span></span> -<span><span class="co">## Date of summary: Sun Apr 16 08:35:16 2023 </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Equations:</span></span> -<span><span class="co">## d_parent/dt = - k_parent * parent</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Model predictions using solution type analytical </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Fitted using 142 model solutions performed in 0.009 s</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Error model: Constant variance </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Error model algorithm: OLS </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Starting values for parameters to be optimised:</span></span> -<span><span class="co">## value type</span></span> -<span><span class="co">## parent_0 96.6 state</span></span> -<span><span class="co">## k_parent 0.1 deparm</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Starting values for the transformed parameters actually optimised:</span></span> -<span><span class="co">## value lower upper</span></span> -<span><span class="co">## parent_0 96.600000 -Inf Inf</span></span> -<span><span class="co">## log_k_parent -2.302585 -Inf Inf</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Fixed parameter values:</span></span> -<span><span class="co">## None</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Results:</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## AIC BIC logLik</span></span> -<span><span class="co">## 47.12133 47.35966 -20.56067</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Optimised, transformed parameters with symmetric confidence intervals:</span></span> -<span><span class="co">## Estimate Std. Error Lower Upper</span></span> -<span><span class="co">## parent_0 96.440 1.69900 92.070 100.800</span></span> -<span><span class="co">## log_k_parent -5.030 0.07059 -5.211 -4.848</span></span> -<span><span class="co">## sigma 3.162 0.79050 1.130 5.194</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Parameter correlation:</span></span> -<span><span class="co">## parent_0 log_k_parent sigma</span></span> -<span><span class="co">## parent_0 1.000e+00 5.938e-01 3.387e-07</span></span> -<span><span class="co">## log_k_parent 5.938e-01 1.000e+00 5.830e-07</span></span> -<span><span class="co">## sigma 3.387e-07 5.830e-07 1.000e+00</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Backtransformed parameters:</span></span> -<span><span class="co">## Confidence intervals for internally transformed parameters are asymmetric.</span></span> -<span><span class="co">## t-test (unrealistically) based on the assumption of normal distribution</span></span> -<span><span class="co">## for estimators of untransformed parameters.</span></span> -<span><span class="co">## Estimate t value Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 96.440000 56.77 1.604e-08 92.070000 1.008e+02</span></span> -<span><span class="co">## k_parent 0.006541 14.17 1.578e-05 0.005455 7.842e-03</span></span> -<span><span class="co">## sigma 3.162000 4.00 5.162e-03 1.130000 5.194e+00</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## FOCUS Chi2 error levels in percent:</span></span> -<span><span class="co">## err.min n.optim df</span></span> -<span><span class="co">## All data 3.287 2 6</span></span> -<span><span class="co">## parent 3.287 2 6</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Estimated disappearance times:</span></span> -<span><span class="co">## DT50 DT90</span></span> -<span><span class="co">## parent 106 352</span></span></code></pre> -<div class="sourceCode" id="cb31"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">mm.L4</span><span class="op">[[</span><span class="st">"FOMC"</span>, <span class="fl">1</span><span class="op">]</span><span class="op">]</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## mkin version used for fitting: 1.2.3 </span></span> -<span><span class="co">## R version used for fitting: 4.2.3 </span></span> -<span><span class="co">## Date of fit: Sun Apr 16 08:35:15 2023 </span></span> -<span><span class="co">## Date of summary: Sun Apr 16 08:35:16 2023 </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Equations:</span></span> -<span><span class="co">## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Model predictions using solution type analytical </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Fitted using 224 model solutions performed in 0.014 s</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Error model: Constant variance </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Error model algorithm: OLS </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Starting values for parameters to be optimised:</span></span> -<span><span class="co">## value type</span></span> -<span><span class="co">## parent_0 96.6 state</span></span> -<span><span class="co">## alpha 1.0 deparm</span></span> -<span><span class="co">## beta 10.0 deparm</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Starting values for the transformed parameters actually optimised:</span></span> -<span><span class="co">## value lower upper</span></span> -<span><span class="co">## parent_0 96.600000 -Inf Inf</span></span> -<span><span class="co">## log_alpha 0.000000 -Inf Inf</span></span> -<span><span class="co">## log_beta 2.302585 -Inf Inf</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Fixed parameter values:</span></span> -<span><span class="co">## None</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Results:</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## AIC BIC logLik</span></span> -<span><span class="co">## 40.37255 40.69032 -16.18628</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Optimised, transformed parameters with symmetric confidence intervals:</span></span> -<span><span class="co">## Estimate Std. Error Lower Upper</span></span> -<span><span class="co">## parent_0 99.1400 1.2670 95.6300 102.7000</span></span> -<span><span class="co">## log_alpha -0.3506 0.2616 -1.0770 0.3756</span></span> -<span><span class="co">## log_beta 4.1740 0.3938 3.0810 5.2670</span></span> -<span><span class="co">## sigma 1.8300 0.4575 0.5598 3.1000</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Parameter correlation:</span></span> -<span><span class="co">## parent_0 log_alpha log_beta sigma</span></span> -<span><span class="co">## parent_0 1.000e+00 -4.696e-01 -5.543e-01 -2.468e-07</span></span> -<span><span class="co">## log_alpha -4.696e-01 1.000e+00 9.889e-01 2.478e-08</span></span> -<span><span class="co">## log_beta -5.543e-01 9.889e-01 1.000e+00 5.211e-08</span></span> -<span><span class="co">## sigma -2.468e-07 2.478e-08 5.211e-08 1.000e+00</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Backtransformed parameters:</span></span> -<span><span class="co">## Confidence intervals for internally transformed parameters are asymmetric.</span></span> -<span><span class="co">## t-test (unrealistically) based on the assumption of normal distribution</span></span> -<span><span class="co">## for estimators of untransformed parameters.</span></span> -<span><span class="co">## Estimate t value Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 99.1400 78.250 7.993e-08 95.6300 102.700</span></span> -<span><span class="co">## alpha 0.7042 3.823 9.365e-03 0.3407 1.456</span></span> -<span><span class="co">## beta 64.9800 2.540 3.201e-02 21.7800 193.900</span></span> -<span><span class="co">## sigma 1.8300 4.000 8.065e-03 0.5598 3.100</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## FOCUS Chi2 error levels in percent:</span></span> -<span><span class="co">## err.min n.optim df</span></span> -<span><span class="co">## All data 2.029 3 5</span></span> -<span><span class="co">## parent 2.029 3 5</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Estimated disappearance times:</span></span> -<span><span class="co">## DT50 DT90 DT50back</span></span> -<span><span class="co">## parent 108.9 1644 494.9</span></span></code></pre> -</div> -<div class="section level2"> -<h2 class="unnumbered" id="references">References<a class="anchor" aria-label="anchor" href="#references"></a> -</h2> -<div id="refs" class="references csl-bib-body hanging-indent"> -<div id="ref-ranke2014" class="csl-entry"> -Ranke, Johannes. 2014. <span>“<span class="nocase">Prüfung und -Validierung von Modellierungssoftware als Alternative zu ModelMaker -4.0</span>.”</span> Umweltbundesamt Projektnummer 27452. -</div> -</div> -</div> - </div> - - <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar"> - - <nav id="toc" data-toggle="toc"><h2 data-toc-skip>Contents</h2> - </nav> -</div> - -</div> - - - - <footer><div class="copyright"> - <p></p> -<p>Developed by Johannes Ranke.</p> -</div> - -<div class="pkgdown"> - <p></p> -<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p> -</div> - - </footer> -</div> - - - - - - - </body> -</html> diff --git a/docs/dev/articles/FOCUS_L_files/accessible-code-block-0.0.1/empty-anchor.js b/docs/dev/articles/FOCUS_L_files/accessible-code-block-0.0.1/empty-anchor.js deleted file mode 100644 index ca349fd6..00000000 --- a/docs/dev/articles/FOCUS_L_files/accessible-code-block-0.0.1/empty-anchor.js +++ /dev/null @@ -1,15 +0,0 @@ -// Hide empty <a> tag within highlighted CodeBlock for screen reader accessibility (see https://github.com/jgm/pandoc/issues/6352#issuecomment-626106786) --> -// v0.0.1 -// Written by JooYoung Seo (jooyoung@psu.edu) and Atsushi Yasumoto on June 1st, 2020. - -document.addEventListener('DOMContentLoaded', function() { - const codeList = document.getElementsByClassName("sourceCode"); 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Articles - - <span class="caret"></span> - </a> - <ul class="dropdown-menu" role="menu"><li> - <a href="../articles/mkin.html">Introduction to mkin</a> - </li> - <li class="divider"> - <li class="dropdown-header">Example evaluations with (generalised) nonlinear least squares</li> - <li> - <a href="../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a> - </li> - <li> - <a href="../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a> - </li> - <li> - <a href="../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> - </li> - <li class="divider"> - <li class="dropdown-header">Example evaluations with hierarchical models (nonlinear mixed-effects models)</li> - <li> - <a href="../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a> - </li> - <li> - <a href="../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a> - </li> - <li> - <a href="../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a> - </li> - <li> - <a href="../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a> - </li> - <li> - <a href="../articles/web_only/multistart.html">Short demo of the multistart method</a> - </li> - <li class="divider"> - <li class="dropdown-header">Performance</li> - <li> - <a href="../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> - </li> - <li> - <a href="../articles/web_only/benchmarks.html">Benchmark timings for mkin</a> - </li> - <li> - <a href="../articles/web_only/saem_benchmarks.html">Benchmark timings for saem.mmkin</a> - </li> - <li class="divider"> - <li class="dropdown-header">Miscellaneous</li> - <li> - <a href="../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> - </li> - 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<dd> - </dd><dt><a href="prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a></dt> - <dd> - </dd><dt><a href="prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a></dt> - <dd> - </dd><dt><a href="twa.html">Calculation of time weighted average concentrations with mkin</a></dt> - <dd> - </dd><dt><a href="web_only/FOCUS_Z.html">Example evaluation of FOCUS dataset Z</a></dt> - <dd> - </dd><dt><a href="web_only/NAFTA_examples.html">Evaluation of example datasets from Attachment 1 to the US EPA SOP for the NAFTA guidance</a></dt> - <dd> - </dd><dt><a href="web_only/benchmarks.html">Benchmark timings for mkin</a></dt> - <dd> - </dd><dt><a href="web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a></dt> - <dd> - </dd><dt><a href="web_only/dimethenamid_2018.html">Example evaluations of the dimethenamid data from 2018</a></dt> - <dd> - </dd><dt><a href="web_only/multistart.html">Short demo of the multistart method</a></dt> - <dd> - </dd><dt><a href="web_only/saem_benchmarks.html">Benchmark timings for saem.mmkin</a></dt> - <dd> - </dd></dl></div> - </div> -</div> - - - <footer><div class="copyright"> - <p></p><p>Developed by Johannes Ranke.</p> -</div> - -<div class="pkgdown"> - <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p> -</div> - - </footer></div> - - - - - - - </body></html> - diff --git a/docs/dev/articles/mkin.html b/docs/dev/articles/mkin.html deleted file mode 100644 index fa3ac11c..00000000 --- a/docs/dev/articles/mkin.html +++ /dev/null @@ -1,472 +0,0 @@ -<!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>Introduction to mkin • 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" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous"> -<script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"> -<script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"> -<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"> -<!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"> -<script src="../pkgdown.js"></script><meta property="og:title" content="Introduction to mkin"> -<meta property="og:description" content="mkin"> -<meta name="robots" content="noindex"> -<!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]> -<script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script> -<script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script> -<![endif]--> -</head> -<body data-spy="scroll" data-target="#toc"> - 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</li> - <li> - <a href="../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a> - </li> - <li> - <a href="../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a> - </li> - <li> - <a href="../articles/web_only/multistart.html">Short demo of the multistart method</a> - </li> - <li class="divider"> - </li> -<li class="dropdown-header">Performance</li> - <li> - <a href="../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> - </li> - <li> - <a href="../articles/web_only/benchmarks.html">Benchmark timings for mkin</a> - </li> - <li> - <a href="../articles/web_only/saem_benchmarks.html">Benchmark timings for saem.mmkin</a> - </li> - <li class="divider"> - </li> -<li class="dropdown-header">Miscellaneous</li> - <li> - <a href="../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> - </li> - <li> - <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> - </li> - </ul> -</li> -<li> - <a href="../news/index.html">News</a> -</li> - </ul> -<ul class="nav navbar-nav navbar-right"> -<li> - <a href="https://github.com/jranke/mkin/" class="external-link"> - <span class="fab fa-github fa-lg"></span> - - </a> -</li> - </ul> -</div> -<!--/.nav-collapse --> - </div> -<!--/.container --> -</div> -<!--/.navbar --> - - - - </header><div class="row"> - <div class="col-md-9 contents"> - <div class="page-header toc-ignore"> - <h1 data-toc-skip>Introduction to mkin</h1> - <h4 data-toc-skip class="author">Johannes -Ranke</h4> - - <h4 data-toc-skip class="date">Last change 15 February 2021 -(rebuilt 2023-04-16)</h4> - - <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/mkin.rmd" class="external-link"><code>vignettes/mkin.rmd</code></a></small> - <div class="hidden name"><code>mkin.rmd</code></div> - - </div> - - - -<p><a href="https://www.jrwb.de" class="external-link">Wissenschaftlicher Berater, Kronacher -Str. 12, 79639 Grenzach-Wyhlen, Germany</a><br> Privatdozent at the -University of Freiburg</p> -<div class="section level2"> -<h2 id="abstract">Abstract<a class="anchor" aria-label="anchor" href="#abstract"></a> -</h2> -<p>In the regulatory evaluation of chemical substances like plant -protection products (pesticides), biocides and other chemicals, -degradation data play an important role. For the evaluation of pesticide -degradation experiments, detailed guidance has been developed, based on -nonlinear optimisation. The <code>R</code> add-on package -<code>mkin</code> implements fitting some of the models recommended in -this guidance from within R and calculates some statistical measures for -data series within one or more compartments, for parent and -metabolites.</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="st"><a href="https://pkgdown.jrwb.de/mkin/">"mkin"</a></span>, quietly <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<span><span class="co"># Define the kinetic model</span></span> -<span><span class="va">m_SFO_SFO_SFO</span> <span class="op"><-</span> <span class="fu"><a href="../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>parent <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">"M1"</span><span class="op">)</span>,</span> -<span> M1 <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">"M2"</span><span class="op">)</span>,</span> -<span> M2 <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> use_of_ff <span class="op">=</span> <span class="st">"max"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<span></span> -<span></span> -<span><span class="co"># Produce model predictions using some arbitrary parameters</span></span> -<span><span class="va">sampling_times</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="fl">0</span>, <span class="fl">1</span>, <span class="fl">3</span>, <span class="fl">7</span>, <span class="fl">14</span>, <span class="fl">28</span>, <span class="fl">60</span>, <span class="fl">90</span>, <span class="fl">120</span><span class="op">)</span></span> -<span><span class="va">d_SFO_SFO_SFO</span> <span class="op"><-</span> <span class="fu"><a href="../reference/mkinpredict.html">mkinpredict</a></span><span class="op">(</span><span class="va">m_SFO_SFO_SFO</span>,</span> -<span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>k_parent <span class="op">=</span> <span class="fl">0.03</span>,</span> -<span> f_parent_to_M1 <span class="op">=</span> <span class="fl">0.5</span>, k_M1 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/Log.html" class="external-link">log</a></span><span class="op">(</span><span class="fl">2</span><span class="op">)</span><span class="op">/</span><span class="fl">100</span>,</span> -<span> f_M1_to_M2 <span class="op">=</span> <span class="fl">0.9</span>, k_M2 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/Log.html" class="external-link">log</a></span><span class="op">(</span><span class="fl">2</span><span class="op">)</span><span class="op">/</span><span class="fl">50</span><span class="op">)</span>,</span> -<span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>parent <span class="op">=</span> <span class="fl">100</span>, M1 <span class="op">=</span> <span class="fl">0</span>, M2 <span class="op">=</span> <span class="fl">0</span><span class="op">)</span>,</span> -<span> <span class="va">sampling_times</span><span class="op">)</span></span> -<span></span> -<span><span class="co"># Generate a dataset by adding normally distributed errors with</span></span> -<span><span class="co"># standard deviation 3, for two replicates at each sampling time</span></span> -<span><span class="va">d_SFO_SFO_SFO_err</span> <span class="op"><-</span> <span class="fu"><a href="../reference/add_err.html">add_err</a></span><span class="op">(</span><span class="va">d_SFO_SFO_SFO</span>, reps <span class="op">=</span> <span class="fl">2</span>,</span> -<span> sdfunc <span class="op">=</span> <span class="kw">function</span><span class="op">(</span><span class="va">x</span><span class="op">)</span> <span class="fl">3</span>,</span> -<span> n <span class="op">=</span> <span class="fl">1</span>, seed <span class="op">=</span> <span class="fl">123456789</span> <span class="op">)</span></span> -<span></span> -<span><span class="co"># Fit the model to the dataset</span></span> -<span><span class="va">f_SFO_SFO_SFO</span> <span class="op"><-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">m_SFO_SFO_SFO</span>, <span class="va">d_SFO_SFO_SFO_err</span><span class="op">[[</span><span class="fl">1</span><span class="op">]</span><span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<span></span> -<span><span class="co"># Plot the results separately for parent and metabolites</span></span> -<span><span class="fu"><a href="../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">f_SFO_SFO_SFO</span>, lpos <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">"topright"</span>, <span class="st">"bottomright"</span>, <span class="st">"bottomright"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> -<p><img src="mkin_files/figure-html/unnamed-chunk-2-1.png" width="768"></p> -</div> -<div class="section level2"> -<h2 id="background">Background<a class="anchor" aria-label="anchor" href="#background"></a> -</h2> -<p>The <code>mkin</code> package <span class="citation">(J. Ranke -2021)</span> implements the approach to degradation kinetics recommended -in the kinetics report provided by the FOrum for Co-ordination of -pesticide fate models and their USe <span class="citation">(FOCUS Work -Group on Degradation Kinetics 2006, 2014)</span>. It covers data series -describing the decline of one compound, data series with transformation -products (commonly termed metabolites) and data series for more than one -compartment. It is possible to include back reactions. Therefore, -equilibrium reactions and equilibrium partitioning can be specified, -although this often leads to an overparameterisation of the model.</p> -<p>When the first <code>mkin</code> code was published in 2010, the most -commonly used tools for fitting more complex kinetic degradation models -to experimental data were KinGUI <span class="citation">(Schäfer et al. -2007)</span>, a MATLAB based tool with a graphical user interface that -was specifically tailored to the task and included some output as -proposed by the FOCUS Kinetics Workgroup, and ModelMaker, a general -purpose compartment based tool providing infrastructure for fitting -dynamic simulation models based on differential equations to data.</p> -<p>The ‘mkin’ code was first uploaded to the BerliOS development -platform. When this was taken down, the version control history was -imported into the R-Forge site (see <em>e.g.</em> <a href="https://cgit.jrwb.de/mkin/commit/?id=30cbb4092f6d2d3beff5800603374a0d009ad770" class="external-link">the -initial commit on 11 May 2010</a>), where the code is still being -updated.</p> -<p>At that time, the R package <code>FME</code> (Flexible Modelling -Environment) <span class="citation">(Soetaert and Petzoldt 2010)</span> -was already available, and provided a good basis for developing a -package specifically tailored to the task. The remaining challenge was -to make it as easy as possible for the users (including the author of -this vignette) to specify the system of differential equations and to -include the output requested by the FOCUS guidance, such as the <span class="math inline">\(\chi^2\)</span> error level as defined in this -guidance.</p> -<p>Also, <code>mkin</code> introduced using analytical solutions for -parent only kinetics for improved optimization speed. Later, Eigenvalue -based solutions were introduced to <code>mkin</code> for the case of -linear differential equations (<em>i.e.</em> where the FOMC or DFOP -models were not used for the parent compound), greatly improving the -optimization speed for these cases. This, has become somehow obsolete, -as the use of compiled code described below gives even faster execution -times.</p> -<p>The possibility to specify back-reactions and a biphasic model -(SFORB) for metabolites were present in <code>mkin</code> from the very -beginning.</p> -<div class="section level3"> -<h3 id="derived-software-tools">Derived software tools<a class="anchor" aria-label="anchor" href="#derived-software-tools"></a> -</h3> -<p>Soon after the publication of <code>mkin</code>, two derived tools -were published, namely KinGUII (developed at Bayer Crop Science) and -CAKE (commissioned to Tessella by Syngenta), which added a graphical -user interface (GUI), and added fitting by iteratively reweighted least -squares (IRLS) and characterisation of likely parameter distributions by -Markov Chain Monte Carlo (MCMC) sampling.</p> -<p>CAKE focuses on a smooth use experience, sacrificing some flexibility -in the model definition, originally allowing only two primary -metabolites in parallel. The current version 3.4 of CAKE released in May -2020 uses a scheme for up to six metabolites in a flexible arrangement -and supports biphasic modelling of metabolites, but does not support -back-reactions (non-instantaneous equilibria).</p> -<p>KinGUI offers an even more flexible widget for specifying complex -kinetic models. Back-reactions (non-instantaneous equilibria) were -supported early on, but until 2014, only simple first-order models could -be specified for transformation products. Starting with KinGUII version -2.1, biphasic modelling of metabolites was also available in -KinGUII.</p> -<p>A further graphical user interface (GUI) that has recently been -brought to a decent degree of maturity is the browser based GUI named -<code>gmkin</code>. Please see its <a href="https://pkgdown.jrwb.de/gmkin/" class="external-link">documentation page</a> and <a href="https://pkgdown.jrwb.de/gmkin/articles/gmkin_manual.html" class="external-link">manual</a> -for further information.</p> -<p>A comparison of scope, usability and numerical results obtained with -these tools has been recently been published by <span class="citation">Johannes Ranke, Wöltjen, and Meinecke -(2018)</span>.</p> -</div> -</div> -<div class="section level2"> -<h2 id="unique-features">Unique features<a class="anchor" aria-label="anchor" href="#unique-features"></a> -</h2> -<p>Currently, the main unique features available in <code>mkin</code> -are</p> -<ul> -<li>the <a href="https://pkgdown.jrwb.de/mkin/articles/web_only/compiled_models.html">speed -increase</a> by using compiled code when a compiler is present,</li> -<li>parallel model fitting on multicore machines using the <a href="https://pkgdown.jrwb.de/mkin/reference/mmkin.html"><code>mmkin</code> -function</a>,</li> -<li>the estimation of parameter confidence intervals based on -transformed parameters (see below) and</li> -<li>the possibility to use the <a href="https://pkgdown.jrwb.de/mkin/reference/sigma_twocomp.html">two-component -error model</a> -</li> -</ul> -<p>The iteratively reweighted least squares fitting of different -variances for each variable as introduced by <span class="citation">Gao -et al. (2011)</span> has been available in mkin since <a href="https://pkgdown.jrwb.de/mkin/news/index.html#mkin-0-9-22-2013-10-26">version -0.9-22</a>. With <a href="https://pkgdown.jrwb.de/mkin/news/index.html#mkin-0-9-49-5-2019-07-04">release -0.9.49.5</a>, the IRLS algorithm has been complemented by direct or -step-wise maximisation of the likelihood function, which makes it -possible not only to fit the variance by variable error model but also a -<a href="https://pkgdown.jrwb.de/mkin/reference/sigma_twocomp.html">two-component -error model</a> inspired by error models developed in analytical -chemistry <span class="citation">(Johannes Ranke and Meinecke -2019)</span>.</p> -</div> -<div class="section level2"> -<h2 id="internal-parameter-transformations">Internal parameter transformations<a class="anchor" aria-label="anchor" href="#internal-parameter-transformations"></a> -</h2> -<p>For rate constants, the log transformation is used, as proposed by -Bates and Watts <span class="citation">(1988, 77, 149)</span>. -Approximate intervals are constructed for the transformed rate constants -<span class="citation">(compare Bates and Watts 1988, 135)</span>, -<em>i.e.</em> for their logarithms. Confidence intervals for the rate -constants are then obtained using the appropriate backtransformation -using the exponential function.</p> -<p>In the first version of <code>mkin</code> allowing for specifying -models using formation fractions, a home-made reparameterisation was -used in order to ensure that the sum of formation fractions would not -exceed unity.</p> -<p>This method is still used in the current version of KinGUII (v2.1 -from April 2014), with a modification that allows for fixing the pathway -to sink to zero. CAKE uses penalties in the objective function in order -to enforce this constraint.</p> -<p>In 2012, an alternative reparameterisation of the formation fractions -was proposed together with René Lehmann <span class="citation">(J. Ranke -and Lehmann 2012)</span>, based on isometric logratio transformation -(ILR). The aim was to improve the validity of the linear approximation -of the objective function during the parameter estimation procedure as -well as in the subsequent calculation of parameter confidence intervals. -In the current version of mkin, a logit transformation is used for -parameters that are bound between 0 and 1, such as the g parameter of -the DFOP model.</p> -<div class="section level3"> -<h3 id="confidence-intervals-based-on-transformed-parameters">Confidence intervals based on transformed parameters<a class="anchor" aria-label="anchor" href="#confidence-intervals-based-on-transformed-parameters"></a> -</h3> -<p>In the first attempt at providing improved parameter confidence -intervals introduced to <code>mkin</code> in 2013, confidence intervals -obtained from FME on the transformed parameters were simply all -backtransformed one by one to yield asymmetric confidence intervals for -the backtransformed parameters.</p> -<p>However, while there is a 1:1 relation between the rate constants in -the model and the transformed parameters fitted in the model, the -parameters obtained by the isometric logratio transformation are -calculated from the set of formation fractions that quantify the paths -to each of the compounds formed from a specific parent compound, and no -such 1:1 relation exists.</p> -<p>Therefore, parameter confidence intervals for formation fractions -obtained with this method only appear valid for the case of a single -transformation product, where currently the logit transformation is used -for the formation fraction.</p> -<p>The confidence intervals obtained by backtransformation for the cases -where a 1:1 relation between transformed and original parameter exist -are considered by the author of this vignette to be more accurate than -those obtained using a re-estimation of the Hessian matrix after -backtransformation, as implemented in the FME package.</p> -</div> -<div class="section level3"> -<h3 id="parameter-t-test-based-on-untransformed-parameters">Parameter t-test based on untransformed parameters<a class="anchor" aria-label="anchor" href="#parameter-t-test-based-on-untransformed-parameters"></a> -</h3> -<p>The standard output of many nonlinear regression software packages -includes the results from a test for significant difference from zero -for all parameters. Such a test is also recommended to check the -validity of rate constants in the FOCUS guidance <span class="citation">(FOCUS Work Group on Degradation Kinetics 2014, -96ff)</span>.</p> -<p>It has been argued that the precondition for this test, <em>i.e.</em> -normal distribution of the estimator for the parameters, is not -fulfilled in the case of nonlinear regression <span class="citation">(J. -Ranke and Lehmann 2015)</span>. However, this test is commonly used by -industry, consultants and national authorities in order to decide on the -reliability of parameter estimates, based on the FOCUS guidance -mentioned above. Therefore, the results of this one-sided t-test are -included in the summary output from <code>mkin</code>.</p> -<p>As it is not reasonable to test for significant difference of the -transformed parameters (<em>e.g.</em> <span class="math inline">\(log(k)\)</span>) from zero, the t-test is -calculated based on the model definition before parameter -transformation, <em>i.e.</em> in a similar way as in packages that do -not apply such an internal parameter transformation. A note is included -in the <code>mkin</code> output, pointing to the fact that the t-test is -based on the unjustified assumption of normal distribution of the -parameter estimators.</p> -</div> -</div> -<div class="section level2"> -<h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a> -</h2> -<!-- vim: set foldmethod=syntax: --> -<div id="refs" class="references csl-bib-body hanging-indent"> -<div id="ref-bates1988" class="csl-entry"> -Bates, D., and D. Watts. 1988. <em>Nonlinear Regression and Its -Applications</em>. Wiley-Interscience. -</div> -<div id="ref-FOCUS2006" class="csl-entry"> -FOCUS Work Group on Degradation Kinetics. 2006. <em>Guidance Document on -Estimating Persistence and Degradation Kinetics from Environmental Fate -Studies on Pesticides in EU Registration. Report of the FOCUS Work Group -on Degradation Kinetics</em>. <a href="http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics" class="external-link">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>. -</div> -<div id="ref-FOCUSkinetics2014" class="csl-entry"> -———. 2014. <em>Generic Guidance for Estimating Persistence and -Degradation Kinetics from Environmental Fate Studies on Pesticides in EU -Registration</em>. 1.1 ed. <a href="http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics" class="external-link">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>. -</div> -<div id="ref-gao11" class="csl-entry"> -Gao, Z., J. W. Green, J. Vanderborght, and W. Schmitt. 2011. -<span>“Improving Uncertainty Analysis in Kinetic Evaluations Using -Iteratively Reweighted Least Squares.”</span> Journal. <em>Environmental -Science and Technology</em> 45: 4429–37. -</div> -<div id="ref-pkg:mkin" class="csl-entry"> -Ranke, J. 2021. <em>‘<span class="nocase">mkin</span>‘: -<span>K</span>inetic Evaluation of Chemical Degradation Data</em>. <a href="https://CRAN.R-project.org/package=mkin" class="external-link">https://CRAN.R-project.org/package=mkin</a>. -</div> -<div id="ref-ranke2012" class="csl-entry"> -Ranke, J., and R. Lehmann. 2012. <span>“Parameter Reliability in Kinetic -Evaluation of Environmental Metabolism Data - Assessment and the -Influence of Model Specification.”</span> In <em>SETAC World 20-24 -May</em>. Berlin. <a href="https://jrwb.de/posters/Poster_SETAC_2012_Kinetic_parameter_uncertainty_model_parameterization_Lehmann_Ranke.pdf" class="external-link">https://jrwb.de/posters/Poster_SETAC_2012_Kinetic_parameter_uncertainty_model_parameterization_Lehmann_Ranke.pdf</a>. -</div> -<div id="ref-ranke2015" class="csl-entry"> -———. 2015. <span>“To t-Test or Not to t-Test, That Is the -Question.”</span> In <em>XV Symposium on Pesticide Chemistry 2-4 -September 2015</em>. Piacenza. <a href="https://jrwb.de/posters/piacenza_2015.pdf" class="external-link">https://jrwb.de/posters/piacenza_2015.pdf</a>. -</div> -<div id="ref-ranke2019" class="csl-entry"> -Ranke, Johannes, and Stefan Meinecke. 2019. <span>“Error Models for the -Kinetic Evaluation of Chemical Degradation Data.”</span> -<em>Environments</em> 6 (12). <a href="https://doi.org/10.3390/environments6120124" class="external-link">https://doi.org/10.3390/environments6120124</a>. -</div> -<div id="ref-ranke2018" class="csl-entry"> -Ranke, Johannes, Janina Wöltjen, and Stefan Meinecke. 2018. -<span>“Comparison of Software Tools for Kinetic Evaluation of Chemical -Degradation Data.”</span> <em>Environmental Sciences Europe</em> 30 (1): -17. <a href="https://doi.org/10.1186/s12302-018-0145-1" class="external-link">https://doi.org/10.1186/s12302-018-0145-1</a>. -</div> -<div id="ref-schaefer2007" class="csl-entry"> -Schäfer, D., B. Mikolasch, P. Rainbird, and B. Harvey. 2007. -<span>“<span>KinGUI</span>: A New Kinetic Software Tool for Evaluations -According to <span>FOCUS</span> Degradation Kinetics.”</span> In -<em>Proceedings of the XIII Symposium Pesticide Chemistry</em>, edited -by Del Re A. A. M., Capri E., Fragoulis G., and Trevisan M., 916–23. -Piacenza. -</div> -<div id="ref-soetaert2010" class="csl-entry"> -Soetaert, Karline, and Thomas Petzoldt. 2010. <span>“Inverse Modelling, -Sensitivity and Monte Carlo Analysis in <span>R</span> Using Package -<span>FME</span>.”</span> <em>Journal of Statistical Software</em> 33 -(3): 1–28. <a href="https://doi.org/10.18637/jss.v033.i03" class="external-link">https://doi.org/10.18637/jss.v033.i03</a>. -</div> -</div> -</div> - </div> - - <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar"> - - <nav id="toc" data-toggle="toc"><h2 data-toc-skip>Contents</h2> - </nav> -</div> - -</div> - - - - <footer><div class="copyright"> - <p></p> -<p>Developed by Johannes Ranke.</p> -</div> - -<div class="pkgdown"> - <p></p> -<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p> -</div> - - </footer> -</div> - - - - - - - </body> -</html> diff --git a/docs/dev/articles/mkin_files/accessible-code-block-0.0.1/empty-anchor.js b/docs/dev/articles/mkin_files/accessible-code-block-0.0.1/empty-anchor.js deleted file mode 100644 index ca349fd6..00000000 --- a/docs/dev/articles/mkin_files/accessible-code-block-0.0.1/empty-anchor.js +++ /dev/null @@ -1,15 +0,0 @@ -// Hide empty <a> tag within highlighted CodeBlock for screen reader accessibility (see https://github.com/jgm/pandoc/issues/6352#issuecomment-626106786) --> -// v0.0.1 -// Written by JooYoung Seo (jooyoung@psu.edu) and Atsushi Yasumoto on June 1st, 2020. - -document.addEventListener('DOMContentLoaded', function() { - const codeList = document.getElementsByClassName("sourceCode"); - for (var i = 0; i < codeList.length; i++) { - var linkList = codeList[i].getElementsByTagName('a'); - for (var j = 0; j < linkList.length; j++) { - if (linkList[j].innerHTML === "") { - linkList[j].setAttribute('aria-hidden', 'true'); - } - } - } -}); diff --git a/docs/dev/articles/mkin_files/anchor-sections-1.0/anchor-sections.css b/docs/dev/articles/mkin_files/anchor-sections-1.0/anchor-sections.css deleted file mode 100644 index 07aee5fc..00000000 --- a/docs/dev/articles/mkin_files/anchor-sections-1.0/anchor-sections.css +++ /dev/null @@ -1,4 +0,0 @@ -/* Styles for section anchors */ -a.anchor-section {margin-left: 10px; visibility: hidden; color: inherit;} -a.anchor-section::before {content: '#';} -.hasAnchor:hover a.anchor-section {visibility: visible;} diff --git a/docs/dev/articles/mkin_files/anchor-sections-1.0/anchor-sections.js b/docs/dev/articles/mkin_files/anchor-sections-1.0/anchor-sections.js deleted file mode 100644 index 570f99a0..00000000 --- a/docs/dev/articles/mkin_files/anchor-sections-1.0/anchor-sections.js +++ /dev/null @@ -1,33 +0,0 @@ -// Anchor sections v1.0 written by Atsushi Yasumoto on Oct 3rd, 2020. -document.addEventListener('DOMContentLoaded', function() { - // Do nothing if AnchorJS is used - if (typeof window.anchors === 'object' && anchors.hasOwnProperty('hasAnchorJSLink')) { - return; - } - - const h = document.querySelectorAll('h1, h2, h3, h4, h5, h6'); - - // Do nothing if sections are already anchored - if (Array.from(h).some(x => x.classList.contains('hasAnchor'))) { - return null; - } - - // Use section id when pandoc runs with --section-divs - const section_id = function(x) { - return ((x.classList.contains('section') || (x.tagName === 'SECTION')) - ? x.id : ''); - }; - - // Add anchors - h.forEach(function(x) { - const id = x.id || section_id(x.parentElement); - if (id === '') { - return null; - } - let anchor = document.createElement('a'); - anchor.href = '#' + id; - anchor.classList = ['anchor-section']; - x.classList.add('hasAnchor'); - x.appendChild(anchor); - }); -}); diff --git a/docs/dev/articles/mkin_files/figure-html/unnamed-chunk-2-1.png b/docs/dev/articles/mkin_files/figure-html/unnamed-chunk-2-1.png Binary files differdeleted file mode 100644 index 7ba861ea..00000000 --- a/docs/dev/articles/mkin_files/figure-html/unnamed-chunk-2-1.png +++ /dev/null diff --git a/docs/dev/articles/mkin_files/header-attrs-2.6/header-attrs.js b/docs/dev/articles/mkin_files/header-attrs-2.6/header-attrs.js deleted file mode 100644 index dd57d92e..00000000 --- a/docs/dev/articles/mkin_files/header-attrs-2.6/header-attrs.js +++ /dev/null @@ -1,12 +0,0 @@ -// Pandoc 2.9 adds attributes on both header and div. 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<div class="hidden name"><code>2022_cyan_pathway.rmd</code></div> - - </div> - - - -<div class="section level2"> -<h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#introduction"></a> -</h2> -<p>The purpose of this document is to test demonstrate how nonlinear -hierarchical models (NLHM) based on the parent degradation models SFO, -FOMC, DFOP and HS, with serial formation of two or more metabolites can -be fitted with the mkin package.</p> -<p>It was assembled in the course of work package 1.2 of Project Number -173340 (Application of nonlinear hierarchical models to the kinetic -evaluation of chemical degradation data) of the German Environment -Agency carried out in 2022 and 2023.</p> -<p>The mkin package is used in version 1.2.4 which is currently under -development. The newly introduced functionality that is used here is a -simplification of excluding random effects for a set of fits based on a -related set of fits with a reduced model, and the documentation of the -starting parameters of the fit, so that all starting parameters of -<code>saem</code> fits are now listed in the summary. The -<code>saemix</code> package is used as a backend for fitting the NLHM, -but is also loaded to make the convergence plot function available.</p> -<p>This document is processed with the <code>knitr</code> package, which -also provides the <code>kable</code> function that is used to improve -the display of tabular data in R markdown documents. For parallel -processing, the <code>parallel</code> package is used.</p> -<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://pkgdown.jrwb.de/mkin/">mkin</a></span><span class="op">)</span></span> -<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://yihui.org/knitr/" class="external-link">knitr</a></span><span class="op">)</span></span> -<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">saemix</span><span class="op">)</span></span> -<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">parallel</span><span class="op">)</span></span> -<span><span class="va">n_cores</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/detectCores.html" class="external-link">detectCores</a></span><span class="op">(</span><span class="op">)</span></span> -<span></span> -<span><span class="co"># We need to start a new cluster after defining a compiled model that is</span></span> -<span><span class="co"># saved as a DLL to the user directory, therefore we define a function</span></span> -<span><span class="co"># This is used again after defining the pathway model</span></span> -<span><span class="va">start_cluster</span> <span class="op"><-</span> <span class="kw">function</span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span> <span class="op">{</span></span> -<span> <span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/Sys.info.html" class="external-link">Sys.info</a></span><span class="op">(</span><span class="op">)</span><span class="op">[</span><span class="st">"sysname"</span><span class="op">]</span> <span class="op">==</span> <span class="st">"Windows"</span><span class="op">)</span> <span class="op">{</span></span> -<span> <span class="va">ret</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makePSOCKcluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> -<span> <span class="op">}</span> <span class="kw">else</span> <span class="op">{</span></span> -<span> <span class="va">ret</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makeForkCluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> -<span> <span class="op">}</span></span> -<span> <span class="kw"><a href="https://rdrr.io/r/base/function.html" class="external-link">return</a></span><span class="op">(</span><span class="va">ret</span><span class="op">)</span></span> -<span><span class="op">}</span></span> -<span><span class="va">cl</span> <span class="op"><-</span> <span class="fu">start_cluster</span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span></code></pre></div> -<div class="section level3"> -<h3 id="test-data">Test data<a class="anchor" aria-label="anchor" href="#test-data"></a> -</h3> -<p>The example data are taken from the final addendum to the DAR from -2014 and are distributed with the mkin package. Residue data and time -step normalisation factors are read in using the function -<code>read_spreadsheet</code> from the mkin package. This function also -performs the time step normalisation.</p> -<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">data_file</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.file.html" class="external-link">system.file</a></span><span class="op">(</span></span> -<span> <span class="st">"testdata"</span>, <span class="st">"cyantraniliprole_soil_efsa_2014.xlsx"</span>,</span> -<span> package <span class="op">=</span> <span class="st">"mkin"</span><span class="op">)</span></span> -<span><span class="va">cyan_ds</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/read_spreadsheet.html">read_spreadsheet</a></span><span class="op">(</span><span class="va">data_file</span>, parent_only <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div> -<p>The following tables show the covariate data and the 5 datasets that -were read in from the spreadsheet file.</p> -<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">pH</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/attr.html" class="external-link">attr</a></span><span class="op">(</span><span class="va">cyan_ds</span>, <span class="st">"covariates"</span><span class="op">)</span></span> -<span><span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="va">pH</span>, caption <span class="op">=</span> <span class="st">"Covariate data"</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<caption>Covariate data</caption> -<thead><tr class="header"> -<th align="left"></th> -<th align="right">pH</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">Nambsheim</td> -<td align="right">7.90</td> -</tr> -<tr class="even"> -<td align="left">Tama</td> -<td align="right">6.20</td> -</tr> -<tr class="odd"> -<td align="left">Gross-Umstadt</td> -<td align="right">7.04</td> -</tr> -<tr class="even"> -<td align="left">Sassafras</td> -<td align="right">4.62</td> -</tr> -<tr class="odd"> -<td align="left">Lleida</td> -<td align="right">8.05</td> -</tr> -</tbody> -</table> -<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="kw">for</span> <span class="op">(</span><span class="va">ds_name</span> <span class="kw">in</span> <span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">cyan_ds</span><span class="op">)</span><span class="op">)</span> <span class="op">{</span></span> -<span> <span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span></span> -<span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="fu"><a href="../../reference/mkin_long_to_wide.html">mkin_long_to_wide</a></span><span class="op">(</span><span class="va">cyan_ds</span><span class="op">[[</span><span class="va">ds_name</span><span class="op">]</span><span class="op">]</span><span class="op">)</span>,</span> -<span> caption <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste</a></span><span class="op">(</span><span class="st">"Dataset"</span>, <span class="va">ds_name</span><span class="op">)</span>,</span> -<span> booktabs <span class="op">=</span> <span class="cn">TRUE</span>, row.names <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">)</span></span> -<span> <span class="fu"><a href="https://rdrr.io/r/base/cat.html" class="external-link">cat</a></span><span class="op">(</span><span class="st">"\n\\clearpage\n"</span><span class="op">)</span></span> -<span><span class="op">}</span></span></code></pre></div> -<table class="table"> -<caption>Dataset Nambsheim</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">cyan</th> -<th align="right">JCZ38</th> -<th align="right">J9C38</th> -<th align="right">JSE76</th> -<th align="right">J9Z38</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.000000</td> -<td align="right">105.79</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">3.210424</td> -<td align="right">77.26</td> -<td align="right">7.92</td> -<td align="right">11.94</td> -<td align="right">5.58</td> -<td align="right">9.12</td> -</tr> -<tr class="odd"> -<td align="right">7.490988</td> -<td align="right">57.13</td> -<td align="right">15.46</td> -<td align="right">16.58</td> -<td align="right">12.59</td> -<td align="right">11.74</td> -</tr> -<tr class="even"> -<td align="right">17.122259</td> -<td align="right">37.74</td> -<td align="right">15.98</td> -<td align="right">13.36</td> -<td align="right">26.05</td> -<td align="right">10.77</td> -</tr> -<tr class="odd"> -<td align="right">23.543105</td> -<td align="right">31.47</td> -<td align="right">6.05</td> -<td align="right">14.49</td> -<td align="right">34.71</td> -<td align="right">4.96</td> -</tr> -<tr class="even"> -<td align="right">43.875788</td> -<td align="right">16.74</td> -<td align="right">6.07</td> -<td align="right">7.57</td> -<td align="right">40.38</td> -<td align="right">6.52</td> -</tr> -<tr class="odd"> -<td align="right">67.418893</td> -<td align="right">8.85</td> -<td align="right">10.34</td> -<td align="right">6.39</td> -<td align="right">30.71</td> -<td align="right">8.90</td> -</tr> -<tr class="even"> -<td align="right">107.014116</td> -<td align="right">5.19</td> -<td align="right">9.61</td> -<td align="right">1.95</td> -<td align="right">20.41</td> -<td align="right">12.93</td> -</tr> -<tr class="odd"> -<td align="right">129.487080</td> -<td align="right">3.45</td> -<td align="right">6.18</td> -<td align="right">1.36</td> -<td align="right">21.78</td> -<td align="right">6.99</td> -</tr> -<tr class="even"> -<td align="right">195.835832</td> -<td align="right">2.15</td> -<td align="right">9.13</td> -<td align="right">0.95</td> -<td align="right">16.29</td> -<td align="right">7.69</td> -</tr> -<tr class="odd"> -<td align="right">254.693596</td> -<td align="right">1.92</td> -<td align="right">6.92</td> -<td align="right">0.20</td> -<td align="right">13.57</td> -<td align="right">7.16</td> -</tr> -<tr class="even"> -<td align="right">321.042348</td> -<td align="right">2.26</td> -<td align="right">7.02</td> -<td align="right">NA</td> -<td align="right">11.12</td> -<td align="right">8.66</td> -</tr> -<tr class="odd"> -<td align="right">383.110535</td> -<td align="right">NA</td> -<td align="right">5.05</td> -<td align="right">NA</td> -<td align="right">10.64</td> -<td align="right">5.56</td> -</tr> -<tr class="even"> -<td align="right">0.000000</td> -<td align="right">105.57</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">3.210424</td> -<td align="right">78.88</td> -<td align="right">12.77</td> -<td align="right">11.94</td> -<td align="right">5.47</td> -<td align="right">9.12</td> -</tr> -<tr class="even"> -<td align="right">7.490988</td> -<td align="right">59.94</td> -<td align="right">15.27</td> -<td align="right">16.58</td> -<td align="right">13.60</td> -<td align="right">11.74</td> -</tr> -<tr class="odd"> -<td align="right">17.122259</td> -<td align="right">39.67</td> -<td align="right">14.26</td> -<td align="right">13.36</td> -<td align="right">29.44</td> -<td align="right">10.77</td> -</tr> -<tr class="even"> -<td align="right">23.543105</td> -<td align="right">30.21</td> -<td align="right">16.07</td> -<td align="right">14.49</td> -<td align="right">35.90</td> -<td align="right">4.96</td> -</tr> -<tr class="odd"> -<td align="right">43.875788</td> -<td align="right">18.06</td> -<td align="right">9.44</td> -<td align="right">7.57</td> -<td align="right">42.30</td> -<td align="right">6.52</td> -</tr> -<tr class="even"> -<td align="right">67.418893</td> -<td align="right">8.54</td> -<td align="right">5.78</td> -<td align="right">6.39</td> -<td align="right">34.70</td> -<td align="right">8.90</td> -</tr> -<tr class="odd"> -<td align="right">107.014116</td> -<td align="right">7.26</td> -<td align="right">4.54</td> -<td align="right">1.95</td> -<td align="right">23.33</td> -<td align="right">12.93</td> -</tr> -<tr class="even"> -<td align="right">129.487080</td> -<td align="right">3.60</td> -<td align="right">4.22</td> -<td align="right">1.36</td> -<td align="right">23.56</td> -<td align="right">6.99</td> -</tr> -<tr class="odd"> -<td align="right">195.835832</td> -<td align="right">2.84</td> -<td align="right">3.05</td> -<td align="right">0.95</td> -<td align="right">16.21</td> -<td align="right">7.69</td> -</tr> -<tr class="even"> -<td align="right">254.693596</td> -<td align="right">2.00</td> -<td align="right">2.90</td> -<td align="right">0.20</td> -<td align="right">15.53</td> -<td align="right">7.16</td> -</tr> -<tr class="odd"> -<td align="right">321.042348</td> -<td align="right">1.79</td> -<td align="right">0.94</td> -<td align="right">NA</td> -<td align="right">9.80</td> -<td align="right">8.66</td> -</tr> -<tr class="even"> -<td align="right">383.110535</td> -<td align="right">NA</td> -<td align="right">1.82</td> -<td align="right">NA</td> -<td align="right">9.49</td> -<td align="right">5.56</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset Tama</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">cyan</th> -<th align="right">JCZ38</th> -<th align="right">J9Z38</th> -<th align="right">JSE76</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.000000</td> -<td align="right">106.14</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">2.400833</td> -<td align="right">93.47</td> -<td align="right">6.46</td> -<td align="right">2.85</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">5.601943</td> -<td align="right">88.39</td> -<td align="right">10.86</td> -<td align="right">4.65</td> -<td align="right">3.85</td> -</tr> -<tr class="even"> -<td align="right">12.804442</td> -<td align="right">72.29</td> -<td align="right">11.97</td> -<td align="right">4.91</td> -<td align="right">11.24</td> -</tr> -<tr class="odd"> -<td align="right">17.606108</td> -<td align="right">65.79</td> -<td align="right">13.11</td> -<td align="right">6.63</td> -<td align="right">13.79</td> -</tr> -<tr class="even"> -<td align="right">32.811382</td> -<td align="right">53.16</td> -<td align="right">11.24</td> -<td align="right">8.90</td> -<td align="right">23.40</td> -</tr> -<tr class="odd"> -<td align="right">50.417490</td> -<td align="right">44.01</td> -<td align="right">11.34</td> -<td align="right">9.98</td> -<td align="right">29.56</td> -</tr> -<tr class="even"> -<td align="right">80.027761</td> -<td align="right">33.23</td> -<td align="right">8.82</td> -<td align="right">11.31</td> -<td align="right">35.63</td> -</tr> -<tr class="odd"> -<td align="right">96.833591</td> -<td align="right">40.68</td> -<td align="right">5.94</td> -<td align="right">8.32</td> -<td align="right">29.09</td> -</tr> -<tr class="even"> -<td align="right">146.450803</td> -<td align="right">20.65</td> -<td align="right">4.49</td> -<td align="right">8.72</td> -<td align="right">36.88</td> -</tr> -<tr class="odd"> -<td align="right">190.466072</td> -<td align="right">17.71</td> -<td align="right">4.66</td> -<td align="right">11.10</td> -<td align="right">40.97</td> -</tr> -<tr class="even"> -<td align="right">240.083284</td> -<td align="right">14.86</td> -<td align="right">2.27</td> -<td align="right">11.62</td> -<td align="right">40.11</td> -</tr> -<tr class="odd"> -<td align="right">286.499386</td> -<td align="right">12.02</td> -<td align="right">NA</td> -<td align="right">10.73</td> -<td align="right">42.58</td> -</tr> -<tr class="even"> -<td align="right">0.000000</td> -<td align="right">109.11</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">2.400833</td> -<td align="right">96.84</td> -<td align="right">5.52</td> -<td align="right">2.04</td> -<td align="right">2.02</td> -</tr> -<tr class="even"> -<td align="right">5.601943</td> -<td align="right">85.29</td> -<td align="right">9.65</td> -<td align="right">2.99</td> -<td align="right">4.39</td> -</tr> -<tr class="odd"> -<td align="right">12.804442</td> -<td align="right">73.68</td> -<td align="right">12.48</td> -<td align="right">5.05</td> -<td align="right">11.47</td> -</tr> -<tr class="even"> -<td align="right">17.606108</td> -<td align="right">64.89</td> -<td align="right">12.44</td> -<td align="right">6.29</td> -<td align="right">15.00</td> -</tr> -<tr class="odd"> -<td align="right">32.811382</td> -<td align="right">52.27</td> -<td align="right">10.86</td> -<td align="right">7.65</td> -<td align="right">23.30</td> -</tr> -<tr class="even"> -<td align="right">50.417490</td> -<td align="right">42.61</td> -<td align="right">10.54</td> -<td align="right">9.37</td> -<td align="right">31.06</td> -</tr> -<tr class="odd"> -<td align="right">80.027761</td> -<td align="right">34.29</td> -<td align="right">10.02</td> -<td align="right">9.04</td> -<td align="right">37.87</td> -</tr> -<tr class="even"> -<td align="right">96.833591</td> -<td align="right">30.50</td> -<td align="right">6.34</td> -<td align="right">8.14</td> -<td align="right">33.97</td> -</tr> -<tr class="odd"> -<td align="right">146.450803</td> -<td align="right">19.21</td> -<td align="right">6.29</td> -<td align="right">8.52</td> -<td align="right">26.15</td> -</tr> -<tr class="even"> -<td align="right">190.466072</td> -<td align="right">17.55</td> -<td align="right">5.81</td> -<td align="right">9.89</td> -<td align="right">32.08</td> -</tr> -<tr class="odd"> -<td align="right">240.083284</td> -<td align="right">13.22</td> -<td align="right">5.99</td> -<td align="right">10.79</td> -<td align="right">40.66</td> -</tr> -<tr class="even"> -<td align="right">286.499386</td> -<td align="right">11.09</td> -<td align="right">6.05</td> -<td align="right">8.82</td> -<td align="right">42.90</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset Gross-Umstadt</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">cyan</th> -<th align="right">JCZ38</th> -<th align="right">J9Z38</th> -<th align="right">JSE76</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.0000000</td> -<td align="right">103.03</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">2.1014681</td> -<td align="right">87.85</td> -<td align="right">4.79</td> -<td align="right">3.26</td> -<td align="right">0.62</td> -</tr> -<tr class="odd"> -<td align="right">4.9034255</td> -<td align="right">77.35</td> -<td align="right">8.05</td> -<td align="right">9.89</td> -<td align="right">1.32</td> -</tr> -<tr class="even"> -<td align="right">10.5073404</td> -<td align="right">69.33</td> -<td align="right">9.74</td> -<td align="right">12.32</td> -<td align="right">4.74</td> -</tr> -<tr class="odd"> -<td align="right">21.0146807</td> -<td align="right">55.65</td> -<td align="right">14.57</td> -<td align="right">13.59</td> -<td align="right">9.84</td> -</tr> -<tr class="even"> -<td align="right">31.5220211</td> -<td align="right">49.03</td> -<td align="right">14.66</td> -<td align="right">16.71</td> -<td align="right">12.32</td> -</tr> -<tr class="odd"> -<td align="right">42.0293615</td> -<td align="right">41.86</td> -<td align="right">15.97</td> -<td align="right">13.64</td> -<td align="right">15.53</td> -</tr> -<tr class="even"> -<td align="right">63.0440422</td> -<td align="right">34.88</td> -<td align="right">18.20</td> -<td align="right">14.12</td> -<td align="right">22.02</td> -</tr> -<tr class="odd"> -<td align="right">84.0587230</td> -<td align="right">28.26</td> -<td align="right">15.64</td> -<td align="right">14.06</td> -<td align="right">25.60</td> -</tr> -<tr class="even"> -<td align="right">0.0000000</td> -<td align="right">104.05</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">2.1014681</td> -<td align="right">85.25</td> -<td align="right">2.68</td> -<td align="right">7.32</td> -<td align="right">0.69</td> -</tr> -<tr class="even"> -<td align="right">4.9034255</td> -<td align="right">77.22</td> -<td align="right">7.28</td> -<td align="right">8.37</td> -<td align="right">1.45</td> -</tr> -<tr class="odd"> -<td align="right">10.5073404</td> -<td align="right">65.23</td> -<td align="right">10.73</td> -<td align="right">10.93</td> -<td align="right">4.74</td> -</tr> -<tr class="even"> -<td align="right">21.0146807</td> -<td align="right">57.78</td> -<td align="right">12.29</td> -<td align="right">14.80</td> -<td align="right">9.05</td> -</tr> -<tr class="odd"> -<td align="right">31.5220211</td> -<td align="right">54.83</td> -<td align="right">14.05</td> -<td align="right">12.01</td> -<td align="right">11.05</td> -</tr> -<tr class="even"> -<td align="right">42.0293615</td> -<td align="right">45.17</td> -<td align="right">12.12</td> -<td align="right">17.89</td> -<td align="right">15.71</td> -</tr> -<tr class="odd"> -<td align="right">63.0440422</td> -<td align="right">34.83</td> -<td align="right">12.90</td> -<td align="right">15.86</td> -<td align="right">22.52</td> -</tr> -<tr class="even"> -<td align="right">84.0587230</td> -<td align="right">26.59</td> -<td align="right">14.28</td> -<td align="right">14.91</td> -<td align="right">28.48</td> -</tr> -<tr class="odd"> -<td align="right">0.0000000</td> -<td align="right">104.62</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">0.8145225</td> -<td align="right">97.21</td> -<td align="right">NA</td> -<td align="right">4.00</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">1.9005525</td> -<td align="right">89.64</td> -<td align="right">3.59</td> -<td align="right">5.24</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">4.0726125</td> -<td align="right">87.90</td> -<td align="right">4.10</td> -<td align="right">9.58</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">8.1452251</td> -<td align="right">86.90</td> -<td align="right">5.96</td> -<td align="right">9.45</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">12.2178376</td> -<td align="right">74.74</td> -<td align="right">7.83</td> -<td align="right">15.03</td> -<td align="right">5.33</td> -</tr> -<tr class="odd"> -<td align="right">16.2904502</td> -<td align="right">74.13</td> -<td align="right">8.84</td> -<td align="right">14.41</td> -<td align="right">5.10</td> -</tr> -<tr class="even"> -<td align="right">24.4356753</td> -<td align="right">65.26</td> -<td align="right">11.84</td> -<td align="right">18.33</td> -<td align="right">6.71</td> -</tr> -<tr class="odd"> -<td align="right">32.5809004</td> -<td align="right">57.70</td> -<td align="right">12.74</td> -<td align="right">19.93</td> -<td align="right">9.74</td> -</tr> -<tr class="even"> -<td align="right">0.0000000</td> -<td align="right">101.94</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">0.8145225</td> -<td align="right">99.94</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">1.9005525</td> -<td align="right">94.87</td> -<td align="right">NA</td> -<td align="right">4.56</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">4.0726125</td> -<td align="right">86.96</td> -<td align="right">6.75</td> -<td align="right">6.90</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">8.1452251</td> -<td align="right">80.51</td> -<td align="right">10.68</td> -<td align="right">7.43</td> -<td align="right">2.58</td> -</tr> -<tr class="odd"> -<td align="right">12.2178376</td> -<td align="right">78.38</td> -<td align="right">10.35</td> -<td align="right">9.46</td> -<td align="right">3.69</td> -</tr> -<tr class="even"> -<td align="right">16.2904502</td> -<td align="right">70.05</td> -<td align="right">13.73</td> -<td align="right">9.27</td> -<td align="right">7.18</td> -</tr> -<tr class="odd"> -<td align="right">24.4356753</td> -<td align="right">61.28</td> -<td align="right">12.57</td> -<td align="right">13.28</td> -<td align="right">13.19</td> -</tr> -<tr class="even"> -<td align="right">32.5809004</td> -<td align="right">52.85</td> -<td align="right">12.67</td> -<td align="right">12.95</td> -<td align="right">13.69</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset Sassafras</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">cyan</th> -<th align="right">JCZ38</th> -<th align="right">J9Z38</th> -<th align="right">JSE76</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.000000</td> -<td align="right">102.17</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">2.216719</td> -<td align="right">95.49</td> -<td align="right">1.11</td> -<td align="right">0.10</td> -<td align="right">0.83</td> -</tr> -<tr class="odd"> -<td align="right">5.172343</td> -<td align="right">83.35</td> -<td align="right">6.43</td> -<td align="right">2.89</td> -<td align="right">3.30</td> -</tr> -<tr class="even"> -<td align="right">11.083593</td> -<td align="right">78.18</td> -<td align="right">10.00</td> -<td align="right">5.59</td> -<td align="right">0.81</td> -</tr> -<tr class="odd"> -<td align="right">22.167186</td> -<td align="right">70.44</td> -<td align="right">17.21</td> -<td align="right">4.23</td> -<td align="right">1.09</td> -</tr> -<tr class="even"> -<td align="right">33.250779</td> -<td align="right">68.00</td> -<td align="right">20.45</td> -<td align="right">5.86</td> -<td align="right">1.17</td> -</tr> -<tr class="odd"> -<td align="right">44.334371</td> -<td align="right">59.64</td> -<td align="right">24.64</td> -<td align="right">3.17</td> -<td align="right">2.72</td> -</tr> -<tr class="even"> -<td align="right">66.501557</td> -<td align="right">50.73</td> -<td align="right">27.50</td> -<td align="right">6.19</td> -<td align="right">1.27</td> -</tr> -<tr class="odd"> -<td align="right">88.668742</td> -<td align="right">45.65</td> -<td align="right">32.77</td> -<td align="right">5.69</td> -<td align="right">4.54</td> -</tr> -<tr class="even"> -<td align="right">0.000000</td> -<td align="right">100.43</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">2.216719</td> -<td align="right">95.34</td> -<td align="right">3.21</td> -<td align="right">0.14</td> -<td align="right">0.46</td> -</tr> -<tr class="even"> -<td align="right">5.172343</td> -<td align="right">84.38</td> -<td align="right">5.73</td> -<td align="right">4.75</td> -<td align="right">0.62</td> -</tr> -<tr class="odd"> -<td align="right">11.083593</td> -<td align="right">78.50</td> -<td align="right">11.89</td> -<td align="right">3.99</td> -<td align="right">0.73</td> -</tr> -<tr class="even"> -<td align="right">22.167186</td> -<td align="right">71.17</td> -<td align="right">17.28</td> -<td align="right">4.39</td> -<td align="right">0.66</td> -</tr> -<tr class="odd"> -<td align="right">33.250779</td> -<td align="right">59.41</td> -<td align="right">18.73</td> -<td align="right">11.85</td> -<td align="right">2.65</td> -</tr> -<tr class="even"> -<td align="right">44.334371</td> -<td align="right">64.57</td> -<td align="right">22.93</td> -<td align="right">5.13</td> -<td align="right">2.01</td> -</tr> -<tr class="odd"> -<td align="right">66.501557</td> -<td align="right">49.08</td> -<td align="right">33.39</td> -<td align="right">5.67</td> -<td align="right">3.63</td> -</tr> -<tr class="even"> -<td align="right">88.668742</td> -<td align="right">40.41</td> -<td align="right">39.60</td> -<td align="right">5.93</td> -<td align="right">6.17</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset Lleida</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">cyan</th> -<th align="right">JCZ38</th> -<th align="right">J9Z38</th> -<th align="right">JSE76</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.000000</td> -<td align="right">102.71</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">2.821051</td> -<td align="right">79.11</td> -<td align="right">5.70</td> -<td align="right">8.07</td> -<td align="right">0.97</td> -</tr> -<tr class="odd"> -<td align="right">6.582451</td> -<td align="right">70.03</td> -<td align="right">7.17</td> -<td align="right">11.31</td> -<td align="right">4.72</td> -</tr> -<tr class="even"> -<td align="right">14.105253</td> -<td align="right">50.93</td> -<td align="right">10.25</td> -<td align="right">14.84</td> -<td align="right">9.95</td> -</tr> -<tr class="odd"> -<td align="right">28.210505</td> -<td align="right">33.43</td> -<td align="right">10.40</td> -<td align="right">14.82</td> -<td align="right">24.06</td> -</tr> -<tr class="even"> -<td align="right">42.315758</td> -<td align="right">24.69</td> -<td align="right">9.75</td> -<td align="right">16.38</td> -<td align="right">29.38</td> -</tr> -<tr class="odd"> -<td align="right">56.421010</td> -<td align="right">22.99</td> -<td align="right">10.06</td> -<td align="right">15.51</td> -<td align="right">29.25</td> -</tr> -<tr class="even"> -<td align="right">84.631516</td> -<td align="right">14.63</td> -<td align="right">5.63</td> -<td align="right">14.74</td> -<td align="right">31.04</td> -</tr> -<tr class="odd"> -<td align="right">112.842021</td> -<td align="right">12.43</td> -<td align="right">4.17</td> -<td align="right">13.53</td> -<td align="right">33.28</td> -</tr> -<tr class="even"> -<td align="right">0.000000</td> -<td align="right">99.31</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">2.821051</td> -<td align="right">82.07</td> -<td align="right">6.55</td> -<td align="right">5.60</td> -<td align="right">1.12</td> -</tr> -<tr class="even"> -<td align="right">6.582451</td> -<td align="right">70.65</td> -<td align="right">7.61</td> -<td align="right">8.01</td> -<td align="right">3.21</td> -</tr> -<tr class="odd"> -<td align="right">14.105253</td> -<td align="right">53.52</td> -<td align="right">11.48</td> -<td align="right">10.82</td> -<td align="right">12.24</td> -</tr> -<tr class="even"> -<td align="right">28.210505</td> -<td align="right">35.60</td> -<td align="right">11.19</td> -<td align="right">15.43</td> -<td align="right">23.53</td> -</tr> -<tr class="odd"> -<td align="right">42.315758</td> -<td align="right">34.26</td> -<td align="right">11.09</td> -<td align="right">13.26</td> -<td align="right">27.42</td> -</tr> -<tr class="even"> -<td align="right">56.421010</td> -<td align="right">21.79</td> -<td align="right">4.80</td> -<td align="right">18.30</td> -<td align="right">30.20</td> -</tr> -<tr class="odd"> -<td align="right">84.631516</td> -<td align="right">14.06</td> -<td align="right">6.30</td> -<td align="right">16.35</td> -<td align="right">32.32</td> -</tr> -<tr class="even"> -<td align="right">112.842021</td> -<td align="right">11.51</td> -<td align="right">5.57</td> -<td align="right">12.64</td> -<td align="right">32.51</td> -</tr> -</tbody> -</table> -</div> -</div> -<div class="section level2"> -<h2 id="parent-only-evaluations">Parent only evaluations<a class="anchor" aria-label="anchor" href="#parent-only-evaluations"></a> -</h2> -<p>As the pathway fits have very long run times, evaluations of the -parent data are performed first, in order to determine for each -hierarchical parent degradation model which random effects on the -degradation model parameters are ill-defined.</p> -<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">cyan_sep_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>, <span class="st">"SFORB"</span>, <span class="st">"HS"</span><span class="op">)</span>,</span> -<span> <span class="va">cyan_ds</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>, cores <span class="op">=</span> <span class="va">n_cores</span><span class="op">)</span></span> -<span><span class="va">cyan_sep_tc</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">cyan_sep_const</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span> -<span><span class="va">cyan_saem_full</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mhmkin.html">mhmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">cyan_sep_const</span>, <span class="va">cyan_sep_tc</span><span class="op">)</span><span class="op">)</span></span> -<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">cyan_saem_full</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">const</th> -<th align="left">tc</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">SFO</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">FOMC</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">DFOP</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">SFORB</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">HS</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -</tbody> -</table> -<p>All fits converged successfully.</p> -<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">cyan_saem_full</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">const</th> -<th align="left">tc</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">SFO</td> -<td align="left">sd(cyan_0)</td> -<td align="left">sd(cyan_0)</td> -</tr> -<tr class="even"> -<td align="left">FOMC</td> -<td align="left">sd(log_beta)</td> -<td align="left">sd(cyan_0)</td> -</tr> -<tr class="odd"> -<td align="left">DFOP</td> -<td align="left">sd(cyan_0)</td> -<td align="left">sd(cyan_0), sd(log_k1)</td> -</tr> -<tr class="even"> -<td align="left">SFORB</td> -<td align="left">sd(cyan_free_0)</td> -<td align="left">sd(cyan_free_0), sd(log_k_cyan_free_bound)</td> -</tr> -<tr class="odd"> -<td align="left">HS</td> -<td align="left">sd(cyan_0)</td> -<td align="left">sd(cyan_0)</td> -</tr> -</tbody> -</table> -<p>In almost all models, the random effect for the initial concentration -of the parent compound is ill-defined. For the biexponential models DFOP -and SFORB, the random effect of one additional parameter is ill-defined -when the two-component error model is used.</p> -<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">cyan_saem_full</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="right">npar</th> -<th align="right">AIC</th> -<th align="right">BIC</th> -<th align="right">Lik</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">SFO const</td> -<td align="right">5</td> -<td align="right">833.9</td> -<td align="right">832.0</td> -<td align="right">-412.0</td> -</tr> -<tr class="even"> -<td align="left">SFO tc</td> -<td align="right">6</td> -<td align="right">831.6</td> -<td align="right">829.3</td> -<td align="right">-409.8</td> -</tr> -<tr class="odd"> -<td align="left">FOMC const</td> -<td align="right">7</td> -<td align="right">709.1</td> -<td align="right">706.4</td> -<td align="right">-347.6</td> -</tr> -<tr class="even"> -<td align="left">FOMC tc</td> -<td align="right">8</td> -<td align="right">689.2</td> -<td align="right">686.1</td> -<td align="right">-336.6</td> -</tr> -<tr class="odd"> -<td align="left">DFOP const</td> -<td align="right">9</td> -<td align="right">703.0</td> -<td align="right">699.5</td> -<td align="right">-342.5</td> -</tr> -<tr class="even"> -<td align="left">SFORB const</td> -<td align="right">9</td> -<td align="right">701.3</td> -<td align="right">697.8</td> -<td align="right">-341.7</td> -</tr> -<tr class="odd"> -<td align="left">HS const</td> -<td align="right">9</td> -<td align="right">718.6</td> -<td align="right">715.1</td> -<td align="right">-350.3</td> -</tr> -<tr class="even"> -<td align="left">DFOP tc</td> -<td align="right">10</td> -<td align="right">703.1</td> -<td align="right">699.2</td> -<td align="right">-341.6</td> -</tr> -<tr class="odd"> -<td align="left">SFORB tc</td> -<td align="right">10</td> -<td align="right">700.1</td> -<td align="right">696.2</td> -<td align="right">-340.1</td> -</tr> -<tr class="even"> -<td align="left">HS tc</td> -<td align="right">10</td> -<td align="right">716.7</td> -<td align="right">712.8</td> -<td align="right">-348.3</td> -</tr> -</tbody> -</table> -<p>Model comparison based on AIC and BIC indicates that the -two-component error model is preferable for all parent models with the -exception of DFOP. The lowest AIC and BIC values are are obtained with -the FOMC model, followed by SFORB and DFOP.</p> -<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">stopCluster</a></span><span class="op">(</span><span class="va">cl</span><span class="op">)</span></span></code></pre></div> -</div> -<div class="section level2"> -<h2 id="pathway-fits">Pathway fits<a class="anchor" aria-label="anchor" href="#pathway-fits"></a> -</h2> -<div class="section level3"> -<h3 id="evaluations-with-pathway-established-previously">Evaluations with pathway established previously<a class="anchor" aria-label="anchor" href="#evaluations-with-pathway-established-previously"></a> -</h3> -<p>To test the technical feasibility of coupling the relevant parent -degradation models with different transformation pathway models, a list -of <code>mkinmod</code> models is set up below. As in the EU evaluation, -parallel formation of metabolites JCZ38 and J9Z38 and secondary -formation of metabolite JSE76 from JCZ38 is used.</p> -<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="kw">if</span> <span class="op">(</span><span class="op">!</span><span class="fu"><a href="https://rdrr.io/r/base/files2.html" class="external-link">dir.exists</a></span><span class="op">(</span><span class="st">"cyan_dlls"</span><span class="op">)</span><span class="op">)</span> <span class="fu"><a href="https://rdrr.io/r/base/files2.html" class="external-link">dir.create</a></span><span class="op">(</span><span class="st">"cyan_dlls"</span><span class="op">)</span></span> -<span><span class="va">cyan_path_1</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span></span> -<span> sfo_path_1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> cyan <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"JCZ38"</span>, <span class="st">"J9Z38"</span><span class="op">)</span><span class="op">)</span>,</span> -<span> JCZ38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JSE76"</span><span class="op">)</span>,</span> -<span> J9Z38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> JSE76 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> name <span class="op">=</span> <span class="st">"sfo_path_1"</span>, dll_dir <span class="op">=</span> <span class="st">"cyan_dlls"</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,</span> -<span> fomc_path_1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> cyan <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"FOMC"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"JCZ38"</span>, <span class="st">"J9Z38"</span><span class="op">)</span><span class="op">)</span>,</span> -<span> JCZ38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JSE76"</span><span class="op">)</span>,</span> -<span> J9Z38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> JSE76 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> name <span class="op">=</span> <span class="st">"fomc_path_1"</span>, dll_dir <span class="op">=</span> <span class="st">"cyan_dlls"</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,</span> -<span> dfop_path_1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> cyan <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"DFOP"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"JCZ38"</span>, <span class="st">"J9Z38"</span><span class="op">)</span><span class="op">)</span>,</span> -<span> JCZ38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JSE76"</span><span class="op">)</span>,</span> -<span> J9Z38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> JSE76 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> name <span class="op">=</span> <span class="st">"dfop_path_1"</span>, dll_dir <span class="op">=</span> <span class="st">"cyan_dlls"</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,</span> -<span> sforb_path_1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> cyan <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"JCZ38"</span>, <span class="st">"J9Z38"</span><span class="op">)</span><span class="op">)</span>,</span> -<span> JCZ38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JSE76"</span><span class="op">)</span>,</span> -<span> J9Z38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> JSE76 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> name <span class="op">=</span> <span class="st">"sforb_path_1"</span>, dll_dir <span class="op">=</span> <span class="st">"cyan_dlls"</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,</span> -<span> hs_path_1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> cyan <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"HS"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"JCZ38"</span>, <span class="st">"J9Z38"</span><span class="op">)</span><span class="op">)</span>,</span> -<span> JCZ38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JSE76"</span><span class="op">)</span>,</span> -<span> J9Z38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> JSE76 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> name <span class="op">=</span> <span class="st">"hs_path_1"</span>, dll_dir <span class="op">=</span> <span class="st">"cyan_dlls"</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<span><span class="op">)</span></span> -<span><span class="va">cl_path_1</span> <span class="op"><-</span> <span class="fu">start_cluster</span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span></code></pre></div> -<p>To obtain suitable starting values for the NLHM fits, separate -pathway fits are performed for all datasets.</p> -<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_sep_1_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span></span> -<span> <span class="va">cyan_path_1</span>,</span> -<span> <span class="va">cyan_ds</span>,</span> -<span> error_model <span class="op">=</span> <span class="st">"const"</span>,</span> -<span> cluster <span class="op">=</span> <span class="va">cl_path_1</span>,</span> -<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_1_const</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">Nambsheim</th> -<th align="left">Tama</th> -<th align="left">Gross-Umstadt</th> -<th align="left">Sassafras</th> -<th align="left">Lleida</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">sfo_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">fomc_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">dfop_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">sforb_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">hs_path_1</td> -<td align="left">C</td> -<td align="left">C</td> -<td align="left">C</td> -<td align="left">C</td> -<td align="left">C</td> -</tr> -</tbody> -</table> -<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_sep_1_tc</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_sep_1_const</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span> -<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_1_tc</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">Nambsheim</th> -<th align="left">Tama</th> -<th align="left">Gross-Umstadt</th> -<th align="left">Sassafras</th> -<th align="left">Lleida</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">sfo_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">fomc_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">C</td> -</tr> -<tr class="odd"> -<td align="left">dfop_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">sforb_path_1</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">hs_path_1</td> -<td align="left">C</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -</tbody> -</table> -<p>Most separate fits converged successfully. The biggest convergence -problems are seen when using the HS model with constant variance.</p> -<p>For the hierarchical pathway fits, those random effects that could -not be quantified in the corresponding parent data analyses are -excluded.</p> -<p>In the code below, the output of the <code>illparms</code> function -for the parent only fits is used as an argument -<code>no_random_effect</code> to the <code>mhmkin</code> function. The -possibility to do so was introduced in mkin version <code>1.2.2</code> -which is currently under development.</p> -<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_saem_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mhmkin.html">mhmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">f_sep_1_const</span>, <span class="va">f_sep_1_tc</span><span class="op">)</span>,</span> -<span> no_random_effect <span class="op">=</span> <span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">cyan_saem_full</span><span class="op">)</span>,</span> -<span> cluster <span class="op">=</span> <span class="va">cl_path_1</span><span class="op">)</span></span></code></pre></div> -<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">const</th> -<th align="left">tc</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">sfo_path_1</td> -<td align="left">Fth, FO</td> -<td align="left">Fth, FO</td> -</tr> -<tr class="even"> -<td align="left">fomc_path_1</td> -<td align="left">OK</td> -<td align="left">Fth, FO</td> -</tr> -<tr class="odd"> -<td align="left">dfop_path_1</td> -<td align="left">Fth, FO</td> -<td align="left">Fth, FO</td> -</tr> -<tr class="even"> -<td align="left">sforb_path_1</td> -<td align="left">Fth, FO</td> -<td align="left">Fth, FO</td> -</tr> -<tr class="odd"> -<td align="left">hs_path_1</td> -<td align="left">Fth, FO</td> -<td align="left">Fth, FO</td> -</tr> -</tbody> -</table> -<p>The status information from the individual fits shows that all fits -completed successfully. The matrix entries Fth and FO indicate that the -Fisher Information Matrix could not be inverted for the fixed effects -(theta) and the random effects (Omega), respectively. For the affected -fits, ill-defined parameters cannot be determined using the -<code>illparms</code> function, because it relies on the Fisher -Information Matrix.</p> -<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<colgroup> -<col width="18%"> -<col width="77%"> -<col width="4%"> -</colgroup> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">const</th> -<th align="left">tc</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">sfo_path_1</td> -<td align="left">NA</td> -<td align="left">NA</td> -</tr> -<tr class="even"> -<td align="left">fomc_path_1</td> -<td align="left">sd(log_k_J9Z38), sd(f_cyan_ilr_2), -sd(f_JCZ38_qlogis)</td> -<td align="left">NA</td> -</tr> -<tr class="odd"> -<td align="left">dfop_path_1</td> -<td align="left">NA</td> -<td align="left">NA</td> -</tr> -<tr class="even"> -<td align="left">sforb_path_1</td> -<td align="left">NA</td> -<td align="left">NA</td> -</tr> -<tr class="odd"> -<td align="left">hs_path_1</td> -<td align="left">NA</td> -<td align="left">NA</td> -</tr> -</tbody> -</table> -<p>The model comparison below suggests that the pathway fits using DFOP -or SFORB for the parent compound provide the best fit.</p> -<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="right">npar</th> -<th align="right">AIC</th> -<th align="right">BIC</th> -<th align="right">Lik</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">sfo_path_1 const</td> -<td align="right">16</td> -<td align="right">2692.8</td> -<td align="right">2686.6</td> -<td align="right">-1330.4</td> -</tr> -<tr class="even"> -<td align="left">sfo_path_1 tc</td> -<td align="right">17</td> -<td align="right">2657.7</td> -<td align="right">2651.1</td> -<td align="right">-1311.9</td> -</tr> -<tr class="odd"> -<td align="left">fomc_path_1 const</td> -<td align="right">18</td> -<td align="right">2427.8</td> -<td align="right">2420.8</td> -<td align="right">-1195.9</td> -</tr> -<tr class="even"> -<td align="left">fomc_path_1 tc</td> -<td align="right">19</td> -<td align="right">2423.4</td> -<td align="right">2416.0</td> -<td align="right">-1192.7</td> -</tr> -<tr class="odd"> -<td align="left">dfop_path_1 const</td> -<td align="right">20</td> -<td align="right">2403.2</td> -<td align="right">2395.4</td> -<td align="right">-1181.6</td> -</tr> -<tr class="even"> -<td align="left">sforb_path_1 const</td> -<td align="right">20</td> -<td align="right">2401.4</td> -<td align="right">2393.6</td> -<td align="right">-1180.7</td> -</tr> -<tr class="odd"> -<td align="left">hs_path_1 const</td> -<td align="right">20</td> -<td align="right">2427.3</td> -<td align="right">2419.5</td> -<td align="right">-1193.7</td> -</tr> -<tr class="even"> -<td align="left">dfop_path_1 tc</td> -<td align="right">20</td> -<td align="right">2398.0</td> -<td align="right">2390.2</td> -<td align="right">-1179.0</td> -</tr> -<tr class="odd"> -<td align="left">sforb_path_1 tc</td> -<td align="right">20</td> -<td align="right">2399.8</td> -<td align="right">2392.0</td> -<td align="right">-1179.9</td> -</tr> -<tr class="even"> -<td align="left">hs_path_1 tc</td> -<td align="right">21</td> -<td align="right">2422.3</td> -<td align="right">2414.1</td> -<td align="right">-1190.2</td> -</tr> -</tbody> -</table> -<p>For these two parent model, successful fits are shown below. Plots of -the fits with the other parent models are shown in the Appendix.</p> -<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">[[</span><span class="st">"dfop_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_cyan_pathway_files/figure-html/unnamed-chunk-7-1.png" alt="DFOP pathway fit with two-component error" width="700"><p class="caption"> -DFOP pathway fit with two-component error -</p> -</div> -<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">[[</span><span class="st">"sforb_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_cyan_pathway_files/figure-html/unnamed-chunk-8-1.png" alt="SFORB pathway fit with two-component error" width="700"><p class="caption"> -SFORB pathway fit with two-component error -</p> -</div> -<p>A closer graphical analysis of these Figures shows that the residues -of transformation product JCZ38 in the soils Tama and Nambsheim observed -at later time points are strongly and systematically underestimated.</p> -<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">stopCluster</a></span><span class="op">(</span><span class="va">cl_path_1</span><span class="op">)</span></span></code></pre></div> -</div> -<div class="section level3"> -<h3 id="alternative-pathway-fits">Alternative pathway fits<a class="anchor" aria-label="anchor" href="#alternative-pathway-fits"></a> -</h3> -<p>To improve the fit for JCZ38, a back-reaction from JSE76 to JCZ38 was -introduced in an alternative version of the transformation pathway, in -analogy to the back-reaction from K5A78 to K5A77. Both pairs of -transformation products are pairs of an organic acid with its -corresponding amide (Addendum 2014, p. 109). As FOMC provided the best -fit for the parent, and the biexponential models DFOP and SFORB provided -the best initial pathway fits, these three parent models are used in the -alternative pathway fits.</p> -<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">cyan_path_2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span></span> -<span> fomc_path_2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> cyan <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"FOMC"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"JCZ38"</span>, <span class="st">"J9Z38"</span><span class="op">)</span><span class="op">)</span>,</span> -<span> JCZ38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JSE76"</span><span class="op">)</span>,</span> -<span> J9Z38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> JSE76 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JCZ38"</span><span class="op">)</span>,</span> -<span> name <span class="op">=</span> <span class="st">"fomc_path_2"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> dll_dir <span class="op">=</span> <span class="st">"cyan_dlls"</span>,</span> -<span> overwrite <span class="op">=</span> <span class="cn">TRUE</span></span> -<span> <span class="op">)</span>,</span> -<span> dfop_path_2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> cyan <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"DFOP"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"JCZ38"</span>, <span class="st">"J9Z38"</span><span class="op">)</span><span class="op">)</span>,</span> -<span> JCZ38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JSE76"</span><span class="op">)</span>,</span> -<span> J9Z38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> JSE76 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JCZ38"</span><span class="op">)</span>,</span> -<span> name <span class="op">=</span> <span class="st">"dfop_path_2"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> dll_dir <span class="op">=</span> <span class="st">"cyan_dlls"</span>,</span> -<span> overwrite <span class="op">=</span> <span class="cn">TRUE</span></span> -<span> <span class="op">)</span>,</span> -<span> sforb_path_2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> cyan <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"JCZ38"</span>, <span class="st">"J9Z38"</span><span class="op">)</span><span class="op">)</span>,</span> -<span> JCZ38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JSE76"</span><span class="op">)</span>,</span> -<span> J9Z38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> JSE76 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JCZ38"</span><span class="op">)</span>,</span> -<span> name <span class="op">=</span> <span class="st">"sforb_path_2"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> dll_dir <span class="op">=</span> <span class="st">"cyan_dlls"</span>,</span> -<span> overwrite <span class="op">=</span> <span class="cn">TRUE</span></span> -<span> <span class="op">)</span></span> -<span><span class="op">)</span></span> -<span></span> -<span><span class="va">cl_path_2</span> <span class="op"><-</span> <span class="fu">start_cluster</span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> -<span><span class="va">f_sep_2_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span></span> -<span> <span class="va">cyan_path_2</span>,</span> -<span> <span class="va">cyan_ds</span>,</span> -<span> error_model <span class="op">=</span> <span class="st">"const"</span>,</span> -<span> cluster <span class="op">=</span> <span class="va">cl_path_2</span>,</span> -<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<span></span> -<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_2_const</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">Nambsheim</th> -<th align="left">Tama</th> -<th align="left">Gross-Umstadt</th> -<th align="left">Sassafras</th> -<th align="left">Lleida</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">fomc_path_2</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">dfop_path_2</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">sforb_path_2</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -</tr> -</tbody> -</table> -<p>Using constant variance, separate fits converge with the exception of -the fits to the Sassafras soil data.</p> -<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_sep_2_tc</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_sep_2_const</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span> -<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_2_tc</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">Nambsheim</th> -<th align="left">Tama</th> -<th align="left">Gross-Umstadt</th> -<th align="left">Sassafras</th> -<th align="left">Lleida</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">fomc_path_2</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">dfop_path_2</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">sforb_path_2</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -</tbody> -</table> -<p>Using the two-component error model, all separate fits converge with -the exception of the alternative pathway fit with DFOP used for the -parent and the Sassafras dataset.</p> -<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_saem_2</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mhmkin.html">mhmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">f_sep_2_const</span>, <span class="va">f_sep_2_tc</span><span class="op">)</span>,</span> -<span> no_random_effect <span class="op">=</span> <span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">cyan_saem_full</span><span class="op">[</span><span class="fl">2</span><span class="op">:</span><span class="fl">4</span>, <span class="op">]</span><span class="op">)</span>,</span> -<span> cluster <span class="op">=</span> <span class="va">cl_path_2</span><span class="op">)</span></span></code></pre></div> -<div class="sourceCode" id="cb22"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">const</th> -<th align="left">tc</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">fomc_path_2</td> -<td align="left">OK</td> -<td align="left">FO</td> -</tr> -<tr class="even"> -<td align="left">dfop_path_2</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">sforb_path_2</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -</tbody> -</table> -<p>The hierarchical fits for the alternative pathway completed -successfully.</p> -<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<colgroup> -<col width="14%"> -<col width="42%"> -<col width="42%"> -</colgroup> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">const</th> -<th align="left">tc</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">fomc_path_2</td> -<td align="left">sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)</td> -<td align="left">NA</td> -</tr> -<tr class="even"> -<td align="left">dfop_path_2</td> -<td align="left">sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)</td> -<td align="left">sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)</td> -</tr> -<tr class="odd"> -<td align="left">sforb_path_2</td> -<td align="left">sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)</td> -<td align="left">sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)</td> -</tr> -</tbody> -</table> -<p>In both fits, the random effects for the formation fractions for the -pathways from JCZ38 to JSE76, and for the reverse pathway from JSE76 to -JCZ38 are ill-defined.</p> -<div class="sourceCode" id="cb24"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="right">npar</th> -<th align="right">AIC</th> -<th align="right">BIC</th> -<th align="right">Lik</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">fomc_path_2 const</td> -<td align="right">20</td> -<td align="right">2308.3</td> -<td align="right">2300.5</td> -<td align="right">-1134.2</td> -</tr> -<tr class="even"> -<td align="left">fomc_path_2 tc</td> -<td align="right">21</td> -<td align="right">2248.3</td> -<td align="right">2240.1</td> -<td align="right">-1103.2</td> -</tr> -<tr class="odd"> -<td align="left">dfop_path_2 const</td> -<td align="right">22</td> -<td align="right">2289.6</td> -<td align="right">2281.0</td> -<td align="right">-1122.8</td> -</tr> -<tr class="even"> -<td align="left">sforb_path_2 const</td> -<td align="right">22</td> -<td align="right">2284.1</td> -<td align="right">2275.5</td> -<td align="right">-1120.0</td> -</tr> -<tr class="odd"> -<td align="left">dfop_path_2 tc</td> -<td align="right">22</td> -<td align="right">2234.4</td> -<td align="right">2225.8</td> -<td align="right">-1095.2</td> -</tr> -<tr class="even"> -<td align="left">sforb_path_2 tc</td> -<td align="right">22</td> -<td align="right">2240.4</td> -<td align="right">2231.8</td> -<td align="right">-1098.2</td> -</tr> -</tbody> -</table> -<p>The variants using the biexponential models DFOP and SFORB for the -parent compound and the two-component error model give the lowest AIC -and BIC values and are plotted below. Compared with the original -pathway, the AIC and BIC values indicate a large improvement. This is -confirmed by the plots, which show that the metabolite JCZ38 is fitted -much better with this model.</p> -<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"fomc_path_2"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_cyan_pathway_files/figure-html/unnamed-chunk-13-1.png" alt="FOMC pathway fit with two-component error, alternative pathway" width="700"><p class="caption"> -FOMC pathway fit with two-component error, alternative pathway -</p> -</div> -<div class="sourceCode" id="cb26"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"dfop_path_2"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_cyan_pathway_files/figure-html/unnamed-chunk-14-1.png" alt="DFOP pathway fit with two-component error, alternative pathway" width="700"><p class="caption"> -DFOP pathway fit with two-component error, alternative pathway -</p> -</div> -<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"sforb_path_2"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_cyan_pathway_files/figure-html/unnamed-chunk-15-1.png" alt="SFORB pathway fit with two-component error, alternative pathway" width="700"><p class="caption"> -SFORB pathway fit with two-component error, alternative pathway -</p> -</div> -</div> -<div class="section level3"> -<h3 id="refinement-of-alternative-pathway-fits">Refinement of alternative pathway fits<a class="anchor" aria-label="anchor" href="#refinement-of-alternative-pathway-fits"></a> -</h3> -<p>All ill-defined random effects that were identified in the parent -only fits and in the above pathway fits, are excluded for the final -evaluations below. For this purpose, a list of character vectors is -created below that can be indexed by row and column indices, and which -contains the degradation parameter names for which random effects should -be excluded for each of the hierarchical fits contained in -<code>f_saem_2</code>.</p> -<div class="sourceCode" id="cb28"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">no_ranef</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/matrix.html" class="external-link">matrix</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="op">)</span>, nrow <span class="op">=</span> <span class="fl">3</span>, ncol <span class="op">=</span> <span class="fl">2</span>, dimnames <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/dimnames.html" class="external-link">dimnames</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">)</span><span class="op">)</span></span> -<span><span class="va">no_ranef</span><span class="op">[[</span><span class="st">"fomc_path_2"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"log_beta"</span>, <span class="st">"f_JCZ38_qlogis"</span>, <span class="st">"f_JSE76_qlogis"</span><span class="op">)</span></span> -<span><span class="va">no_ranef</span><span class="op">[[</span><span class="st">"fomc_path_2"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"cyan_0"</span>, <span class="st">"f_JCZ38_qlogis"</span>, <span class="st">"f_JSE76_qlogis"</span><span class="op">)</span></span> -<span><span class="va">no_ranef</span><span class="op">[[</span><span class="st">"dfop_path_2"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"cyan_0"</span>, <span class="st">"f_JCZ38_qlogis"</span>, <span class="st">"f_JSE76_qlogis"</span><span class="op">)</span></span> -<span><span class="va">no_ranef</span><span class="op">[[</span><span class="st">"dfop_path_2"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"cyan_0"</span>, <span class="st">"log_k1"</span>, <span class="st">"f_JCZ38_qlogis"</span>, <span class="st">"f_JSE76_qlogis"</span><span class="op">)</span></span> -<span><span class="va">no_ranef</span><span class="op">[[</span><span class="st">"sforb_path_2"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"cyan_free_0"</span>,</span> -<span> <span class="st">"f_JCZ38_qlogis"</span>, <span class="st">"f_JSE76_qlogis"</span><span class="op">)</span></span> -<span><span class="va">no_ranef</span><span class="op">[[</span><span class="st">"sforb_path_2"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"cyan_free_0"</span>, <span class="st">"log_k_cyan_free_bound"</span>,</span> -<span> <span class="st">"f_JCZ38_qlogis"</span>, <span class="st">"f_JSE76_qlogis"</span><span class="op">)</span></span> -<span><span class="fu"><a href="https://rdrr.io/r/parallel/clusterApply.html" class="external-link">clusterExport</a></span><span class="op">(</span><span class="va">cl_path_2</span>, <span class="st">"no_ranef"</span><span class="op">)</span></span> -<span></span> -<span><span class="va">f_saem_3</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_saem_2</span>,</span> -<span> no_random_effect <span class="op">=</span> <span class="va">no_ranef</span>,</span> -<span> cluster <span class="op">=</span> <span class="va">cl_path_2</span><span class="op">)</span></span></code></pre></div> -<div class="sourceCode" id="cb29"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_saem_3</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">const</th> -<th align="left">tc</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">fomc_path_2</td> -<td align="left">E</td> -<td align="left">Fth</td> -</tr> -<tr class="even"> -<td align="left">dfop_path_2</td> -<td align="left">Fth</td> -<td align="left">Fth</td> -</tr> -<tr class="odd"> -<td align="left">sforb_path_2</td> -<td align="left">Fth</td> -<td align="left">Fth</td> -</tr> -</tbody> -</table> -<p>With the exception of the FOMC pathway fit with constant variance, -all updated fits completed successfully. However, the Fisher Information -Matrix for the fixed effects (Fth) could not be inverted, so no -confidence intervals for the optimised parameters are available.</p> -<div class="sourceCode" id="cb30"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_3</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">const</th> -<th align="left">tc</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">fomc_path_2</td> -<td align="left">E</td> -<td align="left"></td> -</tr> -<tr class="even"> -<td align="left">dfop_path_2</td> -<td align="left"></td> -<td align="left"></td> -</tr> -<tr class="odd"> -<td align="left">sforb_path_2</td> -<td align="left"></td> -<td align="left"></td> -</tr> -</tbody> -</table> -<div class="sourceCode" id="cb31"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_3</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="right">npar</th> -<th align="right">AIC</th> -<th align="right">BIC</th> -<th align="right">Lik</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">fomc_path_2 tc</td> -<td align="right">19</td> -<td align="right">2250.9</td> -<td align="right">2243.5</td> -<td align="right">-1106.5</td> -</tr> -<tr class="even"> -<td align="left">dfop_path_2 const</td> -<td align="right">20</td> -<td align="right">2281.7</td> -<td align="right">2273.9</td> -<td align="right">-1120.8</td> -</tr> -<tr class="odd"> -<td align="left">sforb_path_2 const</td> -<td align="right">20</td> -<td align="right">2279.5</td> -<td align="right">2271.7</td> -<td align="right">-1119.7</td> -</tr> -<tr class="even"> -<td align="left">dfop_path_2 tc</td> -<td align="right">20</td> -<td align="right">2231.5</td> -<td align="right">2223.7</td> -<td align="right">-1095.8</td> -</tr> -<tr class="odd"> -<td align="left">sforb_path_2 tc</td> -<td align="right">20</td> -<td align="right">2235.7</td> -<td align="right">2227.9</td> -<td align="right">-1097.9</td> -</tr> -</tbody> -</table> -<p>While the AIC and BIC values of the best fit (DFOP pathway fit with -two-component error) are lower than in the previous fits with the -alternative pathway, the practical value of these refined evaluations is -limited as no confidence intervals are obtained.</p> -<div class="sourceCode" id="cb32"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">stopCluster</a></span><span class="op">(</span><span class="va">cl_path_2</span><span class="op">)</span></span></code></pre></div> -</div> -</div> -<div class="section level2"> -<h2 id="conclusion">Conclusion<a class="anchor" aria-label="anchor" href="#conclusion"></a> -</h2> -<p>It was demonstrated that a relatively complex transformation pathway -with parallel formation of two primary metabolites and one secondary -metabolite can be fitted even if the data in the individual datasets are -quite different and partly only cover the formation phase.</p> -<p>The run times of the pathway fits were several hours, limiting the -practical feasibility of iterative refinements based on ill-defined -parameters and of alternative checks of parameter identifiability based -on multistart runs.</p> -</div> -<div class="section level2"> -<h2 id="acknowledgements">Acknowledgements<a class="anchor" aria-label="anchor" href="#acknowledgements"></a> -</h2> -<p>The helpful comments by Janina Wöltjen of the German Environment -Agency are gratefully acknowledged.</p> -</div> -<div class="section level2"> -<h2 id="appendix">Appendix<a class="anchor" aria-label="anchor" href="#appendix"></a> -</h2> -<div class="section level3"> -<h3 id="plots-of-fits-that-were-not-refined-further">Plots of fits that were not refined further<a class="anchor" aria-label="anchor" href="#plots-of-fits-that-were-not-refined-further"></a> -</h3> -<div class="sourceCode" id="cb33"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">[[</span><span class="st">"sfo_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_cyan_pathway_files/figure-html/unnamed-chunk-20-1.png" alt="SFO pathway fit with two-component error" width="700"><p class="caption"> -SFO pathway fit with two-component error -</p> -</div> -<div class="sourceCode" id="cb34"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">[[</span><span class="st">"fomc_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_cyan_pathway_files/figure-html/unnamed-chunk-21-1.png" alt="FOMC pathway fit with two-component error" width="700"><p class="caption"> -FOMC pathway fit with two-component error -</p> -</div> -<div class="sourceCode" id="cb35"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">[[</span><span class="st">"sforb_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_cyan_pathway_files/figure-html/unnamed-chunk-22-1.png" alt="HS pathway fit with two-component error" width="700"><p class="caption"> -HS pathway fit with two-component error -</p> -</div> -</div> -<div class="section level3"> -<h3 id="hierarchical-fit-listings">Hierarchical fit listings<a class="anchor" aria-label="anchor" href="#hierarchical-fit-listings"></a> -</h3> -<div class="section level4"> -<h4 id="pathway-1">Pathway 1<a class="anchor" aria-label="anchor" href="#pathway-1"></a> -</h4> -<caption> -Hierarchical SFO path 1 fit with constant variance -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 20:33:05 2023 -Date of summary: Thu Apr 20 21:04:34 2023 - -Equations: -d_cyan/dt = - k_cyan * cyan -d_JCZ38/dt = + f_cyan_to_JCZ38 * k_cyan * cyan - k_JCZ38 * JCZ38 -d_J9Z38/dt = + f_cyan_to_J9Z38 * k_cyan * cyan - k_J9Z38 * J9Z38 -d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 - -Data: -433 observations of 4 variable(s) grouped in 5 datasets - -Model predictions using solution type deSolve - -Fitted in 438.011 s -Using 300, 100 iterations and 10 chains - -Variance model: Constant variance - -Starting values for degradation parameters: - cyan_0 log_k_cyan log_k_JCZ38 log_k_J9Z38 log_k_JSE76 - 95.3304 -3.8459 -3.1305 -5.0678 -5.3196 - f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis - 0.8158 22.5404 10.4289 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - cyan_0 log_k_cyan log_k_JCZ38 log_k_J9Z38 log_k_JSE76 -cyan_0 4.797 0.0000 0.000 0.000 0.0000 -log_k_cyan 0.000 0.9619 0.000 0.000 0.0000 -log_k_JCZ38 0.000 0.0000 2.139 0.000 0.0000 -log_k_J9Z38 0.000 0.0000 0.000 1.639 0.0000 -log_k_JSE76 0.000 0.0000 0.000 0.000 0.7894 -f_cyan_ilr_1 0.000 0.0000 0.000 0.000 0.0000 -f_cyan_ilr_2 0.000 0.0000 0.000 0.000 0.0000 -f_JCZ38_qlogis 0.000 0.0000 0.000 0.000 0.0000 - f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis -cyan_0 0.0000 0.000 0.00 -log_k_cyan 0.0000 0.000 0.00 -log_k_JCZ38 0.0000 0.000 0.00 -log_k_J9Z38 0.0000 0.000 0.00 -log_k_JSE76 0.0000 0.000 0.00 -f_cyan_ilr_1 0.7714 0.000 0.00 -f_cyan_ilr_2 0.0000 8.684 0.00 -f_JCZ38_qlogis 0.0000 0.000 13.48 - -Starting values for error model parameters: -a.1 - 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 2693 2687 -1330 - -Optimised parameters: - est. lower upper -cyan_0 95.0946 NA NA -log_k_cyan -3.8544 NA NA -log_k_JCZ38 -3.0402 NA NA -log_k_J9Z38 -5.0109 NA NA -log_k_JSE76 -5.2857 NA NA -f_cyan_ilr_1 0.8069 NA NA -f_cyan_ilr_2 16.6623 NA NA -f_JCZ38_qlogis 1.3602 NA NA -a.1 4.8326 NA NA -SD.log_k_cyan 0.5842 NA NA -SD.log_k_JCZ38 1.2680 NA NA -SD.log_k_J9Z38 0.3626 NA NA -SD.log_k_JSE76 0.5244 NA NA -SD.f_cyan_ilr_1 0.2752 NA NA -SD.f_cyan_ilr_2 2.3556 NA NA -SD.f_JCZ38_qlogis 0.2400 NA NA - -Correlation is not available - -Random effects: - est. lower upper -SD.log_k_cyan 0.5842 NA NA -SD.log_k_JCZ38 1.2680 NA NA -SD.log_k_J9Z38 0.3626 NA NA -SD.log_k_JSE76 0.5244 NA NA -SD.f_cyan_ilr_1 0.2752 NA NA -SD.f_cyan_ilr_2 2.3556 NA NA -SD.f_JCZ38_qlogis 0.2400 NA NA - -Variance model: - est. lower upper -a.1 4.833 NA NA - -Backtransformed parameters: - est. lower upper -cyan_0 95.094581 NA NA -k_cyan 0.021186 NA NA -k_JCZ38 0.047825 NA NA -k_J9Z38 0.006665 NA NA -k_JSE76 0.005063 NA NA -f_cyan_to_JCZ38 0.757885 NA NA -f_cyan_to_J9Z38 0.242115 NA NA -f_JCZ38_to_JSE76 0.795792 NA NA - -Resulting formation fractions: - ff -cyan_JCZ38 7.579e-01 -cyan_J9Z38 2.421e-01 -cyan_sink 5.877e-10 -JCZ38_JSE76 7.958e-01 -JCZ38_sink 2.042e-01 - -Estimated disappearance times: - DT50 DT90 -cyan 32.72 108.68 -JCZ38 14.49 48.15 -J9Z38 103.99 345.46 -JSE76 136.90 454.76 - -</code></pre> -<p></p> -<caption> -Hierarchical SFO path 1 fit with two-component error -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 20:32:55 2023 -Date of summary: Thu Apr 20 21:04:34 2023 - -Equations: -d_cyan/dt = - k_cyan * cyan -d_JCZ38/dt = + f_cyan_to_JCZ38 * k_cyan * cyan - k_JCZ38 * JCZ38 -d_J9Z38/dt = + f_cyan_to_J9Z38 * k_cyan * cyan - k_J9Z38 * J9Z38 -d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 - -Data: -433 observations of 4 variable(s) grouped in 5 datasets - -Model predictions using solution type deSolve - -Fitted in 427.249 s -Using 300, 100 iterations and 10 chains - -Variance model: Two-component variance function - -Starting values for degradation parameters: - cyan_0 log_k_cyan log_k_JCZ38 log_k_J9Z38 log_k_JSE76 - 96.0039 -3.8907 -3.1276 -5.0069 -4.9367 - f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis - 0.7937 20.0030 15.1336 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - cyan_0 log_k_cyan log_k_JCZ38 log_k_J9Z38 log_k_JSE76 -cyan_0 4.859 0.000 0.00 0.00 0.0000 -log_k_cyan 0.000 0.962 0.00 0.00 0.0000 -log_k_JCZ38 0.000 0.000 2.04 0.00 0.0000 -log_k_J9Z38 0.000 0.000 0.00 1.72 0.0000 -log_k_JSE76 0.000 0.000 0.00 0.00 0.9076 -f_cyan_ilr_1 0.000 0.000 0.00 0.00 0.0000 -f_cyan_ilr_2 0.000 0.000 0.00 0.00 0.0000 -f_JCZ38_qlogis 0.000 0.000 0.00 0.00 0.0000 - f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis -cyan_0 0.0000 0.000 0.00 -log_k_cyan 0.0000 0.000 0.00 -log_k_JCZ38 0.0000 0.000 0.00 -log_k_J9Z38 0.0000 0.000 0.00 -log_k_JSE76 0.0000 0.000 0.00 -f_cyan_ilr_1 0.7598 0.000 0.00 -f_cyan_ilr_2 0.0000 7.334 0.00 -f_JCZ38_qlogis 0.0000 0.000 11.78 - -Starting values for error model parameters: -a.1 b.1 - 1 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 2658 2651 -1312 - -Optimised parameters: - est. lower upper -cyan_0 94.72923 NA NA -log_k_cyan -3.91670 NA NA -log_k_JCZ38 -3.12917 NA NA -log_k_J9Z38 -5.06070 NA NA -log_k_JSE76 -5.09254 NA NA -f_cyan_ilr_1 0.81116 NA NA -f_cyan_ilr_2 39.97850 NA NA -f_JCZ38_qlogis 3.09728 NA NA -a.1 3.95044 NA NA -b.1 0.07998 NA NA -SD.log_k_cyan 0.58855 NA NA -SD.log_k_JCZ38 1.29753 NA NA -SD.log_k_J9Z38 0.62851 NA NA -SD.log_k_JSE76 0.37235 NA NA -SD.f_cyan_ilr_1 0.37346 NA NA -SD.f_cyan_ilr_2 1.41667 NA NA -SD.f_JCZ38_qlogis 1.81467 NA NA - -Correlation is not available - -Random effects: - est. lower upper -SD.log_k_cyan 0.5886 NA NA -SD.log_k_JCZ38 1.2975 NA NA -SD.log_k_J9Z38 0.6285 NA NA -SD.log_k_JSE76 0.3724 NA NA -SD.f_cyan_ilr_1 0.3735 NA NA -SD.f_cyan_ilr_2 1.4167 NA NA -SD.f_JCZ38_qlogis 1.8147 NA NA - -Variance model: - est. lower upper -a.1 3.95044 NA NA -b.1 0.07998 NA NA - -Backtransformed parameters: - est. lower upper -cyan_0 94.729229 NA NA -k_cyan 0.019907 NA NA -k_JCZ38 0.043754 NA NA -k_J9Z38 0.006341 NA NA -k_JSE76 0.006142 NA NA -f_cyan_to_JCZ38 0.758991 NA NA -f_cyan_to_J9Z38 0.241009 NA NA -f_JCZ38_to_JSE76 0.956781 NA NA - -Resulting formation fractions: - ff -cyan_JCZ38 0.75899 -cyan_J9Z38 0.24101 -cyan_sink 0.00000 -JCZ38_JSE76 0.95678 -JCZ38_sink 0.04322 - -Estimated disappearance times: - DT50 DT90 -cyan 34.82 115.67 -JCZ38 15.84 52.63 -J9Z38 109.31 363.12 -JSE76 112.85 374.87 - -</code></pre> -<p></p> -<caption> -Hierarchical FOMC path 1 fit with constant variance -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 20:33:49 2023 -Date of summary: Thu Apr 20 21:04:34 2023 - -Equations: -d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan -d_JCZ38/dt = + f_cyan_to_JCZ38 * (alpha/beta) * 1/((time/beta) + 1) * - cyan - k_JCZ38 * JCZ38 -d_J9Z38/dt = + f_cyan_to_J9Z38 * (alpha/beta) * 1/((time/beta) + 1) * - cyan - k_J9Z38 * J9Z38 -d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 - -Data: -433 observations of 4 variable(s) grouped in 5 datasets - -Model predictions using solution type deSolve - -Fitted in 481.497 s -Using 300, 100 iterations and 10 chains - -Variance model: Constant variance - -Starting values for degradation parameters: - cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 - 101.2314 -3.3680 -5.1108 -5.9416 0.7144 - f_cyan_ilr_2 f_JCZ38_qlogis log_alpha log_beta - 7.3870 15.7604 -0.1791 2.9811 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 -cyan_0 5.416 0.000 0.0 0.000 0.0000 -log_k_JCZ38 0.000 2.439 0.0 0.000 0.0000 -log_k_J9Z38 0.000 0.000 1.7 0.000 0.0000 -log_k_JSE76 0.000 0.000 0.0 1.856 0.0000 -f_cyan_ilr_1 0.000 0.000 0.0 0.000 0.7164 -f_cyan_ilr_2 0.000 0.000 0.0 0.000 0.0000 -f_JCZ38_qlogis 0.000 0.000 0.0 0.000 0.0000 -log_alpha 0.000 0.000 0.0 0.000 0.0000 -log_beta 0.000 0.000 0.0 0.000 0.0000 - f_cyan_ilr_2 f_JCZ38_qlogis log_alpha log_beta -cyan_0 0.00 0.00 0.0000 0.0000 -log_k_JCZ38 0.00 0.00 0.0000 0.0000 -log_k_J9Z38 0.00 0.00 0.0000 0.0000 -log_k_JSE76 0.00 0.00 0.0000 0.0000 -f_cyan_ilr_1 0.00 0.00 0.0000 0.0000 -f_cyan_ilr_2 12.33 0.00 0.0000 0.0000 -f_JCZ38_qlogis 0.00 20.42 0.0000 0.0000 -log_alpha 0.00 0.00 0.4144 0.0000 -log_beta 0.00 0.00 0.0000 0.5077 - -Starting values for error model parameters: -a.1 - 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 2428 2421 -1196 - -Optimised parameters: - est. lower upper -cyan_0 101.0225 98.306270 103.7387 -log_k_JCZ38 -3.3786 -4.770657 -1.9866 -log_k_J9Z38 -5.2603 -5.902085 -4.6186 -log_k_JSE76 -6.1427 -7.318336 -4.9671 -f_cyan_ilr_1 0.7437 0.421215 1.0663 -f_cyan_ilr_2 0.9108 0.267977 1.5537 -f_JCZ38_qlogis 2.0487 0.524897 3.5724 -log_alpha -0.2268 -0.618049 0.1644 -log_beta 2.8986 2.700701 3.0964 -a.1 3.4058 3.169913 3.6416 -SD.cyan_0 2.5279 0.454190 4.6016 -SD.log_k_JCZ38 1.5636 0.572824 2.5543 -SD.log_k_J9Z38 0.5316 -0.004405 1.0677 -SD.log_k_JSE76 0.9903 0.106325 1.8742 -SD.f_cyan_ilr_1 0.3464 0.112066 0.5807 -SD.f_cyan_ilr_2 0.2804 -0.393900 0.9546 -SD.f_JCZ38_qlogis 0.9416 -0.152986 2.0362 -SD.log_alpha 0.4273 0.161044 0.6936 - -Correlation: - cyan_0 l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 log_lph -log_k_JCZ38 -0.0156 -log_k_J9Z38 -0.0493 0.0073 -log_k_JSE76 -0.0329 0.0018 0.0069 -f_cyan_ilr_1 -0.0086 0.0180 -0.1406 0.0012 -f_cyan_ilr_2 -0.2629 0.0779 0.2826 0.0274 0.0099 -f_JCZ38_qlogis 0.0713 -0.0747 -0.0505 0.1169 -0.1022 -0.4893 -log_alpha -0.0556 0.0120 0.0336 0.0193 0.0036 0.0840 -0.0489 -log_beta -0.2898 0.0460 0.1305 0.0768 0.0190 0.4071 -0.1981 0.2772 - -Random effects: - est. lower upper -SD.cyan_0 2.5279 0.454190 4.6016 -SD.log_k_JCZ38 1.5636 0.572824 2.5543 -SD.log_k_J9Z38 0.5316 -0.004405 1.0677 -SD.log_k_JSE76 0.9903 0.106325 1.8742 -SD.f_cyan_ilr_1 0.3464 0.112066 0.5807 -SD.f_cyan_ilr_2 0.2804 -0.393900 0.9546 -SD.f_JCZ38_qlogis 0.9416 -0.152986 2.0362 -SD.log_alpha 0.4273 0.161044 0.6936 - -Variance model: - est. lower upper -a.1 3.406 3.17 3.642 - -Backtransformed parameters: - est. lower upper -cyan_0 1.010e+02 9.831e+01 1.037e+02 -k_JCZ38 3.409e-02 8.475e-03 1.372e-01 -k_J9Z38 5.194e-03 2.734e-03 9.867e-03 -k_JSE76 2.149e-03 6.633e-04 6.963e-03 -f_cyan_to_JCZ38 6.481e-01 NA NA -f_cyan_to_J9Z38 2.264e-01 NA NA -f_JCZ38_to_JSE76 8.858e-01 6.283e-01 9.727e-01 -alpha 7.971e-01 5.390e-01 1.179e+00 -beta 1.815e+01 1.489e+01 2.212e+01 - -Resulting formation fractions: - ff -cyan_JCZ38 0.6481 -cyan_J9Z38 0.2264 -cyan_sink 0.1255 -JCZ38_JSE76 0.8858 -JCZ38_sink 0.1142 - -Estimated disappearance times: - DT50 DT90 DT50back -cyan 25.15 308.01 92.72 -JCZ38 20.33 67.54 NA -J9Z38 133.46 443.35 NA -JSE76 322.53 1071.42 NA - -</code></pre> -<p></p> -<caption> -Hierarchical FOMC path 1 fit with two-component error -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 20:33:59 2023 -Date of summary: Thu Apr 20 21:04:34 2023 - -Equations: -d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan -d_JCZ38/dt = + f_cyan_to_JCZ38 * (alpha/beta) * 1/((time/beta) + 1) * - cyan - k_JCZ38 * JCZ38 -d_J9Z38/dt = + f_cyan_to_J9Z38 * (alpha/beta) * 1/((time/beta) + 1) * - cyan - k_J9Z38 * J9Z38 -d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 - -Data: -433 observations of 4 variable(s) grouped in 5 datasets - -Model predictions using solution type deSolve - -Fitted in 491.071 s -Using 300, 100 iterations and 10 chains - -Variance model: Two-component variance function - -Starting values for degradation parameters: - cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 - 101.13827 -3.32493 -5.08921 -5.93478 0.71330 - f_cyan_ilr_2 f_JCZ38_qlogis log_alpha log_beta - 10.05989 12.79248 -0.09621 3.10646 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 -cyan_0 5.643 0.000 0.000 0.00 0.0000 -log_k_JCZ38 0.000 2.319 0.000 0.00 0.0000 -log_k_J9Z38 0.000 0.000 1.731 0.00 0.0000 -log_k_JSE76 0.000 0.000 0.000 1.86 0.0000 -f_cyan_ilr_1 0.000 0.000 0.000 0.00 0.7186 -f_cyan_ilr_2 0.000 0.000 0.000 0.00 0.0000 -f_JCZ38_qlogis 0.000 0.000 0.000 0.00 0.0000 -log_alpha 0.000 0.000 0.000 0.00 0.0000 -log_beta 0.000 0.000 0.000 0.00 0.0000 - f_cyan_ilr_2 f_JCZ38_qlogis log_alpha log_beta -cyan_0 0.00 0.00 0.0000 0.0000 -log_k_JCZ38 0.00 0.00 0.0000 0.0000 -log_k_J9Z38 0.00 0.00 0.0000 0.0000 -log_k_JSE76 0.00 0.00 0.0000 0.0000 -f_cyan_ilr_1 0.00 0.00 0.0000 0.0000 -f_cyan_ilr_2 12.49 0.00 0.0000 0.0000 -f_JCZ38_qlogis 0.00 20.19 0.0000 0.0000 -log_alpha 0.00 0.00 0.3142 0.0000 -log_beta 0.00 0.00 0.0000 0.7331 - -Starting values for error model parameters: -a.1 b.1 - 1 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 2423 2416 -1193 - -Optimised parameters: - est. lower upper -cyan_0 100.57649 NA NA -log_k_JCZ38 -3.46250 NA NA -log_k_J9Z38 -5.24442 NA NA -log_k_JSE76 -5.75229 NA NA -f_cyan_ilr_1 0.68480 NA NA -f_cyan_ilr_2 0.61670 NA NA -f_JCZ38_qlogis 87.97407 NA NA -log_alpha -0.15699 NA NA -log_beta 3.01540 NA NA -a.1 3.11518 NA NA -b.1 0.04445 NA NA -SD.log_k_JCZ38 1.40732 NA NA -SD.log_k_J9Z38 0.56510 NA NA -SD.log_k_JSE76 0.72067 NA NA -SD.f_cyan_ilr_1 0.31199 NA NA -SD.f_cyan_ilr_2 0.36894 NA NA -SD.f_JCZ38_qlogis 6.92892 NA NA -SD.log_alpha 0.25662 NA NA -SD.log_beta 0.35845 NA NA - -Correlation is not available - -Random effects: - est. lower upper -SD.log_k_JCZ38 1.4073 NA NA -SD.log_k_J9Z38 0.5651 NA NA -SD.log_k_JSE76 0.7207 NA NA -SD.f_cyan_ilr_1 0.3120 NA NA -SD.f_cyan_ilr_2 0.3689 NA NA -SD.f_JCZ38_qlogis 6.9289 NA NA -SD.log_alpha 0.2566 NA NA -SD.log_beta 0.3585 NA NA - -Variance model: - est. lower upper -a.1 3.11518 NA NA -b.1 0.04445 NA NA - -Backtransformed parameters: - est. lower upper -cyan_0 1.006e+02 NA NA -k_JCZ38 3.135e-02 NA NA -k_J9Z38 5.277e-03 NA NA -k_JSE76 3.175e-03 NA NA -f_cyan_to_JCZ38 5.991e-01 NA NA -f_cyan_to_J9Z38 2.275e-01 NA NA -f_JCZ38_to_JSE76 1.000e+00 NA NA -alpha 8.547e-01 NA NA -beta 2.040e+01 NA NA - -Resulting formation fractions: - ff -cyan_JCZ38 0.5991 -cyan_J9Z38 0.2275 -cyan_sink 0.1734 -JCZ38_JSE76 1.0000 -JCZ38_sink 0.0000 - -Estimated disappearance times: - DT50 DT90 DT50back -cyan 25.50 281.29 84.68 -JCZ38 22.11 73.44 NA -J9Z38 131.36 436.35 NA -JSE76 218.28 725.11 NA - -</code></pre> -<p></p> -<caption> -Hierarchical DFOP path 1 fit with constant variance -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 20:34:33 2023 -Date of summary: Thu Apr 20 21:04:34 2023 - -Equations: -d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * - time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) - * cyan -d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - - g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * - exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38 -d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - - g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * - exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38 -d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 - -Data: -433 observations of 4 variable(s) grouped in 5 datasets - -Model predictions using solution type deSolve - -Fitted in 525.551 s -Using 300, 100 iterations and 10 chains - -Variance model: Constant variance - -Starting values for degradation parameters: - cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 - 102.0644 -3.4008 -5.0024 -5.8613 0.6855 - f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 g_qlogis - 1.2365 13.7245 -1.8641 -4.5063 -0.6468 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 -cyan_0 4.466 0.000 0.000 0.000 0.0000 -log_k_JCZ38 0.000 2.382 0.000 0.000 0.0000 -log_k_J9Z38 0.000 0.000 1.595 0.000 0.0000 -log_k_JSE76 0.000 0.000 0.000 1.245 0.0000 -f_cyan_ilr_1 0.000 0.000 0.000 0.000 0.6852 -f_cyan_ilr_2 0.000 0.000 0.000 0.000 0.0000 -f_JCZ38_qlogis 0.000 0.000 0.000 0.000 0.0000 -log_k1 0.000 0.000 0.000 0.000 0.0000 -log_k2 0.000 0.000 0.000 0.000 0.0000 -g_qlogis 0.000 0.000 0.000 0.000 0.0000 - f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 g_qlogis -cyan_0 0.00 0.00 0.0000 0.0000 0.000 -log_k_JCZ38 0.00 0.00 0.0000 0.0000 0.000 -log_k_J9Z38 0.00 0.00 0.0000 0.0000 0.000 -log_k_JSE76 0.00 0.00 0.0000 0.0000 0.000 -f_cyan_ilr_1 0.00 0.00 0.0000 0.0000 0.000 -f_cyan_ilr_2 1.28 0.00 0.0000 0.0000 0.000 -f_JCZ38_qlogis 0.00 16.11 0.0000 0.0000 0.000 -log_k1 0.00 0.00 0.9866 0.0000 0.000 -log_k2 0.00 0.00 0.0000 0.5953 0.000 -g_qlogis 0.00 0.00 0.0000 0.0000 1.583 - -Starting values for error model parameters: -a.1 - 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 2403 2395 -1182 - -Optimised parameters: - est. lower upper -cyan_0 102.6079 NA NA -log_k_JCZ38 -3.4855 NA NA -log_k_J9Z38 -5.1686 NA NA -log_k_JSE76 -5.6697 NA NA -f_cyan_ilr_1 0.6714 NA NA -f_cyan_ilr_2 0.4986 NA NA -f_JCZ38_qlogis 55.4760 NA NA -log_k1 -1.8409 NA NA -log_k2 -4.4915 NA NA -g_qlogis -0.6403 NA NA -a.1 3.2387 NA NA -SD.log_k_JCZ38 1.4524 NA NA -SD.log_k_J9Z38 0.5151 NA NA -SD.log_k_JSE76 0.6514 NA NA -SD.f_cyan_ilr_1 0.3023 NA NA -SD.f_cyan_ilr_2 0.2959 NA NA -SD.f_JCZ38_qlogis 1.9984 NA NA -SD.log_k1 0.5188 NA NA -SD.log_k2 0.3894 NA NA -SD.g_qlogis 0.8579 NA NA - -Correlation is not available - -Random effects: - est. lower upper -SD.log_k_JCZ38 1.4524 NA NA -SD.log_k_J9Z38 0.5151 NA NA -SD.log_k_JSE76 0.6514 NA NA -SD.f_cyan_ilr_1 0.3023 NA NA -SD.f_cyan_ilr_2 0.2959 NA NA -SD.f_JCZ38_qlogis 1.9984 NA NA -SD.log_k1 0.5188 NA NA -SD.log_k2 0.3894 NA NA -SD.g_qlogis 0.8579 NA NA - -Variance model: - est. lower upper -a.1 3.239 NA NA - -Backtransformed parameters: - est. lower upper -cyan_0 1.026e+02 NA NA -k_JCZ38 3.064e-02 NA NA -k_J9Z38 5.692e-03 NA NA -k_JSE76 3.449e-03 NA NA -f_cyan_to_JCZ38 5.798e-01 NA NA -f_cyan_to_J9Z38 2.243e-01 NA NA -f_JCZ38_to_JSE76 1.000e+00 NA NA -k1 1.587e-01 NA NA -k2 1.120e-02 NA NA -g 3.452e-01 NA NA - -Resulting formation fractions: - ff -cyan_JCZ38 0.5798 -cyan_J9Z38 0.2243 -cyan_sink 0.1958 -JCZ38_JSE76 1.0000 -JCZ38_sink 0.0000 - -Estimated disappearance times: - DT50 DT90 DT50back DT50_k1 DT50_k2 -cyan 25.21 167.73 50.49 4.368 61.87 -JCZ38 22.62 75.15 NA NA NA -J9Z38 121.77 404.50 NA NA NA -JSE76 200.98 667.64 NA NA NA - -</code></pre> -<p></p> -<caption> -Hierarchical DFOP path 1 fit with two-component error -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 20:37:03 2023 -Date of summary: Thu Apr 20 21:04:34 2023 - -Equations: -d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * - time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) - * cyan -d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - - g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * - exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38 -d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - - g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * - exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38 -d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 - -Data: -433 observations of 4 variable(s) grouped in 5 datasets - -Model predictions using solution type deSolve - -Fitted in 675.804 s -Using 300, 100 iterations and 10 chains - -Variance model: Two-component variance function - -Starting values for degradation parameters: - cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 - 101.3964 -3.3626 -4.9792 -5.8727 0.6814 - f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 g_qlogis - 6.7799 13.7245 -1.9222 -4.5035 -0.7172 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 -cyan_0 5.317 0.000 0.000 0.000 0.0000 -log_k_JCZ38 0.000 2.272 0.000 0.000 0.0000 -log_k_J9Z38 0.000 0.000 1.633 0.000 0.0000 -log_k_JSE76 0.000 0.000 0.000 1.271 0.0000 -f_cyan_ilr_1 0.000 0.000 0.000 0.000 0.6838 -f_cyan_ilr_2 0.000 0.000 0.000 0.000 0.0000 -f_JCZ38_qlogis 0.000 0.000 0.000 0.000 0.0000 -log_k1 0.000 0.000 0.000 0.000 0.0000 -log_k2 0.000 0.000 0.000 0.000 0.0000 -g_qlogis 0.000 0.000 0.000 0.000 0.0000 - f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 g_qlogis -cyan_0 0.00 0.00 0.0000 0.0000 0.000 -log_k_JCZ38 0.00 0.00 0.0000 0.0000 0.000 -log_k_J9Z38 0.00 0.00 0.0000 0.0000 0.000 -log_k_JSE76 0.00 0.00 0.0000 0.0000 0.000 -f_cyan_ilr_1 0.00 0.00 0.0000 0.0000 0.000 -f_cyan_ilr_2 11.77 0.00 0.0000 0.0000 0.000 -f_JCZ38_qlogis 0.00 16.11 0.0000 0.0000 0.000 -log_k1 0.00 0.00 0.9496 0.0000 0.000 -log_k2 0.00 0.00 0.0000 0.5846 0.000 -g_qlogis 0.00 0.00 0.0000 0.0000 1.719 - -Starting values for error model parameters: -a.1 b.1 - 1 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 2398 2390 -1179 - -Optimised parameters: - est. lower upper -cyan_0 100.8076 NA NA -log_k_JCZ38 -3.4684 NA NA -log_k_J9Z38 -5.0844 NA NA -log_k_JSE76 -5.5743 NA NA -f_cyan_ilr_1 0.6669 NA NA -f_cyan_ilr_2 0.7912 NA NA -f_JCZ38_qlogis 84.1825 NA NA -log_k1 -2.1671 NA NA -log_k2 -4.5447 NA NA -g_qlogis -0.5631 NA NA -a.1 2.9627 NA NA -b.1 0.0444 NA NA -SD.log_k_JCZ38 1.4044 NA NA -SD.log_k_J9Z38 0.6410 NA NA -SD.log_k_JSE76 0.5391 NA NA -SD.f_cyan_ilr_1 0.3203 NA NA -SD.f_cyan_ilr_2 0.5038 NA NA -SD.f_JCZ38_qlogis 3.5865 NA NA -SD.log_k2 0.3119 NA NA -SD.g_qlogis 0.8276 NA NA - -Correlation is not available - -Random effects: - est. lower upper -SD.log_k_JCZ38 1.4044 NA NA -SD.log_k_J9Z38 0.6410 NA NA -SD.log_k_JSE76 0.5391 NA NA -SD.f_cyan_ilr_1 0.3203 NA NA -SD.f_cyan_ilr_2 0.5038 NA NA -SD.f_JCZ38_qlogis 3.5865 NA NA -SD.log_k2 0.3119 NA NA -SD.g_qlogis 0.8276 NA NA - -Variance model: - est. lower upper -a.1 2.9627 NA NA -b.1 0.0444 NA NA - -Backtransformed parameters: - est. lower upper -cyan_0 1.008e+02 NA NA -k_JCZ38 3.117e-02 NA NA -k_J9Z38 6.193e-03 NA NA -k_JSE76 3.794e-03 NA NA -f_cyan_to_JCZ38 6.149e-01 NA NA -f_cyan_to_J9Z38 2.395e-01 NA NA -f_JCZ38_to_JSE76 1.000e+00 NA NA -k1 1.145e-01 NA NA -k2 1.062e-02 NA NA -g 3.628e-01 NA NA - -Resulting formation fractions: - ff -cyan_JCZ38 0.6149 -cyan_J9Z38 0.2395 -cyan_sink 0.1456 -JCZ38_JSE76 1.0000 -JCZ38_sink 0.0000 - -Estimated disappearance times: - DT50 DT90 DT50back DT50_k1 DT50_k2 -cyan 26.26 174.32 52.47 6.053 65.25 -JCZ38 22.24 73.88 NA NA NA -J9Z38 111.93 371.82 NA NA NA -JSE76 182.69 606.88 NA NA NA - -</code></pre> -<p></p> -<caption> -Hierarchical SFORB path 1 fit with constant variance -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 20:34:43 2023 -Date of summary: Thu Apr 20 21:04:34 2023 - -Equations: -d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound * - cyan_free + k_cyan_bound_free * cyan_bound -d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free * - cyan_bound -d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38 - * JCZ38 -d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38 - * J9Z38 -d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 - -Data: -433 observations of 4 variable(s) grouped in 5 datasets - -Model predictions using solution type deSolve - -Fitted in 535.818 s -Using 300, 100 iterations and 10 chains - -Variance model: Constant variance - -Starting values for degradation parameters: - cyan_free_0 log_k_cyan_free log_k_cyan_free_bound - 102.0643 -2.8987 -2.7077 -log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 - -3.4717 -3.4008 -5.0024 - log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 - -5.8613 0.6855 1.2366 - f_JCZ38_qlogis - 13.7418 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - cyan_free_0 log_k_cyan_free log_k_cyan_free_bound -cyan_free_0 4.466 0.0000 0.000 -log_k_cyan_free 0.000 0.6158 0.000 -log_k_cyan_free_bound 0.000 0.0000 1.463 -log_k_cyan_bound_free 0.000 0.0000 0.000 -log_k_JCZ38 0.000 0.0000 0.000 -log_k_J9Z38 0.000 0.0000 0.000 -log_k_JSE76 0.000 0.0000 0.000 -f_cyan_ilr_1 0.000 0.0000 0.000 -f_cyan_ilr_2 0.000 0.0000 0.000 -f_JCZ38_qlogis 0.000 0.0000 0.000 - log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 -cyan_free_0 0.000 0.000 0.000 0.000 -log_k_cyan_free 0.000 0.000 0.000 0.000 -log_k_cyan_free_bound 0.000 0.000 0.000 0.000 -log_k_cyan_bound_free 1.058 0.000 0.000 0.000 -log_k_JCZ38 0.000 2.382 0.000 0.000 -log_k_J9Z38 0.000 0.000 1.595 0.000 -log_k_JSE76 0.000 0.000 0.000 1.245 -f_cyan_ilr_1 0.000 0.000 0.000 0.000 -f_cyan_ilr_2 0.000 0.000 0.000 0.000 -f_JCZ38_qlogis 0.000 0.000 0.000 0.000 - f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis -cyan_free_0 0.0000 0.00 0.00 -log_k_cyan_free 0.0000 0.00 0.00 -log_k_cyan_free_bound 0.0000 0.00 0.00 -log_k_cyan_bound_free 0.0000 0.00 0.00 -log_k_JCZ38 0.0000 0.00 0.00 -log_k_J9Z38 0.0000 0.00 0.00 -log_k_JSE76 0.0000 0.00 0.00 -f_cyan_ilr_1 0.6852 0.00 0.00 -f_cyan_ilr_2 0.0000 1.28 0.00 -f_JCZ38_qlogis 0.0000 0.00 16.14 - -Starting values for error model parameters: -a.1 - 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 2401 2394 -1181 - -Optimised parameters: - est. lower upper -cyan_free_0 102.7803 NA NA -log_k_cyan_free -2.8068 NA NA -log_k_cyan_free_bound -2.5714 NA NA -log_k_cyan_bound_free -3.4426 NA NA -log_k_JCZ38 -3.4994 NA NA -log_k_J9Z38 -5.1148 NA NA -log_k_JSE76 -5.6335 NA NA -f_cyan_ilr_1 0.6597 NA NA -f_cyan_ilr_2 0.5132 NA NA -f_JCZ38_qlogis 37.2090 NA NA -a.1 3.2367 NA NA -SD.log_k_cyan_free 0.3161 NA NA -SD.log_k_cyan_free_bound 0.8103 NA NA -SD.log_k_cyan_bound_free 0.5554 NA NA -SD.log_k_JCZ38 1.4858 NA NA -SD.log_k_J9Z38 0.5859 NA NA -SD.log_k_JSE76 0.6195 NA NA -SD.f_cyan_ilr_1 0.3118 NA NA -SD.f_cyan_ilr_2 0.3344 NA NA -SD.f_JCZ38_qlogis 0.5518 NA NA - -Correlation is not available - -Random effects: - est. lower upper -SD.log_k_cyan_free 0.3161 NA NA -SD.log_k_cyan_free_bound 0.8103 NA NA -SD.log_k_cyan_bound_free 0.5554 NA NA -SD.log_k_JCZ38 1.4858 NA NA -SD.log_k_J9Z38 0.5859 NA NA -SD.log_k_JSE76 0.6195 NA NA -SD.f_cyan_ilr_1 0.3118 NA NA -SD.f_cyan_ilr_2 0.3344 NA NA -SD.f_JCZ38_qlogis 0.5518 NA NA - -Variance model: - est. lower upper -a.1 3.237 NA NA - -Backtransformed parameters: - est. lower upper -cyan_free_0 1.028e+02 NA NA -k_cyan_free 6.040e-02 NA NA -k_cyan_free_bound 7.643e-02 NA NA -k_cyan_bound_free 3.198e-02 NA NA -k_JCZ38 3.022e-02 NA NA -k_J9Z38 6.007e-03 NA NA -k_JSE76 3.576e-03 NA NA -f_cyan_free_to_JCZ38 5.787e-01 NA NA -f_cyan_free_to_J9Z38 2.277e-01 NA NA -f_JCZ38_to_JSE76 1.000e+00 NA NA - -Estimated Eigenvalues of SFORB model(s): -cyan_b1 cyan_b2 cyan_g -0.15646 0.01235 0.33341 - -Resulting formation fractions: - ff -cyan_free_JCZ38 0.5787 -cyan_free_J9Z38 0.2277 -cyan_free_sink 0.1936 -cyan_free 1.0000 -JCZ38_JSE76 1.0000 -JCZ38_sink 0.0000 - -Estimated disappearance times: - DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 -cyan 24.48 153.7 46.26 4.43 56.15 -JCZ38 22.94 76.2 NA NA NA -J9Z38 115.39 383.3 NA NA NA -JSE76 193.84 643.9 NA NA NA - -</code></pre> -<p></p> -<caption> -Hierarchical SFORB path 1 fit with two-component error -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 20:37:02 2023 -Date of summary: Thu Apr 20 21:04:34 2023 - -Equations: -d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound * - cyan_free + k_cyan_bound_free * cyan_bound -d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free * - cyan_bound -d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38 - * JCZ38 -d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38 - * J9Z38 -d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 - -Data: -433 observations of 4 variable(s) grouped in 5 datasets - -Model predictions using solution type deSolve - -Fitted in 674.859 s -Using 300, 100 iterations and 10 chains - -Variance model: Two-component variance function - -Starting values for degradation parameters: - cyan_free_0 log_k_cyan_free log_k_cyan_free_bound - 101.3964 -2.9881 -2.7949 -log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 - -3.4376 -3.3626 -4.9792 - log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 - -5.8727 0.6814 6.8139 - f_JCZ38_qlogis - 13.7419 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - cyan_free_0 log_k_cyan_free log_k_cyan_free_bound -cyan_free_0 5.317 0.0000 0.000 -log_k_cyan_free 0.000 0.7301 0.000 -log_k_cyan_free_bound 0.000 0.0000 1.384 -log_k_cyan_bound_free 0.000 0.0000 0.000 -log_k_JCZ38 0.000 0.0000 0.000 -log_k_J9Z38 0.000 0.0000 0.000 -log_k_JSE76 0.000 0.0000 0.000 -f_cyan_ilr_1 0.000 0.0000 0.000 -f_cyan_ilr_2 0.000 0.0000 0.000 -f_JCZ38_qlogis 0.000 0.0000 0.000 - log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 -cyan_free_0 0.000 0.000 0.000 0.000 -log_k_cyan_free 0.000 0.000 0.000 0.000 -log_k_cyan_free_bound 0.000 0.000 0.000 0.000 -log_k_cyan_bound_free 1.109 0.000 0.000 0.000 -log_k_JCZ38 0.000 2.272 0.000 0.000 -log_k_J9Z38 0.000 0.000 1.633 0.000 -log_k_JSE76 0.000 0.000 0.000 1.271 -f_cyan_ilr_1 0.000 0.000 0.000 0.000 -f_cyan_ilr_2 0.000 0.000 0.000 0.000 -f_JCZ38_qlogis 0.000 0.000 0.000 0.000 - f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis -cyan_free_0 0.0000 0.00 0.00 -log_k_cyan_free 0.0000 0.00 0.00 -log_k_cyan_free_bound 0.0000 0.00 0.00 -log_k_cyan_bound_free 0.0000 0.00 0.00 -log_k_JCZ38 0.0000 0.00 0.00 -log_k_J9Z38 0.0000 0.00 0.00 -log_k_JSE76 0.0000 0.00 0.00 -f_cyan_ilr_1 0.6838 0.00 0.00 -f_cyan_ilr_2 0.0000 11.84 0.00 -f_JCZ38_qlogis 0.0000 0.00 16.14 - -Starting values for error model parameters: -a.1 b.1 - 1 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 2400 2392 -1180 - -Optimised parameters: - est. lower upper -cyan_free_0 100.69983 NA NA -log_k_cyan_free -3.11584 NA NA -log_k_cyan_free_bound -3.15216 NA NA -log_k_cyan_bound_free -3.65986 NA NA -log_k_JCZ38 -3.47811 NA NA -log_k_J9Z38 -5.08835 NA NA -log_k_JSE76 -5.55514 NA NA -f_cyan_ilr_1 0.66764 NA NA -f_cyan_ilr_2 0.78329 NA NA -f_JCZ38_qlogis 25.35245 NA NA -a.1 2.99088 NA NA -b.1 0.04346 NA NA -SD.log_k_cyan_free 0.48797 NA NA -SD.log_k_cyan_bound_free 0.27243 NA NA -SD.log_k_JCZ38 1.42450 NA NA -SD.log_k_J9Z38 0.63496 NA NA -SD.log_k_JSE76 0.55951 NA NA -SD.f_cyan_ilr_1 0.32687 NA NA -SD.f_cyan_ilr_2 0.48056 NA NA -SD.f_JCZ38_qlogis 0.43818 NA NA - -Correlation is not available - -Random effects: - est. lower upper -SD.log_k_cyan_free 0.4880 NA NA -SD.log_k_cyan_bound_free 0.2724 NA NA -SD.log_k_JCZ38 1.4245 NA NA -SD.log_k_J9Z38 0.6350 NA NA -SD.log_k_JSE76 0.5595 NA NA -SD.f_cyan_ilr_1 0.3269 NA NA -SD.f_cyan_ilr_2 0.4806 NA NA -SD.f_JCZ38_qlogis 0.4382 NA NA - -Variance model: - est. lower upper -a.1 2.99088 NA NA -b.1 0.04346 NA NA - -Backtransformed parameters: - est. lower upper -cyan_free_0 1.007e+02 NA NA -k_cyan_free 4.434e-02 NA NA -k_cyan_free_bound 4.276e-02 NA NA -k_cyan_bound_free 2.574e-02 NA NA -k_JCZ38 3.087e-02 NA NA -k_J9Z38 6.168e-03 NA NA -k_JSE76 3.868e-03 NA NA -f_cyan_free_to_JCZ38 6.143e-01 NA NA -f_cyan_free_to_J9Z38 2.389e-01 NA NA -f_JCZ38_to_JSE76 1.000e+00 NA NA - -Estimated Eigenvalues of SFORB model(s): -cyan_b1 cyan_b2 cyan_g -0.10161 0.01123 0.36636 - -Resulting formation fractions: - ff -cyan_free_JCZ38 6.143e-01 -cyan_free_J9Z38 2.389e-01 -cyan_free_sink 1.468e-01 -cyan_free 1.000e+00 -JCZ38_JSE76 1.000e+00 -JCZ38_sink 9.763e-12 - -Estimated disappearance times: - DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 -cyan 25.91 164.4 49.49 6.822 61.72 -JCZ38 22.46 74.6 NA NA NA -J9Z38 112.37 373.3 NA NA NA -JSE76 179.22 595.4 NA NA NA - -</code></pre> -<p></p> -<caption> -Hierarchical HS path 1 fit with constant variance -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 20:34:41 2023 -Date of summary: Thu Apr 20 21:04:34 2023 - -Equations: -d_cyan/dt = - ifelse(time <= tb, k1, k2) * cyan -d_JCZ38/dt = + f_cyan_to_JCZ38 * ifelse(time <= tb, k1, k2) * cyan - - k_JCZ38 * JCZ38 -d_J9Z38/dt = + f_cyan_to_J9Z38 * ifelse(time <= tb, k1, k2) * cyan - - k_J9Z38 * J9Z38 -d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 - -Data: -433 observations of 4 variable(s) grouped in 5 datasets - -Model predictions using solution type deSolve - -Fitted in 533.787 s -Using 300, 100 iterations and 10 chains - -Variance model: Constant variance - -Starting values for degradation parameters: - cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 - 102.8738 -3.4490 -4.9348 -5.5989 0.6469 - f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 log_tb - 1.2854 9.7193 -2.9084 -4.1810 1.7813 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 -cyan_0 5.409 0.00 0.00 0.000 0.0000 -log_k_JCZ38 0.000 2.33 0.00 0.000 0.0000 -log_k_J9Z38 0.000 0.00 1.59 0.000 0.0000 -log_k_JSE76 0.000 0.00 0.00 1.006 0.0000 -f_cyan_ilr_1 0.000 0.00 0.00 0.000 0.6371 -f_cyan_ilr_2 0.000 0.00 0.00 0.000 0.0000 -f_JCZ38_qlogis 0.000 0.00 0.00 0.000 0.0000 -log_k1 0.000 0.00 0.00 0.000 0.0000 -log_k2 0.000 0.00 0.00 0.000 0.0000 -log_tb 0.000 0.00 0.00 0.000 0.0000 - f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 log_tb -cyan_0 0.000 0.00 0.0000 0.0000 0.0000 -log_k_JCZ38 0.000 0.00 0.0000 0.0000 0.0000 -log_k_J9Z38 0.000 0.00 0.0000 0.0000 0.0000 -log_k_JSE76 0.000 0.00 0.0000 0.0000 0.0000 -f_cyan_ilr_1 0.000 0.00 0.0000 0.0000 0.0000 -f_cyan_ilr_2 2.167 0.00 0.0000 0.0000 0.0000 -f_JCZ38_qlogis 0.000 10.22 0.0000 0.0000 0.0000 -log_k1 0.000 0.00 0.7003 0.0000 0.0000 -log_k2 0.000 0.00 0.0000 0.8928 0.0000 -log_tb 0.000 0.00 0.0000 0.0000 0.6774 - -Starting values for error model parameters: -a.1 - 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 2427 2420 -1194 - -Optimised parameters: - est. lower upper -cyan_0 101.84849 NA NA -log_k_JCZ38 -3.47365 NA NA -log_k_J9Z38 -5.10562 NA NA -log_k_JSE76 -5.60318 NA NA -f_cyan_ilr_1 0.66127 NA NA -f_cyan_ilr_2 0.60283 NA NA -f_JCZ38_qlogis 45.06408 NA NA -log_k1 -3.10124 NA NA -log_k2 -4.39028 NA NA -log_tb 2.32256 NA NA -a.1 3.32683 NA NA -SD.log_k_JCZ38 1.41427 NA NA -SD.log_k_J9Z38 0.54767 NA NA -SD.log_k_JSE76 0.62147 NA NA -SD.f_cyan_ilr_1 0.30189 NA NA -SD.f_cyan_ilr_2 0.34960 NA NA -SD.f_JCZ38_qlogis 0.04644 NA NA -SD.log_k1 0.39534 NA NA -SD.log_k2 0.43468 NA NA -SD.log_tb 0.60781 NA NA - -Correlation is not available - -Random effects: - est. lower upper -SD.log_k_JCZ38 1.41427 NA NA -SD.log_k_J9Z38 0.54767 NA NA -SD.log_k_JSE76 0.62147 NA NA -SD.f_cyan_ilr_1 0.30189 NA NA -SD.f_cyan_ilr_2 0.34960 NA NA -SD.f_JCZ38_qlogis 0.04644 NA NA -SD.log_k1 0.39534 NA NA -SD.log_k2 0.43468 NA NA -SD.log_tb 0.60781 NA NA - -Variance model: - est. lower upper -a.1 3.327 NA NA - -Backtransformed parameters: - est. lower upper -cyan_0 1.018e+02 NA NA -k_JCZ38 3.100e-02 NA NA -k_J9Z38 6.063e-03 NA NA -k_JSE76 3.686e-03 NA NA -f_cyan_to_JCZ38 5.910e-01 NA NA -f_cyan_to_J9Z38 2.320e-01 NA NA -f_JCZ38_to_JSE76 1.000e+00 NA NA -k1 4.499e-02 NA NA -k2 1.240e-02 NA NA -tb 1.020e+01 NA NA - -Resulting formation fractions: - ff -cyan_JCZ38 0.591 -cyan_J9Z38 0.232 -cyan_sink 0.177 -JCZ38_JSE76 1.000 -JCZ38_sink 0.000 - -Estimated disappearance times: - DT50 DT90 DT50back DT50_k1 DT50_k2 -cyan 29.09 158.91 47.84 15.41 55.91 -JCZ38 22.36 74.27 NA NA NA -J9Z38 114.33 379.80 NA NA NA -JSE76 188.04 624.66 NA NA NA - -</code></pre> -<p></p> -<caption> -Hierarchical HS path 1 fit with two-component error -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 20:34:39 2023 -Date of summary: Thu Apr 20 21:04:34 2023 - -Equations: -d_cyan/dt = - ifelse(time <= tb, k1, k2) * cyan -d_JCZ38/dt = + f_cyan_to_JCZ38 * ifelse(time <= tb, k1, k2) * cyan - - k_JCZ38 * JCZ38 -d_J9Z38/dt = + f_cyan_to_J9Z38 * ifelse(time <= tb, k1, k2) * cyan - - k_J9Z38 * J9Z38 -d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 - -Data: -433 observations of 4 variable(s) grouped in 5 datasets - -Model predictions using solution type deSolve - -Fitted in 531.084 s -Using 300, 100 iterations and 10 chains - -Variance model: Two-component variance function - -Starting values for degradation parameters: - cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 - 101.168 -3.358 -4.941 -5.794 0.676 - f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 log_tb - 5.740 13.863 -3.147 -4.262 2.173 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 -cyan_0 5.79 0.000 0.000 0.000 0.0000 -log_k_JCZ38 0.00 2.271 0.000 0.000 0.0000 -log_k_J9Z38 0.00 0.000 1.614 0.000 0.0000 -log_k_JSE76 0.00 0.000 0.000 1.264 0.0000 -f_cyan_ilr_1 0.00 0.000 0.000 0.000 0.6761 -f_cyan_ilr_2 0.00 0.000 0.000 0.000 0.0000 -f_JCZ38_qlogis 0.00 0.000 0.000 0.000 0.0000 -log_k1 0.00 0.000 0.000 0.000 0.0000 -log_k2 0.00 0.000 0.000 0.000 0.0000 -log_tb 0.00 0.000 0.000 0.000 0.0000 - f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 log_tb -cyan_0 0.000 0.00 0.0000 0.0000 0.000 -log_k_JCZ38 0.000 0.00 0.0000 0.0000 0.000 -log_k_J9Z38 0.000 0.00 0.0000 0.0000 0.000 -log_k_JSE76 0.000 0.00 0.0000 0.0000 0.000 -f_cyan_ilr_1 0.000 0.00 0.0000 0.0000 0.000 -f_cyan_ilr_2 9.572 0.00 0.0000 0.0000 0.000 -f_JCZ38_qlogis 0.000 19.19 0.0000 0.0000 0.000 -log_k1 0.000 0.00 0.8705 0.0000 0.000 -log_k2 0.000 0.00 0.0000 0.9288 0.000 -log_tb 0.000 0.00 0.0000 0.0000 1.065 - -Starting values for error model parameters: -a.1 b.1 - 1 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 2422 2414 -1190 - -Optimised parameters: - est. lower upper -cyan_0 100.9521 NA NA -log_k_JCZ38 -3.4629 NA NA -log_k_J9Z38 -5.0346 NA NA -log_k_JSE76 -5.5722 NA NA -f_cyan_ilr_1 0.6560 NA NA -f_cyan_ilr_2 0.7983 NA NA -f_JCZ38_qlogis 42.7949 NA NA -log_k1 -3.1721 NA NA -log_k2 -4.4039 NA NA -log_tb 2.3994 NA NA -a.1 3.0586 NA NA -b.1 0.0380 NA NA -SD.log_k_JCZ38 1.3754 NA NA -SD.log_k_J9Z38 0.6703 NA NA -SD.log_k_JSE76 0.5876 NA NA -SD.f_cyan_ilr_1 0.3272 NA NA -SD.f_cyan_ilr_2 0.5300 NA NA -SD.f_JCZ38_qlogis 6.4465 NA NA -SD.log_k1 0.4135 NA NA -SD.log_k2 0.4182 NA NA -SD.log_tb 0.6035 NA NA - -Correlation is not available - -Random effects: - est. lower upper -SD.log_k_JCZ38 1.3754 NA NA -SD.log_k_J9Z38 0.6703 NA NA -SD.log_k_JSE76 0.5876 NA NA -SD.f_cyan_ilr_1 0.3272 NA NA -SD.f_cyan_ilr_2 0.5300 NA NA -SD.f_JCZ38_qlogis 6.4465 NA NA -SD.log_k1 0.4135 NA NA -SD.log_k2 0.4182 NA NA -SD.log_tb 0.6035 NA NA - -Variance model: - est. lower upper -a.1 3.059 NA NA -b.1 0.038 NA NA - -Backtransformed parameters: - est. lower upper -cyan_0 1.010e+02 NA NA -k_JCZ38 3.134e-02 NA NA -k_J9Z38 6.509e-03 NA NA -k_JSE76 3.802e-03 NA NA -f_cyan_to_JCZ38 6.127e-01 NA NA -f_cyan_to_J9Z38 2.423e-01 NA NA -f_JCZ38_to_JSE76 1.000e+00 NA NA -k1 4.191e-02 NA NA -k2 1.223e-02 NA NA -tb 1.102e+01 NA NA - -Resulting formation fractions: - ff -cyan_JCZ38 0.6127 -cyan_J9Z38 0.2423 -cyan_sink 0.1449 -JCZ38_JSE76 1.0000 -JCZ38_sink 0.0000 - -Estimated disappearance times: - DT50 DT90 DT50back DT50_k1 DT50_k2 -cyan 29.94 161.54 48.63 16.54 56.68 -JCZ38 22.12 73.47 NA NA NA -J9Z38 106.50 353.77 NA NA NA -JSE76 182.30 605.60 NA NA NA - -</code></pre> -<p></p> -</div> -<div class="section level4"> -<h4 id="pathway-2">Pathway 2<a class="anchor" aria-label="anchor" href="#pathway-2"></a> -</h4> -<caption> -Hierarchical FOMC path 2 fit with constant variance -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 20:45:51 2023 -Date of summary: Thu Apr 20 21:04:34 2023 - -Equations: -d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan -d_JCZ38/dt = + f_cyan_to_JCZ38 * (alpha/beta) * 1/((time/beta) + 1) * - cyan - k_JCZ38 * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76 -d_J9Z38/dt = + f_cyan_to_J9Z38 * (alpha/beta) * 1/((time/beta) + 1) * - cyan - k_J9Z38 * J9Z38 -d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 - -Data: -433 observations of 4 variable(s) grouped in 5 datasets - -Model predictions using solution type deSolve - -Fitted in 517.002 s -Using 300, 100 iterations and 10 chains - -Variance model: Constant variance - -Starting values for degradation parameters: - cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 - 101.8173 -1.8998 -5.1449 -2.5415 0.6705 - f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta - 4.4669 16.1281 13.3327 -0.2314 2.8738 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 -cyan_0 5.742 0.000 0.000 0.00 0.0000 -log_k_JCZ38 0.000 1.402 0.000 0.00 0.0000 -log_k_J9Z38 0.000 0.000 1.718 0.00 0.0000 -log_k_JSE76 0.000 0.000 0.000 3.57 0.0000 -f_cyan_ilr_1 0.000 0.000 0.000 0.00 0.5926 -f_cyan_ilr_2 0.000 0.000 0.000 0.00 0.0000 -f_JCZ38_qlogis 0.000 0.000 0.000 0.00 0.0000 -f_JSE76_qlogis 0.000 0.000 0.000 0.00 0.0000 -log_alpha 0.000 0.000 0.000 0.00 0.0000 -log_beta 0.000 0.000 0.000 0.00 0.0000 - f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta -cyan_0 0.00 0.00 0.00 0.0000 0.0000 -log_k_JCZ38 0.00 0.00 0.00 0.0000 0.0000 -log_k_J9Z38 0.00 0.00 0.00 0.0000 0.0000 -log_k_JSE76 0.00 0.00 0.00 0.0000 0.0000 -f_cyan_ilr_1 0.00 0.00 0.00 0.0000 0.0000 -f_cyan_ilr_2 10.56 0.00 0.00 0.0000 0.0000 -f_JCZ38_qlogis 0.00 12.04 0.00 0.0000 0.0000 -f_JSE76_qlogis 0.00 0.00 15.26 0.0000 0.0000 -log_alpha 0.00 0.00 0.00 0.4708 0.0000 -log_beta 0.00 0.00 0.00 0.0000 0.4432 - -Starting values for error model parameters: -a.1 - 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 2308 2301 -1134 - -Optimised parameters: - est. lower upper -cyan_0 101.9586 99.22024 104.69700 -log_k_JCZ38 -2.4861 -3.17661 -1.79560 -log_k_J9Z38 -5.3926 -6.08842 -4.69684 -log_k_JSE76 -3.1193 -4.12904 -2.10962 -f_cyan_ilr_1 0.7368 0.42085 1.05276 -f_cyan_ilr_2 0.6196 0.06052 1.17861 -f_JCZ38_qlogis 4.8970 -4.68003 14.47398 -f_JSE76_qlogis 4.4066 -1.02087 9.83398 -log_alpha -0.3021 -0.68264 0.07838 -log_beta 2.7438 2.57970 2.90786 -a.1 2.9008 2.69920 3.10245 -SD.cyan_0 2.7081 0.64216 4.77401 -SD.log_k_JCZ38 0.7043 0.19951 1.20907 -SD.log_k_J9Z38 0.6248 0.05790 1.19180 -SD.log_k_JSE76 1.0750 0.33157 1.81839 -SD.f_cyan_ilr_1 0.3429 0.11688 0.56892 -SD.f_cyan_ilr_2 0.4774 0.09381 0.86097 -SD.f_JCZ38_qlogis 1.5565 -7.83970 10.95279 -SD.f_JSE76_qlogis 1.6871 -1.25577 4.63000 -SD.log_alpha 0.4216 0.15913 0.68405 - -Correlation: - cyan_0 l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76 -log_k_JCZ38 -0.0167 -log_k_J9Z38 -0.0307 0.0057 -log_k_JSE76 -0.0032 0.1358 0.0009 -f_cyan_ilr_1 -0.0087 0.0206 -0.1158 -0.0009 -f_cyan_ilr_2 -0.1598 0.0690 0.1770 0.0002 -0.0007 -f_JCZ38_qlogis 0.0966 -0.1132 -0.0440 0.0182 -0.1385 -0.4583 -f_JSE76_qlogis -0.0647 0.1157 0.0333 -0.0026 0.1110 0.3620 -0.8586 -log_alpha -0.0389 0.0113 0.0209 0.0021 0.0041 0.0451 -0.0605 0.0412 -log_beta -0.2508 0.0533 0.0977 0.0098 0.0220 0.2741 -0.2934 0.1999 - log_lph -log_k_JCZ38 -log_k_J9Z38 -log_k_JSE76 -f_cyan_ilr_1 -f_cyan_ilr_2 -f_JCZ38_qlogis -f_JSE76_qlogis -log_alpha -log_beta 0.2281 - -Random effects: - est. lower upper -SD.cyan_0 2.7081 0.64216 4.7740 -SD.log_k_JCZ38 0.7043 0.19951 1.2091 -SD.log_k_J9Z38 0.6248 0.05790 1.1918 -SD.log_k_JSE76 1.0750 0.33157 1.8184 -SD.f_cyan_ilr_1 0.3429 0.11688 0.5689 -SD.f_cyan_ilr_2 0.4774 0.09381 0.8610 -SD.f_JCZ38_qlogis 1.5565 -7.83970 10.9528 -SD.f_JSE76_qlogis 1.6871 -1.25577 4.6300 -SD.log_alpha 0.4216 0.15913 0.6840 - -Variance model: - est. lower upper -a.1 2.901 2.699 3.102 - -Backtransformed parameters: - est. lower upper -cyan_0 101.95862 99.220240 1.047e+02 -k_JCZ38 0.08323 0.041727 1.660e-01 -k_J9Z38 0.00455 0.002269 9.124e-03 -k_JSE76 0.04419 0.016098 1.213e-01 -f_cyan_to_JCZ38 0.61318 NA NA -f_cyan_to_J9Z38 0.21630 NA NA -f_JCZ38_to_JSE76 0.99259 0.009193 1.000e+00 -f_JSE76_to_JCZ38 0.98795 0.264857 9.999e-01 -alpha 0.73924 0.505281 1.082e+00 -beta 15.54568 13.193194 1.832e+01 - -Resulting formation fractions: - ff -cyan_JCZ38 0.613182 -cyan_J9Z38 0.216298 -cyan_sink 0.170519 -JCZ38_JSE76 0.992586 -JCZ38_sink 0.007414 -JSE76_JCZ38 0.987950 -JSE76_sink 0.012050 - -Estimated disappearance times: - DT50 DT90 DT50back -cyan 24.157 334.68 100.7 -JCZ38 8.328 27.66 NA -J9Z38 152.341 506.06 NA -JSE76 15.687 52.11 NA - -</code></pre> -<p></p> -<caption> -Hierarchical FOMC path 2 fit with two-component error -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 20:45:39 2023 -Date of summary: Thu Apr 20 21:04:34 2023 - -Equations: -d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan -d_JCZ38/dt = + f_cyan_to_JCZ38 * (alpha/beta) * 1/((time/beta) + 1) * - cyan - k_JCZ38 * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76 -d_J9Z38/dt = + f_cyan_to_J9Z38 * (alpha/beta) * 1/((time/beta) + 1) * - cyan - k_J9Z38 * J9Z38 -d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 - -Data: -433 observations of 4 variable(s) grouped in 5 datasets - -Model predictions using solution type deSolve - -Fitted in 505.619 s -Using 300, 100 iterations and 10 chains - -Variance model: Two-component variance function - -Starting values for degradation parameters: - cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 - 101.9028 -1.9055 -5.0249 -2.5646 0.6807 - f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta - 4.8883 16.0676 9.3923 -0.1346 3.0364 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 -cyan_0 6.321 0.000 0.000 0.000 0.0000 -log_k_JCZ38 0.000 1.392 0.000 0.000 0.0000 -log_k_J9Z38 0.000 0.000 1.561 0.000 0.0000 -log_k_JSE76 0.000 0.000 0.000 3.614 0.0000 -f_cyan_ilr_1 0.000 0.000 0.000 0.000 0.6339 -f_cyan_ilr_2 0.000 0.000 0.000 0.000 0.0000 -f_JCZ38_qlogis 0.000 0.000 0.000 0.000 0.0000 -f_JSE76_qlogis 0.000 0.000 0.000 0.000 0.0000 -log_alpha 0.000 0.000 0.000 0.000 0.0000 -log_beta 0.000 0.000 0.000 0.000 0.0000 - f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta -cyan_0 0.00 0.00 0.00 0.0000 0.0000 -log_k_JCZ38 0.00 0.00 0.00 0.0000 0.0000 -log_k_J9Z38 0.00 0.00 0.00 0.0000 0.0000 -log_k_JSE76 0.00 0.00 0.00 0.0000 0.0000 -f_cyan_ilr_1 0.00 0.00 0.00 0.0000 0.0000 -f_cyan_ilr_2 10.41 0.00 0.00 0.0000 0.0000 -f_JCZ38_qlogis 0.00 12.24 0.00 0.0000 0.0000 -f_JSE76_qlogis 0.00 0.00 15.13 0.0000 0.0000 -log_alpha 0.00 0.00 0.00 0.3701 0.0000 -log_beta 0.00 0.00 0.00 0.0000 0.5662 - -Starting values for error model parameters: -a.1 b.1 - 1 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 2248 2240 -1103 - -Optimised parameters: - est. lower upper -cyan_0 101.55545 9.920e+01 1.039e+02 -log_k_JCZ38 -2.37354 -2.928e+00 -1.819e+00 -log_k_J9Z38 -5.14736 -5.960e+00 -4.335e+00 -log_k_JSE76 -3.07802 -4.243e+00 -1.913e+00 -f_cyan_ilr_1 0.71263 3.655e-01 1.060e+00 -f_cyan_ilr_2 0.95202 2.701e-01 1.634e+00 -f_JCZ38_qlogis 3.58473 1.251e+00 5.919e+00 -f_JSE76_qlogis 19.03623 -1.037e+07 1.037e+07 -log_alpha -0.15297 -4.490e-01 1.431e-01 -log_beta 2.99230 2.706e+00 3.278e+00 -a.1 2.04816 NA NA -b.1 0.06886 NA NA -SD.log_k_JCZ38 0.56174 NA NA -SD.log_k_J9Z38 0.86509 NA NA -SD.log_k_JSE76 1.28450 NA NA -SD.f_cyan_ilr_1 0.38705 NA NA -SD.f_cyan_ilr_2 0.54153 NA NA -SD.f_JCZ38_qlogis 1.65311 NA NA -SD.f_JSE76_qlogis 7.51468 NA NA -SD.log_alpha 0.31586 NA NA -SD.log_beta 0.24696 NA NA - -Correlation is not available - -Random effects: - est. lower upper -SD.log_k_JCZ38 0.5617 NA NA -SD.log_k_J9Z38 0.8651 NA NA -SD.log_k_JSE76 1.2845 NA NA -SD.f_cyan_ilr_1 0.3870 NA NA -SD.f_cyan_ilr_2 0.5415 NA NA -SD.f_JCZ38_qlogis 1.6531 NA NA -SD.f_JSE76_qlogis 7.5147 NA NA -SD.log_alpha 0.3159 NA NA -SD.log_beta 0.2470 NA NA - -Variance model: - est. lower upper -a.1 2.04816 NA NA -b.1 0.06886 NA NA - -Backtransformed parameters: - est. lower upper -cyan_0 1.016e+02 99.20301 103.9079 -k_JCZ38 9.315e-02 0.05349 0.1622 -k_J9Z38 5.815e-03 0.00258 0.0131 -k_JSE76 4.605e-02 0.01436 0.1477 -f_cyan_to_JCZ38 6.438e-01 NA NA -f_cyan_to_J9Z38 2.350e-01 NA NA -f_JCZ38_to_JSE76 9.730e-01 0.77745 0.9973 -f_JSE76_to_JCZ38 1.000e+00 0.00000 1.0000 -alpha 8.582e-01 0.63824 1.1538 -beta 1.993e+01 14.97621 26.5262 - -Resulting formation fractions: - ff -cyan_JCZ38 6.438e-01 -cyan_J9Z38 2.350e-01 -cyan_sink 1.212e-01 -JCZ38_JSE76 9.730e-01 -JCZ38_sink 2.700e-02 -JSE76_JCZ38 1.000e+00 -JSE76_sink 5.403e-09 - -Estimated disappearance times: - DT50 DT90 DT50back -cyan 24.771 271.70 81.79 -JCZ38 7.441 24.72 NA -J9Z38 119.205 395.99 NA -JSE76 15.052 50.00 NA - -</code></pre> -<p></p> -<caption> -Hierarchical DFOP path 2 fit with constant variance -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 20:46:46 2023 -Date of summary: Thu Apr 20 21:04:34 2023 - -Equations: -d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * - time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) - * cyan -d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - - g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * - exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38 + - f_JSE76_to_JCZ38 * k_JSE76 * JSE76 -d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - - g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * - exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38 -d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 - -Data: -433 observations of 4 variable(s) grouped in 5 datasets - -Model predictions using solution type deSolve - -Fitted in 572.382 s -Using 300, 100 iterations and 10 chains - -Variance model: Constant variance - -Starting values for degradation parameters: - cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 - 102.4358 -2.3107 -5.3123 -3.7120 0.6753 - f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 - 1.1462 12.4095 12.3630 -1.9317 -4.4557 - g_qlogis - -0.5648 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 -cyan_0 4.594 0.0000 0.000 0.0 0.0000 -log_k_JCZ38 0.000 0.7966 0.000 0.0 0.0000 -log_k_J9Z38 0.000 0.0000 1.561 0.0 0.0000 -log_k_JSE76 0.000 0.0000 0.000 0.8 0.0000 -f_cyan_ilr_1 0.000 0.0000 0.000 0.0 0.6349 -f_cyan_ilr_2 0.000 0.0000 0.000 0.0 0.0000 -f_JCZ38_qlogis 0.000 0.0000 0.000 0.0 0.0000 -f_JSE76_qlogis 0.000 0.0000 0.000 0.0 0.0000 -log_k1 0.000 0.0000 0.000 0.0 0.0000 -log_k2 0.000 0.0000 0.000 0.0 0.0000 -g_qlogis 0.000 0.0000 0.000 0.0 0.0000 - f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 -cyan_0 0.000 0.00 0.0 0.000 0.0000 -log_k_JCZ38 0.000 0.00 0.0 0.000 0.0000 -log_k_J9Z38 0.000 0.00 0.0 0.000 0.0000 -log_k_JSE76 0.000 0.00 0.0 0.000 0.0000 -f_cyan_ilr_1 0.000 0.00 0.0 0.000 0.0000 -f_cyan_ilr_2 1.797 0.00 0.0 0.000 0.0000 -f_JCZ38_qlogis 0.000 13.85 0.0 0.000 0.0000 -f_JSE76_qlogis 0.000 0.00 14.1 0.000 0.0000 -log_k1 0.000 0.00 0.0 1.106 0.0000 -log_k2 0.000 0.00 0.0 0.000 0.6141 -g_qlogis 0.000 0.00 0.0 0.000 0.0000 - g_qlogis -cyan_0 0.000 -log_k_JCZ38 0.000 -log_k_J9Z38 0.000 -log_k_JSE76 0.000 -f_cyan_ilr_1 0.000 -f_cyan_ilr_2 0.000 -f_JCZ38_qlogis 0.000 -f_JSE76_qlogis 0.000 -log_k1 0.000 -log_k2 0.000 -g_qlogis 1.595 - -Starting values for error model parameters: -a.1 - 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 2290 2281 -1123 - -Optimised parameters: - est. lower upper -cyan_0 102.6903 101.44420 103.9365 -log_k_JCZ38 -2.4018 -2.98058 -1.8230 -log_k_J9Z38 -5.1865 -5.92931 -4.4437 -log_k_JSE76 -3.0784 -4.25226 -1.9045 -f_cyan_ilr_1 0.7157 0.37625 1.0551 -f_cyan_ilr_2 0.7073 0.20136 1.2132 -f_JCZ38_qlogis 4.6797 0.43240 8.9269 -f_JSE76_qlogis 5.0080 -1.01380 11.0299 -log_k1 -1.9620 -2.62909 -1.2949 -log_k2 -4.4894 -4.94958 -4.0292 -g_qlogis -0.4658 -1.34443 0.4129 -a.1 2.7158 2.52576 2.9059 -SD.log_k_JCZ38 0.5818 0.15679 1.0067 -SD.log_k_J9Z38 0.7421 0.16751 1.3167 -SD.log_k_JSE76 1.2841 0.43247 2.1356 -SD.f_cyan_ilr_1 0.3748 0.13040 0.6192 -SD.f_cyan_ilr_2 0.4550 0.08396 0.8261 -SD.f_JCZ38_qlogis 2.0862 -0.73390 4.9062 -SD.f_JSE76_qlogis 1.9585 -3.14773 7.0647 -SD.log_k1 0.7389 0.25761 1.2201 -SD.log_k2 0.5132 0.18143 0.8450 -SD.g_qlogis 0.9870 0.35773 1.6164 - -Correlation: - cyan_0 l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76 -log_k_JCZ38 -0.0170 -log_k_J9Z38 -0.0457 0.0016 -log_k_JSE76 -0.0046 0.1183 0.0005 -f_cyan_ilr_1 0.0079 0.0072 -0.0909 0.0003 -f_cyan_ilr_2 -0.3114 0.0343 0.1542 0.0023 -0.0519 -f_JCZ38_qlogis 0.0777 -0.0601 -0.0152 0.0080 -0.0520 -0.2524 -f_JSE76_qlogis -0.0356 0.0817 0.0073 0.0051 0.0388 0.1959 -0.6236 -log_k1 0.0848 -0.0028 0.0010 -0.0010 -0.0014 -0.0245 0.0121 -0.0177 -log_k2 0.0274 -0.0001 0.0075 0.0000 -0.0023 -0.0060 0.0000 -0.0130 -g_qlogis 0.0159 0.0002 -0.0095 0.0002 0.0029 -0.0140 -0.0001 0.0149 - log_k1 log_k2 -log_k_JCZ38 -log_k_J9Z38 -log_k_JSE76 -f_cyan_ilr_1 -f_cyan_ilr_2 -f_JCZ38_qlogis -f_JSE76_qlogis -log_k1 -log_k2 0.0280 -g_qlogis -0.0278 -0.0310 - -Random effects: - est. lower upper -SD.log_k_JCZ38 0.5818 0.15679 1.0067 -SD.log_k_J9Z38 0.7421 0.16751 1.3167 -SD.log_k_JSE76 1.2841 0.43247 2.1356 -SD.f_cyan_ilr_1 0.3748 0.13040 0.6192 -SD.f_cyan_ilr_2 0.4550 0.08396 0.8261 -SD.f_JCZ38_qlogis 2.0862 -0.73390 4.9062 -SD.f_JSE76_qlogis 1.9585 -3.14773 7.0647 -SD.log_k1 0.7389 0.25761 1.2201 -SD.log_k2 0.5132 0.18143 0.8450 -SD.g_qlogis 0.9870 0.35773 1.6164 - -Variance model: - est. lower upper -a.1 2.716 2.526 2.906 - -Backtransformed parameters: - est. lower upper -cyan_0 1.027e+02 1.014e+02 103.93649 -k_JCZ38 9.056e-02 5.076e-02 0.16154 -k_J9Z38 5.591e-03 2.660e-03 0.01175 -k_JSE76 4.603e-02 1.423e-02 0.14890 -f_cyan_to_JCZ38 6.184e-01 NA NA -f_cyan_to_J9Z38 2.248e-01 NA NA -f_JCZ38_to_JSE76 9.908e-01 6.064e-01 0.99987 -f_JSE76_to_JCZ38 9.934e-01 2.662e-01 0.99998 -k1 1.406e-01 7.214e-02 0.27393 -k2 1.123e-02 7.086e-03 0.01779 -g 3.856e-01 2.068e-01 0.60177 - -Resulting formation fractions: - ff -cyan_JCZ38 0.618443 -cyan_J9Z38 0.224770 -cyan_sink 0.156787 -JCZ38_JSE76 0.990803 -JCZ38_sink 0.009197 -JSE76_JCZ38 0.993360 -JSE76_sink 0.006640 - -Estimated disappearance times: - DT50 DT90 DT50back DT50_k1 DT50_k2 -cyan 21.674 161.70 48.68 4.931 61.74 -JCZ38 7.654 25.43 NA NA NA -J9Z38 123.966 411.81 NA NA NA -JSE76 15.057 50.02 NA NA NA - -</code></pre> -<p></p> -<caption> -Hierarchical DFOP path 2 fit with two-component error -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 20:49:18 2023 -Date of summary: Thu Apr 20 21:04:34 2023 - -Equations: -d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * - time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) - * cyan -d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - - g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * - exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38 + - f_JSE76_to_JCZ38 * k_JSE76 * JSE76 -d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - - g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * - exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38 -d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 - -Data: -433 observations of 4 variable(s) grouped in 5 datasets - -Model predictions using solution type deSolve - -Fitted in 724.515 s -Using 300, 100 iterations and 10 chains - -Variance model: Two-component variance function - -Starting values for degradation parameters: - cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 - 101.7523 -1.5948 -5.0119 -2.2723 0.6719 - f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 - 5.1681 12.8238 12.4130 -2.0057 -4.5526 - g_qlogis - -0.5805 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 -cyan_0 5.627 0.000 0.000 0.000 0.0000 -log_k_JCZ38 0.000 2.327 0.000 0.000 0.0000 -log_k_J9Z38 0.000 0.000 1.664 0.000 0.0000 -log_k_JSE76 0.000 0.000 0.000 4.566 0.0000 -f_cyan_ilr_1 0.000 0.000 0.000 0.000 0.6519 -f_cyan_ilr_2 0.000 0.000 0.000 0.000 0.0000 -f_JCZ38_qlogis 0.000 0.000 0.000 0.000 0.0000 -f_JSE76_qlogis 0.000 0.000 0.000 0.000 0.0000 -log_k1 0.000 0.000 0.000 0.000 0.0000 -log_k2 0.000 0.000 0.000 0.000 0.0000 -g_qlogis 0.000 0.000 0.000 0.000 0.0000 - f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 -cyan_0 0.0 0.00 0.00 0.0000 0.0000 -log_k_JCZ38 0.0 0.00 0.00 0.0000 0.0000 -log_k_J9Z38 0.0 0.00 0.00 0.0000 0.0000 -log_k_JSE76 0.0 0.00 0.00 0.0000 0.0000 -f_cyan_ilr_1 0.0 0.00 0.00 0.0000 0.0000 -f_cyan_ilr_2 10.1 0.00 0.00 0.0000 0.0000 -f_JCZ38_qlogis 0.0 13.99 0.00 0.0000 0.0000 -f_JSE76_qlogis 0.0 0.00 14.15 0.0000 0.0000 -log_k1 0.0 0.00 0.00 0.8452 0.0000 -log_k2 0.0 0.00 0.00 0.0000 0.5968 -g_qlogis 0.0 0.00 0.00 0.0000 0.0000 - g_qlogis -cyan_0 0.000 -log_k_JCZ38 0.000 -log_k_J9Z38 0.000 -log_k_JSE76 0.000 -f_cyan_ilr_1 0.000 -f_cyan_ilr_2 0.000 -f_JCZ38_qlogis 0.000 -f_JSE76_qlogis 0.000 -log_k1 0.000 -log_k2 0.000 -g_qlogis 1.691 - -Starting values for error model parameters: -a.1 b.1 - 1 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 2234 2226 -1095 - -Optimised parameters: - est. lower upper -cyan_0 101.10667 9.903e+01 103.18265 -log_k_JCZ38 -2.49437 -3.297e+00 -1.69221 -log_k_J9Z38 -5.08171 -5.875e+00 -4.28846 -log_k_JSE76 -3.20072 -4.180e+00 -2.22163 -f_cyan_ilr_1 0.71059 3.639e-01 1.05727 -f_cyan_ilr_2 1.15398 2.981e-01 2.00984 -f_JCZ38_qlogis 3.18027 1.056e+00 5.30452 -f_JSE76_qlogis 5.61578 -2.505e+01 36.28077 -log_k1 -2.38875 -2.517e+00 -2.26045 -log_k2 -4.67246 -4.928e+00 -4.41715 -g_qlogis -0.28231 -1.135e+00 0.57058 -a.1 2.08190 1.856e+00 2.30785 -b.1 0.06114 5.015e-02 0.07214 -SD.log_k_JCZ38 0.84622 2.637e-01 1.42873 -SD.log_k_J9Z38 0.84564 2.566e-01 1.43464 -SD.log_k_JSE76 1.04385 3.242e-01 1.76351 -SD.f_cyan_ilr_1 0.38568 1.362e-01 0.63514 -SD.f_cyan_ilr_2 0.68046 7.166e-02 1.28925 -SD.f_JCZ38_qlogis 1.25244 -4.213e-02 2.54700 -SD.f_JSE76_qlogis 0.28202 -1.515e+03 1515.87968 -SD.log_k2 0.25749 7.655e-02 0.43843 -SD.g_qlogis 0.94535 3.490e-01 1.54174 - -Correlation: - cyan_0 l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76 -log_k_JCZ38 -0.0086 -log_k_J9Z38 -0.0363 -0.0007 -log_k_JSE76 0.0015 0.1210 -0.0017 -f_cyan_ilr_1 -0.0048 0.0095 -0.0572 0.0030 -f_cyan_ilr_2 -0.4788 0.0328 0.1143 0.0027 -0.0316 -f_JCZ38_qlogis 0.0736 -0.0664 -0.0137 0.0145 -0.0444 -0.2175 -f_JSE76_qlogis -0.0137 0.0971 0.0035 0.0009 0.0293 0.1333 -0.6767 -log_k1 0.2345 -0.0350 -0.0099 -0.0113 -0.0126 -0.1652 0.1756 -0.2161 -log_k2 0.0440 -0.0133 0.0199 -0.0040 -0.0097 -0.0119 0.0604 -0.1306 -g_qlogis 0.0438 0.0078 -0.0123 0.0029 0.0046 -0.0363 -0.0318 0.0736 - log_k1 log_k2 -log_k_JCZ38 -log_k_J9Z38 -log_k_JSE76 -f_cyan_ilr_1 -f_cyan_ilr_2 -f_JCZ38_qlogis -f_JSE76_qlogis -log_k1 -log_k2 0.3198 -g_qlogis -0.1666 -0.0954 - -Random effects: - est. lower upper -SD.log_k_JCZ38 0.8462 2.637e-01 1.4287 -SD.log_k_J9Z38 0.8456 2.566e-01 1.4346 -SD.log_k_JSE76 1.0439 3.242e-01 1.7635 -SD.f_cyan_ilr_1 0.3857 1.362e-01 0.6351 -SD.f_cyan_ilr_2 0.6805 7.166e-02 1.2893 -SD.f_JCZ38_qlogis 1.2524 -4.213e-02 2.5470 -SD.f_JSE76_qlogis 0.2820 -1.515e+03 1515.8797 -SD.log_k2 0.2575 7.655e-02 0.4384 -SD.g_qlogis 0.9453 3.490e-01 1.5417 - -Variance model: - est. lower upper -a.1 2.08190 1.85595 2.30785 -b.1 0.06114 0.05015 0.07214 - -Backtransformed parameters: - est. lower upper -cyan_0 1.011e+02 9.903e+01 103.18265 -k_JCZ38 8.255e-02 3.701e-02 0.18411 -k_J9Z38 6.209e-03 2.809e-03 0.01373 -k_JSE76 4.073e-02 1.530e-02 0.10843 -f_cyan_to_JCZ38 6.608e-01 NA NA -f_cyan_to_J9Z38 2.419e-01 NA NA -f_JCZ38_to_JSE76 9.601e-01 7.419e-01 0.99506 -f_JSE76_to_JCZ38 9.964e-01 1.322e-11 1.00000 -k1 9.174e-02 8.070e-02 0.10430 -k2 9.349e-03 7.243e-03 0.01207 -g 4.299e-01 2.432e-01 0.63890 - -Resulting formation fractions: - ff -cyan_JCZ38 0.660808 -cyan_J9Z38 0.241904 -cyan_sink 0.097288 -JCZ38_JSE76 0.960085 -JCZ38_sink 0.039915 -JSE76_JCZ38 0.996373 -JSE76_sink 0.003627 - -Estimated disappearance times: - DT50 DT90 DT50back DT50_k1 DT50_k2 -cyan 24.359 186.18 56.05 7.555 74.14 -JCZ38 8.397 27.89 NA NA NA -J9Z38 111.631 370.83 NA NA NA -JSE76 17.017 56.53 NA NA NA - -</code></pre> -<p></p> -<caption> -Hierarchical SFORB path 2 fit with constant variance -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 20:46:33 2023 -Date of summary: Thu Apr 20 21:04:34 2023 - -Equations: -d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound * - cyan_free + k_cyan_bound_free * cyan_bound -d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free * - cyan_bound -d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38 - * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76 -d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38 - * J9Z38 -d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 - -Data: -433 observations of 4 variable(s) grouped in 5 datasets - -Model predictions using solution type deSolve - -Fitted in 559.097 s -Using 300, 100 iterations and 10 chains - -Variance model: Constant variance - -Starting values for degradation parameters: - cyan_free_0 log_k_cyan_free log_k_cyan_free_bound - 102.4394 -2.7673 -2.8942 -log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 - -3.6201 -2.3107 -5.3123 - log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 - -3.7120 0.6754 1.1448 - f_JCZ38_qlogis f_JSE76_qlogis - 13.2672 13.3538 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - cyan_free_0 log_k_cyan_free log_k_cyan_free_bound -cyan_free_0 4.589 0.0000 0.00 -log_k_cyan_free 0.000 0.4849 0.00 -log_k_cyan_free_bound 0.000 0.0000 1.62 -log_k_cyan_bound_free 0.000 0.0000 0.00 -log_k_JCZ38 0.000 0.0000 0.00 -log_k_J9Z38 0.000 0.0000 0.00 -log_k_JSE76 0.000 0.0000 0.00 -f_cyan_ilr_1 0.000 0.0000 0.00 -f_cyan_ilr_2 0.000 0.0000 0.00 -f_JCZ38_qlogis 0.000 0.0000 0.00 -f_JSE76_qlogis 0.000 0.0000 0.00 - log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 -cyan_free_0 0.000 0.0000 0.000 0.0 -log_k_cyan_free 0.000 0.0000 0.000 0.0 -log_k_cyan_free_bound 0.000 0.0000 0.000 0.0 -log_k_cyan_bound_free 1.197 0.0000 0.000 0.0 -log_k_JCZ38 0.000 0.7966 0.000 0.0 -log_k_J9Z38 0.000 0.0000 1.561 0.0 -log_k_JSE76 0.000 0.0000 0.000 0.8 -f_cyan_ilr_1 0.000 0.0000 0.000 0.0 -f_cyan_ilr_2 0.000 0.0000 0.000 0.0 -f_JCZ38_qlogis 0.000 0.0000 0.000 0.0 -f_JSE76_qlogis 0.000 0.0000 0.000 0.0 - f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis -cyan_free_0 0.0000 0.000 0.00 0.00 -log_k_cyan_free 0.0000 0.000 0.00 0.00 -log_k_cyan_free_bound 0.0000 0.000 0.00 0.00 -log_k_cyan_bound_free 0.0000 0.000 0.00 0.00 -log_k_JCZ38 0.0000 0.000 0.00 0.00 -log_k_J9Z38 0.0000 0.000 0.00 0.00 -log_k_JSE76 0.0000 0.000 0.00 0.00 -f_cyan_ilr_1 0.6349 0.000 0.00 0.00 -f_cyan_ilr_2 0.0000 1.797 0.00 0.00 -f_JCZ38_qlogis 0.0000 0.000 13.84 0.00 -f_JSE76_qlogis 0.0000 0.000 0.00 14.66 - -Starting values for error model parameters: -a.1 - 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 2284 2275 -1120 - -Optimised parameters: - est. lower upper -cyan_free_0 102.7730 1.015e+02 1.041e+02 -log_k_cyan_free -2.8530 -3.167e+00 -2.539e+00 -log_k_cyan_free_bound -2.7326 -3.543e+00 -1.922e+00 -log_k_cyan_bound_free -3.5582 -4.126e+00 -2.990e+00 -log_k_JCZ38 -2.3810 -2.921e+00 -1.841e+00 -log_k_J9Z38 -5.2301 -5.963e+00 -4.497e+00 -log_k_JSE76 -3.0286 -4.286e+00 -1.771e+00 -f_cyan_ilr_1 0.7081 3.733e-01 1.043e+00 -f_cyan_ilr_2 0.5847 7.846e-03 1.162e+00 -f_JCZ38_qlogis 9.5676 -1.323e+03 1.342e+03 -f_JSE76_qlogis 3.7042 7.254e-02 7.336e+00 -a.1 2.7222 2.532e+00 2.913e+00 -SD.log_k_cyan_free 0.3338 1.086e-01 5.589e-01 -SD.log_k_cyan_free_bound 0.8888 3.023e-01 1.475e+00 -SD.log_k_cyan_bound_free 0.6220 2.063e-01 1.038e+00 -SD.log_k_JCZ38 0.5221 1.334e-01 9.108e-01 -SD.log_k_J9Z38 0.7104 1.371e-01 1.284e+00 -SD.log_k_JSE76 1.3837 4.753e-01 2.292e+00 -SD.f_cyan_ilr_1 0.3620 1.248e-01 5.992e-01 -SD.f_cyan_ilr_2 0.4259 8.145e-02 7.704e-01 -SD.f_JCZ38_qlogis 3.5332 -1.037e+05 1.037e+05 -SD.f_JSE76_qlogis 1.6990 -2.771e-01 3.675e+00 - -Correlation: - cyn_f_0 lg_k_c_ lg_k_cyn_f_ lg_k_cyn_b_ l__JCZ3 l__J9Z3 -log_k_cyan_free 0.2126 -log_k_cyan_free_bound 0.0894 0.0871 -log_k_cyan_bound_free 0.0033 0.0410 0.0583 -log_k_JCZ38 -0.0708 -0.0280 -0.0147 0.0019 -log_k_J9Z38 -0.0535 -0.0138 0.0012 0.0148 0.0085 -log_k_JSE76 -0.0066 -0.0030 -0.0021 -0.0005 0.1090 0.0010 -f_cyan_ilr_1 -0.0364 -0.0157 -0.0095 -0.0015 0.0458 -0.0960 -f_cyan_ilr_2 -0.3814 -0.1104 -0.0423 0.0146 0.1540 0.1526 -f_JCZ38_qlogis 0.2507 0.0969 0.0482 -0.0097 -0.2282 -0.0363 -f_JSE76_qlogis -0.1648 -0.0710 -0.0443 -0.0087 0.2002 0.0226 - l__JSE7 f_cy__1 f_cy__2 f_JCZ38 -log_k_cyan_free -log_k_cyan_free_bound -log_k_cyan_bound_free -log_k_JCZ38 -log_k_J9Z38 -log_k_JSE76 -f_cyan_ilr_1 0.0001 -f_cyan_ilr_2 0.0031 0.0586 -f_JCZ38_qlogis 0.0023 -0.1867 -0.6255 -f_JSE76_qlogis 0.0082 0.1356 0.4519 -0.7951 - -Random effects: - est. lower upper -SD.log_k_cyan_free 0.3338 1.086e-01 5.589e-01 -SD.log_k_cyan_free_bound 0.8888 3.023e-01 1.475e+00 -SD.log_k_cyan_bound_free 0.6220 2.063e-01 1.038e+00 -SD.log_k_JCZ38 0.5221 1.334e-01 9.108e-01 -SD.log_k_J9Z38 0.7104 1.371e-01 1.284e+00 -SD.log_k_JSE76 1.3837 4.753e-01 2.292e+00 -SD.f_cyan_ilr_1 0.3620 1.248e-01 5.992e-01 -SD.f_cyan_ilr_2 0.4259 8.145e-02 7.704e-01 -SD.f_JCZ38_qlogis 3.5332 -1.037e+05 1.037e+05 -SD.f_JSE76_qlogis 1.6990 -2.771e-01 3.675e+00 - -Variance model: - est. lower upper -a.1 2.722 2.532 2.913 - -Backtransformed parameters: - est. lower upper -cyan_free_0 1.028e+02 1.015e+02 104.06475 -k_cyan_free 5.767e-02 4.213e-02 0.07894 -k_cyan_free_bound 6.505e-02 2.892e-02 0.14633 -k_cyan_bound_free 2.849e-02 1.614e-02 0.05028 -k_JCZ38 9.246e-02 5.390e-02 0.15859 -k_J9Z38 5.353e-03 2.572e-03 0.01114 -k_JSE76 4.838e-02 1.376e-02 0.17009 -f_cyan_free_to_JCZ38 6.011e-01 5.028e-01 0.83792 -f_cyan_free_to_J9Z38 2.208e-01 5.028e-01 0.83792 -f_JCZ38_to_JSE76 9.999e-01 0.000e+00 1.00000 -f_JSE76_to_JCZ38 9.760e-01 5.181e-01 0.99935 - -Estimated Eigenvalues of SFORB model(s): -cyan_b1 cyan_b2 cyan_g -0.13942 0.01178 0.35948 - -Resulting formation fractions: - ff -cyan_free_JCZ38 6.011e-01 -cyan_free_J9Z38 2.208e-01 -cyan_free_sink 1.780e-01 -cyan_free 1.000e+00 -JCZ38_JSE76 9.999e-01 -JCZ38_sink 6.996e-05 -JSE76_JCZ38 9.760e-01 -JSE76_sink 2.403e-02 - -Estimated disappearance times: - DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 -cyan 23.390 157.60 47.44 4.971 58.82 -JCZ38 7.497 24.90 NA NA NA -J9Z38 129.482 430.13 NA NA NA -JSE76 14.326 47.59 NA NA NA - -</code></pre> -<p></p> -<caption> -Hierarchical SFORB path 2 fit with two-component error -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 20:49:20 2023 -Date of summary: Thu Apr 20 21:04:34 2023 - -Equations: -d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound * - cyan_free + k_cyan_bound_free * cyan_bound -d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free * - cyan_bound -d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38 - * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76 -d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38 - * J9Z38 -d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 - -Data: -433 observations of 4 variable(s) grouped in 5 datasets - -Model predictions using solution type deSolve - -Fitted in 726.293 s -Using 300, 100 iterations and 10 chains - -Variance model: Two-component variance function - -Starting values for degradation parameters: - cyan_free_0 log_k_cyan_free log_k_cyan_free_bound - 101.751 -2.837 -3.016 -log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 - -3.660 -2.299 -5.313 - log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 - -3.699 0.672 5.873 - f_JCZ38_qlogis f_JSE76_qlogis - 13.216 13.338 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - cyan_free_0 log_k_cyan_free log_k_cyan_free_bound -cyan_free_0 5.629 0.000 0.000 -log_k_cyan_free 0.000 0.446 0.000 -log_k_cyan_free_bound 0.000 0.000 1.449 -log_k_cyan_bound_free 0.000 0.000 0.000 -log_k_JCZ38 0.000 0.000 0.000 -log_k_J9Z38 0.000 0.000 0.000 -log_k_JSE76 0.000 0.000 0.000 -f_cyan_ilr_1 0.000 0.000 0.000 -f_cyan_ilr_2 0.000 0.000 0.000 -f_JCZ38_qlogis 0.000 0.000 0.000 -f_JSE76_qlogis 0.000 0.000 0.000 - log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 -cyan_free_0 0.000 0.0000 0.000 0.0000 -log_k_cyan_free 0.000 0.0000 0.000 0.0000 -log_k_cyan_free_bound 0.000 0.0000 0.000 0.0000 -log_k_cyan_bound_free 1.213 0.0000 0.000 0.0000 -log_k_JCZ38 0.000 0.7801 0.000 0.0000 -log_k_J9Z38 0.000 0.0000 1.575 0.0000 -log_k_JSE76 0.000 0.0000 0.000 0.8078 -f_cyan_ilr_1 0.000 0.0000 0.000 0.0000 -f_cyan_ilr_2 0.000 0.0000 0.000 0.0000 -f_JCZ38_qlogis 0.000 0.0000 0.000 0.0000 -f_JSE76_qlogis 0.000 0.0000 0.000 0.0000 - f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis -cyan_free_0 0.0000 0.00 0.00 0.00 -log_k_cyan_free 0.0000 0.00 0.00 0.00 -log_k_cyan_free_bound 0.0000 0.00 0.00 0.00 -log_k_cyan_bound_free 0.0000 0.00 0.00 0.00 -log_k_JCZ38 0.0000 0.00 0.00 0.00 -log_k_J9Z38 0.0000 0.00 0.00 0.00 -log_k_JSE76 0.0000 0.00 0.00 0.00 -f_cyan_ilr_1 0.6519 0.00 0.00 0.00 -f_cyan_ilr_2 0.0000 10.78 0.00 0.00 -f_JCZ38_qlogis 0.0000 0.00 13.96 0.00 -f_JSE76_qlogis 0.0000 0.00 0.00 14.69 - -Starting values for error model parameters: -a.1 b.1 - 1 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 2240 2232 -1098 - -Optimised parameters: - est. lower upper -cyan_free_0 101.10205 98.99221 103.2119 -log_k_cyan_free -3.16929 -3.61395 -2.7246 -log_k_cyan_free_bound -3.38259 -3.63022 -3.1350 -log_k_cyan_bound_free -3.81075 -4.13888 -3.4826 -log_k_JCZ38 -2.42057 -3.00756 -1.8336 -log_k_J9Z38 -5.07501 -5.85138 -4.2986 -log_k_JSE76 -3.12442 -4.21277 -2.0361 -f_cyan_ilr_1 0.70577 0.35788 1.0537 -f_cyan_ilr_2 1.14824 0.15810 2.1384 -f_JCZ38_qlogis 3.52245 0.43257 6.6123 -f_JSE76_qlogis 5.65140 -21.22295 32.5257 -a.1 2.07062 1.84329 2.2980 -b.1 0.06227 0.05124 0.0733 -SD.log_k_cyan_free 0.49468 0.18566 0.8037 -SD.log_k_cyan_bound_free 0.28972 0.07188 0.5076 -SD.log_k_JCZ38 0.58852 0.16800 1.0090 -SD.log_k_J9Z38 0.82500 0.24730 1.4027 -SD.log_k_JSE76 1.19201 0.40313 1.9809 -SD.f_cyan_ilr_1 0.38534 0.13640 0.6343 -SD.f_cyan_ilr_2 0.72463 0.10076 1.3485 -SD.f_JCZ38_qlogis 1.38223 -0.20997 2.9744 -SD.f_JSE76_qlogis 2.07989 -72.53027 76.6901 - -Correlation: - cyn_f_0 lg_k_c_ lg_k_cyn_f_ lg_k_cyn_b_ l__JCZ3 l__J9Z3 -log_k_cyan_free 0.1117 -log_k_cyan_free_bound 0.1763 0.1828 -log_k_cyan_bound_free 0.0120 0.0593 0.5030 -log_k_JCZ38 -0.0459 -0.0230 -0.0931 -0.0337 -log_k_J9Z38 -0.0381 -0.0123 -0.0139 0.0237 0.0063 -log_k_JSE76 -0.0044 -0.0038 -0.0175 -0.0072 0.1120 0.0003 -f_cyan_ilr_1 -0.0199 -0.0087 -0.0407 -0.0233 0.0268 -0.0552 -f_cyan_ilr_2 -0.4806 -0.1015 -0.2291 -0.0269 0.1156 0.1113 -f_JCZ38_qlogis 0.1805 0.0825 0.3085 0.0963 -0.1674 -0.0314 -f_JSE76_qlogis -0.1586 -0.0810 -0.3560 -0.1563 0.2025 0.0278 - l__JSE7 f_cy__1 f_cy__2 f_JCZ38 -log_k_cyan_free -log_k_cyan_free_bound -log_k_cyan_bound_free -log_k_JCZ38 -log_k_J9Z38 -log_k_JSE76 -f_cyan_ilr_1 0.0024 -f_cyan_ilr_2 0.0087 0.0172 -f_JCZ38_qlogis -0.0016 -0.1047 -0.4656 -f_JSE76_qlogis 0.0119 0.1034 0.4584 -0.8137 - -Random effects: - est. lower upper -SD.log_k_cyan_free 0.4947 0.18566 0.8037 -SD.log_k_cyan_bound_free 0.2897 0.07188 0.5076 -SD.log_k_JCZ38 0.5885 0.16800 1.0090 -SD.log_k_J9Z38 0.8250 0.24730 1.4027 -SD.log_k_JSE76 1.1920 0.40313 1.9809 -SD.f_cyan_ilr_1 0.3853 0.13640 0.6343 -SD.f_cyan_ilr_2 0.7246 0.10076 1.3485 -SD.f_JCZ38_qlogis 1.3822 -0.20997 2.9744 -SD.f_JSE76_qlogis 2.0799 -72.53027 76.6901 - -Variance model: - est. lower upper -a.1 2.07062 1.84329 2.2980 -b.1 0.06227 0.05124 0.0733 - -Backtransformed parameters: - est. lower upper -cyan_free_0 1.011e+02 9.899e+01 103.21190 -k_cyan_free 4.203e-02 2.695e-02 0.06557 -k_cyan_free_bound 3.396e-02 2.651e-02 0.04350 -k_cyan_bound_free 2.213e-02 1.594e-02 0.03073 -k_JCZ38 8.887e-02 4.941e-02 0.15984 -k_J9Z38 6.251e-03 2.876e-03 0.01359 -k_JSE76 4.396e-02 1.481e-02 0.13054 -f_cyan_free_to_JCZ38 6.590e-01 5.557e-01 0.95365 -f_cyan_free_to_J9Z38 2.429e-01 5.557e-01 0.95365 -f_JCZ38_to_JSE76 9.713e-01 6.065e-01 0.99866 -f_JSE76_to_JCZ38 9.965e-01 6.067e-10 1.00000 - -Estimated Eigenvalues of SFORB model(s): -cyan_b1 cyan_b2 cyan_g -0.08749 0.01063 0.40855 - -Resulting formation fractions: - ff -cyan_free_JCZ38 0.65905 -cyan_free_J9Z38 0.24291 -cyan_free_sink 0.09805 -cyan_free 1.00000 -JCZ38_JSE76 0.97132 -JCZ38_sink 0.02868 -JSE76_JCZ38 0.99650 -JSE76_sink 0.00350 - -Estimated disappearance times: - DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 -cyan 24.91 167.16 50.32 7.922 65.19 -JCZ38 7.80 25.91 NA NA NA -J9Z38 110.89 368.36 NA NA NA -JSE76 15.77 52.38 NA NA NA - -</code></pre> -<p></p> -</div> -<div class="section level4"> -<h4 id="pathway-2-refined-fits">Pathway 2, refined fits<a class="anchor" aria-label="anchor" href="#pathway-2-refined-fits"></a> -</h4> -<caption> -Hierarchical FOMC path 2 fit with reduced random effects, two-component -error -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 21:02:39 2023 -Date of summary: Thu Apr 20 21:04:34 2023 - -Equations: -d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan -d_JCZ38/dt = + f_cyan_to_JCZ38 * (alpha/beta) * 1/((time/beta) + 1) * - cyan - k_JCZ38 * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76 -d_J9Z38/dt = + f_cyan_to_J9Z38 * (alpha/beta) * 1/((time/beta) + 1) * - cyan - k_J9Z38 * J9Z38 -d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 - -Data: -433 observations of 4 variable(s) grouped in 5 datasets - -Model predictions using solution type deSolve - -Fitted in 796.615 s -Using 300, 100 iterations and 10 chains - -Variance model: Two-component variance function - -Starting values for degradation parameters: - cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 - 101.9028 -1.9055 -5.0249 -2.5646 0.6807 - f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta - 4.8883 16.0676 9.3923 -0.1346 3.0364 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 -cyan_0 6.321 0.000 0.000 0.000 0.0000 -log_k_JCZ38 0.000 1.392 0.000 0.000 0.0000 -log_k_J9Z38 0.000 0.000 1.561 0.000 0.0000 -log_k_JSE76 0.000 0.000 0.000 3.614 0.0000 -f_cyan_ilr_1 0.000 0.000 0.000 0.000 0.6339 -f_cyan_ilr_2 0.000 0.000 0.000 0.000 0.0000 -f_JCZ38_qlogis 0.000 0.000 0.000 0.000 0.0000 -f_JSE76_qlogis 0.000 0.000 0.000 0.000 0.0000 -log_alpha 0.000 0.000 0.000 0.000 0.0000 -log_beta 0.000 0.000 0.000 0.000 0.0000 - f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta -cyan_0 0.00 0.00 0.00 0.0000 0.0000 -log_k_JCZ38 0.00 0.00 0.00 0.0000 0.0000 -log_k_J9Z38 0.00 0.00 0.00 0.0000 0.0000 -log_k_JSE76 0.00 0.00 0.00 0.0000 0.0000 -f_cyan_ilr_1 0.00 0.00 0.00 0.0000 0.0000 -f_cyan_ilr_2 10.41 0.00 0.00 0.0000 0.0000 -f_JCZ38_qlogis 0.00 12.24 0.00 0.0000 0.0000 -f_JSE76_qlogis 0.00 0.00 15.13 0.0000 0.0000 -log_alpha 0.00 0.00 0.00 0.3701 0.0000 -log_beta 0.00 0.00 0.00 0.0000 0.5662 - -Starting values for error model parameters: -a.1 b.1 - 1 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 2251 2244 -1106 - -Optimised parameters: - est. lower upper -cyan_0 101.05768 NA NA -log_k_JCZ38 -2.73252 NA NA -log_k_J9Z38 -5.07399 NA NA -log_k_JSE76 -3.52863 NA NA -f_cyan_ilr_1 0.72176 NA NA -f_cyan_ilr_2 1.34610 NA NA -f_JCZ38_qlogis 2.08337 NA NA -f_JSE76_qlogis 1590.31880 NA NA -log_alpha -0.09336 NA NA -log_beta 3.10191 NA NA -a.1 2.08557 1.85439 2.31675 -b.1 0.06998 0.05800 0.08197 -SD.log_k_JCZ38 1.20053 0.43329 1.96777 -SD.log_k_J9Z38 0.85854 0.26708 1.45000 -SD.log_k_JSE76 0.62528 0.16061 1.08995 -SD.f_cyan_ilr_1 0.35190 0.12340 0.58039 -SD.f_cyan_ilr_2 0.85385 0.15391 1.55378 -SD.log_alpha 0.28971 0.08718 0.49225 -SD.log_beta 0.31614 0.05938 0.57290 - -Correlation is not available - -Random effects: - est. lower upper -SD.log_k_JCZ38 1.2005 0.43329 1.9678 -SD.log_k_J9Z38 0.8585 0.26708 1.4500 -SD.log_k_JSE76 0.6253 0.16061 1.0900 -SD.f_cyan_ilr_1 0.3519 0.12340 0.5804 -SD.f_cyan_ilr_2 0.8538 0.15391 1.5538 -SD.log_alpha 0.2897 0.08718 0.4923 -SD.log_beta 0.3161 0.05938 0.5729 - -Variance model: - est. lower upper -a.1 2.08557 1.854 2.31675 -b.1 0.06998 0.058 0.08197 - -Backtransformed parameters: - est. lower upper -cyan_0 1.011e+02 NA NA -k_JCZ38 6.506e-02 NA NA -k_J9Z38 6.257e-03 NA NA -k_JSE76 2.935e-02 NA NA -f_cyan_to_JCZ38 6.776e-01 NA NA -f_cyan_to_J9Z38 2.442e-01 NA NA -f_JCZ38_to_JSE76 8.893e-01 NA NA -f_JSE76_to_JCZ38 1.000e+00 NA NA -alpha 9.109e-01 NA NA -beta 2.224e+01 NA NA - -Resulting formation fractions: - ff -cyan_JCZ38 0.67761 -cyan_J9Z38 0.24417 -cyan_sink 0.07822 -JCZ38_JSE76 0.88928 -JCZ38_sink 0.11072 -JSE76_JCZ38 1.00000 -JSE76_sink 0.00000 - -Estimated disappearance times: - DT50 DT90 DT50back -cyan 25.36 256.37 77.18 -JCZ38 10.65 35.39 NA -J9Z38 110.77 367.98 NA -JSE76 23.62 78.47 NA - -</code></pre> -<p></p> -<caption> -Hierarchical DFOP path 2 fit with reduced random effects, constant -variance -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 21:04:15 2023 -Date of summary: Thu Apr 20 21:04:34 2023 - -Equations: -d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * - time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) - * cyan -d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - - g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * - exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38 + - f_JSE76_to_JCZ38 * k_JSE76 * JSE76 -d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - - g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * - exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38 -d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 - -Data: -433 observations of 4 variable(s) grouped in 5 datasets - -Model predictions using solution type deSolve - -Fitted in 893.328 s -Using 300, 100 iterations and 10 chains - -Variance model: Constant variance - -Starting values for degradation parameters: - cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 - 102.4358 -2.3107 -5.3123 -3.7120 0.6753 - f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 - 1.1462 12.4095 12.3630 -1.9317 -4.4557 - g_qlogis - -0.5648 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 -cyan_0 4.594 0.0000 0.000 0.0 0.0000 -log_k_JCZ38 0.000 0.7966 0.000 0.0 0.0000 -log_k_J9Z38 0.000 0.0000 1.561 0.0 0.0000 -log_k_JSE76 0.000 0.0000 0.000 0.8 0.0000 -f_cyan_ilr_1 0.000 0.0000 0.000 0.0 0.6349 -f_cyan_ilr_2 0.000 0.0000 0.000 0.0 0.0000 -f_JCZ38_qlogis 0.000 0.0000 0.000 0.0 0.0000 -f_JSE76_qlogis 0.000 0.0000 0.000 0.0 0.0000 -log_k1 0.000 0.0000 0.000 0.0 0.0000 -log_k2 0.000 0.0000 0.000 0.0 0.0000 -g_qlogis 0.000 0.0000 0.000 0.0 0.0000 - f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 -cyan_0 0.000 0.00 0.0 0.000 0.0000 -log_k_JCZ38 0.000 0.00 0.0 0.000 0.0000 -log_k_J9Z38 0.000 0.00 0.0 0.000 0.0000 -log_k_JSE76 0.000 0.00 0.0 0.000 0.0000 -f_cyan_ilr_1 0.000 0.00 0.0 0.000 0.0000 -f_cyan_ilr_2 1.797 0.00 0.0 0.000 0.0000 -f_JCZ38_qlogis 0.000 13.85 0.0 0.000 0.0000 -f_JSE76_qlogis 0.000 0.00 14.1 0.000 0.0000 -log_k1 0.000 0.00 0.0 1.106 0.0000 -log_k2 0.000 0.00 0.0 0.000 0.6141 -g_qlogis 0.000 0.00 0.0 0.000 0.0000 - g_qlogis -cyan_0 0.000 -log_k_JCZ38 0.000 -log_k_J9Z38 0.000 -log_k_JSE76 0.000 -f_cyan_ilr_1 0.000 -f_cyan_ilr_2 0.000 -f_JCZ38_qlogis 0.000 -f_JSE76_qlogis 0.000 -log_k1 0.000 -log_k2 0.000 -g_qlogis 1.595 - -Starting values for error model parameters: -a.1 - 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 2282 2274 -1121 - -Optimised parameters: - est. lower upper -cyan_0 102.5254 NA NA -log_k_JCZ38 -2.9358 NA NA -log_k_J9Z38 -5.1424 NA NA -log_k_JSE76 -3.6458 NA NA -f_cyan_ilr_1 0.6957 NA NA -f_cyan_ilr_2 0.6635 NA NA -f_JCZ38_qlogis 4984.8163 NA NA -f_JSE76_qlogis 1.9415 NA NA -log_k1 -1.9456 NA NA -log_k2 -4.4705 NA NA -g_qlogis -0.5117 NA NA -a.1 2.7455 2.55392 2.9370 -SD.log_k_JCZ38 1.3163 0.47635 2.1563 -SD.log_k_J9Z38 0.7162 0.16133 1.2711 -SD.log_k_JSE76 0.6457 0.15249 1.1390 -SD.f_cyan_ilr_1 0.3424 0.11714 0.5677 -SD.f_cyan_ilr_2 0.4524 0.09709 0.8077 -SD.log_k1 0.7353 0.25445 1.2161 -SD.log_k2 0.5137 0.18206 0.8453 -SD.g_qlogis 0.9857 0.35651 1.6148 - -Correlation is not available - -Random effects: - est. lower upper -SD.log_k_JCZ38 1.3163 0.47635 2.1563 -SD.log_k_J9Z38 0.7162 0.16133 1.2711 -SD.log_k_JSE76 0.6457 0.15249 1.1390 -SD.f_cyan_ilr_1 0.3424 0.11714 0.5677 -SD.f_cyan_ilr_2 0.4524 0.09709 0.8077 -SD.log_k1 0.7353 0.25445 1.2161 -SD.log_k2 0.5137 0.18206 0.8453 -SD.g_qlogis 0.9857 0.35651 1.6148 - -Variance model: - est. lower upper -a.1 2.745 2.554 2.937 - -Backtransformed parameters: - est. lower upper -cyan_0 1.025e+02 NA NA -k_JCZ38 5.309e-02 NA NA -k_J9Z38 5.844e-03 NA NA -k_JSE76 2.610e-02 NA NA -f_cyan_to_JCZ38 6.079e-01 NA NA -f_cyan_to_J9Z38 2.272e-01 NA NA -f_JCZ38_to_JSE76 1.000e+00 NA NA -f_JSE76_to_JCZ38 8.745e-01 NA NA -k1 1.429e-01 NA NA -k2 1.144e-02 NA NA -g 3.748e-01 NA NA - -Resulting formation fractions: - ff -cyan_JCZ38 0.6079 -cyan_J9Z38 0.2272 -cyan_sink 0.1649 -JCZ38_JSE76 1.0000 -JCZ38_sink 0.0000 -JSE76_JCZ38 0.8745 -JSE76_sink 0.1255 - -Estimated disappearance times: - DT50 DT90 DT50back DT50_k1 DT50_k2 -cyan 22.29 160.20 48.22 4.85 60.58 -JCZ38 13.06 43.37 NA NA NA -J9Z38 118.61 394.02 NA NA NA -JSE76 26.56 88.22 NA NA NA - -</code></pre> -<p></p> -<caption> -Hierarchical DFOP path 2 fit with reduced random effects, two-component -error -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 21:04:33 2023 -Date of summary: Thu Apr 20 21:04:34 2023 - -Equations: -d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * - time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) - * cyan -d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - - g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * - exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38 + - f_JSE76_to_JCZ38 * k_JSE76 * JSE76 -d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - - g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * - exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38 -d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 - -Data: -433 observations of 4 variable(s) grouped in 5 datasets - -Model predictions using solution type deSolve - -Fitted in 910.788 s -Using 300, 100 iterations and 10 chains - -Variance model: Two-component variance function - -Starting values for degradation parameters: - cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 - 101.7523 -1.5948 -5.0119 -2.2723 0.6719 - f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 - 5.1681 12.8238 12.4130 -2.0057 -4.5526 - g_qlogis - -0.5805 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 -cyan_0 5.627 0.000 0.000 0.000 0.0000 -log_k_JCZ38 0.000 2.327 0.000 0.000 0.0000 -log_k_J9Z38 0.000 0.000 1.664 0.000 0.0000 -log_k_JSE76 0.000 0.000 0.000 4.566 0.0000 -f_cyan_ilr_1 0.000 0.000 0.000 0.000 0.6519 -f_cyan_ilr_2 0.000 0.000 0.000 0.000 0.0000 -f_JCZ38_qlogis 0.000 0.000 0.000 0.000 0.0000 -f_JSE76_qlogis 0.000 0.000 0.000 0.000 0.0000 -log_k1 0.000 0.000 0.000 0.000 0.0000 -log_k2 0.000 0.000 0.000 0.000 0.0000 -g_qlogis 0.000 0.000 0.000 0.000 0.0000 - f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 -cyan_0 0.0 0.00 0.00 0.0000 0.0000 -log_k_JCZ38 0.0 0.00 0.00 0.0000 0.0000 -log_k_J9Z38 0.0 0.00 0.00 0.0000 0.0000 -log_k_JSE76 0.0 0.00 0.00 0.0000 0.0000 -f_cyan_ilr_1 0.0 0.00 0.00 0.0000 0.0000 -f_cyan_ilr_2 10.1 0.00 0.00 0.0000 0.0000 -f_JCZ38_qlogis 0.0 13.99 0.00 0.0000 0.0000 -f_JSE76_qlogis 0.0 0.00 14.15 0.0000 0.0000 -log_k1 0.0 0.00 0.00 0.8452 0.0000 -log_k2 0.0 0.00 0.00 0.0000 0.5968 -g_qlogis 0.0 0.00 0.00 0.0000 0.0000 - g_qlogis -cyan_0 0.000 -log_k_JCZ38 0.000 -log_k_J9Z38 0.000 -log_k_JSE76 0.000 -f_cyan_ilr_1 0.000 -f_cyan_ilr_2 0.000 -f_JCZ38_qlogis 0.000 -f_JSE76_qlogis 0.000 -log_k1 0.000 -log_k2 0.000 -g_qlogis 1.691 - -Starting values for error model parameters: -a.1 b.1 - 1 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 2232 2224 -1096 - -Optimised parameters: - est. lower upper -cyan_0 101.20051 NA NA -log_k_JCZ38 -2.93542 NA NA -log_k_J9Z38 -5.03151 NA NA -log_k_JSE76 -3.67679 NA NA -f_cyan_ilr_1 0.67290 NA NA -f_cyan_ilr_2 0.99787 NA NA -f_JCZ38_qlogis 348.32484 NA NA -f_JSE76_qlogis 1.87846 NA NA -log_k1 -2.32738 NA NA -log_k2 -4.61295 NA NA -g_qlogis -0.38342 NA NA -a.1 2.06184 1.83746 2.28622 -b.1 0.06329 0.05211 0.07447 -SD.log_k_JCZ38 1.29042 0.47468 2.10617 -SD.log_k_J9Z38 0.84235 0.25903 1.42566 -SD.log_k_JSE76 0.56930 0.13934 0.99926 -SD.f_cyan_ilr_1 0.35183 0.12298 0.58068 -SD.f_cyan_ilr_2 0.77269 0.17908 1.36631 -SD.log_k2 0.28549 0.09210 0.47888 -SD.g_qlogis 0.93830 0.34568 1.53093 - -Correlation is not available - -Random effects: - est. lower upper -SD.log_k_JCZ38 1.2904 0.4747 2.1062 -SD.log_k_J9Z38 0.8423 0.2590 1.4257 -SD.log_k_JSE76 0.5693 0.1393 0.9993 -SD.f_cyan_ilr_1 0.3518 0.1230 0.5807 -SD.f_cyan_ilr_2 0.7727 0.1791 1.3663 -SD.log_k2 0.2855 0.0921 0.4789 -SD.g_qlogis 0.9383 0.3457 1.5309 - -Variance model: - est. lower upper -a.1 2.06184 1.83746 2.28622 -b.1 0.06329 0.05211 0.07447 - -Backtransformed parameters: - est. lower upper -cyan_0 1.012e+02 NA NA -k_JCZ38 5.311e-02 NA NA -k_J9Z38 6.529e-03 NA NA -k_JSE76 2.530e-02 NA NA -f_cyan_to_JCZ38 6.373e-01 NA NA -f_cyan_to_J9Z38 2.461e-01 NA NA -f_JCZ38_to_JSE76 1.000e+00 NA NA -f_JSE76_to_JCZ38 8.674e-01 NA NA -k1 9.755e-02 NA NA -k2 9.922e-03 NA NA -g 4.053e-01 NA NA - -Resulting formation fractions: - ff -cyan_JCZ38 0.6373 -cyan_J9Z38 0.2461 -cyan_sink 0.1167 -JCZ38_JSE76 1.0000 -JCZ38_sink 0.0000 -JSE76_JCZ38 0.8674 -JSE76_sink 0.1326 - -Estimated disappearance times: - DT50 DT90 DT50back DT50_k1 DT50_k2 -cyan 24.93 179.68 54.09 7.105 69.86 -JCZ38 13.05 43.36 NA NA NA -J9Z38 106.16 352.67 NA NA NA -JSE76 27.39 91.00 NA NA NA - -</code></pre> -<p></p> -<caption> -Hierarchical SFORB path 2 fit with reduced random effects, constant -variance -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 21:04:09 2023 -Date of summary: Thu Apr 20 21:04:34 2023 - -Equations: -d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound * - cyan_free + k_cyan_bound_free * cyan_bound -d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free * - cyan_bound -d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38 - * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76 -d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38 - * J9Z38 -d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 - -Data: -433 observations of 4 variable(s) grouped in 5 datasets - -Model predictions using solution type deSolve - -Fitted in 887.369 s -Using 300, 100 iterations and 10 chains - -Variance model: Constant variance - -Starting values for degradation parameters: - cyan_free_0 log_k_cyan_free log_k_cyan_free_bound - 102.4394 -2.7673 -2.8942 -log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 - -3.6201 -2.3107 -5.3123 - log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 - -3.7120 0.6754 1.1448 - f_JCZ38_qlogis f_JSE76_qlogis - 13.2672 13.3538 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - cyan_free_0 log_k_cyan_free log_k_cyan_free_bound -cyan_free_0 4.589 0.0000 0.00 -log_k_cyan_free 0.000 0.4849 0.00 -log_k_cyan_free_bound 0.000 0.0000 1.62 -log_k_cyan_bound_free 0.000 0.0000 0.00 -log_k_JCZ38 0.000 0.0000 0.00 -log_k_J9Z38 0.000 0.0000 0.00 -log_k_JSE76 0.000 0.0000 0.00 -f_cyan_ilr_1 0.000 0.0000 0.00 -f_cyan_ilr_2 0.000 0.0000 0.00 -f_JCZ38_qlogis 0.000 0.0000 0.00 -f_JSE76_qlogis 0.000 0.0000 0.00 - log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 -cyan_free_0 0.000 0.0000 0.000 0.0 -log_k_cyan_free 0.000 0.0000 0.000 0.0 -log_k_cyan_free_bound 0.000 0.0000 0.000 0.0 -log_k_cyan_bound_free 1.197 0.0000 0.000 0.0 -log_k_JCZ38 0.000 0.7966 0.000 0.0 -log_k_J9Z38 0.000 0.0000 1.561 0.0 -log_k_JSE76 0.000 0.0000 0.000 0.8 -f_cyan_ilr_1 0.000 0.0000 0.000 0.0 -f_cyan_ilr_2 0.000 0.0000 0.000 0.0 -f_JCZ38_qlogis 0.000 0.0000 0.000 0.0 -f_JSE76_qlogis 0.000 0.0000 0.000 0.0 - f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis -cyan_free_0 0.0000 0.000 0.00 0.00 -log_k_cyan_free 0.0000 0.000 0.00 0.00 -log_k_cyan_free_bound 0.0000 0.000 0.00 0.00 -log_k_cyan_bound_free 0.0000 0.000 0.00 0.00 -log_k_JCZ38 0.0000 0.000 0.00 0.00 -log_k_J9Z38 0.0000 0.000 0.00 0.00 -log_k_JSE76 0.0000 0.000 0.00 0.00 -f_cyan_ilr_1 0.6349 0.000 0.00 0.00 -f_cyan_ilr_2 0.0000 1.797 0.00 0.00 -f_JCZ38_qlogis 0.0000 0.000 13.84 0.00 -f_JSE76_qlogis 0.0000 0.000 0.00 14.66 - -Starting values for error model parameters: -a.1 - 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 2279 2272 -1120 - -Optimised parameters: - est. lower upper -cyan_free_0 102.5621 NA NA -log_k_cyan_free -2.8531 NA NA -log_k_cyan_free_bound -2.6916 NA NA -log_k_cyan_bound_free -3.5032 NA NA -log_k_JCZ38 -2.9436 NA NA -log_k_J9Z38 -5.1140 NA NA -log_k_JSE76 -3.6472 NA NA -f_cyan_ilr_1 0.6887 NA NA -f_cyan_ilr_2 0.6874 NA NA -f_JCZ38_qlogis 4063.6389 NA NA -f_JSE76_qlogis 1.9556 NA NA -a.1 2.7460 2.55451 2.9376 -SD.log_k_cyan_free 0.3131 0.09841 0.5277 -SD.log_k_cyan_free_bound 0.8850 0.29909 1.4710 -SD.log_k_cyan_bound_free 0.6167 0.20391 1.0295 -SD.log_k_JCZ38 1.3555 0.49101 2.2200 -SD.log_k_J9Z38 0.7200 0.16166 1.2783 -SD.log_k_JSE76 0.6252 0.14619 1.1042 -SD.f_cyan_ilr_1 0.3386 0.11447 0.5627 -SD.f_cyan_ilr_2 0.4699 0.09810 0.8417 - -Correlation is not available - -Random effects: - est. lower upper -SD.log_k_cyan_free 0.3131 0.09841 0.5277 -SD.log_k_cyan_free_bound 0.8850 0.29909 1.4710 -SD.log_k_cyan_bound_free 0.6167 0.20391 1.0295 -SD.log_k_JCZ38 1.3555 0.49101 2.2200 -SD.log_k_J9Z38 0.7200 0.16166 1.2783 -SD.log_k_JSE76 0.6252 0.14619 1.1042 -SD.f_cyan_ilr_1 0.3386 0.11447 0.5627 -SD.f_cyan_ilr_2 0.4699 0.09810 0.8417 - -Variance model: - est. lower upper -a.1 2.746 2.555 2.938 - -Backtransformed parameters: - est. lower upper -cyan_free_0 1.026e+02 NA NA -k_cyan_free 5.767e-02 NA NA -k_cyan_free_bound 6.777e-02 NA NA -k_cyan_bound_free 3.010e-02 NA NA -k_JCZ38 5.267e-02 NA NA -k_J9Z38 6.012e-03 NA NA -k_JSE76 2.606e-02 NA NA -f_cyan_free_to_JCZ38 6.089e-01 NA NA -f_cyan_free_to_J9Z38 2.299e-01 NA NA -f_JCZ38_to_JSE76 1.000e+00 NA NA -f_JSE76_to_JCZ38 8.761e-01 NA NA - -Estimated Eigenvalues of SFORB model(s): -cyan_b1 cyan_b2 cyan_g - 0.1434 0.0121 0.3469 - -Resulting formation fractions: - ff -cyan_free_JCZ38 0.6089 -cyan_free_J9Z38 0.2299 -cyan_free_sink 0.1612 -cyan_free 1.0000 -JCZ38_JSE76 1.0000 -JCZ38_sink 0.0000 -JSE76_JCZ38 0.8761 -JSE76_sink 0.1239 - -Estimated disappearance times: - DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 -cyan 23.94 155.06 46.68 4.832 57.28 -JCZ38 13.16 43.71 NA NA NA -J9Z38 115.30 383.02 NA NA NA -JSE76 26.59 88.35 NA NA NA - -</code></pre> -<p></p> -<caption> -Hierarchical SFORB path 2 fit with reduced random effects, two-component -error -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.4 -R version used for fitting: 4.2.3 -Date of fit: Thu Apr 20 21:04:32 2023 -Date of summary: Thu Apr 20 21:04:34 2023 - -Equations: -d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound * - cyan_free + k_cyan_bound_free * cyan_bound -d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free * - cyan_bound -d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38 - * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76 -d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38 - * J9Z38 -d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 - -Data: -433 observations of 4 variable(s) grouped in 5 datasets - -Model predictions using solution type deSolve - -Fitted in 910.017 s -Using 300, 100 iterations and 10 chains - -Variance model: Two-component variance function - -Starting values for degradation parameters: - cyan_free_0 log_k_cyan_free log_k_cyan_free_bound - 101.751 -2.837 -3.016 -log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 - -3.660 -2.299 -5.313 - log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 - -3.699 0.672 5.873 - f_JCZ38_qlogis f_JSE76_qlogis - 13.216 13.338 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - cyan_free_0 log_k_cyan_free log_k_cyan_free_bound -cyan_free_0 5.629 0.000 0.000 -log_k_cyan_free 0.000 0.446 0.000 -log_k_cyan_free_bound 0.000 0.000 1.449 -log_k_cyan_bound_free 0.000 0.000 0.000 -log_k_JCZ38 0.000 0.000 0.000 -log_k_J9Z38 0.000 0.000 0.000 -log_k_JSE76 0.000 0.000 0.000 -f_cyan_ilr_1 0.000 0.000 0.000 -f_cyan_ilr_2 0.000 0.000 0.000 -f_JCZ38_qlogis 0.000 0.000 0.000 -f_JSE76_qlogis 0.000 0.000 0.000 - log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 -cyan_free_0 0.000 0.0000 0.000 0.0000 -log_k_cyan_free 0.000 0.0000 0.000 0.0000 -log_k_cyan_free_bound 0.000 0.0000 0.000 0.0000 -log_k_cyan_bound_free 1.213 0.0000 0.000 0.0000 -log_k_JCZ38 0.000 0.7801 0.000 0.0000 -log_k_J9Z38 0.000 0.0000 1.575 0.0000 -log_k_JSE76 0.000 0.0000 0.000 0.8078 -f_cyan_ilr_1 0.000 0.0000 0.000 0.0000 -f_cyan_ilr_2 0.000 0.0000 0.000 0.0000 -f_JCZ38_qlogis 0.000 0.0000 0.000 0.0000 -f_JSE76_qlogis 0.000 0.0000 0.000 0.0000 - f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis -cyan_free_0 0.0000 0.00 0.00 0.00 -log_k_cyan_free 0.0000 0.00 0.00 0.00 -log_k_cyan_free_bound 0.0000 0.00 0.00 0.00 -log_k_cyan_bound_free 0.0000 0.00 0.00 0.00 -log_k_JCZ38 0.0000 0.00 0.00 0.00 -log_k_J9Z38 0.0000 0.00 0.00 0.00 -log_k_JSE76 0.0000 0.00 0.00 0.00 -f_cyan_ilr_1 0.6519 0.00 0.00 0.00 -f_cyan_ilr_2 0.0000 10.78 0.00 0.00 -f_JCZ38_qlogis 0.0000 0.00 13.96 0.00 -f_JSE76_qlogis 0.0000 0.00 0.00 14.69 - -Starting values for error model parameters: -a.1 b.1 - 1 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 2236 2228 -1098 - -Optimised parameters: - est. lower upper -cyan_free_0 100.72760 NA NA -log_k_cyan_free -3.18281 NA NA -log_k_cyan_free_bound -3.37924 NA NA -log_k_cyan_bound_free -3.77107 NA NA -log_k_JCZ38 -2.92811 NA NA -log_k_J9Z38 -5.02759 NA NA -log_k_JSE76 -3.65835 NA NA -f_cyan_ilr_1 0.67390 NA NA -f_cyan_ilr_2 1.15106 NA NA -f_JCZ38_qlogis 827.82299 NA NA -f_JSE76_qlogis 1.83064 NA NA -a.1 2.06921 1.84443 2.29399 -b.1 0.06391 0.05267 0.07515 -SD.log_k_cyan_free 0.50518 0.18962 0.82075 -SD.log_k_cyan_bound_free 0.30991 0.08170 0.53813 -SD.log_k_JCZ38 1.26661 0.46578 2.06744 -SD.log_k_J9Z38 0.88272 0.27813 1.48730 -SD.log_k_JSE76 0.53050 0.12561 0.93538 -SD.f_cyan_ilr_1 0.35547 0.12461 0.58633 -SD.f_cyan_ilr_2 0.91446 0.20131 1.62761 - -Correlation is not available - -Random effects: - est. lower upper -SD.log_k_cyan_free 0.5052 0.1896 0.8207 -SD.log_k_cyan_bound_free 0.3099 0.0817 0.5381 -SD.log_k_JCZ38 1.2666 0.4658 2.0674 -SD.log_k_J9Z38 0.8827 0.2781 1.4873 -SD.log_k_JSE76 0.5305 0.1256 0.9354 -SD.f_cyan_ilr_1 0.3555 0.1246 0.5863 -SD.f_cyan_ilr_2 0.9145 0.2013 1.6276 - -Variance model: - est. lower upper -a.1 2.06921 1.84443 2.29399 -b.1 0.06391 0.05267 0.07515 - -Backtransformed parameters: - est. lower upper -cyan_free_0 1.007e+02 NA NA -k_cyan_free 4.147e-02 NA NA -k_cyan_free_bound 3.407e-02 NA NA -k_cyan_bound_free 2.303e-02 NA NA -k_JCZ38 5.350e-02 NA NA -k_J9Z38 6.555e-03 NA NA -k_JSE76 2.578e-02 NA NA -f_cyan_free_to_JCZ38 6.505e-01 NA NA -f_cyan_free_to_J9Z38 2.508e-01 NA NA -f_JCZ38_to_JSE76 1.000e+00 NA NA -f_JSE76_to_JCZ38 8.618e-01 NA NA - -Estimated Eigenvalues of SFORB model(s): -cyan_b1 cyan_b2 cyan_g -0.08768 0.01089 0.39821 - -Resulting formation fractions: - ff -cyan_free_JCZ38 0.65053 -cyan_free_J9Z38 0.25082 -cyan_free_sink 0.09864 -cyan_free 1.00000 -JCZ38_JSE76 1.00000 -JCZ38_sink 0.00000 -JSE76_JCZ38 0.86184 -JSE76_sink 0.13816 - -Estimated disappearance times: - DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 -cyan 25.32 164.79 49.61 7.906 63.64 -JCZ38 12.96 43.04 NA NA NA -J9Z38 105.75 351.29 NA NA NA -JSE76 26.89 89.33 NA NA NA - -</code></pre> -<p></p> -</div> -</div> -<div class="section level3"> -<h3 id="session-info">Session info<a class="anchor" aria-label="anchor" href="#session-info"></a> -</h3> -<pre><code>R version 4.2.3 (2023-03-15) -Platform: x86_64-pc-linux-gnu (64-bit) -Running under: Debian GNU/Linux 12 (bookworm) - -Matrix products: default -BLAS: /usr/lib/x86_64-linux-gnu/openblas-serial/libblas.so.3 -LAPACK: /usr/lib/x86_64-linux-gnu/openblas-serial/libopenblas-r0.3.21.so - -locale: - [1] LC_CTYPE=de_DE.UTF-8 LC_NUMERIC=C - [3] LC_TIME=de_DE.UTF-8 LC_COLLATE=de_DE.UTF-8 - [5] LC_MONETARY=de_DE.UTF-8 LC_MESSAGES=de_DE.UTF-8 - [7] LC_PAPER=de_DE.UTF-8 LC_NAME=C - [9] LC_ADDRESS=C LC_TELEPHONE=C -[11] LC_MEASUREMENT=de_DE.UTF-8 LC_IDENTIFICATION=C - -attached base packages: -[1] parallel stats graphics grDevices utils datasets methods -[8] base - -other attached packages: -[1] saemix_3.2 npde_3.3 knitr_1.42 mkin_1.2.4 - -loaded via a namespace (and not attached): - [1] deSolve_1.35 zoo_1.8-12 tidyselect_1.2.0 xfun_0.38 - [5] bslib_0.4.2 purrr_1.0.1 lattice_0.21-8 colorspace_2.1-0 - [9] vctrs_0.6.1 generics_0.1.3 htmltools_0.5.5 yaml_2.3.7 -[13] utf8_1.2.3 rlang_1.1.0 pkgbuild_1.4.0 pkgdown_2.0.7 -[17] jquerylib_0.1.4 pillar_1.9.0 glue_1.6.2 DBI_1.1.3 -[21] readxl_1.4.2 lifecycle_1.0.3 stringr_1.5.0 munsell_0.5.0 -[25] gtable_0.3.3 cellranger_1.1.0 ragg_1.2.5 codetools_0.2-19 -[29] memoise_2.0.1 evaluate_0.20 inline_0.3.19 callr_3.7.3 -[33] fastmap_1.1.1 ps_1.7.4 lmtest_0.9-40 fansi_1.0.4 -[37] highr_0.10 scales_1.2.1 cachem_1.0.7 desc_1.4.2 -[41] jsonlite_1.8.4 systemfonts_1.0.4 fs_1.6.1 textshaping_0.3.6 -[45] gridExtra_2.3 ggplot2_3.4.2 digest_0.6.31 stringi_1.7.12 -[49] processx_3.8.0 dplyr_1.1.1 grid_4.2.3 rprojroot_2.0.3 -[53] cli_3.6.1 tools_4.2.3 magrittr_2.0.3 sass_0.4.5 -[57] tibble_3.2.1 crayon_1.5.2 pkgconfig_2.0.3 prettyunits_1.1.1 -[61] rmarkdown_2.21 R6_2.5.1 mclust_6.0.0 nlme_3.1-162 -[65] compiler_4.2.3 </code></pre> -</div> -<div class="section level3"> -<h3 id="hardware-info">Hardware info<a class="anchor" aria-label="anchor" href="#hardware-info"></a> -</h3> -<pre><code>CPU model: AMD Ryzen 9 7950X 16-Core Processor</code></pre> -<pre><code>MemTotal: 64936316 kB</code></pre> -</div> -</div> - </div> - - <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar"> - - <nav id="toc" data-toggle="toc"><h2 data-toc-skip>Contents</h2> - </nav> -</div> - -</div> - - - - <footer><div class="copyright"> - <p></p> -<p>Developed by Johannes Ranke.</p> -</div> - -<div class="pkgdown"> - <p></p> -<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p> -</div> - - </footer> -</div> - - - - - - - </body> -</html> diff --git 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NAFTA SOP Attachment examples</a> - </li> - </ul> -</li> -<li> - <a href="../../news/index.html">News</a> -</li> - </ul> -<ul class="nav navbar-nav navbar-right"> -<li> - <a href="https://github.com/jranke/mkin/" class="external-link"> - <span class="fab fa-github fa-lg"></span> - - </a> -</li> - </ul> -</div> -<!--/.nav-collapse --> - </div> -<!--/.container --> -</div> -<!--/.navbar --> - - - - </header><div class="row"> - <div class="col-md-9 contents"> - <div class="page-header toc-ignore"> - <h1 data-toc-skip>Testing hierarchical parent degradation kinetics -with residue data on dimethenamid and dimethenamid-P</h1> - <h4 data-toc-skip class="author">Johannes -Ranke</h4> - - <h4 data-toc-skip class="date">Last change on 5 January -2023, last compiled on 16 April 2023</h4> - - <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/prebuilt/2022_dmta_parent.rmd" class="external-link"><code>vignettes/prebuilt/2022_dmta_parent.rmd</code></a></small> - <div class="hidden name"><code>2022_dmta_parent.rmd</code></div> - - </div> - - - -<div class="section level2"> -<h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#introduction"></a> -</h2> -<p>The purpose of this document is to demonstrate how nonlinear -hierarchical models (NLHM) based on the parent degradation models SFO, -FOMC, DFOP and HS can be fitted with the mkin package.</p> -<p>It was assembled in the course of work package 1.1 of Project Number -173340 (Application of nonlinear hierarchical models to the kinetic -evaluation of chemical degradation data) of the German Environment -Agency carried out in 2022 and 2023.</p> -<p>The mkin package is used in version 1.2.3. It contains the test data -and the functions used in the evaluations. The <code>saemix</code> -package is used as a backend for fitting the NLHM, but is also loaded to -make the convergence plot function available.</p> -<p>This document is processed with the <code>knitr</code> package, which -also provides the <code>kable</code> function that is used to improve -the display of tabular data in R markdown documents. For parallel -processing, the <code>parallel</code> package is used.</p> -<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://pkgdown.jrwb.de/mkin/">mkin</a></span><span class="op">)</span></span> -<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://yihui.org/knitr/" class="external-link">knitr</a></span><span class="op">)</span></span> -<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">saemix</span><span class="op">)</span></span> -<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">parallel</span><span class="op">)</span></span> -<span><span class="va">n_cores</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/detectCores.html" class="external-link">detectCores</a></span><span class="op">(</span><span class="op">)</span></span> -<span><span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/Sys.info.html" class="external-link">Sys.info</a></span><span class="op">(</span><span class="op">)</span><span class="op">[</span><span class="st">"sysname"</span><span class="op">]</span> <span class="op">==</span> <span class="st">"Windows"</span><span class="op">)</span> <span class="op">{</span></span> -<span> <span class="va">cl</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makePSOCKcluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> -<span><span class="op">}</span> <span class="kw">else</span> <span class="op">{</span></span> -<span> <span class="va">cl</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makeForkCluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> -<span><span class="op">}</span></span></code></pre></div> -</div> -<div class="section level2"> -<h2 id="data">Data<a class="anchor" aria-label="anchor" href="#data"></a> -</h2> -<p>The test data are available in the mkin package as an object of class -<code>mkindsg</code> (mkin dataset group) under the identifier -<code>dimethenamid_2018</code>. The following preprocessing steps are -still necessary:</p> -<ul> -<li>The data available for the enantiomer dimethenamid-P (DMTAP) are -renamed to have the same substance name as the data for the racemic -mixture dimethenamid (DMTA). The reason for this is that no difference -between their degradation behaviour was identified in the EU risk -assessment.</li> -<li>The data for transformation products and unnecessary columns are -discarded</li> -<li>The observation times of each dataset are multiplied with the -corresponding normalisation factor also available in the dataset, in -order to make it possible to describe all datasets with a single set of -parameters that are independent of temperature</li> -<li>Finally, datasets observed in the same soil (<code>Elliot 1</code> -and <code>Elliot 2</code>) are combined, resulting in dimethenamid -(DMTA) data from six soils.</li> -</ul> -<p>The following commented R code performs this preprocessing.</p> -<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="co"># Apply a function to each of the seven datasets in the mkindsg object to create a list</span></span> -<span><span class="va">dmta_ds</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">lapply</a></span><span class="op">(</span><span class="fl">1</span><span class="op">:</span><span class="fl">7</span>, <span class="kw">function</span><span class="op">(</span><span class="va">i</span><span class="op">)</span> <span class="op">{</span></span> -<span> <span class="va">ds_i</span> <span class="op"><-</span> <span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">ds</span><span class="op">[[</span><span class="va">i</span><span class="op">]</span><span class="op">]</span><span class="op">$</span><span class="va">data</span> <span class="co"># Get a dataset</span></span> -<span> <span class="va">ds_i</span><span class="op">[</span><span class="va">ds_i</span><span class="op">$</span><span class="va">name</span> <span class="op">==</span> <span class="st">"DMTAP"</span>, <span class="st">"name"</span><span class="op">]</span> <span class="op"><-</span> <span class="st">"DMTA"</span> <span class="co"># Rename DMTAP to DMTA</span></span> -<span> <span class="va">ds_i</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/subset.html" class="external-link">subset</a></span><span class="op">(</span><span class="va">ds_i</span>, <span class="va">name</span> <span class="op">==</span> <span class="st">"DMTA"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"name"</span>, <span class="st">"time"</span>, <span class="st">"value"</span><span class="op">)</span><span class="op">)</span> <span class="co"># Select data</span></span> -<span> <span class="va">ds_i</span><span class="op">$</span><span class="va">time</span> <span class="op"><-</span> <span class="va">ds_i</span><span class="op">$</span><span class="va">time</span> <span class="op">*</span> <span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">f_time_norm</span><span class="op">[</span><span class="va">i</span><span class="op">]</span> <span class="co"># Normalise time</span></span> -<span> <span class="va">ds_i</span> <span class="co"># Return the dataset</span></span> -<span><span class="op">}</span><span class="op">)</span></span> -<span></span> -<span><span class="co"># Use dataset titles as names for the list elements</span></span> -<span><span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">)</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</span><span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">ds</span>, <span class="kw">function</span><span class="op">(</span><span class="va">ds</span><span class="op">)</span> <span class="va">ds</span><span class="op">$</span><span class="va">title</span><span class="op">)</span></span> -<span></span> -<span><span class="co"># Combine data for Elliot soil to obtain a named list with six elements</span></span> -<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/cbind.html" class="external-link">rbind</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 1"</span><span class="op">]</span><span class="op">]</span>, <span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 2"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span> <span class="co">#</span></span> -<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 1"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="cn">NULL</span></span> -<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 2"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="cn">NULL</span></span></code></pre></div> -<p>The following tables show the 6 datasets.</p> -<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="kw">for</span> <span class="op">(</span><span class="va">ds_name</span> <span class="kw">in</span> <span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">)</span><span class="op">)</span> <span class="op">{</span></span> -<span> <span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="fu"><a href="../../reference/mkin_long_to_wide.html">mkin_long_to_wide</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">[[</span><span class="va">ds_name</span><span class="op">]</span><span class="op">]</span><span class="op">)</span>,</span> -<span> caption <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste</a></span><span class="op">(</span><span class="st">"Dataset"</span>, <span class="va">ds_name</span><span class="op">)</span>,</span> -<span> label <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste0</a></span><span class="op">(</span><span class="st">"tab:"</span>, <span class="va">ds_name</span><span class="op">)</span>, booktabs <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span><span class="op">)</span></span> -<span> <span class="fu"><a href="https://rdrr.io/r/base/cat.html" class="external-link">cat</a></span><span class="op">(</span><span class="st">"\n\\clearpage\n"</span><span class="op">)</span></span> -<span><span class="op">}</span></span></code></pre></div> -<table class="table"> -<caption>Dataset Calke</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">DMTA</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0</td> -<td align="right">95.8</td> -</tr> -<tr class="even"> -<td align="right">0</td> -<td align="right">98.7</td> -</tr> -<tr class="odd"> -<td align="right">14</td> -<td align="right">60.5</td> -</tr> -<tr class="even"> -<td align="right">30</td> -<td align="right">39.1</td> -</tr> -<tr class="odd"> -<td align="right">59</td> -<td align="right">15.2</td> -</tr> -<tr class="even"> -<td align="right">120</td> -<td align="right">4.8</td> -</tr> -<tr class="odd"> -<td align="right">120</td> -<td align="right">4.6</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset Borstel</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">DMTA</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.000000</td> -<td align="right">100.5</td> -</tr> -<tr class="even"> -<td align="right">0.000000</td> -<td align="right">99.6</td> -</tr> -<tr class="odd"> -<td align="right">1.941295</td> -<td align="right">91.9</td> -</tr> -<tr class="even"> -<td align="right">1.941295</td> -<td align="right">91.3</td> -</tr> -<tr class="odd"> -<td align="right">6.794534</td> -<td align="right">81.8</td> -</tr> -<tr class="even"> -<td align="right">6.794534</td> -<td align="right">82.1</td> -</tr> -<tr class="odd"> -<td align="right">13.589067</td> -<td align="right">69.1</td> -</tr> -<tr class="even"> -<td align="right">13.589067</td> -<td align="right">68.0</td> -</tr> -<tr class="odd"> -<td align="right">27.178135</td> -<td align="right">51.4</td> -</tr> -<tr class="even"> -<td align="right">27.178135</td> -<td align="right">51.4</td> -</tr> -<tr class="odd"> -<td align="right">56.297565</td> -<td align="right">27.6</td> -</tr> -<tr class="even"> -<td align="right">56.297565</td> -<td align="right">26.8</td> -</tr> -<tr class="odd"> -<td align="right">86.387643</td> -<td align="right">15.7</td> -</tr> -<tr class="even"> -<td align="right">86.387643</td> -<td align="right">15.3</td> -</tr> -<tr class="odd"> -<td align="right">115.507073</td> -<td align="right">7.9</td> -</tr> -<tr class="even"> -<td align="right">115.507073</td> -<td align="right">8.1</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset Flaach</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">DMTA</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.0000000</td> -<td align="right">96.5</td> -</tr> -<tr class="even"> -<td align="right">0.0000000</td> -<td align="right">96.8</td> -</tr> -<tr class="odd"> -<td align="right">0.0000000</td> -<td align="right">97.0</td> -</tr> -<tr class="even"> -<td align="right">0.6233856</td> -<td align="right">82.9</td> -</tr> -<tr class="odd"> -<td align="right">0.6233856</td> -<td align="right">86.7</td> -</tr> -<tr class="even"> -<td align="right">0.6233856</td> -<td align="right">87.4</td> -</tr> -<tr class="odd"> -<td align="right">1.8701567</td> -<td align="right">72.8</td> -</tr> -<tr class="even"> -<td align="right">1.8701567</td> -<td align="right">69.9</td> -</tr> -<tr class="odd"> -<td align="right">1.8701567</td> -<td align="right">71.9</td> -</tr> -<tr class="even"> -<td align="right">4.3636989</td> -<td align="right">51.4</td> -</tr> -<tr class="odd"> -<td align="right">4.3636989</td> -<td align="right">52.9</td> -</tr> -<tr class="even"> -<td align="right">4.3636989</td> -<td align="right">48.6</td> -</tr> -<tr class="odd"> -<td align="right">8.7273979</td> -<td align="right">28.5</td> -</tr> -<tr class="even"> -<td align="right">8.7273979</td> -<td align="right">27.3</td> -</tr> -<tr class="odd"> -<td align="right">8.7273979</td> -<td align="right">27.5</td> -</tr> -<tr class="even"> -<td align="right">13.0910968</td> -<td align="right">14.8</td> -</tr> -<tr class="odd"> -<td align="right">13.0910968</td> -<td align="right">13.4</td> -</tr> -<tr class="even"> -<td align="right">13.0910968</td> -<td align="right">14.4</td> -</tr> -<tr class="odd"> -<td align="right">17.4547957</td> -<td align="right">7.7</td> -</tr> -<tr class="even"> -<td align="right">17.4547957</td> -<td align="right">7.3</td> -</tr> -<tr class="odd"> -<td align="right">17.4547957</td> -<td align="right">8.1</td> -</tr> -<tr class="even"> -<td align="right">26.1821936</td> -<td align="right">2.0</td> -</tr> -<tr class="odd"> -<td align="right">26.1821936</td> -<td align="right">1.5</td> -</tr> -<tr class="even"> -<td align="right">26.1821936</td> -<td align="right">1.9</td> -</tr> -<tr class="odd"> -<td align="right">34.9095915</td> -<td align="right">1.3</td> -</tr> -<tr class="even"> -<td align="right">34.9095915</td> -<td align="right">1.0</td> -</tr> -<tr class="odd"> -<td align="right">34.9095915</td> -<td align="right">1.1</td> -</tr> -<tr class="even"> -<td align="right">43.6369893</td> -<td align="right">0.9</td> -</tr> -<tr class="odd"> -<td align="right">43.6369893</td> -<td align="right">0.7</td> -</tr> -<tr class="even"> -<td align="right">43.6369893</td> -<td align="right">0.7</td> -</tr> -<tr class="odd"> -<td align="right">52.3643872</td> -<td align="right">0.6</td> -</tr> -<tr class="even"> -<td align="right">52.3643872</td> -<td align="right">0.4</td> -</tr> -<tr class="odd"> -<td align="right">52.3643872</td> -<td align="right">0.5</td> -</tr> -<tr class="even"> -<td align="right">74.8062674</td> -<td align="right">0.4</td> -</tr> -<tr class="odd"> -<td align="right">74.8062674</td> -<td align="right">0.3</td> -</tr> -<tr class="even"> -<td align="right">74.8062674</td> -<td align="right">0.3</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset BBA 2.2</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">DMTA</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.0000000</td> -<td align="right">98.09</td> -</tr> -<tr class="even"> -<td align="right">0.0000000</td> -<td align="right">98.77</td> -</tr> -<tr class="odd"> -<td align="right">0.7678922</td> -<td align="right">93.52</td> -</tr> -<tr class="even"> -<td align="right">0.7678922</td> -<td align="right">92.03</td> -</tr> -<tr class="odd"> -<td align="right">2.3036765</td> -<td align="right">88.39</td> -</tr> -<tr class="even"> -<td align="right">2.3036765</td> -<td align="right">87.18</td> -</tr> -<tr class="odd"> -<td align="right">5.3752452</td> -<td align="right">69.38</td> -</tr> -<tr class="even"> -<td align="right">5.3752452</td> -<td align="right">71.06</td> -</tr> -<tr class="odd"> -<td align="right">10.7504904</td> -<td align="right">45.21</td> -</tr> -<tr class="even"> -<td align="right">10.7504904</td> -<td align="right">46.81</td> -</tr> -<tr class="odd"> -<td align="right">16.1257355</td> -<td align="right">30.54</td> -</tr> -<tr class="even"> -<td align="right">16.1257355</td> -<td align="right">30.07</td> -</tr> -<tr class="odd"> -<td align="right">21.5009807</td> -<td align="right">21.60</td> -</tr> -<tr class="even"> -<td align="right">21.5009807</td> -<td align="right">20.41</td> -</tr> -<tr class="odd"> -<td align="right">32.2514711</td> -<td align="right">9.10</td> -</tr> -<tr class="even"> -<td align="right">32.2514711</td> -<td align="right">9.70</td> -</tr> -<tr class="odd"> -<td align="right">43.0019614</td> -<td align="right">6.58</td> -</tr> -<tr class="even"> -<td align="right">43.0019614</td> -<td align="right">6.31</td> -</tr> -<tr class="odd"> -<td align="right">53.7524518</td> -<td align="right">3.47</td> -</tr> -<tr class="even"> -<td align="right">53.7524518</td> -<td align="right">3.52</td> -</tr> -<tr class="odd"> -<td align="right">64.5029421</td> -<td align="right">3.40</td> -</tr> -<tr class="even"> -<td align="right">64.5029421</td> -<td align="right">3.67</td> -</tr> -<tr class="odd"> -<td align="right">91.3791680</td> -<td align="right">1.62</td> -</tr> -<tr class="even"> -<td align="right">91.3791680</td> -<td align="right">1.62</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset BBA 2.3</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">DMTA</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.0000000</td> -<td align="right">99.33</td> -</tr> -<tr class="even"> -<td align="right">0.0000000</td> -<td align="right">97.44</td> -</tr> -<tr class="odd"> -<td align="right">0.6733938</td> -<td align="right">93.73</td> -</tr> -<tr class="even"> -<td align="right">0.6733938</td> -<td align="right">93.77</td> -</tr> -<tr class="odd"> -<td align="right">2.0201814</td> -<td align="right">87.84</td> -</tr> -<tr class="even"> -<td align="right">2.0201814</td> -<td align="right">89.82</td> -</tr> -<tr class="odd"> -<td align="right">4.7137565</td> -<td align="right">71.61</td> -</tr> -<tr class="even"> -<td align="right">4.7137565</td> -<td align="right">71.42</td> -</tr> -<tr class="odd"> -<td align="right">9.4275131</td> -<td align="right">45.60</td> -</tr> -<tr class="even"> -<td align="right">9.4275131</td> -<td align="right">45.42</td> -</tr> -<tr class="odd"> -<td align="right">14.1412696</td> -<td align="right">31.12</td> -</tr> -<tr class="even"> -<td align="right">14.1412696</td> -<td align="right">31.68</td> -</tr> -<tr class="odd"> -<td align="right">18.8550262</td> -<td align="right">23.20</td> -</tr> -<tr class="even"> -<td align="right">18.8550262</td> -<td align="right">24.13</td> -</tr> -<tr class="odd"> -<td align="right">28.2825393</td> -<td align="right">9.43</td> -</tr> -<tr class="even"> -<td align="right">28.2825393</td> -<td align="right">9.82</td> -</tr> -<tr class="odd"> -<td align="right">37.7100523</td> -<td align="right">7.08</td> -</tr> -<tr class="even"> -<td align="right">37.7100523</td> -<td align="right">8.64</td> -</tr> -<tr class="odd"> -<td align="right">47.1375654</td> -<td align="right">4.41</td> -</tr> -<tr class="even"> -<td align="right">47.1375654</td> -<td align="right">4.78</td> -</tr> -<tr class="odd"> -<td align="right">56.5650785</td> -<td align="right">4.92</td> -</tr> -<tr class="even"> -<td align="right">56.5650785</td> -<td align="right">5.08</td> -</tr> -<tr class="odd"> -<td align="right">80.1338612</td> -<td align="right">2.13</td> -</tr> -<tr class="even"> -<td align="right">80.1338612</td> -<td align="right">2.23</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset Elliot</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">DMTA</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.000000</td> -<td align="right">97.5</td> -</tr> -<tr class="even"> -<td align="right">0.000000</td> -<td align="right">100.7</td> -</tr> -<tr class="odd"> -<td align="right">1.228478</td> -<td align="right">86.4</td> -</tr> -<tr class="even"> -<td align="right">1.228478</td> -<td align="right">88.5</td> -</tr> -<tr class="odd"> -<td align="right">3.685435</td> -<td align="right">69.8</td> -</tr> -<tr class="even"> -<td align="right">3.685435</td> -<td align="right">77.1</td> -</tr> -<tr class="odd"> -<td align="right">8.599349</td> -<td align="right">59.0</td> -</tr> -<tr class="even"> -<td align="right">8.599349</td> -<td align="right">54.2</td> -</tr> -<tr class="odd"> -<td align="right">17.198697</td> -<td align="right">31.3</td> -</tr> -<tr class="even"> -<td align="right">17.198697</td> -<td align="right">33.5</td> -</tr> -<tr class="odd"> -<td align="right">25.798046</td> -<td align="right">19.6</td> -</tr> -<tr class="even"> -<td align="right">25.798046</td> -<td align="right">20.9</td> -</tr> -<tr class="odd"> -<td align="right">34.397395</td> -<td align="right">13.3</td> -</tr> -<tr class="even"> -<td align="right">34.397395</td> -<td align="right">15.8</td> -</tr> -<tr class="odd"> -<td align="right">51.596092</td> -<td align="right">6.7</td> -</tr> -<tr class="even"> -<td align="right">51.596092</td> -<td align="right">8.7</td> -</tr> -<tr class="odd"> -<td align="right">68.794789</td> -<td align="right">8.8</td> -</tr> -<tr class="even"> -<td align="right">68.794789</td> -<td align="right">8.7</td> -</tr> -<tr class="odd"> -<td align="right">103.192184</td> -<td align="right">6.0</td> -</tr> -<tr class="even"> -<td align="right">103.192184</td> -<td align="right">4.4</td> -</tr> -<tr class="odd"> -<td align="right">146.188928</td> -<td align="right">3.3</td> -</tr> -<tr class="even"> -<td align="right">146.188928</td> -<td align="right">2.8</td> -</tr> -<tr class="odd"> -<td align="right">223.583066</td> -<td align="right">1.4</td> -</tr> -<tr class="even"> -<td align="right">223.583066</td> -<td align="right">1.8</td> -</tr> -<tr class="odd"> -<td align="right">0.000000</td> -<td align="right">93.4</td> -</tr> -<tr class="even"> -<td align="right">0.000000</td> -<td align="right">103.2</td> -</tr> -<tr class="odd"> -<td align="right">1.228478</td> -<td align="right">89.2</td> -</tr> -<tr class="even"> -<td align="right">1.228478</td> -<td align="right">86.6</td> -</tr> -<tr class="odd"> -<td align="right">3.685435</td> -<td align="right">78.2</td> -</tr> -<tr class="even"> -<td align="right">3.685435</td> -<td align="right">78.1</td> -</tr> -<tr class="odd"> -<td align="right">8.599349</td> -<td align="right">55.6</td> -</tr> -<tr class="even"> -<td align="right">8.599349</td> -<td align="right">53.0</td> -</tr> -<tr class="odd"> -<td align="right">17.198697</td> -<td align="right">33.7</td> -</tr> -<tr class="even"> -<td align="right">17.198697</td> -<td align="right">33.2</td> -</tr> -<tr class="odd"> -<td align="right">25.798046</td> -<td align="right">20.9</td> -</tr> -<tr class="even"> -<td align="right">25.798046</td> -<td align="right">19.9</td> -</tr> -<tr class="odd"> -<td align="right">34.397395</td> -<td align="right">18.2</td> -</tr> -<tr class="even"> -<td align="right">34.397395</td> -<td align="right">12.7</td> -</tr> -<tr class="odd"> -<td align="right">51.596092</td> -<td align="right">7.8</td> -</tr> -<tr class="even"> -<td align="right">51.596092</td> -<td align="right">9.0</td> -</tr> -<tr class="odd"> -<td align="right">68.794789</td> -<td align="right">11.4</td> -</tr> -<tr class="even"> -<td align="right">68.794789</td> -<td align="right">9.0</td> -</tr> -<tr class="odd"> -<td align="right">103.192184</td> -<td align="right">3.9</td> -</tr> -<tr class="even"> -<td align="right">103.192184</td> -<td align="right">4.4</td> -</tr> -<tr class="odd"> -<td align="right">146.188928</td> -<td align="right">2.6</td> -</tr> -<tr class="even"> -<td align="right">146.188928</td> -<td align="right">3.4</td> -</tr> -<tr class="odd"> -<td align="right">223.583066</td> -<td align="right">2.0</td> -</tr> -<tr class="even"> -<td align="right">223.583066</td> -<td align="right">1.7</td> -</tr> -</tbody> -</table> -</div> -<div class="section level2"> -<h2 id="separate-evaluations">Separate evaluations<a class="anchor" aria-label="anchor" href="#separate-evaluations"></a> -</h2> -<p>In order to obtain suitable starting parameters for the NLHM fits, -separate fits of the four models to the data for each soil are generated -using the <code>mmkin</code> function from the <code>mkin</code> -package. In a first step, constant variance is assumed. Convergence is -checked with the <code>status</code> function.</p> -<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">deg_mods</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>, <span class="st">"HS"</span><span class="op">)</span></span> -<span><span class="va">f_sep_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span></span> -<span> <span class="va">deg_mods</span>,</span> -<span> <span class="va">dmta_ds</span>,</span> -<span> error_model <span class="op">=</span> <span class="st">"const"</span>,</span> -<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<span></span> -<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">Calke</th> -<th align="left">Borstel</th> -<th align="left">Flaach</th> -<th align="left">BBA 2.2</th> -<th align="left">BBA 2.3</th> -<th align="left">Elliot</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">SFO</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">FOMC</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">DFOP</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">HS</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -</tbody> -</table> -<p>In the table above, OK indicates convergence, and C indicates failure -to converge. All separate fits with constant variance converged, with -the sole exception of the HS fit to the BBA 2.2 data. To prepare for -fitting NLHM using the two-component error model, the separate fits are -updated assuming two-component error.</p> -<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_sep_tc</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_sep_const</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span> -<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_tc</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">Calke</th> -<th align="left">Borstel</th> -<th align="left">Flaach</th> -<th align="left">BBA 2.2</th> -<th align="left">BBA 2.3</th> -<th align="left">Elliot</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">SFO</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">FOMC</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">DFOP</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">HS</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -</tbody> -</table> -<p>Using the two-component error model, the one fit that did not -converge with constant variance did converge, but other non-SFO fits -failed to converge.</p> -</div> -<div class="section level2"> -<h2 id="hierarchichal-model-fits">Hierarchichal model fits<a class="anchor" aria-label="anchor" href="#hierarchichal-model-fits"></a> -</h2> -<p>The following code fits eight versions of hierarchical models to the -data, using SFO, FOMC, DFOP and HS for the parent compound, and using -either constant variance or two-component error for the error model. The -default parameter distribution model in mkin allows for variation of all -degradation parameters across the assumed population of soils. In other -words, each degradation parameter is associated with a random effect as -a first step. The <code>mhmkin</code> function makes it possible to fit -all eight versions in parallel (given a sufficient number of computing -cores being available) to save execution time.</p> -<p>Convergence plots and summaries for these fits are shown in the -appendix.</p> -<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_saem</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mhmkin.html">mhmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">f_sep_const</span>, <span class="va">f_sep_tc</span><span class="op">)</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span></span></code></pre></div> -<p>The output of the <code>status</code> function shows that all fits -terminated successfully.</p> -<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_saem</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">const</th> -<th align="left">tc</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">SFO</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">FOMC</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">DFOP</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">HS</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -</tbody> -</table> -<p>The AIC and BIC values show that the biphasic models DFOP and HS give -the best fits.</p> -<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="right">npar</th> -<th align="right">AIC</th> -<th align="right">BIC</th> -<th align="right">Lik</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">SFO const</td> -<td align="right">5</td> -<td align="right">796.3</td> -<td align="right">795.3</td> -<td align="right">-393.2</td> -</tr> -<tr class="even"> -<td align="left">SFO tc</td> -<td align="right">6</td> -<td align="right">798.3</td> -<td align="right">797.1</td> -<td align="right">-393.2</td> -</tr> -<tr class="odd"> -<td align="left">FOMC const</td> -<td align="right">7</td> -<td align="right">734.2</td> -<td align="right">732.7</td> -<td align="right">-360.1</td> -</tr> -<tr class="even"> -<td align="left">FOMC tc</td> -<td align="right">8</td> -<td align="right">720.4</td> -<td align="right">718.8</td> -<td align="right">-352.2</td> -</tr> -<tr class="odd"> -<td align="left">DFOP const</td> -<td align="right">9</td> -<td align="right">711.8</td> -<td align="right">710.0</td> -<td align="right">-346.9</td> -</tr> -<tr class="even"> -<td align="left">HS const</td> -<td align="right">9</td> -<td align="right">714.0</td> -<td align="right">712.1</td> -<td align="right">-348.0</td> -</tr> -<tr class="odd"> -<td align="left">DFOP tc</td> -<td align="right">10</td> -<td align="right">665.5</td> -<td align="right">663.4</td> -<td align="right">-322.8</td> -</tr> -<tr class="even"> -<td align="left">HS tc</td> -<td align="right">10</td> -<td align="right">667.1</td> -<td align="right">665.0</td> -<td align="right">-323.6</td> -</tr> -</tbody> -</table> -<p>The DFOP model is preferred here, as it has a better mechanistic -basis for batch experiments with constant incubation conditions. Also, -it shows the lowest AIC and BIC values in the first set of fits when -combined with the two-component error model. Therefore, the DFOP model -was selected for further refinements of the fits with the aim to make -the model fully identifiable.</p> -<div class="section level3"> -<h3 id="parameter-identifiability-based-on-the-fisher-information-matrix">Parameter identifiability based on the Fisher Information -Matrix<a class="anchor" aria-label="anchor" href="#parameter-identifiability-based-on-the-fisher-information-matrix"></a> -</h3> -<p>Using the <code>illparms</code> function, ill-defined statistical -model parameters such as standard deviations of the degradation -parameters in the population and error model parameters can be -found.</p> -<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">const</th> -<th align="left">tc</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">SFO</td> -<td align="left"></td> -<td align="left">b.1</td> -</tr> -<tr class="even"> -<td align="left">FOMC</td> -<td align="left"></td> -<td align="left">sd(DMTA_0)</td> -</tr> -<tr class="odd"> -<td align="left">DFOP</td> -<td align="left">sd(k2)</td> -<td align="left">sd(k2)</td> -</tr> -<tr class="even"> -<td align="left">HS</td> -<td align="left"></td> -<td align="left">sd(tb)</td> -</tr> -</tbody> -</table> -<p>According to the <code>illparms</code> function, the fitted standard -deviation of the second kinetic rate constant <code>k2</code> is -ill-defined in both DFOP fits. This suggests that different values would -be obtained for this standard deviation when using different starting -values.</p> -<p>The thus identified overparameterisation is addressed by removing the -random effect for <code>k2</code> from the parameter model.</p> -<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_saem_dfop_tc_no_ranef_k2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_saem</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span>,</span> -<span> no_random_effect <span class="op">=</span> <span class="st">"k2"</span><span class="op">)</span></span></code></pre></div> -<p>For the resulting fit, it is checked whether there are still -ill-defined parameters,</p> -<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_dfop_tc_no_ranef_k2</span><span class="op">)</span></span></code></pre></div> -<p>which is not the case. Below, the refined model is compared with the -previous best model. The model without random effect for <code>k2</code> -is a reduced version of the previous model. Therefore, the models are -nested and can be compared using the likelihood ratio test. This is -achieved with the argument <code>test = TRUE</code> to the -<code>anova</code> function.</p> -<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span>, <span class="va">f_saem_dfop_tc_no_ranef_k2</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|></span></span> -<span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>format.args <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">4</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<colgroup> -<col width="37%"> -<col width="6%"> -<col width="8%"> -<col width="8%"> -<col width="9%"> -<col width="9%"> -<col width="4%"> -<col width="15%"> -</colgroup> -<thead><tr class="header"> -<th align="left"></th> -<th align="right">npar</th> -<th align="right">AIC</th> -<th align="right">BIC</th> -<th align="right">Lik</th> -<th align="right">Chisq</th> -<th align="right">Df</th> -<th align="right">Pr(>Chisq)</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">f_saem_dfop_tc_no_ranef_k2</td> -<td align="right">9</td> -<td align="right">663.8</td> -<td align="right">661.9</td> -<td align="right">-322.9</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="left">f_saem[[“DFOP”, “tc”]]</td> -<td align="right">10</td> -<td align="right">665.5</td> -<td align="right">663.4</td> -<td align="right">-322.8</td> -<td align="right">0.2809</td> -<td align="right">1</td> -<td align="right">0.5961</td> -</tr> -</tbody> -</table> -<p>The AIC and BIC criteria are lower after removal of the ill-defined -random effect for <code>k2</code>. The p value of the likelihood ratio -test is much greater than 0.05, indicating that the model with the -higher likelihood (here the model with random effects for all -degradation parameters <code>f_saem[["DFOP", "tc"]]</code>) does not fit -significantly better than the model with the lower likelihood (the -reduced model <code>f_saem_dfop_tc_no_ranef_k2</code>).</p> -<p>Therefore, AIC, BIC and likelihood ratio test suggest the use of the -reduced model.</p> -<p>The convergence of the fit is checked visually.</p> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_parent_files/figure-html/convergence-saem-dfop-tc-no-ranef-k2-1.png" alt="Convergence plot for the NLHM DFOP fit with two-component error and without a random effect on 'k2'" width="864"><p class="caption"> -Convergence plot for the NLHM DFOP fit with two-component error and -without a random effect on ‘k2’ -</p> -</div> -<p>All parameters appear to have converged to a satisfactory degree. The -final fit is plotted using the plot method from the mkin package.</p> -<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_dfop_tc_no_ranef_k2</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_parent_files/figure-html/plot-saem-dfop-tc-no-ranef-k2-1.png" alt="Plot of the final NLHM DFOP fit" width="864"><p class="caption"> -Plot of the final NLHM DFOP fit -</p> -</div> -<p>Finally, a summary report of the fit is produced.</p> -<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">f_saem_dfop_tc_no_ranef_k2</span><span class="op">)</span></span></code></pre></div> -<pre><code>saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.2 -R version used for fitting: 4.2.2 -Date of fit: Sat Jan 28 11:22:51 2023 -Date of summary: Sat Jan 28 11:22:52 2023 - -Equations: -d_DMTA/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * - time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) - * DMTA - -Data: -155 observations of 1 variable(s) grouped in 6 datasets - -Model predictions using solution type analytical - -Fitted in 3.74 s -Using 300, 100 iterations and 9 chains - -Variance model: Two-component variance function - -Starting values for degradation parameters: - DMTA_0 k1 k2 g -98.759266 0.087034 0.009933 0.930827 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - DMTA_0 k1 k2 g -DMTA_0 98.76 0 0 0 -k1 0.00 1 0 0 -k2 0.00 0 1 0 -g 0.00 0 0 1 - -Starting values for error model parameters: -a.1 b.1 - 1 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 663.8 661.9 -322.9 - -Optimised parameters: - est. lower upper -DMTA_0 98.228939 96.285869 100.17201 -k1 0.064063 0.033477 0.09465 -k2 0.008297 0.005824 0.01077 -g 0.953821 0.914328 0.99331 -a.1 1.068479 0.869538 1.26742 -b.1 0.029424 0.022406 0.03644 -SD.DMTA_0 2.030437 0.404824 3.65605 -SD.k1 0.594692 0.256660 0.93272 -SD.g 1.006754 0.361327 1.65218 - -Correlation: - DMTA_0 k1 k2 -k1 0.0218 -k2 0.0556 0.0355 -g -0.0516 -0.0284 -0.2800 - -Random effects: - est. lower upper -SD.DMTA_0 2.0304 0.4048 3.6560 -SD.k1 0.5947 0.2567 0.9327 -SD.g 1.0068 0.3613 1.6522 - -Variance model: - est. lower upper -a.1 1.06848 0.86954 1.26742 -b.1 0.02942 0.02241 0.03644 - -Estimated disappearance times: - DT50 DT90 DT50back DT50_k1 DT50_k2 -DMTA 11.45 41.4 12.46 10.82 83.54</code></pre> -</div> -<div class="section level3"> -<h3 id="alternative-check-of-parameter-identifiability">Alternative check of parameter identifiability<a class="anchor" aria-label="anchor" href="#alternative-check-of-parameter-identifiability"></a> -</h3> -<p>The parameter check used in the <code>illparms</code> function is -based on a quadratic approximation of the likelihood surface near its -optimum, which is calculated using the Fisher Information Matrix (FIM). -An alternative way to check parameter identifiability <span class="citation">(Duchesne et al. 2021)</span> based on a multistart -approach has recently been implemented in mkin.</p> -<p>The graph below shows boxplots of the parameters obtained in 50 runs -of the saem algorithm with different parameter combinations, sampled -from the range of the parameters obtained for the individual datasets -fitted separately using nonlinear regression.</p> -<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_saem_dfop_tc_multi</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/multistart.html">multistart</a></span><span class="op">(</span><span class="va">f_saem</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span>, n <span class="op">=</span> <span class="fl">50</span>, cores <span class="op">=</span> <span class="fl">15</span><span class="op">)</span></span></code></pre></div> -<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/par.html" class="external-link">par</a></span><span class="op">(</span>mar <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">6.1</span>, <span class="fl">4.1</span>, <span class="fl">2.1</span>, <span class="fl">2.1</span><span class="op">)</span><span class="op">)</span></span> -<span><span class="fu"><a href="../../reference/parplot.html">parplot</a></span><span class="op">(</span><span class="va">f_saem_dfop_tc_multi</span>, lpos <span class="op">=</span> <span class="st">"bottomright"</span>, ylim <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.3</span>, <span class="fl">10</span><span class="op">)</span>, las <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_parent_files/figure-html/multistart-full-par-1.png" alt="Scaled parameters from the multistart runs, full model" width="960"><p class="caption"> -Scaled parameters from the multistart runs, full model -</p> -</div> -<p>The graph clearly confirms the lack of identifiability of the -variance of <code>k2</code> in the full model. The overparameterisation -of the model also indicates a lack of identifiability of the variance of -parameter <code>g</code>.</p> -<p>The parameter boxplots of the multistart runs with the reduced model -shown below indicate that all runs give similar results, regardless of -the starting parameters.</p> -<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_saem_dfop_tc_no_ranef_k2_multi</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/multistart.html">multistart</a></span><span class="op">(</span><span class="va">f_saem_dfop_tc_no_ranef_k2</span>,</span> -<span> n <span class="op">=</span> <span class="fl">50</span>, cores <span class="op">=</span> <span class="fl">15</span><span class="op">)</span></span></code></pre></div> -<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/par.html" class="external-link">par</a></span><span class="op">(</span>mar <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">6.1</span>, <span class="fl">4.1</span>, <span class="fl">2.1</span>, <span class="fl">2.1</span><span class="op">)</span><span class="op">)</span></span> -<span><span class="fu"><a href="../../reference/parplot.html">parplot</a></span><span class="op">(</span><span class="va">f_saem_dfop_tc_no_ranef_k2_multi</span>, ylim <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.5</span>, <span class="fl">2</span><span class="op">)</span>, las <span class="op">=</span> <span class="fl">2</span>,</span> -<span> lpos <span class="op">=</span> <span class="st">"bottomright"</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_parent_files/figure-html/multistart-reduced-par-1.png" alt="Scaled parameters from the multistart runs, reduced model" width="960"><p class="caption"> -Scaled parameters from the multistart runs, reduced model -</p> -</div> -<p>When only the parameters of the top 25% of the fits are shown (based -on a feature introduced in mkin 1.2.2 currently under development), the -scatter is even less as shown below.</p> -<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/par.html" class="external-link">par</a></span><span class="op">(</span>mar <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">6.1</span>, <span class="fl">4.1</span>, <span class="fl">2.1</span>, <span class="fl">2.1</span><span class="op">)</span><span class="op">)</span></span> -<span><span class="fu"><a href="../../reference/parplot.html">parplot</a></span><span class="op">(</span><span class="va">f_saem_dfop_tc_no_ranef_k2_multi</span>, ylim <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.5</span>, <span class="fl">2</span><span class="op">)</span>, las <span class="op">=</span> <span class="fl">2</span>, llquant <span class="op">=</span> <span class="fl">0.25</span>,</span> -<span> lpos <span class="op">=</span> <span class="st">"bottomright"</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_parent_files/figure-html/multistart-reduced-par-llquant-1.png" alt="Scaled parameters from the multistart runs, reduced model, fits with the top 25\% likelihood values" width="960"><p class="caption"> -Scaled parameters from the multistart runs, reduced model, fits with the -top 25% likelihood values -</p> -</div> -</div> -</div> -<div class="section level2"> -<h2 id="conclusions">Conclusions<a class="anchor" aria-label="anchor" href="#conclusions"></a> -</h2> -<p>Fitting the four parent degradation models SFO, FOMC, DFOP and HS as -part of hierarchical model fits with two different error models and -normal distributions of the transformed degradation parameters works -without technical problems. The biphasic models DFOP and HS gave the -best fit to the data, but the default parameter distribution model was -not fully identifiable. Removing the random effect for the second -kinetic rate constant of the DFOP model resulted in a reduced model that -was fully identifiable and showed the lowest values for the model -selection criteria AIC and BIC. The reliability of the identification of -all model parameters was confirmed using multiple starting values.</p> -</div> -<div class="section level2"> -<h2 id="acknowledgements">Acknowledgements<a class="anchor" aria-label="anchor" href="#acknowledgements"></a> -</h2> -<p>The helpful comments by Janina Wöltjen of the German Environment -Agency are gratefully acknowledged.</p> -</div> -<div class="section level2"> -<h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a> -</h2> -<div id="refs" class="references csl-bib-body hanging-indent"> -<div id="ref-duchesne_2021" class="csl-entry"> -Duchesne, Ronan, Anissa Guillemin, Olivier Gandrillon, and Fabien -Crauste. 2021. <span>“Practical Identifiability in the Frame of -Nonlinear Mixed Effects Models: The Example of the in Vitro -Erythropoiesis.”</span> <em>BMC Bioinformatics</em> 22 (478). <a href="https://doi.org/10.1186/s12859-021-04373-4" class="external-link">https://doi.org/10.1186/s12859-021-04373-4</a>. -</div> -</div> -</div> -<div class="section level2"> -<h2 id="appendix">Appendix<a class="anchor" aria-label="anchor" href="#appendix"></a> -</h2> -<div class="section level3"> -<h3 id="hierarchical-model-fit-listings">Hierarchical model fit listings<a class="anchor" aria-label="anchor" href="#hierarchical-model-fit-listings"></a> -</h3> -<caption> -Hierarchical mkin fit of the SFO model with error model const -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.2 -R version used for fitting: 4.2.2 -Date of fit: Sat Jan 28 11:22:44 2023 -Date of summary: Sat Jan 28 11:23:57 2023 - -Equations: -d_DMTA/dt = - k_DMTA * DMTA - -Data: -155 observations of 1 variable(s) grouped in 6 datasets - -Model predictions using solution type analytical - -Fitted in 0.982 s -Using 300, 100 iterations and 9 chains - -Variance model: Constant variance - -Starting values for degradation parameters: - DMTA_0 k_DMTA -97.2953 0.0566 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - DMTA_0 k_DMTA -DMTA_0 97.3 0 -k_DMTA 0.0 1 - -Starting values for error model parameters: -a.1 - 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 796.3 795.3 -393.2 - -Optimised parameters: - est. lower upper -DMTA_0 97.28130 95.71113 98.8515 -k_DMTA 0.05665 0.02909 0.0842 -a.1 2.66442 2.35579 2.9731 -SD.DMTA_0 1.54776 0.15447 2.9411 -SD.k_DMTA 0.60690 0.26248 0.9513 - -Correlation: - DMTA_0 -k_DMTA 0.0168 - -Random effects: - est. lower upper -SD.DMTA_0 1.5478 0.1545 2.9411 -SD.k_DMTA 0.6069 0.2625 0.9513 - -Variance model: - est. lower upper -a.1 2.664 2.356 2.973 - -Estimated disappearance times: - DT50 DT90 -DMTA 12.24 40.65 - -</code></pre> -<p></p> -<caption> -Hierarchical mkin fit of the SFO model with error model tc -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.2 -R version used for fitting: 4.2.2 -Date of fit: Sat Jan 28 11:22:46 2023 -Date of summary: Sat Jan 28 11:23:57 2023 - -Equations: -d_DMTA/dt = - k_DMTA * DMTA - -Data: -155 observations of 1 variable(s) grouped in 6 datasets - -Model predictions using solution type analytical - -Fitted in 2.39 s -Using 300, 100 iterations and 9 chains - -Variance model: Two-component variance function - -Starting values for degradation parameters: - DMTA_0 k_DMTA -96.99175 0.05603 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - DMTA_0 k_DMTA -DMTA_0 96.99 0 -k_DMTA 0.00 1 - -Starting values for error model parameters: -a.1 b.1 - 1 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 798.3 797.1 -393.2 - -Optimised parameters: - est. lower upper -DMTA_0 97.271822 95.703157 98.84049 -k_DMTA 0.056638 0.029110 0.08417 -a.1 2.660081 2.230398 3.08976 -b.1 0.001665 -0.006911 0.01024 -SD.DMTA_0 1.545520 0.145035 2.94601 -SD.k_DMTA 0.606422 0.262274 0.95057 - -Correlation: - DMTA_0 -k_DMTA 0.0169 - -Random effects: - est. lower upper -SD.DMTA_0 1.5455 0.1450 2.9460 -SD.k_DMTA 0.6064 0.2623 0.9506 - -Variance model: - est. lower upper -a.1 2.660081 2.230398 3.08976 -b.1 0.001665 -0.006911 0.01024 - -Estimated disappearance times: - DT50 DT90 -DMTA 12.24 40.65 - -</code></pre> -<p></p> -<caption> -Hierarchical mkin fit of the FOMC model with error model const -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.2 -R version used for fitting: 4.2.2 -Date of fit: Sat Jan 28 11:22:45 2023 -Date of summary: Sat Jan 28 11:23:57 2023 - -Equations: -d_DMTA/dt = - (alpha/beta) * 1/((time/beta) + 1) * DMTA - -Data: -155 observations of 1 variable(s) grouped in 6 datasets - -Model predictions using solution type analytical - -Fitted in 1.552 s -Using 300, 100 iterations and 9 chains - -Variance model: Constant variance - -Starting values for degradation parameters: - DMTA_0 alpha beta - 98.292 9.909 156.341 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - DMTA_0 alpha beta -DMTA_0 98.29 0 0 -alpha 0.00 1 0 -beta 0.00 0 1 - -Starting values for error model parameters: -a.1 - 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 734.2 732.7 -360.1 - -Optimised parameters: - est. lower upper -DMTA_0 98.3435 96.9033 99.784 -alpha 7.2007 2.5889 11.812 -beta 112.8746 34.8816 190.868 -a.1 2.0459 1.8054 2.286 -SD.DMTA_0 1.4795 0.2717 2.687 -SD.alpha 0.6396 0.1509 1.128 -SD.beta 0.6874 0.1587 1.216 - -Correlation: - DMTA_0 alpha -alpha -0.1125 -beta -0.1227 0.3632 - -Random effects: - est. lower upper -SD.DMTA_0 1.4795 0.2717 2.687 -SD.alpha 0.6396 0.1509 1.128 -SD.beta 0.6874 0.1587 1.216 - -Variance model: - est. lower upper -a.1 2.046 1.805 2.286 - -Estimated disappearance times: - DT50 DT90 DT50back -DMTA 11.41 42.53 12.8 - -</code></pre> -<p></p> -<caption> -Hierarchical mkin fit of the FOMC model with error model tc -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.2 -R version used for fitting: 4.2.2 -Date of fit: Sat Jan 28 11:22:46 2023 -Date of summary: Sat Jan 28 11:23:57 2023 - -Equations: -d_DMTA/dt = - (alpha/beta) * 1/((time/beta) + 1) * DMTA - -Data: -155 observations of 1 variable(s) grouped in 6 datasets - -Model predictions using solution type analytical - -Fitted in 2.764 s -Using 300, 100 iterations and 9 chains - -Variance model: Two-component variance function - -Starting values for degradation parameters: -DMTA_0 alpha beta -98.772 4.663 92.597 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - DMTA_0 alpha beta -DMTA_0 98.77 0 0 -alpha 0.00 1 0 -beta 0.00 0 1 - -Starting values for error model parameters: -a.1 b.1 - 1 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 720.4 718.8 -352.2 - -Optimised parameters: - est. lower upper -DMTA_0 98.99136 97.26011 100.72261 -alpha 5.86312 2.57485 9.15138 -beta 88.55571 29.20889 147.90254 -a.1 1.51063 1.24384 1.77741 -b.1 0.02824 0.02040 0.03609 -SD.DMTA_0 1.57436 -0.04867 3.19739 -SD.alpha 0.59871 0.17132 1.02611 -SD.beta 0.72994 0.22849 1.23139 - -Correlation: - DMTA_0 alpha -alpha -0.1363 -beta -0.1414 0.2542 - -Random effects: - est. lower upper -SD.DMTA_0 1.5744 -0.04867 3.197 -SD.alpha 0.5987 0.17132 1.026 -SD.beta 0.7299 0.22849 1.231 - -Variance model: - est. lower upper -a.1 1.51063 1.2438 1.77741 -b.1 0.02824 0.0204 0.03609 - -Estimated disappearance times: - DT50 DT90 DT50back -DMTA 11.11 42.6 12.82 - -</code></pre> -<p></p> -<caption> -Hierarchical mkin fit of the DFOP model with error model const -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.2 -R version used for fitting: 4.2.2 -Date of fit: Sat Jan 28 11:22:45 2023 -Date of summary: Sat Jan 28 11:23:57 2023 - -Equations: -d_DMTA/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * - time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) - * DMTA - -Data: -155 observations of 1 variable(s) grouped in 6 datasets - -Model predictions using solution type analytical - -Fitted in 1.649 s -Using 300, 100 iterations and 9 chains - -Variance model: Constant variance - -Starting values for degradation parameters: - DMTA_0 k1 k2 g -98.64383 0.09211 0.02999 0.76814 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - DMTA_0 k1 k2 g -DMTA_0 98.64 0 0 0 -k1 0.00 1 0 0 -k2 0.00 0 1 0 -g 0.00 0 0 1 - -Starting values for error model parameters: -a.1 - 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 711.8 710 -346.9 - -Optimised parameters: - est. lower upper -DMTA_0 98.092481 96.573898 99.61106 -k1 0.062499 0.030336 0.09466 -k2 0.009065 -0.005133 0.02326 -g 0.948967 0.862079 1.03586 -a.1 1.821671 1.604774 2.03857 -SD.DMTA_0 1.677785 0.472066 2.88350 -SD.k1 0.634962 0.270788 0.99914 -SD.k2 1.033498 -0.205994 2.27299 -SD.g 1.710046 0.428642 2.99145 - -Correlation: - DMTA_0 k1 k2 -k1 0.0246 -k2 0.0491 0.0953 -g -0.0552 -0.0889 -0.4795 - -Random effects: - est. lower upper -SD.DMTA_0 1.678 0.4721 2.8835 -SD.k1 0.635 0.2708 0.9991 -SD.k2 1.033 -0.2060 2.2730 -SD.g 1.710 0.4286 2.9914 - -Variance model: - est. lower upper -a.1 1.822 1.605 2.039 - -Estimated disappearance times: - DT50 DT90 DT50back DT50_k1 DT50_k2 -DMTA 11.79 42.8 12.88 11.09 76.46 - -</code></pre> -<p></p> -<caption> -Hierarchical mkin fit of the DFOP model with error model tc -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.2 -R version used for fitting: 4.2.2 -Date of fit: Sat Jan 28 11:22:46 2023 -Date of summary: Sat Jan 28 11:23:57 2023 - -Equations: -d_DMTA/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * - time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) - * DMTA - -Data: -155 observations of 1 variable(s) grouped in 6 datasets - -Model predictions using solution type analytical - -Fitted in 3.288 s -Using 300, 100 iterations and 9 chains - -Variance model: Two-component variance function - -Starting values for degradation parameters: - DMTA_0 k1 k2 g -98.759266 0.087034 0.009933 0.930827 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - DMTA_0 k1 k2 g -DMTA_0 98.76 0 0 0 -k1 0.00 1 0 0 -k2 0.00 0 1 0 -g 0.00 0 0 1 - -Starting values for error model parameters: -a.1 b.1 - 1 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 665.5 663.4 -322.8 - -Optimised parameters: - est. lower upper -DMTA_0 98.377019 96.447952 100.30609 -k1 0.064843 0.034607 0.09508 -k2 0.008895 0.006368 0.01142 -g 0.949696 0.903815 0.99558 -a.1 1.065241 0.865754 1.26473 -b.1 0.029340 0.022336 0.03634 -SD.DMTA_0 2.007754 0.387982 3.62753 -SD.k1 0.580473 0.250286 0.91066 -SD.k2 0.006105 -4.920337 4.93255 -SD.g 1.097149 0.412779 1.78152 - -Correlation: - DMTA_0 k1 k2 -k1 0.0235 -k2 0.0595 0.0424 -g -0.0470 -0.0278 -0.2731 - -Random effects: - est. lower upper -SD.DMTA_0 2.007754 0.3880 3.6275 -SD.k1 0.580473 0.2503 0.9107 -SD.k2 0.006105 -4.9203 4.9325 -SD.g 1.097149 0.4128 1.7815 - -Variance model: - est. lower upper -a.1 1.06524 0.86575 1.26473 -b.1 0.02934 0.02234 0.03634 - -Estimated disappearance times: - DT50 DT90 DT50back DT50_k1 DT50_k2 -DMTA 11.36 41.32 12.44 10.69 77.92 - -</code></pre> -<p></p> -<caption> -Hierarchical mkin fit of the HS model with error model const -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.2 -R version used for fitting: 4.2.2 -Date of fit: Sat Jan 28 11:22:45 2023 -Date of summary: Sat Jan 28 11:23:57 2023 - -Equations: -d_DMTA/dt = - ifelse(time <= tb, k1, k2) * DMTA - -Data: -155 observations of 1 variable(s) grouped in 6 datasets - -Model predictions using solution type analytical - -Fitted in 2.006 s -Using 300, 100 iterations and 9 chains - -Variance model: Constant variance - -Starting values for degradation parameters: - DMTA_0 k1 k2 tb -97.82176 0.06931 0.02997 11.13945 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - DMTA_0 k1 k2 tb -DMTA_0 97.82 0 0 0 -k1 0.00 1 0 0 -k2 0.00 0 1 0 -tb 0.00 0 0 1 - -Starting values for error model parameters: -a.1 - 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 714 712.1 -348 - -Optimised parameters: - est. lower upper -DMTA_0 98.16102 96.47747 99.84456 -k1 0.07876 0.05261 0.10491 -k2 0.02227 0.01706 0.02747 -tb 13.99089 -7.40049 35.38228 -a.1 1.82305 1.60700 2.03910 -SD.DMTA_0 1.88413 0.56204 3.20622 -SD.k1 0.34292 0.10482 0.58102 -SD.k2 0.19851 0.01718 0.37985 -SD.tb 1.68168 0.58064 2.78272 - -Correlation: - DMTA_0 k1 k2 -k1 0.0142 -k2 0.0001 -0.0025 -tb 0.0165 -0.1256 -0.0301 - -Random effects: - est. lower upper -SD.DMTA_0 1.8841 0.56204 3.2062 -SD.k1 0.3429 0.10482 0.5810 -SD.k2 0.1985 0.01718 0.3798 -SD.tb 1.6817 0.58064 2.7827 - -Variance model: - est. lower upper -a.1 1.823 1.607 2.039 - -Estimated disappearance times: - DT50 DT90 DT50back DT50_k1 DT50_k2 -DMTA 8.801 67.91 20.44 8.801 31.13 - -</code></pre> -<p></p> -<caption> -Hierarchical mkin fit of the HS model with error model tc -</caption> -<pre><code> -saemix version used for fitting: 3.2 -mkin version used for pre-fitting: 1.2.2 -R version used for fitting: 4.2.2 -Date of fit: Sat Jan 28 11:22:46 2023 -Date of summary: Sat Jan 28 11:23:57 2023 - -Equations: -d_DMTA/dt = - ifelse(time <= tb, k1, k2) * DMTA - -Data: -155 observations of 1 variable(s) grouped in 6 datasets - -Model predictions using solution type analytical - -Fitted in 3.267 s -Using 300, 100 iterations and 9 chains - -Variance model: Two-component variance function - -Starting values for degradation parameters: - DMTA_0 k1 k2 tb -98.45190 0.07525 0.02576 19.19375 - -Fixed degradation parameter values: -None - -Starting values for random effects (square root of initial entries in omega): - DMTA_0 k1 k2 tb -DMTA_0 98.45 0 0 0 -k1 0.00 1 0 0 -k2 0.00 0 1 0 -tb 0.00 0 0 1 - -Starting values for error model parameters: -a.1 b.1 - 1 1 - -Results: - -Likelihood computed by importance sampling - AIC BIC logLik - 667.1 665 -323.6 - -Optimised parameters: - est. lower upper -DMTA_0 97.76570 95.81350 99.71791 -k1 0.05855 0.03080 0.08630 -k2 0.02337 0.01664 0.03010 -tb 31.09638 29.38289 32.80987 -a.1 1.08835 0.88590 1.29080 -b.1 0.02964 0.02257 0.03671 -SD.DMTA_0 2.04877 0.42607 3.67147 -SD.k1 0.59166 0.25621 0.92711 -SD.k2 0.30698 0.09561 0.51835 -SD.tb 0.01274 -0.10914 0.13462 - -Correlation: - DMTA_0 k1 k2 -k1 0.0160 -k2 -0.0070 -0.0024 -tb -0.0668 -0.0103 -0.2013 - -Random effects: - est. lower upper -SD.DMTA_0 2.04877 0.42607 3.6715 -SD.k1 0.59166 0.25621 0.9271 -SD.k2 0.30698 0.09561 0.5183 -SD.tb 0.01274 -0.10914 0.1346 - -Variance model: - est. lower upper -a.1 1.08835 0.88590 1.29080 -b.1 0.02964 0.02257 0.03671 - -Estimated disappearance times: - DT50 DT90 DT50back DT50_k1 DT50_k2 -DMTA 11.84 51.71 15.57 11.84 29.66 - -</code></pre> -<p></p> -</div> -<div class="section level3"> -<h3 id="hierarchical-model-convergence-plots">Hierarchical model convergence plots<a class="anchor" aria-label="anchor" href="#hierarchical-model-convergence-plots"></a> -</h3> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_parent_files/figure-html/convergence-saem-sfo-const-1.png" alt="Convergence plot for the NLHM SFO fit with constant variance" width="864"><p class="caption"> -Convergence plot for the NLHM SFO fit with constant variance -</p> -</div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_parent_files/figure-html/convergence-saem-sfo-tc-1.png" alt="Convergence plot for the NLHM SFO fit with two-component error" width="864"><p class="caption"> -Convergence plot for the NLHM SFO fit with two-component error -</p> -</div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_parent_files/figure-html/convergence-saem-fomc-const-1.png" alt="Convergence plot for the NLHM FOMC fit with constant variance" width="864"><p class="caption"> -Convergence plot for the NLHM FOMC fit with constant variance -</p> -</div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_parent_files/figure-html/convergence-saem-fomc-tc-1.png" alt="Convergence plot for the NLHM FOMC fit with two-component error" width="864"><p class="caption"> -Convergence plot for the NLHM FOMC fit with two-component error -</p> -</div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_parent_files/figure-html/convergence-saem-dfop-const-1.png" alt="Convergence plot for the NLHM DFOP fit with constant variance" width="864"><p class="caption"> -Convergence plot for the NLHM DFOP fit with constant variance -</p> -</div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_parent_files/figure-html/convergence-saem-dfop-tc-1.png" alt="Convergence plot for the NLHM DFOP fit with two-component error" width="864"><p class="caption"> -Convergence plot for the NLHM DFOP fit with two-component error -</p> -</div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_parent_files/figure-html/convergence-saem-hs-const-1.png" alt="Convergence plot for the NLHM HS fit with constant variance" width="864"><p class="caption"> -Convergence plot for the NLHM HS fit with constant variance -</p> -</div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_parent_files/figure-html/convergence-saem-hs-tc-1.png" alt="Convergence plot for the NLHM HS fit with two-component error" width="864"><p class="caption"> -Convergence plot for the NLHM HS fit with two-component error -</p> -</div> -</div> -<div class="section level3"> -<h3 id="session-info">Session info<a class="anchor" aria-label="anchor" href="#session-info"></a> -</h3> -<pre><code>R version 4.2.2 Patched (2022-11-10 r83330) -Platform: x86_64-pc-linux-gnu (64-bit) -Running under: Debian GNU/Linux bookworm/sid - -Matrix products: default -BLAS: /usr/lib/x86_64-linux-gnu/openblas-serial/libblas.so.3 -LAPACK: /usr/lib/x86_64-linux-gnu/openblas-serial/libopenblas-r0.3.21.so - -locale: - [1] LC_CTYPE=de_DE.UTF-8 LC_NUMERIC=C - [3] LC_TIME=de_DE.UTF-8 LC_COLLATE=de_DE.UTF-8 - [5] LC_MONETARY=de_DE.UTF-8 LC_MESSAGES=de_DE.UTF-8 - [7] LC_PAPER=de_DE.UTF-8 LC_NAME=C - [9] LC_ADDRESS=C LC_TELEPHONE=C -[11] LC_MEASUREMENT=de_DE.UTF-8 LC_IDENTIFICATION=C - -attached base packages: -[1] parallel stats graphics grDevices utils datasets methods -[8] base - -other attached packages: -[1] saemix_3.2 npde_3.3 knitr_1.41 mkin_1.2.2 - -loaded via a namespace (and not attached): - [1] deSolve_1.34 zoo_1.8-11 tidyselect_1.2.0 xfun_0.35 - [5] bslib_0.4.2 purrr_1.0.0 lattice_0.20-45 colorspace_2.0-3 - [9] vctrs_0.5.1 generics_0.1.3 htmltools_0.5.4 yaml_2.3.6 -[13] utf8_1.2.2 rlang_1.0.6 pkgdown_2.0.7 jquerylib_0.1.4 -[17] pillar_1.8.1 glue_1.6.2 DBI_1.1.3 lifecycle_1.0.3 -[21] stringr_1.5.0 munsell_0.5.0 gtable_0.3.1 ragg_1.2.4 -[25] codetools_0.2-18 memoise_2.0.1 evaluate_0.19 fastmap_1.1.0 -[29] lmtest_0.9-40 fansi_1.0.3 highr_0.9 scales_1.2.1 -[33] cachem_1.0.6 desc_1.4.2 jsonlite_1.8.4 systemfonts_1.0.4 -[37] fs_1.5.2 textshaping_0.3.6 gridExtra_2.3 ggplot2_3.4.0 -[41] digest_0.6.31 stringi_1.7.8 dplyr_1.0.10 grid_4.2.2 -[45] rprojroot_2.0.3 cli_3.5.0 tools_4.2.2 magrittr_2.0.3 -[49] sass_0.4.4 tibble_3.1.8 pkgconfig_2.0.3 assertthat_0.2.1 -[53] rmarkdown_2.19 R6_2.5.1 mclust_6.0.0 nlme_3.1-161 -[57] compiler_4.2.2 </code></pre> -</div> -<div class="section level3"> -<h3 id="hardware-info">Hardware info<a class="anchor" aria-label="anchor" href="#hardware-info"></a> -</h3> -<pre><code>CPU model: AMD Ryzen 9 7950X 16-Core Processor</code></pre> -<pre><code>MemTotal: 64940452 kB</code></pre> -</div> -</div> - </div> - - <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar"> - - <nav id="toc" data-toggle="toc"><h2 data-toc-skip>Contents</h2> - </nav> -</div> - -</div> - - - - <footer><div class="copyright"> - <p></p> -<p>Developed by Johannes Ranke.</p> -</div> - -<div class="pkgdown"> - <p></p> -<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p> -</div> - - </footer> -</div> - - - - - - - </body> -</html> diff --git a/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-dfop-const-1.png b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-dfop-const-1.png Binary files differdeleted file mode 100644 index 3f145074..00000000 --- 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fa-lg"></span> - - </a> -</li> - </ul> -</div> -<!--/.nav-collapse --> - </div> -<!--/.container --> -</div> -<!--/.navbar --> - - - - </header><div class="row"> - <div class="col-md-9 contents"> - <div class="page-header toc-ignore"> - <h1 data-toc-skip>Testing hierarchical pathway kinetics with -residue data on dimethenamid and dimethenamid-P</h1> - <h4 data-toc-skip class="author">Johannes -Ranke</h4> - - <h4 data-toc-skip class="date">Last change on 20 April 2023, -last compiled on 20 April 2023</h4> - - <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/prebuilt/2022_dmta_pathway.rmd" class="external-link"><code>vignettes/prebuilt/2022_dmta_pathway.rmd</code></a></small> - <div class="hidden name"><code>2022_dmta_pathway.rmd</code></div> - - </div> - - - -<div class="section level2"> -<h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#introduction"></a> -</h2> -<p>The purpose of this document is to test demonstrate how nonlinear -hierarchical models (NLHM) based on the parent degradation models SFO, -FOMC, DFOP and HS, with parallel formation of two or more metabolites -can be fitted with the mkin package.</p> -<p>It was assembled in the course of work package 1.2 of Project Number -173340 (Application of nonlinear hierarchical models to the kinetic -evaluation of chemical degradation data) of the German Environment -Agency carried out in 2022 and 2023.</p> -<p>The mkin package is used in version 1.2.4, which is currently under -development. It contains the test data, and the functions used in the -evaluations. The <code>saemix</code> package is used as a backend for -fitting the NLHM, but is also loaded to make the convergence plot -function available.</p> -<p>This document is processed with the <code>knitr</code> package, which -also provides the <code>kable</code> function that is used to improve -the display of tabular data in R markdown documents. For parallel -processing, the <code>parallel</code> package is used.</p> -<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://pkgdown.jrwb.de/mkin/">mkin</a></span><span class="op">)</span></span> -<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://yihui.org/knitr/" class="external-link">knitr</a></span><span class="op">)</span></span> -<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">saemix</span><span class="op">)</span></span> -<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">parallel</span><span class="op">)</span></span> -<span><span class="va">n_cores</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/detectCores.html" class="external-link">detectCores</a></span><span class="op">(</span><span class="op">)</span></span> -<span></span> -<span><span class="co"># We need to start a new cluster after defining a compiled model that is</span></span> -<span><span class="co"># saved as a DLL to the user directory, therefore we define a function</span></span> -<span><span class="co"># This is used again after defining the pathway model</span></span> -<span><span class="va">start_cluster</span> <span class="op"><-</span> <span class="kw">function</span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span> <span class="op">{</span></span> -<span> <span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/Sys.info.html" class="external-link">Sys.info</a></span><span class="op">(</span><span class="op">)</span><span class="op">[</span><span class="st">"sysname"</span><span class="op">]</span> <span class="op">==</span> <span class="st">"Windows"</span><span class="op">)</span> <span class="op">{</span></span> -<span> <span class="va">ret</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makePSOCKcluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> -<span> <span class="op">}</span> <span class="kw">else</span> <span class="op">{</span></span> -<span> <span class="va">ret</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makeForkCluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> -<span> <span class="op">}</span></span> -<span> <span class="kw"><a href="https://rdrr.io/r/base/function.html" class="external-link">return</a></span><span class="op">(</span><span class="va">ret</span><span class="op">)</span></span> -<span><span class="op">}</span></span></code></pre></div> -</div> -<div class="section level2"> -<h2 id="data">Data<a class="anchor" aria-label="anchor" href="#data"></a> -</h2> -<p>The test data are available in the mkin package as an object of class -<code>mkindsg</code> (mkin dataset group) under the identifier -<code>dimethenamid_2018</code>. The following preprocessing steps are -done in this document.</p> -<ul> -<li>The data available for the enantiomer dimethenamid-P (DMTAP) are -renamed to have the same substance name as the data for the racemic -mixture dimethenamid (DMTA). The reason for this is that no difference -between their degradation behaviour was identified in the EU risk -assessment.</li> -<li>Unnecessary columns are discarded</li> -<li>The observation times of each dataset are multiplied with the -corresponding normalisation factor also available in the dataset, in -order to make it possible to describe all datasets with a single set of -parameters that are independent of temperature</li> -<li>Finally, datasets observed in the same soil (<code>Elliot 1</code> -and <code>Elliot 2</code>) are combined, resulting in dimethenamid -(DMTA) data from six soils.</li> -</ul> -<p>The following commented R code performs this preprocessing.</p> -<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="co"># Apply a function to each of the seven datasets in the mkindsg object to create a list</span></span> -<span><span class="va">dmta_ds</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">lapply</a></span><span class="op">(</span><span class="fl">1</span><span class="op">:</span><span class="fl">7</span>, <span class="kw">function</span><span class="op">(</span><span class="va">i</span><span class="op">)</span> <span class="op">{</span></span> -<span> <span class="va">ds_i</span> <span class="op"><-</span> <span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">ds</span><span class="op">[[</span><span class="va">i</span><span class="op">]</span><span class="op">]</span><span class="op">$</span><span class="va">data</span> <span class="co"># Get a dataset</span></span> -<span> <span class="va">ds_i</span><span class="op">[</span><span class="va">ds_i</span><span class="op">$</span><span class="va">name</span> <span class="op">==</span> <span class="st">"DMTAP"</span>, <span class="st">"name"</span><span class="op">]</span> <span class="op"><-</span> <span class="st">"DMTA"</span> <span class="co"># Rename DMTAP to DMTA</span></span> -<span> <span class="va">ds_i</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/subset.html" class="external-link">subset</a></span><span class="op">(</span><span class="va">ds_i</span>, select <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"name"</span>, <span class="st">"time"</span>, <span class="st">"value"</span><span class="op">)</span><span class="op">)</span> <span class="co"># Select data</span></span> -<span> <span class="va">ds_i</span><span class="op">$</span><span class="va">time</span> <span class="op"><-</span> <span class="va">ds_i</span><span class="op">$</span><span class="va">time</span> <span class="op">*</span> <span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">f_time_norm</span><span class="op">[</span><span class="va">i</span><span class="op">]</span> <span class="co"># Normalise time</span></span> -<span> <span class="va">ds_i</span> <span class="co"># Return the dataset</span></span> -<span><span class="op">}</span><span class="op">)</span></span> -<span></span> -<span><span class="co"># Use dataset titles as names for the list elements</span></span> -<span><span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">)</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</span><span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">ds</span>, <span class="kw">function</span><span class="op">(</span><span class="va">ds</span><span class="op">)</span> <span class="va">ds</span><span class="op">$</span><span class="va">title</span><span class="op">)</span></span> -<span></span> -<span><span class="co"># Combine data for Elliot soil to obtain a named list with six elements</span></span> -<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/cbind.html" class="external-link">rbind</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 1"</span><span class="op">]</span><span class="op">]</span>, <span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 2"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span> <span class="co">#</span></span> -<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 1"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="cn">NULL</span></span> -<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 2"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="cn">NULL</span></span></code></pre></div> -<p>The following tables show the 6 datasets.</p> -<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="kw">for</span> <span class="op">(</span><span class="va">ds_name</span> <span class="kw">in</span> <span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">)</span><span class="op">)</span> <span class="op">{</span></span> -<span> <span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span></span> -<span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="fu"><a href="../../reference/mkin_long_to_wide.html">mkin_long_to_wide</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">[[</span><span class="va">ds_name</span><span class="op">]</span><span class="op">]</span><span class="op">)</span>,</span> -<span> caption <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste</a></span><span class="op">(</span><span class="st">"Dataset"</span>, <span class="va">ds_name</span><span class="op">)</span>,</span> -<span> booktabs <span class="op">=</span> <span class="cn">TRUE</span>, row.names <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">)</span></span> -<span> <span class="fu"><a href="https://rdrr.io/r/base/cat.html" class="external-link">cat</a></span><span class="op">(</span><span class="st">"\n\\clearpage\n"</span><span class="op">)</span></span> -<span><span class="op">}</span></span></code></pre></div> -<table class="table"> -<caption>Dataset Calke</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">DMTA</th> -<th align="right">M23</th> -<th align="right">M27</th> -<th align="right">M31</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0</td> -<td align="right">95.8</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">0</td> -<td align="right">98.7</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">14</td> -<td align="right">60.5</td> -<td align="right">4.1</td> -<td align="right">1.5</td> -<td align="right">2.0</td> -</tr> -<tr class="even"> -<td align="right">30</td> -<td align="right">39.1</td> -<td align="right">5.3</td> -<td align="right">2.4</td> -<td align="right">2.1</td> -</tr> -<tr class="odd"> -<td align="right">59</td> -<td align="right">15.2</td> -<td align="right">6.0</td> -<td align="right">3.2</td> -<td align="right">2.2</td> -</tr> -<tr class="even"> -<td align="right">120</td> -<td align="right">4.8</td> -<td align="right">4.3</td> -<td align="right">3.8</td> -<td align="right">1.8</td> -</tr> -<tr class="odd"> -<td align="right">120</td> -<td align="right">4.6</td> -<td align="right">4.1</td> -<td align="right">3.7</td> -<td align="right">2.1</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset Borstel</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">DMTA</th> -<th align="right">M23</th> -<th align="right">M27</th> -<th align="right">M31</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.000000</td> -<td align="right">100.5</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">0.000000</td> -<td align="right">99.6</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">1.941295</td> -<td align="right">91.9</td> -<td align="right">0.4</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">1.941295</td> -<td align="right">91.3</td> -<td align="right">0.5</td> -<td align="right">0.3</td> -<td align="right">0.1</td> -</tr> -<tr class="odd"> -<td align="right">6.794534</td> -<td align="right">81.8</td> -<td align="right">1.2</td> -<td align="right">0.8</td> -<td align="right">1.0</td> -</tr> -<tr class="even"> -<td align="right">6.794534</td> -<td align="right">82.1</td> -<td align="right">1.3</td> -<td align="right">0.9</td> -<td align="right">0.9</td> -</tr> -<tr class="odd"> -<td align="right">13.589067</td> -<td align="right">69.1</td> -<td align="right">2.8</td> -<td align="right">1.4</td> -<td align="right">2.0</td> -</tr> -<tr class="even"> -<td align="right">13.589067</td> -<td align="right">68.0</td> -<td align="right">2.0</td> -<td align="right">1.4</td> -<td align="right">2.5</td> -</tr> -<tr class="odd"> -<td align="right">27.178135</td> -<td align="right">51.4</td> -<td align="right">2.9</td> -<td align="right">2.7</td> -<td align="right">4.3</td> -</tr> -<tr class="even"> -<td align="right">27.178135</td> -<td align="right">51.4</td> -<td align="right">4.9</td> -<td align="right">2.6</td> -<td align="right">3.2</td> -</tr> -<tr class="odd"> -<td align="right">56.297565</td> -<td align="right">27.6</td> -<td align="right">12.2</td> -<td align="right">4.4</td> -<td align="right">4.3</td> -</tr> -<tr class="even"> -<td align="right">56.297565</td> -<td align="right">26.8</td> -<td align="right">12.2</td> -<td align="right">4.7</td> -<td align="right">4.8</td> -</tr> -<tr class="odd"> -<td align="right">86.387643</td> -<td align="right">15.7</td> -<td align="right">12.2</td> -<td align="right">5.4</td> -<td align="right">5.0</td> -</tr> -<tr class="even"> -<td align="right">86.387643</td> -<td align="right">15.3</td> -<td align="right">12.0</td> -<td align="right">5.2</td> -<td align="right">5.1</td> -</tr> -<tr class="odd"> -<td align="right">115.507073</td> -<td align="right">7.9</td> -<td align="right">10.4</td> -<td align="right">5.4</td> -<td align="right">4.3</td> -</tr> -<tr class="even"> -<td align="right">115.507073</td> -<td align="right">8.1</td> -<td align="right">11.6</td> -<td align="right">5.4</td> -<td align="right">4.4</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset Flaach</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">DMTA</th> -<th align="right">M23</th> -<th align="right">M27</th> -<th align="right">M31</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.0000000</td> -<td align="right">96.5</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">0.0000000</td> -<td align="right">96.8</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">0.0000000</td> -<td align="right">97.0</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">0.6233856</td> -<td align="right">82.9</td> -<td align="right">0.7</td> -<td align="right">1.1</td> -<td align="right">0.3</td> -</tr> -<tr class="odd"> -<td align="right">0.6233856</td> -<td align="right">86.7</td> -<td align="right">0.7</td> -<td align="right">1.1</td> -<td align="right">0.3</td> -</tr> -<tr class="even"> -<td align="right">0.6233856</td> -<td align="right">87.4</td> -<td align="right">0.2</td> -<td align="right">0.3</td> -<td align="right">0.1</td> -</tr> -<tr class="odd"> -<td align="right">1.8701567</td> -<td align="right">72.8</td> -<td align="right">2.2</td> -<td align="right">2.6</td> -<td align="right">0.7</td> -</tr> -<tr class="even"> -<td align="right">1.8701567</td> -<td align="right">69.9</td> -<td align="right">1.8</td> -<td align="right">2.4</td> -<td align="right">0.6</td> -</tr> -<tr class="odd"> -<td align="right">1.8701567</td> -<td align="right">71.9</td> -<td align="right">1.6</td> -<td align="right">2.3</td> -<td align="right">0.7</td> -</tr> -<tr class="even"> -<td align="right">4.3636989</td> -<td align="right">51.4</td> -<td align="right">4.1</td> -<td align="right">5.0</td> -<td align="right">1.3</td> -</tr> -<tr class="odd"> -<td align="right">4.3636989</td> -<td align="right">52.9</td> -<td align="right">4.2</td> -<td align="right">5.9</td> -<td align="right">1.2</td> -</tr> -<tr class="even"> -<td align="right">4.3636989</td> -<td align="right">48.6</td> -<td align="right">4.2</td> -<td align="right">4.8</td> -<td align="right">1.4</td> -</tr> -<tr class="odd"> -<td align="right">8.7273979</td> -<td align="right">28.5</td> -<td align="right">7.5</td> -<td align="right">8.5</td> -<td align="right">2.4</td> -</tr> -<tr class="even"> -<td align="right">8.7273979</td> -<td align="right">27.3</td> -<td align="right">7.1</td> -<td align="right">8.5</td> -<td align="right">2.1</td> -</tr> -<tr class="odd"> -<td align="right">8.7273979</td> -<td align="right">27.5</td> -<td align="right">7.5</td> -<td align="right">8.3</td> -<td align="right">2.3</td> -</tr> -<tr class="even"> -<td align="right">13.0910968</td> -<td align="right">14.8</td> -<td align="right">8.4</td> -<td align="right">9.3</td> -<td align="right">3.3</td> -</tr> -<tr class="odd"> -<td align="right">13.0910968</td> -<td align="right">13.4</td> -<td align="right">6.8</td> -<td align="right">8.7</td> -<td align="right">2.4</td> -</tr> -<tr class="even"> -<td align="right">13.0910968</td> -<td align="right">14.4</td> -<td align="right">8.0</td> -<td align="right">9.1</td> -<td align="right">2.6</td> -</tr> -<tr class="odd"> -<td align="right">17.4547957</td> -<td align="right">7.7</td> -<td align="right">7.2</td> -<td align="right">8.6</td> -<td align="right">4.0</td> -</tr> -<tr class="even"> -<td align="right">17.4547957</td> -<td align="right">7.3</td> -<td align="right">7.2</td> -<td align="right">8.5</td> -<td align="right">3.6</td> -</tr> -<tr class="odd"> -<td align="right">17.4547957</td> -<td align="right">8.1</td> -<td align="right">6.9</td> -<td align="right">8.9</td> -<td align="right">3.3</td> -</tr> -<tr class="even"> -<td align="right">26.1821936</td> -<td align="right">2.0</td> -<td align="right">4.9</td> -<td align="right">8.1</td> -<td align="right">2.1</td> -</tr> -<tr class="odd"> -<td align="right">26.1821936</td> -<td align="right">1.5</td> -<td align="right">4.3</td> -<td align="right">7.7</td> -<td align="right">1.7</td> -</tr> -<tr class="even"> -<td align="right">26.1821936</td> -<td align="right">1.9</td> -<td align="right">4.5</td> -<td align="right">7.4</td> -<td align="right">1.8</td> -</tr> -<tr class="odd"> -<td align="right">34.9095915</td> -<td align="right">1.3</td> -<td align="right">3.8</td> -<td align="right">5.9</td> -<td align="right">1.6</td> -</tr> -<tr class="even"> -<td align="right">34.9095915</td> -<td align="right">1.0</td> -<td align="right">3.1</td> -<td align="right">6.0</td> -<td align="right">1.6</td> -</tr> -<tr class="odd"> -<td align="right">34.9095915</td> -<td align="right">1.1</td> -<td align="right">3.1</td> -<td align="right">5.9</td> -<td align="right">1.4</td> -</tr> -<tr class="even"> -<td align="right">43.6369893</td> -<td align="right">0.9</td> -<td align="right">2.7</td> -<td align="right">5.6</td> -<td align="right">1.8</td> -</tr> -<tr class="odd"> -<td align="right">43.6369893</td> -<td align="right">0.7</td> -<td align="right">2.3</td> -<td align="right">5.2</td> -<td align="right">1.5</td> -</tr> -<tr class="even"> -<td align="right">43.6369893</td> -<td align="right">0.7</td> -<td align="right">2.1</td> -<td align="right">5.6</td> -<td align="right">1.3</td> -</tr> -<tr class="odd"> -<td align="right">52.3643872</td> -<td align="right">0.6</td> -<td align="right">1.6</td> -<td align="right">4.3</td> -<td align="right">1.2</td> -</tr> -<tr class="even"> -<td align="right">52.3643872</td> -<td align="right">0.4</td> -<td align="right">1.1</td> -<td align="right">3.7</td> -<td align="right">0.9</td> -</tr> -<tr class="odd"> -<td align="right">52.3643872</td> -<td align="right">0.5</td> -<td align="right">1.3</td> -<td align="right">3.9</td> -<td align="right">1.1</td> -</tr> -<tr class="even"> -<td align="right">74.8062674</td> -<td align="right">0.4</td> -<td align="right">0.4</td> -<td align="right">2.5</td> -<td align="right">0.5</td> -</tr> -<tr class="odd"> -<td align="right">74.8062674</td> -<td align="right">0.3</td> -<td align="right">0.4</td> -<td align="right">2.4</td> -<td align="right">0.5</td> -</tr> -<tr class="even"> -<td align="right">74.8062674</td> -<td align="right">0.3</td> -<td align="right">0.3</td> -<td align="right">2.2</td> -<td align="right">0.3</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset BBA 2.2</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">DMTA</th> -<th align="right">M23</th> -<th align="right">M27</th> -<th align="right">M31</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.0000000</td> -<td align="right">98.09</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">0.0000000</td> -<td align="right">98.77</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">0.7678922</td> -<td align="right">93.52</td> -<td align="right">0.36</td> -<td align="right">0.42</td> -<td align="right">0.36</td> -</tr> -<tr class="even"> -<td align="right">0.7678922</td> -<td align="right">92.03</td> -<td align="right">0.40</td> -<td align="right">0.47</td> -<td align="right">0.33</td> -</tr> -<tr class="odd"> -<td align="right">2.3036765</td> -<td align="right">88.39</td> -<td align="right">1.03</td> -<td align="right">0.71</td> -<td align="right">0.55</td> -</tr> -<tr class="even"> -<td align="right">2.3036765</td> -<td align="right">87.18</td> -<td align="right">1.07</td> -<td align="right">0.82</td> -<td align="right">0.64</td> -</tr> -<tr class="odd"> -<td align="right">5.3752452</td> -<td align="right">69.38</td> -<td align="right">3.60</td> -<td align="right">2.19</td> -<td align="right">1.94</td> -</tr> -<tr class="even"> -<td align="right">5.3752452</td> -<td align="right">71.06</td> -<td align="right">3.66</td> -<td align="right">2.28</td> -<td align="right">1.62</td> -</tr> -<tr class="odd"> -<td align="right">10.7504904</td> -<td align="right">45.21</td> -<td align="right">6.97</td> -<td align="right">5.45</td> -<td align="right">4.22</td> -</tr> -<tr class="even"> -<td align="right">10.7504904</td> -<td align="right">46.81</td> -<td align="right">7.22</td> -<td align="right">5.19</td> -<td align="right">4.37</td> -</tr> -<tr class="odd"> -<td align="right">16.1257355</td> -<td align="right">30.54</td> -<td align="right">8.65</td> -<td align="right">8.81</td> -<td align="right">6.31</td> -</tr> -<tr class="even"> -<td align="right">16.1257355</td> -<td align="right">30.07</td> -<td align="right">8.38</td> -<td align="right">7.93</td> -<td align="right">6.85</td> -</tr> -<tr class="odd"> -<td align="right">21.5009807</td> -<td align="right">21.60</td> -<td align="right">9.10</td> -<td align="right">10.25</td> -<td align="right">7.05</td> -</tr> -<tr class="even"> -<td align="right">21.5009807</td> -<td align="right">20.41</td> -<td align="right">8.63</td> -<td align="right">10.77</td> -<td align="right">6.84</td> -</tr> -<tr class="odd"> -<td align="right">32.2514711</td> -<td align="right">9.10</td> -<td align="right">7.63</td> -<td align="right">10.89</td> -<td align="right">6.53</td> -</tr> -<tr class="even"> -<td align="right">32.2514711</td> -<td align="right">9.70</td> -<td align="right">8.01</td> -<td align="right">10.85</td> -<td align="right">7.11</td> -</tr> -<tr class="odd"> -<td align="right">43.0019614</td> -<td align="right">6.58</td> -<td align="right">6.40</td> -<td align="right">10.41</td> -<td align="right">6.06</td> -</tr> -<tr class="even"> -<td align="right">43.0019614</td> -<td align="right">6.31</td> -<td align="right">6.35</td> -<td align="right">10.35</td> -<td align="right">6.05</td> -</tr> -<tr class="odd"> -<td align="right">53.7524518</td> -<td align="right">3.47</td> -<td align="right">5.35</td> -<td align="right">9.92</td> -<td align="right">5.50</td> -</tr> -<tr class="even"> -<td align="right">53.7524518</td> -<td align="right">3.52</td> -<td align="right">5.06</td> -<td align="right">9.42</td> -<td align="right">5.07</td> -</tr> -<tr class="odd"> -<td align="right">64.5029421</td> -<td align="right">3.40</td> -<td align="right">5.14</td> -<td align="right">9.15</td> -<td align="right">4.94</td> -</tr> -<tr class="even"> -<td align="right">64.5029421</td> -<td align="right">3.67</td> -<td align="right">5.91</td> -<td align="right">9.25</td> -<td align="right">4.39</td> -</tr> -<tr class="odd"> -<td align="right">91.3791680</td> -<td align="right">1.62</td> -<td align="right">3.35</td> -<td align="right">7.14</td> -<td align="right">3.64</td> -</tr> -<tr class="even"> -<td align="right">91.3791680</td> -<td align="right">1.62</td> -<td align="right">2.87</td> -<td align="right">7.13</td> -<td align="right">3.55</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset BBA 2.3</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">DMTA</th> -<th align="right">M23</th> -<th align="right">M27</th> -<th align="right">M31</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.0000000</td> -<td align="right">99.33</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">0.0000000</td> -<td align="right">97.44</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">0.6733938</td> -<td align="right">93.73</td> -<td align="right">0.18</td> -<td align="right">0.50</td> -<td align="right">0.47</td> -</tr> -<tr class="even"> -<td align="right">0.6733938</td> -<td align="right">93.77</td> -<td align="right">0.18</td> -<td align="right">0.83</td> -<td align="right">0.34</td> -</tr> -<tr class="odd"> -<td align="right">2.0201814</td> -<td align="right">87.84</td> -<td align="right">0.52</td> -<td align="right">1.25</td> -<td align="right">1.00</td> -</tr> -<tr class="even"> -<td align="right">2.0201814</td> -<td align="right">89.82</td> -<td align="right">0.43</td> -<td align="right">1.09</td> -<td align="right">0.89</td> -</tr> -<tr class="odd"> -<td align="right">4.7137565</td> -<td align="right">71.61</td> -<td align="right">1.19</td> -<td align="right">3.28</td> -<td align="right">3.58</td> -</tr> -<tr class="even"> -<td align="right">4.7137565</td> -<td align="right">71.42</td> -<td align="right">1.11</td> -<td align="right">3.24</td> -<td align="right">3.41</td> -</tr> -<tr class="odd"> -<td align="right">9.4275131</td> -<td align="right">45.60</td> -<td align="right">2.26</td> -<td align="right">7.17</td> -<td align="right">8.74</td> -</tr> -<tr class="even"> -<td align="right">9.4275131</td> -<td align="right">45.42</td> -<td align="right">1.99</td> -<td align="right">7.91</td> -<td align="right">8.28</td> -</tr> -<tr class="odd"> -<td align="right">14.1412696</td> -<td align="right">31.12</td> -<td align="right">2.81</td> -<td align="right">10.15</td> -<td align="right">9.67</td> -</tr> -<tr class="even"> -<td align="right">14.1412696</td> -<td align="right">31.68</td> -<td align="right">2.83</td> -<td align="right">9.55</td> -<td align="right">8.95</td> -</tr> -<tr class="odd"> -<td align="right">18.8550262</td> -<td align="right">23.20</td> -<td align="right">3.39</td> -<td align="right">12.09</td> -<td align="right">10.34</td> -</tr> -<tr class="even"> -<td align="right">18.8550262</td> -<td align="right">24.13</td> -<td align="right">3.56</td> -<td align="right">11.89</td> -<td align="right">10.00</td> -</tr> -<tr class="odd"> -<td align="right">28.2825393</td> -<td align="right">9.43</td> -<td align="right">3.49</td> -<td align="right">13.32</td> -<td align="right">7.89</td> -</tr> -<tr class="even"> -<td align="right">28.2825393</td> -<td align="right">9.82</td> -<td align="right">3.28</td> -<td align="right">12.05</td> -<td align="right">8.13</td> -</tr> -<tr class="odd"> -<td align="right">37.7100523</td> -<td align="right">7.08</td> -<td align="right">2.80</td> -<td align="right">10.04</td> -<td align="right">5.06</td> -</tr> -<tr class="even"> -<td align="right">37.7100523</td> -<td align="right">8.64</td> -<td align="right">2.97</td> -<td align="right">10.78</td> -<td align="right">5.54</td> -</tr> -<tr class="odd"> -<td align="right">47.1375654</td> -<td align="right">4.41</td> -<td align="right">2.42</td> -<td align="right">9.32</td> -<td align="right">3.79</td> -</tr> -<tr class="even"> -<td align="right">47.1375654</td> -<td align="right">4.78</td> -<td align="right">2.51</td> -<td align="right">9.62</td> -<td align="right">4.11</td> -</tr> -<tr class="odd"> -<td align="right">56.5650785</td> -<td align="right">4.92</td> -<td align="right">2.22</td> -<td align="right">8.00</td> -<td align="right">3.11</td> -</tr> -<tr class="even"> -<td align="right">56.5650785</td> -<td align="right">5.08</td> -<td align="right">1.95</td> -<td align="right">8.45</td> -<td align="right">2.98</td> -</tr> -<tr class="odd"> -<td align="right">80.1338612</td> -<td align="right">2.13</td> -<td align="right">1.28</td> -<td align="right">5.71</td> -<td align="right">1.78</td> -</tr> -<tr class="even"> -<td align="right">80.1338612</td> -<td align="right">2.23</td> -<td align="right">0.99</td> -<td align="right">3.33</td> -<td align="right">1.55</td> -</tr> -</tbody> -</table> -<table class="table"> -<caption>Dataset Elliot</caption> -<thead><tr class="header"> -<th align="right">time</th> -<th align="right">DMTA</th> -<th align="right">M23</th> -<th align="right">M27</th> -<th align="right">M31</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="right">0.000000</td> -<td align="right">97.5</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">0.000000</td> -<td align="right">100.7</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">1.228478</td> -<td align="right">86.4</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">1.228478</td> -<td align="right">88.5</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">1.5</td> -</tr> -<tr class="odd"> -<td align="right">3.685435</td> -<td align="right">69.8</td> -<td align="right">2.8</td> -<td align="right">2.3</td> -<td align="right">5.0</td> -</tr> -<tr class="even"> -<td align="right">3.685435</td> -<td align="right">77.1</td> -<td align="right">1.7</td> -<td align="right">2.1</td> -<td align="right">2.4</td> -</tr> -<tr class="odd"> -<td align="right">8.599349</td> -<td align="right">59.0</td> -<td align="right">4.3</td> -<td align="right">4.0</td> -<td align="right">4.3</td> -</tr> -<tr class="even"> -<td align="right">8.599349</td> -<td align="right">54.2</td> -<td align="right">5.8</td> -<td align="right">3.4</td> -<td align="right">5.0</td> -</tr> -<tr class="odd"> -<td align="right">17.198697</td> -<td align="right">31.3</td> -<td align="right">8.2</td> -<td align="right">6.6</td> -<td align="right">8.0</td> -</tr> -<tr class="even"> -<td align="right">17.198697</td> -<td align="right">33.5</td> -<td align="right">5.2</td> -<td align="right">6.9</td> -<td align="right">7.7</td> -</tr> -<tr class="odd"> -<td align="right">25.798046</td> -<td align="right">19.6</td> -<td align="right">5.1</td> -<td align="right">8.2</td> -<td align="right">7.8</td> -</tr> -<tr class="even"> -<td align="right">25.798046</td> -<td align="right">20.9</td> -<td align="right">6.1</td> -<td align="right">8.8</td> -<td align="right">6.5</td> -</tr> -<tr class="odd"> -<td align="right">34.397395</td> -<td align="right">13.3</td> -<td align="right">6.0</td> -<td align="right">9.7</td> -<td align="right">8.0</td> -</tr> -<tr class="even"> -<td align="right">34.397395</td> -<td align="right">15.8</td> -<td align="right">6.0</td> -<td align="right">8.8</td> -<td align="right">7.4</td> -</tr> -<tr class="odd"> -<td align="right">51.596092</td> -<td align="right">6.7</td> -<td align="right">5.0</td> -<td align="right">8.3</td> -<td align="right">6.9</td> -</tr> -<tr class="even"> -<td align="right">51.596092</td> -<td align="right">8.7</td> -<td align="right">4.2</td> -<td align="right">9.2</td> -<td align="right">9.0</td> -</tr> -<tr class="odd"> -<td align="right">68.794789</td> -<td align="right">8.8</td> -<td align="right">3.9</td> -<td align="right">9.3</td> -<td align="right">5.5</td> -</tr> -<tr class="even"> -<td align="right">68.794789</td> -<td align="right">8.7</td> -<td align="right">2.9</td> -<td align="right">8.5</td> -<td align="right">6.1</td> -</tr> -<tr class="odd"> -<td align="right">103.192184</td> -<td align="right">6.0</td> -<td align="right">1.9</td> -<td align="right">8.6</td> -<td align="right">6.1</td> -</tr> -<tr class="even"> -<td align="right">103.192184</td> -<td align="right">4.4</td> -<td align="right">1.5</td> -<td align="right">6.0</td> -<td align="right">4.0</td> -</tr> -<tr class="odd"> -<td align="right">146.188928</td> -<td align="right">3.3</td> -<td align="right">2.0</td> -<td align="right">5.6</td> -<td align="right">3.1</td> -</tr> -<tr class="even"> -<td align="right">146.188928</td> -<td align="right">2.8</td> -<td align="right">2.3</td> -<td align="right">4.5</td> -<td align="right">2.9</td> -</tr> -<tr class="odd"> -<td align="right">223.583066</td> -<td align="right">1.4</td> -<td align="right">1.2</td> -<td align="right">4.1</td> -<td align="right">1.8</td> -</tr> -<tr class="even"> -<td align="right">223.583066</td> -<td align="right">1.8</td> -<td align="right">1.9</td> -<td align="right">3.9</td> -<td align="right">2.6</td> -</tr> -<tr class="odd"> -<td align="right">0.000000</td> -<td align="right">93.4</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="even"> -<td align="right">0.000000</td> -<td align="right">103.2</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">1.228478</td> -<td align="right">89.2</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">1.3</td> -</tr> -<tr class="even"> -<td align="right">1.228478</td> -<td align="right">86.6</td> -<td align="right">NA</td> -<td align="right">NA</td> -<td align="right">NA</td> -</tr> -<tr class="odd"> -<td align="right">3.685435</td> -<td align="right">78.2</td> -<td align="right">2.6</td> -<td align="right">1.0</td> -<td align="right">3.1</td> -</tr> -<tr class="even"> -<td align="right">3.685435</td> -<td align="right">78.1</td> -<td align="right">2.4</td> -<td align="right">2.6</td> -<td align="right">2.3</td> -</tr> -<tr class="odd"> -<td align="right">8.599349</td> -<td align="right">55.6</td> -<td align="right">5.5</td> -<td align="right">4.5</td> -<td align="right">3.4</td> -</tr> -<tr class="even"> -<td align="right">8.599349</td> -<td align="right">53.0</td> -<td align="right">5.6</td> -<td align="right">4.6</td> -<td align="right">4.3</td> -</tr> -<tr class="odd"> -<td align="right">17.198697</td> -<td align="right">33.7</td> -<td align="right">7.3</td> -<td align="right">7.6</td> -<td align="right">7.8</td> -</tr> -<tr class="even"> -<td align="right">17.198697</td> -<td align="right">33.2</td> -<td align="right">6.5</td> -<td align="right">6.7</td> -<td align="right">8.7</td> -</tr> -<tr class="odd"> -<td align="right">25.798046</td> -<td align="right">20.9</td> -<td align="right">5.8</td> -<td align="right">8.7</td> -<td align="right">7.7</td> -</tr> -<tr class="even"> -<td align="right">25.798046</td> -<td align="right">19.9</td> -<td align="right">7.7</td> -<td align="right">7.6</td> -<td align="right">6.5</td> -</tr> -<tr class="odd"> -<td align="right">34.397395</td> -<td align="right">18.2</td> -<td align="right">7.8</td> -<td align="right">8.0</td> -<td align="right">6.3</td> -</tr> -<tr class="even"> -<td align="right">34.397395</td> -<td align="right">12.7</td> -<td align="right">7.3</td> -<td align="right">8.6</td> -<td align="right">8.7</td> -</tr> -<tr class="odd"> -<td align="right">51.596092</td> -<td align="right">7.8</td> -<td align="right">7.0</td> -<td align="right">7.4</td> -<td align="right">5.7</td> -</tr> -<tr class="even"> -<td align="right">51.596092</td> -<td align="right">9.0</td> -<td align="right">6.3</td> -<td align="right">7.2</td> -<td align="right">4.2</td> -</tr> -<tr class="odd"> -<td align="right">68.794789</td> -<td align="right">11.4</td> -<td align="right">4.3</td> -<td align="right">10.3</td> -<td align="right">3.2</td> -</tr> -<tr class="even"> -<td align="right">68.794789</td> -<td align="right">9.0</td> -<td align="right">3.8</td> -<td align="right">9.4</td> -<td align="right">4.2</td> -</tr> -<tr class="odd"> -<td align="right">103.192184</td> -<td align="right">3.9</td> -<td align="right">2.6</td> -<td align="right">6.5</td> -<td align="right">3.8</td> -</tr> -<tr class="even"> -<td align="right">103.192184</td> -<td align="right">4.4</td> -<td align="right">2.8</td> -<td align="right">6.9</td> -<td align="right">4.0</td> -</tr> -<tr class="odd"> -<td align="right">146.188928</td> -<td align="right">2.6</td> -<td align="right">1.6</td> -<td align="right">4.6</td> -<td align="right">4.5</td> -</tr> -<tr class="even"> -<td align="right">146.188928</td> -<td align="right">3.4</td> -<td align="right">1.1</td> -<td align="right">4.5</td> -<td align="right">4.5</td> -</tr> -<tr class="odd"> -<td align="right">223.583066</td> -<td align="right">2.0</td> -<td align="right">1.4</td> -<td align="right">4.3</td> -<td align="right">3.8</td> -</tr> -<tr class="even"> -<td align="right">223.583066</td> -<td align="right">1.7</td> -<td align="right">1.3</td> -<td align="right">4.2</td> -<td align="right">2.3</td> -</tr> -</tbody> -</table> -</div> -<div class="section level2"> -<h2 id="separate-evaluations">Separate evaluations<a class="anchor" aria-label="anchor" href="#separate-evaluations"></a> -</h2> -<p>As a first step to obtain suitable starting parameters for the NLHM -fits, we do separate fits of several variants of the pathway model used -previously <span class="citation">(Ranke et al. 2021)</span>, varying -the kinetic model for the parent compound. Because the SFORB model often -provides faster convergence than the DFOP model, and can sometimes be -fitted where the DFOP model results in errors, it is included in the set -of parent models tested here.</p> -<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="kw">if</span> <span class="op">(</span><span class="op">!</span><span class="fu"><a href="https://rdrr.io/r/base/files2.html" class="external-link">dir.exists</a></span><span class="op">(</span><span class="st">"dmta_dlls"</span><span class="op">)</span><span class="op">)</span> <span class="fu"><a href="https://rdrr.io/r/base/files2.html" class="external-link">dir.create</a></span><span class="op">(</span><span class="st">"dmta_dlls"</span><span class="op">)</span></span> -<span><span class="va">m_sfo_path_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> DMTA <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"M23"</span>, <span class="st">"M27"</span>, <span class="st">"M31"</span><span class="op">)</span><span class="op">)</span>,</span> -<span> M23 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> M27 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> M31 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M27"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> name <span class="op">=</span> <span class="st">"m_sfo_path"</span>, dll_dir <span class="op">=</span> <span class="st">"dmta_dlls"</span>,</span> -<span> unload <span class="op">=</span> <span class="cn">TRUE</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> quiet <span class="op">=</span> <span class="cn">TRUE</span></span> -<span><span class="op">)</span></span> -<span><span class="va">m_fomc_path_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> DMTA <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"FOMC"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"M23"</span>, <span class="st">"M27"</span>, <span class="st">"M31"</span><span class="op">)</span><span class="op">)</span>,</span> -<span> M23 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> M27 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> M31 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M27"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> name <span class="op">=</span> <span class="st">"m_fomc_path"</span>, dll_dir <span class="op">=</span> <span class="st">"dmta_dlls"</span>,</span> -<span> unload <span class="op">=</span> <span class="cn">TRUE</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> quiet <span class="op">=</span> <span class="cn">TRUE</span></span> -<span><span class="op">)</span></span> -<span><span class="va">m_dfop_path_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> DMTA <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"DFOP"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"M23"</span>, <span class="st">"M27"</span>, <span class="st">"M31"</span><span class="op">)</span><span class="op">)</span>,</span> -<span> M23 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> M27 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> M31 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M27"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> name <span class="op">=</span> <span class="st">"m_dfop_path"</span>, dll_dir <span class="op">=</span> <span class="st">"dmta_dlls"</span>,</span> -<span> unload <span class="op">=</span> <span class="cn">TRUE</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> quiet <span class="op">=</span> <span class="cn">TRUE</span></span> -<span><span class="op">)</span></span> -<span><span class="va">m_sforb_path_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> DMTA <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"M23"</span>, <span class="st">"M27"</span>, <span class="st">"M31"</span><span class="op">)</span><span class="op">)</span>,</span> -<span> M23 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> M27 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> M31 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M27"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> name <span class="op">=</span> <span class="st">"m_sforb_path"</span>, dll_dir <span class="op">=</span> <span class="st">"dmta_dlls"</span>,</span> -<span> unload <span class="op">=</span> <span class="cn">TRUE</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> quiet <span class="op">=</span> <span class="cn">TRUE</span></span> -<span><span class="op">)</span></span> -<span><span class="va">m_hs_path_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> DMTA <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"HS"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"M23"</span>, <span class="st">"M27"</span>, <span class="st">"M31"</span><span class="op">)</span><span class="op">)</span>,</span> -<span> M23 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> M27 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> M31 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M27"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> name <span class="op">=</span> <span class="st">"m_hs_path"</span>, dll_dir <span class="op">=</span> <span class="st">"dmta_dlls"</span>,</span> -<span> unload <span class="op">=</span> <span class="cn">TRUE</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> quiet <span class="op">=</span> <span class="cn">TRUE</span></span> -<span><span class="op">)</span></span> -<span><span class="va">cl</span> <span class="op"><-</span> <span class="fu">start_cluster</span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> -<span></span> -<span><span class="va">deg_mods_1</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span></span> -<span> sfo_path_1 <span class="op">=</span> <span class="va">m_sfo_path_1</span>,</span> -<span> fomc_path_1 <span class="op">=</span> <span class="va">m_fomc_path_1</span>,</span> -<span> dfop_path_1 <span class="op">=</span> <span class="va">m_dfop_path_1</span>,</span> -<span> sforb_path_1 <span class="op">=</span> <span class="va">m_sforb_path_1</span>,</span> -<span> hs_path_1 <span class="op">=</span> <span class="va">m_hs_path_1</span><span class="op">)</span></span> -<span></span> -<span><span class="va">sep_1_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span></span> -<span> <span class="va">deg_mods_1</span>,</span> -<span> <span class="va">dmta_ds</span>,</span> -<span> error_model <span class="op">=</span> <span class="st">"const"</span>,</span> -<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<span></span> -<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">sep_1_const</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">Calke</th> -<th align="left">Borstel</th> -<th align="left">Flaach</th> -<th align="left">BBA 2.2</th> -<th align="left">BBA 2.3</th> -<th align="left">Elliot</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">sfo_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">fomc_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">dfop_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">sforb_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">hs_path_1</td> -<td align="left">C</td> -<td align="left">C</td> -<td align="left">C</td> -<td align="left">C</td> -<td align="left">C</td> -<td align="left">C</td> -</tr> -</tbody> -</table> -<p>All separate pathway fits with SFO or FOMC for the parent and -constant variance converged (status OK). Most fits with DFOP or SFORB -for the parent converged as well. The fits with HS for the parent did -not converge with default settings.</p> -<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">sep_1_tc</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">sep_1_const</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span> -<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">sep_1_tc</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">Calke</th> -<th align="left">Borstel</th> -<th align="left">Flaach</th> -<th align="left">BBA 2.2</th> -<th align="left">BBA 2.3</th> -<th align="left">Elliot</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">sfo_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">fomc_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">C</td> -</tr> -<tr class="odd"> -<td align="left">dfop_path_1</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">sforb_path_1</td> -<td align="left">OK</td> -<td align="left">C</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">hs_path_1</td> -<td align="left">C</td> -<td align="left">C</td> -<td align="left">C</td> -<td align="left">C</td> -<td align="left">C</td> -<td align="left">OK</td> -</tr> -</tbody> -</table> -<p>With the two-component error model, the set of fits with convergence -problems is slightly different, with convergence problems appearing for -different data sets when applying the DFOP and SFORB model and some -additional convergence problems when using the FOMC model for the -parent.</p> -</div> -<div class="section level2"> -<h2 id="hierarchichal-model-fits">Hierarchichal model fits<a class="anchor" aria-label="anchor" href="#hierarchichal-model-fits"></a> -</h2> -<p>The following code fits two sets of the corresponding hierarchical -models to the data, one assuming constant variance, and one assuming -two-component error.</p> -<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">saem_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mhmkin.html">mhmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">sep_1_const</span>, <span class="va">sep_1_tc</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> -<p>The run time for these fits was around two hours on five year old -hardware. After a recent hardware upgrade these fits complete in less -than twenty minutes.</p> -<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">const</th> -<th align="left">tc</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">sfo_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">fomc_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">dfop_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="even"> -<td align="left">sforb_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -<tr class="odd"> -<td align="left">hs_path_1</td> -<td align="left">OK</td> -<td align="left">OK</td> -</tr> -</tbody> -</table> -<p>According to the <code>status</code> function, all fits terminated -successfully.</p> -<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> -<pre><code>Warning in FUN(X[[i]], ...): Could not obtain log likelihood with 'is' method -for sforb_path_1 const</code></pre> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="right">npar</th> -<th align="right">AIC</th> -<th align="right">BIC</th> -<th align="right">Lik</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">sfo_path_1 const</td> -<td align="right">17</td> -<td align="right">2291.8</td> -<td align="right">2288.3</td> -<td align="right">-1128.9</td> -</tr> -<tr class="even"> -<td align="left">sfo_path_1 tc</td> -<td align="right">18</td> -<td align="right">2276.3</td> -<td align="right">2272.5</td> -<td align="right">-1120.1</td> -</tr> -<tr class="odd"> -<td align="left">fomc_path_1 const</td> -<td align="right">19</td> -<td align="right">2099.0</td> -<td align="right">2095.0</td> -<td align="right">-1030.5</td> -</tr> -<tr class="even"> -<td align="left">fomc_path_1 tc</td> -<td align="right">20</td> -<td align="right">1939.6</td> -<td align="right">1935.5</td> -<td align="right">-949.8</td> -</tr> -<tr class="odd"> -<td align="left">dfop_path_1 const</td> -<td align="right">21</td> -<td align="right">2038.8</td> -<td align="right">2034.4</td> -<td align="right">-998.4</td> -</tr> -<tr class="even"> -<td align="left">hs_path_1 const</td> -<td align="right">21</td> -<td align="right">2024.2</td> -<td align="right">2019.8</td> -<td align="right">-991.1</td> -</tr> -<tr class="odd"> -<td align="left">dfop_path_1 tc</td> -<td align="right">22</td> -<td align="right">1879.8</td> -<td align="right">1875.2</td> -<td align="right">-917.9</td> -</tr> -<tr class="even"> -<td align="left">sforb_path_1 tc</td> -<td align="right">22</td> -<td align="right">1832.9</td> -<td align="right">1828.3</td> -<td align="right">-894.4</td> -</tr> -<tr class="odd"> -<td align="left">hs_path_1 tc</td> -<td align="right">22</td> -<td align="right">1831.4</td> -<td align="right">1826.8</td> -<td align="right">-893.7</td> -</tr> -</tbody> -</table> -<p>When the goodness-of-fit of the models is compared, a warning is -obtained, indicating that the likelihood of the pathway fit with SFORB -for the parent compound and constant variance could not be calculated -with importance sampling (method ‘is’). As this is the default method on -which all AIC and BIC comparisons are based, this variant is not -included in the model comparison table. Comparing the goodness-of-fit of -the remaining models, HS model model with two-component error provides -the best fit. However, for batch experiments performed with constant -conditions such as the experiments evaluated here, there is no reason to -assume a discontinuity, so the SFORB model is preferable from a -mechanistic viewpoint. In addition, the information criteria AIC and BIC -are very similar for HS and SFORB. Therefore, the SFORB model is -selected here for further refinements.</p> -<div class="section level3"> -<h3 id="parameter-identifiability-based-on-the-fisher-information-matrix">Parameter identifiability based on the Fisher Information -Matrix<a class="anchor" aria-label="anchor" href="#parameter-identifiability-based-on-the-fisher-information-matrix"></a> -</h3> -<p>Using the <code>illparms</code> function, ill-defined statistical -model parameters such as standard deviations of the degradation -parameters in the population and error model parameters can be -found.</p> -<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="left">const</th> -<th align="left">tc</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">sfo_path_1</td> -<td align="left"></td> -<td align="left">sd(DMTA_0)</td> -</tr> -<tr class="even"> -<td align="left">fomc_path_1</td> -<td align="left"></td> -<td align="left">sd(DMTA_0)</td> -</tr> -<tr class="odd"> -<td align="left">dfop_path_1</td> -<td align="left"></td> -<td align="left"></td> -</tr> -<tr class="even"> -<td align="left">sforb_path_1</td> -<td align="left"></td> -<td align="left">sd(log_k_DMTA_bound_free)</td> -</tr> -<tr class="odd"> -<td align="left">hs_path_1</td> -<td align="left"></td> -<td align="left">sd(log_tb)</td> -</tr> -</tbody> -</table> -<p>When using constant variance, no ill-defined variance parameters are -identified with the <code>illparms</code> function in any of the -degradation models. When using the two-component error model, there is -one ill-defined variance parameter in all variants except for the -variant using DFOP for the parent compound.</p> -<p>For the selected combination of the SFORB pathway model with -two-component error, the random effect for the rate constant from -reversibly bound DMTA to the free DMTA (<code>k_DMTA_bound_free</code>) -is not well-defined. Therefore, the fit is updated without assuming a -random effect for this parameter.</p> -<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">saem_sforb_path_1_tc_reduced</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">[[</span><span class="st">"sforb_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span>,</span> -<span> no_random_effect <span class="op">=</span> <span class="st">"log_k_DMTA_bound_free"</span><span class="op">)</span></span> -<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">saem_sforb_path_1_tc_reduced</span><span class="op">)</span></span></code></pre></div> -<p>As expected, no ill-defined parameters remain. The model comparison -below shows that the reduced model is preferable.</p> -<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">[[</span><span class="st">"sforb_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span>, <span class="va">saem_sforb_path_1_tc_reduced</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="right">npar</th> -<th align="right">AIC</th> -<th align="right">BIC</th> -<th align="right">Lik</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">saem_sforb_path_1_tc_reduced</td> -<td align="right">21</td> -<td align="right">1830.3</td> -<td align="right">1825.9</td> -<td align="right">-894.2</td> -</tr> -<tr class="even"> -<td align="left">saem_1[[“sforb_path_1”, “tc”]]</td> -<td align="right">22</td> -<td align="right">1832.9</td> -<td align="right">1828.3</td> -<td align="right">-894.4</td> -</tr> -</tbody> -</table> -<p>The convergence plot of the refined fit is shown below.</p> -<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">saem_sforb_path_1_tc_reduced</span><span class="op">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></span></code></pre></div> -<p><img src="2022_dmta_pathway_files/figure-html/saem-sforb-path-1-tc-reduced-convergence-1.png" width="700" style="display: block; margin: auto;"></p> -<p>For some parameters, for example for <code>f_DMTA_ilr_1</code> and -<code>f_DMTA_ilr_2</code>, i.e. for two of the parameters determining -the formation fractions of the parallel formation of the three -metabolites, some movement of the parameters is still visible in the -second phase of the algorithm. However, the amplitude of this movement -is in the range of the amplitude towards the end of the first phase. -Therefore, it is likely that an increase in iterations would not improve -the parameter estimates very much, and it is proposed that the fit is -acceptable. No numeric convergence criterion is implemented in -saemix.</p> -</div> -<div class="section level3"> -<h3 id="alternative-check-of-parameter-identifiability">Alternative check of parameter identifiability<a class="anchor" aria-label="anchor" href="#alternative-check-of-parameter-identifiability"></a> -</h3> -<p>As an alternative check of parameter identifiability <span class="citation">(Duchesne et al. 2021)</span>, multistart runs were -performed on the basis of the refined fit shown above.</p> -<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">saem_sforb_path_1_tc_reduced_multi</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/multistart.html">multistart</a></span><span class="op">(</span><span class="va">saem_sforb_path_1_tc_reduced</span>,</span> -<span> n <span class="op">=</span> <span class="fl">32</span>, cores <span class="op">=</span> <span class="fl">10</span><span class="op">)</span></span></code></pre></div> -<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">saem_sforb_path_1_tc_reduced_multi</span><span class="op">)</span></span></code></pre></div> -<pre><code><multistart> object with 32 fits: - E OK -15 17 -OK: Fit terminated successfully -E: Error</code></pre> -<p>Out of the 32 fits that were initiated, only 17 terminated without an -error. The reason for this is that the wide variation of starting -parameters in combination with the parameter variation that is used in -the SAEM algorithm leads to parameter combinations for the degradation -model that the numerical integration routine cannot cope with. Because -of this variation of initial parameters, some of the model fits take up -to two times more time than the original fit.</p> -<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/par.html" class="external-link">par</a></span><span class="op">(</span>mar <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">12.1</span>, <span class="fl">4.1</span>, <span class="fl">2.1</span>, <span class="fl">2.1</span><span class="op">)</span><span class="op">)</span></span> -<span><span class="fu"><a href="../../reference/parplot.html">parplot</a></span><span class="op">(</span><span class="va">saem_sforb_path_1_tc_reduced_multi</span>, ylim <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.5</span>, <span class="fl">2</span><span class="op">)</span>, las <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_pathway_files/figure-html/unnamed-chunk-2-1.png" alt="Parameter boxplots for the multistart runs that succeeded" width="960"><p class="caption"> -Parameter boxplots for the multistart runs that succeeded -</p> -</div> -<p>However, visual analysis of the boxplot of the parameters obtained in -the successful fits confirms that the results are sufficiently -independent of the starting parameters, and there are no remaining -ill-defined parameters.</p> -</div> -</div> -<div class="section level2"> -<h2 id="plots-of-selected-fits">Plots of selected fits<a class="anchor" aria-label="anchor" href="#plots-of-selected-fits"></a> -</h2> -<p>The SFORB pathway fits with full and reduced parameter distribution -model are shown below.</p> -<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">[[</span><span class="st">"sforb_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_pathway_files/figure-html/unnamed-chunk-3-1.png" alt="SFORB pathway fit with two-component error" width="700"><p class="caption"> -SFORB pathway fit with two-component error -</p> -</div> -<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">saem_sforb_path_1_tc_reduced</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_pathway_files/figure-html/unnamed-chunk-4-1.png" alt="SFORB pathway fit with two-component error, reduced parameter model" width="700"><p class="caption"> -SFORB pathway fit with two-component error, reduced parameter model -</p> -</div> -<p>Plots of the remaining fits and listings for all successful fits are -shown in the Appendix.</p> -<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">stopCluster</a></span><span class="op">(</span><span class="va">cl</span><span class="op">)</span></span></code></pre></div> -</div> -<div class="section level2"> -<h2 id="conclusions">Conclusions<a class="anchor" aria-label="anchor" href="#conclusions"></a> -</h2> -<p>Pathway fits with SFO, FOMC, DFOP, SFORB and HS models for the parent -compound could be successfully performed.</p> -</div> -<div class="section level2"> -<h2 id="acknowledgements">Acknowledgements<a class="anchor" aria-label="anchor" href="#acknowledgements"></a> -</h2> -<p>The helpful comments by Janina Wöltjen of the German Environment -Agency on earlier versions of this document are gratefully -acknowledged.</p> -</div> -<div class="section level2"> -<h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a> -</h2> -<div id="refs" class="references csl-bib-body hanging-indent"> -<div id="ref-duchesne_2021" class="csl-entry"> -Duchesne, Ronan, Anissa Guillemin, Olivier Gandrillon, and Fabien -Crauste. 2021. <span>“Practical Identifiability in the Frame of -Nonlinear Mixed Effects Models: The Example of the in Vitro -Erythropoiesis.”</span> <em>BMC Bioinformatics</em> 22 (478). <a href="https://doi.org/10.1186/s12859-021-04373-4" class="external-link">https://doi.org/10.1186/s12859-021-04373-4</a>. -</div> -<div id="ref-ranke2021" class="csl-entry"> -Ranke, Johannes, Janina Wöltjen, Jana Schmidt, and Emmanuelle Comets. -2021. <span>“Taking Kinetic Evaluations of Degradation Data to the Next -Level with Nonlinear Mixed-Effects Models.”</span> <em>Environments</em> -8 (8). <a href="https://doi.org/10.3390/environments8080071" class="external-link">https://doi.org/10.3390/environments8080071</a>. -</div> -</div> -</div> -<div class="section level2"> -<h2 id="appendix">Appendix<a class="anchor" aria-label="anchor" href="#appendix"></a> -</h2> -<div class="section level3"> -<h3 id="plots-of-hierarchical-fits-not-selected-for-refinement">Plots of hierarchical fits not selected for refinement<a class="anchor" aria-label="anchor" href="#plots-of-hierarchical-fits-not-selected-for-refinement"></a> -</h3> -<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">[[</span><span class="st">"sfo_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_pathway_files/figure-html/unnamed-chunk-6-1.png" alt="SFO pathway fit with two-component error" width="700"><p class="caption"> -SFO pathway fit with two-component error -</p> -</div> -<div class="sourceCode" id="cb22"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">[[</span><span class="st">"fomc_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_pathway_files/figure-html/unnamed-chunk-7-1.png" alt="FOMC pathway fit with two-component error" width="700"><p class="caption"> -FOMC pathway fit with two-component error -</p> -</div> -<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">[[</span><span class="st">"sforb_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<div class="figure" style="text-align: center"> -<img src="2022_dmta_pathway_files/figure-html/unnamed-chunk-8-1.png" alt="HS pathway fit with two-component error" width="700"><p class="caption"> -HS pathway fit with two-component error -</p> -</div> -</div> -<div class="section level3"> -<h3 id="hierarchical-model-fit-listings">Hierarchical model fit listings<a class="anchor" aria-label="anchor" href="#hierarchical-model-fit-listings"></a> -</h3> -<div class="section level4"> -<h4 id="fits-with-random-effects-for-all-degradation-parameters">Fits with random effects for all degradation parameters<a class="anchor" aria-label="anchor" href="#fits-with-random-effects-for-all-degradation-parameters"></a> -</h4> - -</div> -<div class="section level4"> -<h4 id="improved-fit-of-the-sforb-pathway-model-with-two-component-error">Improved fit of the SFORB pathway model with two-component -error<a class="anchor" aria-label="anchor" href="#improved-fit-of-the-sforb-pathway-model-with-two-component-error"></a> -</h4> - -</div> -</div> -<div class="section level3"> -<h3 id="session-info">Session info<a class="anchor" aria-label="anchor" href="#session-info"></a> -</h3> -<pre><code>R version 4.2.3 (2023-03-15) -Platform: x86_64-pc-linux-gnu (64-bit) -Running under: Debian GNU/Linux 12 (bookworm) - -Matrix products: default -BLAS: /usr/lib/x86_64-linux-gnu/openblas-serial/libblas.so.3 -LAPACK: /usr/lib/x86_64-linux-gnu/openblas-serial/libopenblas-r0.3.21.so - -locale: - [1] LC_CTYPE=de_DE.UTF-8 LC_NUMERIC=C - [3] LC_TIME=de_DE.UTF-8 LC_COLLATE=de_DE.UTF-8 - [5] LC_MONETARY=de_DE.UTF-8 LC_MESSAGES=de_DE.UTF-8 - [7] LC_PAPER=de_DE.UTF-8 LC_NAME=C - [9] LC_ADDRESS=C LC_TELEPHONE=C -[11] LC_MEASUREMENT=de_DE.UTF-8 LC_IDENTIFICATION=C - -attached base packages: -[1] parallel stats graphics grDevices utils datasets methods -[8] base - -other attached packages: -[1] saemix_3.2 npde_3.3 knitr_1.42 mkin_1.2.4 - -loaded via a namespace (and not attached): - [1] deSolve_1.35 zoo_1.8-12 tidyselect_1.2.0 xfun_0.38 - [5] bslib_0.4.2 purrr_1.0.1 lattice_0.21-8 colorspace_2.1-0 - [9] vctrs_0.6.1 generics_0.1.3 htmltools_0.5.5 yaml_2.3.7 -[13] utf8_1.2.3 rlang_1.1.0 pkgbuild_1.4.0 pkgdown_2.0.7 -[17] jquerylib_0.1.4 pillar_1.9.0 glue_1.6.2 DBI_1.1.3 -[21] lifecycle_1.0.3 stringr_1.5.0 munsell_0.5.0 gtable_0.3.3 -[25] ragg_1.2.5 codetools_0.2-19 memoise_2.0.1 evaluate_0.20 -[29] inline_0.3.19 callr_3.7.3 fastmap_1.1.1 ps_1.7.4 -[33] lmtest_0.9-40 fansi_1.0.4 highr_0.10 scales_1.2.1 -[37] cachem_1.0.7 desc_1.4.2 jsonlite_1.8.4 systemfonts_1.0.4 -[41] fs_1.6.1 textshaping_0.3.6 gridExtra_2.3 ggplot2_3.4.2 -[45] digest_0.6.31 stringi_1.7.12 processx_3.8.0 dplyr_1.1.1 -[49] grid_4.2.3 rprojroot_2.0.3 cli_3.6.1 tools_4.2.3 -[53] magrittr_2.0.3 sass_0.4.5 tibble_3.2.1 crayon_1.5.2 -[57] pkgconfig_2.0.3 prettyunits_1.1.1 rmarkdown_2.21 R6_2.5.1 -[61] mclust_6.0.0 nlme_3.1-162 compiler_4.2.3 </code></pre> -</div> -<div class="section level3"> -<h3 id="hardware-info">Hardware info<a class="anchor" aria-label="anchor" href="#hardware-info"></a> -</h3> -<pre><code>CPU model: AMD Ryzen 9 7950X 16-Core Processor</code></pre> -<pre><code>MemTotal: 64936316 kB</code></pre> -</div> -</div> - </div> - - <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar"> - - 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href="../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a> - </li> - <li> - <a href="../articles/web_only/multistart.html">Short demo of the multistart method</a> - </li> - <li class="divider"> - </li> -<li class="dropdown-header">Performance</li> - <li> - <a href="../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> - </li> - <li> - <a href="../articles/web_only/benchmarks.html">Benchmark timings for mkin</a> - </li> - <li> - <a href="../articles/web_only/saem_benchmarks.html">Benchmark timings for saem.mmkin</a> - </li> - <li class="divider"> - </li> -<li class="dropdown-header">Miscellaneous</li> - <li> - <a href="../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> - </li> - <li> - <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> - </li> - </ul> -</li> -<li> - <a href="../news/index.html">News</a> -</li> - </ul> -<ul class="nav navbar-nav navbar-right"> -<li> - <a href="https://github.com/jranke/mkin/" class="external-link"> - <span class="fab fa-github fa-lg"></span> - - </a> -</li> - </ul> -</div> -<!--/.nav-collapse --> - </div> -<!--/.container --> -</div> -<!--/.navbar --> - - - - </header><div class="row"> - <div class="col-md-9 contents"> - <div class="page-header toc-ignore"> - <h1 data-toc-skip>Calculation of time weighted average -concentrations with mkin</h1> - <h4 data-toc-skip class="author">Johannes -Ranke</h4> - - <h4 data-toc-skip class="date">Last change 18 September 2019 -(rebuilt 2023-04-16)</h4> - - <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/twa.rmd" class="external-link"><code>vignettes/twa.rmd</code></a></small> - <div class="hidden name"><code>twa.rmd</code></div> - - </div> - - - -<p>Since version 0.9.45.1 of the ‘mkin’ package, a function for -calculating time weighted average concentrations for decline kinetics -(<em>i.e.</em> only for the compound applied in the experiment) is -included. Strictly speaking, they are maximum moving window time -weighted average concentrations, <em>i.e.</em> the maximum time weighted -average concentration that can be found when moving a time window of a -specified width over the decline curve.</p> -<p>Time weighted average concentrations for the SFO, FOMC and the DFOP -model are calculated using the formulas given in the FOCUS kinetics -guidance <span class="citation">(FOCUS Work Group on Degradation -Kinetics 2014, 251)</span>:</p> -<p>SFO:</p> -<p><span class="math display">\[c_\textrm{twa} = c_0 \frac{\left( 1 - -e^{- k t} \right)}{ k t} \]</span></p> -<p>FOMC:</p> -<p><span class="math display">\[c_\textrm{twa} = c_0 \frac{\beta}{t (1 - -\alpha)} - \left( \left(\frac{t}{\beta} + 1 \right)^{1 - \alpha} -- 1 \right) \]</span></p> -<p>DFOP:</p> -<p><span class="math display">\[c_\textrm{twa} = \frac{c_0}{t} \left( - \frac{g}{k_1} \left( 1 - e^{- k_1 t} \right) + - \frac{1-g}{k_2} \left( 1 - e^{- k_2 t} \right) \right) \]</span></p> -<p>HS for <span class="math inline">\(t > t_b\)</span>:</p> -<p><span class="math display">\[c_\textrm{twa} = \frac{c_0}{t} \left( - \frac{1}{k_1} \left( 1 - e^{- k_1 t_b} \right) + - \frac{e^{- k_1 t_b}}{k_2} \left( 1 - e^{- k_2 (t - t_b)} -\right) \right) \]</span></p> -<p>Often, the ratio between the time weighted average concentration -<span class="math inline">\(c_\textrm{twa}\)</span> and the initial -concentration <span class="math inline">\(c_0\)</span></p> -<p><span class="math display">\[f_\textrm{twa} = -\frac{c_\textrm{twa}}{c_0}\]</span></p> -<p>is needed. This can be calculated from the fitted initial -concentration <span class="math inline">\(c_0\)</span> and the time -weighted average concentration <span class="math inline">\(c_\textrm{twa}\)</span>, or directly from the -model parameters using the following formulas:</p> -<p>SFO:</p> -<p><span class="math display">\[f_\textrm{twa} = \frac{\left( 1 - e^{- k -t} \right)}{k t} \]</span></p> -<p>FOMC:</p> -<p><span class="math display">\[f_\textrm{twa} = \frac{\beta}{t (1 - -\alpha)} - \left( \left(\frac{t}{\beta} + 1 \right)^{1 - \alpha} -- 1 \right) \]</span></p> -<p>DFOP:</p> -<p><span class="math display">\[f_\textrm{twa} = \frac{1}{t} \left( - \frac{g}{k_1} \left( 1 - e^{- k_1 t} \right) + - \frac{1-g}{k_2} \left( 1 - e^{- k_2 t} \right) \right) \]</span></p> -<p>HS for <span class="math inline">\(t > t_b\)</span>:</p> -<p><span class="math display">\[f_\textrm{twa} = \frac{1}{t} \left( - \frac{1}{k_1} \left( 1 - e^{- k_1 t_b} \right) + - \frac{e^{- k_1 t_b}}{k_2} \left( 1 - e^{- k_2 (t - t_b)} -\right) \right) \]</span></p> -<p>Note that a method for calculating maximum moving window time -weighted average concentrations for a model fitted by ‘mkinfit’ or from -parent decline model parameters is included in the -<code><a href="../reference/max_twa_parent.html">max_twa_parent()</a></code> function. If the same is needed for -metabolites, the function <code><a href="https://pkgdown.jrwb.de/pfm/reference/max_twa.html" class="external-link">pfm::max_twa()</a></code> from the ‘pfm’ -package can be used.</p> -<div id="refs" class="references csl-bib-body hanging-indent"> -<div id="ref-FOCUSkinetics2014" class="csl-entry"> -FOCUS Work Group on Degradation Kinetics. 2014. <em>Generic Guidance for -Estimating Persistence and Degradation Kinetics from Environmental Fate -Studies on Pesticides in EU Registration</em>. 1.1 ed. <a href="http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics" class="external-link">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>. -</div> -</div> - </div> - - <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar"> - - </div> - -</div> - - - - <footer><div class="copyright"> - <p></p> -<p>Developed by Johannes Ranke.</p> -</div> - -<div class="pkgdown"> - <p></p> -<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p> -</div> - - </footer> -</div> - - - - - - - </body> -</html> diff --git a/docs/dev/articles/twa_files/accessible-code-block-0.0.1/empty-anchor.js b/docs/dev/articles/twa_files/accessible-code-block-0.0.1/empty-anchor.js deleted file mode 100644 index ca349fd6..00000000 --- a/docs/dev/articles/twa_files/accessible-code-block-0.0.1/empty-anchor.js +++ /dev/null @@ -1,15 +0,0 @@ -// Hide empty <a> tag within highlighted CodeBlock for screen reader accessibility (see https://github.com/jgm/pandoc/issues/6352#issuecomment-626106786) --> -// v0.0.1 -// Written by JooYoung Seo (jooyoung@psu.edu) and Atsushi Yasumoto on June 1st, 2020. - -document.addEventListener('DOMContentLoaded', function() { - const codeList = document.getElementsByClassName("sourceCode"); - for (var i = 0; i < codeList.length; i++) { - var linkList = codeList[i].getElementsByTagName('a'); - for (var j = 0; j < linkList.length; j++) { - if (linkList[j].innerHTML === "") { - linkList[j].setAttribute('aria-hidden', 'true'); - } - } - } -}); diff --git a/docs/dev/articles/twa_files/anchor-sections-1.0/anchor-sections.css b/docs/dev/articles/twa_files/anchor-sections-1.0/anchor-sections.css deleted file mode 100644 index 07aee5fc..00000000 --- a/docs/dev/articles/twa_files/anchor-sections-1.0/anchor-sections.css +++ /dev/null @@ -1,4 +0,0 @@ -/* Styles for section anchors */ -a.anchor-section {margin-left: 10px; visibility: hidden; color: inherit;} -a.anchor-section::before {content: '#';} -.hasAnchor:hover a.anchor-section {visibility: visible;} diff --git a/docs/dev/articles/twa_files/anchor-sections-1.0/anchor-sections.js b/docs/dev/articles/twa_files/anchor-sections-1.0/anchor-sections.js deleted file mode 100644 index 570f99a0..00000000 --- a/docs/dev/articles/twa_files/anchor-sections-1.0/anchor-sections.js +++ /dev/null @@ -1,33 +0,0 @@ -// Anchor sections v1.0 written by Atsushi Yasumoto on Oct 3rd, 2020. -document.addEventListener('DOMContentLoaded', function() { - // Do nothing if AnchorJS is used - if (typeof window.anchors === 'object' && anchors.hasOwnProperty('hasAnchorJSLink')) { - return; - } - - const h = document.querySelectorAll('h1, h2, h3, h4, h5, h6'); - - // Do nothing if sections are already anchored - if (Array.from(h).some(x => x.classList.contains('hasAnchor'))) { - return null; - } - - // Use section id when pandoc runs with --section-divs - const section_id = function(x) { - return ((x.classList.contains('section') || (x.tagName === 'SECTION')) - ? x.id : ''); - }; - - // Add anchors - h.forEach(function(x) { - const id = x.id || section_id(x.parentElement); - if (id === '') { - return null; - } - let anchor = document.createElement('a'); - anchor.href = '#' + id; - anchor.classList = ['anchor-section']; - x.classList.add('hasAnchor'); - x.appendChild(anchor); - }); -}); diff --git a/docs/dev/articles/twa_files/header-attrs-2.6/header-attrs.js b/docs/dev/articles/twa_files/header-attrs-2.6/header-attrs.js deleted file mode 100644 index dd57d92e..00000000 --- a/docs/dev/articles/twa_files/header-attrs-2.6/header-attrs.js +++ /dev/null @@ -1,12 +0,0 @@ -// Pandoc 2.9 adds attributes on both header and div. 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-</li> -<li> - <a href="../../news/index.html">News</a> -</li> - </ul> -<ul class="nav navbar-nav navbar-right"> -<li> - <a href="https://github.com/jranke/mkin/" class="external-link"> - <span class="fab fa-github fa-lg"></span> - - </a> -</li> - </ul> -</div> -<!--/.nav-collapse --> - </div> -<!--/.container --> -</div> -<!--/.navbar --> - - - - </header><div class="row"> - <div class="col-md-9 contents"> - <div class="page-header toc-ignore"> - <h1 data-toc-skip>Example evaluation of FOCUS dataset Z</h1> - <h4 data-toc-skip class="author">Johannes -Ranke</h4> - - <h4 data-toc-skip class="date">Last change 16 January 2018 -(rebuilt 2023-04-16)</h4> - - <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/FOCUS_Z.rmd" class="external-link"><code>vignettes/web_only/FOCUS_Z.rmd</code></a></small> - <div class="hidden name"><code>FOCUS_Z.rmd</code></div> - - </div> - - - -<p><a href="http://www.jrwb.de" class="external-link">Wissenschaftlicher Berater, Kronacher -Str. 12, 79639 Grenzach-Wyhlen, Germany</a><br><a href="http://chem.uft.uni-bremen.de/ranke" class="external-link">Privatdozent at the -University of Bremen</a></p> -<div class="section level2"> -<h2 id="the-data">The data<a class="anchor" aria-label="anchor" href="#the-data"></a> -</h2> -<p>The following code defines the example dataset from Appendix 7 to the -FOCUS kinetics report <span class="citation">(FOCUS Work Group on -Degradation Kinetics 2014, 354)</span>.</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>, quietly <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<span><span class="va">LOD</span> <span class="op">=</span> <span class="fl">0.5</span></span> -<span><span class="va">FOCUS_2006_Z</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span></span> -<span> t <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">0.04</span>, <span class="fl">0.125</span>, <span class="fl">0.29</span>, <span class="fl">0.54</span>, <span class="fl">1</span>, <span class="fl">2</span>, <span class="fl">3</span>, <span class="fl">4</span>, <span class="fl">7</span>, <span class="fl">10</span>, <span class="fl">14</span>, <span class="fl">21</span>,</span> -<span> <span class="fl">42</span>, <span class="fl">61</span>, <span class="fl">96</span>, <span class="fl">124</span><span class="op">)</span>,</span> -<span> Z0 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">100</span>, <span class="fl">81.7</span>, <span class="fl">70.4</span>, <span class="fl">51.1</span>, <span class="fl">41.2</span>, <span class="fl">6.6</span>, <span class="fl">4.6</span>, <span class="fl">3.9</span>, <span class="fl">4.6</span>, <span class="fl">4.3</span>, <span class="fl">6.8</span>,</span> -<span> <span class="fl">2.9</span>, <span class="fl">3.5</span>, <span class="fl">5.3</span>, <span class="fl">4.4</span>, <span class="fl">1.2</span>, <span class="fl">0.7</span><span class="op">)</span>,</span> -<span> Z1 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">18.3</span>, <span class="fl">29.6</span>, <span class="fl">46.3</span>, <span class="fl">55.1</span>, <span class="fl">65.7</span>, <span class="fl">39.1</span>, <span class="fl">36</span>, <span class="fl">15.3</span>, <span class="fl">5.6</span>, <span class="fl">1.1</span>,</span> -<span> <span class="fl">1.6</span>, <span class="fl">0.6</span>, <span class="fl">0.5</span> <span class="op">*</span> <span class="va">LOD</span>, <span class="cn">NA</span>, <span class="cn">NA</span>, <span class="cn">NA</span><span class="op">)</span>,</span> -<span> Z2 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="cn">NA</span>, <span class="fl">0.5</span> <span class="op">*</span> <span class="va">LOD</span>, <span class="fl">2.6</span>, <span class="fl">3.8</span>, <span class="fl">15.3</span>, <span class="fl">37.2</span>, <span class="fl">31.7</span>, <span class="fl">35.6</span>, <span class="fl">14.5</span>,</span> -<span> <span class="fl">0.8</span>, <span class="fl">2.1</span>, <span class="fl">1.9</span>, <span class="fl">0.5</span> <span class="op">*</span> <span class="va">LOD</span>, <span class="cn">NA</span>, <span class="cn">NA</span>, <span class="cn">NA</span><span class="op">)</span>,</span> -<span> Z3 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="cn">NA</span>, <span class="cn">NA</span>, <span class="cn">NA</span>, <span class="cn">NA</span>, <span class="fl">0.5</span> <span class="op">*</span> <span class="va">LOD</span>, <span class="fl">9.2</span>, <span class="fl">13.1</span>, <span class="fl">22.3</span>, <span class="fl">28.4</span>, <span class="fl">32.5</span>,</span> -<span> <span class="fl">25.2</span>, <span class="fl">17.2</span>, <span class="fl">4.8</span>, <span class="fl">4.5</span>, <span class="fl">2.8</span>, <span class="fl">4.4</span><span class="op">)</span><span class="op">)</span></span> -<span></span> -<span><span class="va">FOCUS_2006_Z_mkin</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span><span class="op">(</span><span class="va">FOCUS_2006_Z</span><span class="op">)</span></span></code></pre></div> -</div> -<div class="section level2"> -<h2 id="parent-and-one-metabolite">Parent and one metabolite<a class="anchor" aria-label="anchor" href="#parent-and-one-metabolite"></a> -</h2> -<p>The next step is to set up the models used for the kinetic analysis. -As the simultaneous fit of parent and the first metabolite is usually -straightforward, Step 1 (SFO for parent only) is skipped here. We start -with the model 2a, with formation and decline of metabolite Z1 and the -pathway from parent directly to sink included (default in mkin).</p> -<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">Z.2a</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <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">"Z1"</span><span class="op">)</span>,</span> -<span> Z1 <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 class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre> -<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">m.Z.2a</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.2a</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Warning in mkinfit(Z.2a, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with</span></span> -<span><span class="co">## value of zero were removed from the data</span></span></code></pre> -<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.2a</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png" width="700"></p> -<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.2a</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></code></pre></div> -<pre><code><span><span class="co">## Estimate se_notrans t value Pr(>t) Lower Upper</span></span> -<span><span class="co">## Z0_0 97.01488 3.301084 29.3888 3.2971e-21 91.66556 102.3642</span></span> -<span><span class="co">## k_Z0 2.23601 0.207078 10.7979 3.3309e-11 1.95303 2.5600</span></span> -<span><span class="co">## k_Z1 0.48212 0.063265 7.6207 2.8154e-08 0.40341 0.5762</span></span> -<span><span class="co">## f_Z0_to_Z1 1.00000 0.094764 10.5525 5.3560e-11 0.00000 1.0000</span></span> -<span><span class="co">## sigma 4.80411 0.635638 7.5579 3.2592e-08 3.52677 6.0815</span></span></code></pre> -<p>As obvious from the parameter summary (the component of the summary), -the kinetic rate constant from parent compound Z to sink is very small -and the t-test for this parameter suggests that it is not significantly -different from zero. This suggests, in agreement with the analysis in -the FOCUS kinetics report, to simplify the model by removing the pathway -to sink.</p> -<p>A similar result can be obtained when formation fractions are used in -the model formulation:</p> -<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">Z.2a.ff</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <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">"Z1"</span><span class="op">)</span>,</span> -<span> Z1 <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> use_of_ff <span class="op">=</span> <span class="st">"max"</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre> -<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">m.Z.2a.ff</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.2a.ff</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Warning in mkinfit(Z.2a.ff, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with</span></span> -<span><span class="co">## value of zero were removed from the data</span></span></code></pre> -<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.2a.ff</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png" width="700"></p> -<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.2a.ff</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></code></pre></div> -<pre><code><span><span class="co">## Estimate se_notrans t value Pr(>t) Lower Upper</span></span> -<span><span class="co">## Z0_0 97.01488 3.301084 29.3888 3.2971e-21 91.66556 102.3642</span></span> -<span><span class="co">## k_Z0 2.23601 0.207078 10.7979 3.3309e-11 1.95303 2.5600</span></span> -<span><span class="co">## k_Z1 0.48212 0.063265 7.6207 2.8154e-08 0.40341 0.5762</span></span> -<span><span class="co">## f_Z0_to_Z1 1.00000 0.094764 10.5525 5.3560e-11 0.00000 1.0000</span></span> -<span><span class="co">## sigma 4.80411 0.635638 7.5579 3.2592e-08 3.52677 6.0815</span></span></code></pre> -<p>Here, the ilr transformed formation fraction fitted in the model -takes a very large value, and the backtransformed formation fraction -from parent Z to Z1 is practically unity. Here, the covariance matrix -used for the calculation of confidence intervals is not returned as the -model is overparameterised.</p> -<p>A simplified model is obtained by removing the pathway to the sink. -</p> -<p>In the following, we use the parameterisation with formation -fractions in order to be able to compare with the results in the FOCUS -guidance, and as it makes it easier to use parameters obtained in a -previous fit when adding a further metabolite.</p> -<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">Z.3</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <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">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> Z1 <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>, use_of_ff <span class="op">=</span> <span class="st">"max"</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre> -<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">m.Z.3</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.3</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Warning in mkinfit(Z.3, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with</span></span> -<span><span class="co">## value of zero were removed from the data</span></span></code></pre> -<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.3</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png" width="700"></p> -<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.3</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></code></pre></div> -<pre><code><span><span class="co">## Estimate se_notrans t value Pr(>t) Lower Upper</span></span> -<span><span class="co">## Z0_0 97.01488 2.597342 37.352 2.0106e-24 91.67597 102.3538</span></span> -<span><span class="co">## k_Z0 2.23601 0.146904 15.221 9.1477e-15 1.95354 2.5593</span></span> -<span><span class="co">## k_Z1 0.48212 0.041727 11.554 4.8268e-12 0.40355 0.5760</span></span> -<span><span class="co">## sigma 4.80411 0.620208 7.746 1.6110e-08 3.52925 6.0790</span></span></code></pre> -<p>As there is only one transformation product for Z0 and no pathway to -sink, the formation fraction is internally fixed to unity.</p> -</div> -<div class="section level2"> -<h2 id="metabolites-z2-and-z3">Metabolites Z2 and Z3<a class="anchor" aria-label="anchor" href="#metabolites-z2-and-z3"></a> -</h2> -<p>As suggested in the FOCUS report, the pathway to sink was removed for -metabolite Z1 as well in the next step. While this step appears -questionable on the basis of the above results, it is followed here for -the purpose of comparison. Also, in the FOCUS report, it is assumed that -there is additional empirical evidence that Z1 quickly and exclusively -hydrolyses to Z2.</p> -<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">Z.5</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <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">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> Z1 <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">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> Z2 <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>, use_of_ff <span class="op">=</span> <span class="st">"max"</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre> -<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">m.Z.5</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.5</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Warning in mkinfit(Z.5, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with</span></span> -<span><span class="co">## value of zero were removed from the data</span></span></code></pre> -<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.5</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png" width="700"></p> -<p>Finally, metabolite Z3 is added to the model. We use the optimised -differential equation parameter values from the previous fit in order to -accelerate the optimization.</p> -<div class="sourceCode" id="cb28"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">Z.FOCUS</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <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">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> Z1 <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">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> Z2 <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">"Z3"</span><span class="op">)</span>,</span> -<span> Z3 <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> use_of_ff <span class="op">=</span> <span class="st">"max"</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre> -<div class="sourceCode" id="cb30"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">m.Z.FOCUS</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.FOCUS</span>, <span class="va">FOCUS_2006_Z_mkin</span>,</span> -<span> parms.ini <span class="op">=</span> <span class="va">m.Z.5</span><span class="op">$</span><span class="va">bparms.ode</span>,</span> -<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.5$bparms.ode, :</span></span> -<span><span class="co">## Observations with value of zero were removed from the data</span></span></code></pre> -<pre><code><span><span class="co">## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.5$bparms.ode, : Optimisation did not converge:</span></span> -<span><span class="co">## false convergence (8)</span></span></code></pre> -<div class="sourceCode" id="cb33"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.FOCUS</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png" width="700"></p> -<div class="sourceCode" id="cb34"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.FOCUS</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></code></pre></div> -<pre><code><span><span class="co">## Estimate se_notrans t value Pr(>t) Lower Upper</span></span> -<span><span class="co">## Z0_0 96.838822 1.994274 48.5584 4.0280e-42 92.826981 100.850664</span></span> -<span><span class="co">## k_Z0 2.215393 0.118458 18.7019 1.0413e-23 1.989456 2.466989</span></span> -<span><span class="co">## k_Z1 0.478305 0.028258 16.9266 6.2418e-22 0.424708 0.538666</span></span> -<span><span class="co">## k_Z2 0.451627 0.042139 10.7176 1.6314e-14 0.374339 0.544872</span></span> -<span><span class="co">## k_Z3 0.058692 0.015245 3.8499 1.7803e-04 0.034808 0.098965</span></span> -<span><span class="co">## f_Z2_to_Z3 0.471502 0.058351 8.0805 9.6608e-11 0.357769 0.588274</span></span> -<span><span class="co">## sigma 3.984431 0.383402 10.3923 4.5575e-14 3.213126 4.755736</span></span></code></pre> -<div class="sourceCode" id="cb36"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">m.Z.FOCUS</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## $ff</span></span> -<span><span class="co">## Z2_Z3 Z2_sink </span></span> -<span><span class="co">## 0.4715 0.5285 </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $distimes</span></span> -<span><span class="co">## DT50 DT90</span></span> -<span><span class="co">## Z0 0.31288 1.0394</span></span> -<span><span class="co">## Z1 1.44917 4.8141</span></span> -<span><span class="co">## Z2 1.53478 5.0984</span></span> -<span><span class="co">## Z3 11.80986 39.2315</span></span></code></pre> -<p>This fit corresponds to the final result chosen in Appendix 7 of the -FOCUS report. Confidence intervals returned by mkin are based on -internally transformed parameters, however.</p> -</div> -<div class="section level2"> -<h2 id="using-the-sforb-model">Using the SFORB model<a class="anchor" aria-label="anchor" href="#using-the-sforb-model"></a> -</h2> -<p>As the FOCUS report states, there is a certain tailing of the time -course of metabolite Z3. Also, the time course of the parent compound is -not fitted very well using the SFO model, as residues at a certain low -level remain.</p> -<p>Therefore, an additional model is offered here, using the single -first-order reversible binding (SFORB) model for metabolite Z3. As -expected, the <span class="math inline">\(\chi^2\)</span> error level is -lower for metabolite Z3 using this model and the graphical fit for Z3 is -improved. However, the covariance matrix is not returned.</p> -<div class="sourceCode" id="cb38"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">Z.mkin.1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <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">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> Z1 <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">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> Z2 <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">"Z3"</span><span class="op">)</span>,</span> -<span> Z3 <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="op">)</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre> -<div class="sourceCode" id="cb40"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">m.Z.mkin.1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.mkin.1</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Warning in mkinfit(Z.mkin.1, FOCUS_2006_Z_mkin, quiet = TRUE): Observations</span></span> -<span><span class="co">## with value of zero were removed from the data</span></span></code></pre> -<div class="sourceCode" id="cb42"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.1</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png" width="700"></p> -<div class="sourceCode" id="cb43"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.mkin.1</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">cov.unscaled</span></span></code></pre></div> -<pre><code><span><span class="co">## NULL</span></span></code></pre> -<p>Therefore, a further stepwise model building is performed starting -from the stage of parent and two metabolites, starting from the -assumption that the model fit for the parent compound can be improved by -using the SFORB model.</p> -<div class="sourceCode" id="cb45"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">Z.mkin.3</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <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="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> Z1 <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">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> Z2 <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 class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre> -<div class="sourceCode" id="cb47"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">m.Z.mkin.3</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.mkin.3</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Warning in mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE): Observations</span></span> -<span><span class="co">## with value of zero were removed from the data</span></span></code></pre> -<div class="sourceCode" id="cb49"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.3</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png" width="700"></p> -<p>This results in a much better representation of the behaviour of the -parent compound Z0.</p> -<p>Finally, Z3 is added as well. These models appear overparameterised -(no covariance matrix returned) if the sink for Z1 is left in the -models.</p> -<div class="sourceCode" id="cb50"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">Z.mkin.4</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <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="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> Z1 <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">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> Z2 <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">"Z3"</span><span class="op">)</span>,</span> -<span> Z3 <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 class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre> -<div class="sourceCode" id="cb52"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">m.Z.mkin.4</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.mkin.4</span>, <span class="va">FOCUS_2006_Z_mkin</span>,</span> -<span> parms.ini <span class="op">=</span> <span class="va">m.Z.mkin.3</span><span class="op">$</span><span class="va">bparms.ode</span>,</span> -<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Warning in mkinfit(Z.mkin.4, FOCUS_2006_Z_mkin, parms.ini =</span></span> -<span><span class="co">## m.Z.mkin.3$bparms.ode, : Observations with value of zero were removed from the</span></span> -<span><span class="co">## data</span></span></code></pre> -<div class="sourceCode" id="cb54"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.4</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png" width="700"></p> -<p>The error level of the fit, but especially of metabolite Z3, can be -improved if the SFORB model is chosen for this metabolite, as this model -is capable of representing the tailing of the metabolite decline -phase.</p> -<div class="sourceCode" id="cb55"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">Z.mkin.5</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <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="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> Z1 <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">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> -<span> Z2 <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">"Z3"</span><span class="op">)</span>,</span> -<span> Z3 <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="op">)</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre> -<div class="sourceCode" id="cb57"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">m.Z.mkin.5</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.mkin.5</span>, <span class="va">FOCUS_2006_Z_mkin</span>,</span> -<span> parms.ini <span class="op">=</span> <span class="va">m.Z.mkin.4</span><span class="op">$</span><span class="va">bparms.ode</span><span class="op">[</span><span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span>,</span> -<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini =</span></span> -<span><span class="co">## m.Z.mkin.4$bparms.ode[1:4], : Observations with value of zero were removed from</span></span> -<span><span class="co">## the data</span></span></code></pre> -<div class="sourceCode" id="cb59"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.5</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png" width="700"></p> -<p>The summary view of the backtransformed parameters shows that we get -no confidence intervals due to overparameterisation. As the optimized is -excessively small, it seems reasonable to fix it to zero.</p> -<div class="sourceCode" id="cb60"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">m.Z.mkin.5a</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.mkin.5</span>, <span class="va">FOCUS_2006_Z_mkin</span>,</span> -<span> parms.ini <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="va">m.Z.mkin.5</span><span class="op">$</span><span class="va">bparms.ode</span><span class="op">[</span><span class="fl">1</span><span class="op">:</span><span class="fl">7</span><span class="op">]</span>,</span> -<span> k_Z3_bound_free <span class="op">=</span> <span class="fl">0</span><span class="op">)</span>,</span> -<span> fixed_parms <span class="op">=</span> <span class="st">"k_Z3_bound_free"</span>,</span> -<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini =</span></span> -<span><span class="co">## c(m.Z.mkin.5$bparms.ode[1:7], : Observations with value of zero were removed</span></span> -<span><span class="co">## from the data</span></span></code></pre> -<div class="sourceCode" id="cb62"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.5a</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png" width="700"></p> -<p>As expected, the residual plots for Z0 and Z3 are more random than in -the case of the all SFO model for which they were shown above. In -conclusion, the model is proposed as the best-fit model for the dataset -from Appendix 7 of the FOCUS report.</p> -<p>A graphical representation of the confidence intervals can finally be -obtained.</p> -<div class="sourceCode" id="cb63"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/mkinparplot.html">mkinparplot</a></span><span class="op">(</span><span class="va">m.Z.mkin.5a</span><span class="op">)</span></span></code></pre></div> -<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png" width="700"></p> -<p>The endpoints obtained with this model are</p> -<div class="sourceCode" id="cb64"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">m.Z.mkin.5a</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## $ff</span></span> -<span><span class="co">## Z0_free Z2_Z3 Z2_sink Z3_free </span></span> -<span><span class="co">## 1.00000 0.53656 0.46344 1.00000 </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $SFORB</span></span> -<span><span class="co">## Z0_b1 Z0_b2 Z0_g Z3_b1 Z3_b2 Z3_g </span></span> -<span><span class="co">## 2.4471322 0.0075125 0.9519862 0.0800069 0.0000000 0.9347820 </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $distimes</span></span> -<span><span class="co">## DT50 DT90 DT50back DT50_Z0_b1 DT50_Z0_b2 DT50_Z3_b1 DT50_Z3_b2</span></span> -<span><span class="co">## Z0 0.3043 1.1848 0.35666 0.28325 92.266 NA NA</span></span> -<span><span class="co">## Z1 1.5148 5.0320 NA NA NA NA NA</span></span> -<span><span class="co">## Z2 1.6414 5.4526 NA NA NA NA NA</span></span> -<span><span class="co">## Z3 NA NA NA NA NA 8.6636 Inf</span></span></code></pre> -<p>It is clear the degradation rate of Z3 towards the end of the -experiment is very low as DT50_Z3_b2 (the second Eigenvalue of the -system of two differential equations representing the SFORB system for -Z3, corresponding to the slower rate constant of the DFOP model) is -reported to be infinity. However, this appears to be a feature of the -data.</p> -</div> -<div class="section level2"> -<h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a> -</h2> -<!-- vim: set foldmethod=syntax: --> -<div id="refs" class="references csl-bib-body hanging-indent"> -<div id="ref-FOCUSkinetics2014" class="csl-entry"> -FOCUS Work Group on Degradation Kinetics. 2014. <em>Generic Guidance for -Estimating Persistence and Degradation Kinetics from Environmental Fate -Studies on Pesticides in EU Registration</em>. 1.1 ed. <a href="http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics" class="external-link">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>. -</div> -</div> -</div> - </div> - - <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar"> - - <nav id="toc" data-toggle="toc"><h2 data-toc-skip>Contents</h2> - </nav> -</div> - -</div> - - - - <footer><div class="copyright"> - <p></p> -<p>Developed by Johannes Ranke.</p> -</div> - -<div class="pkgdown"> - <p></p> -<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p> -</div> - - </footer> -</div> - - - - - - - </body> -</html> diff --git a/docs/dev/articles/web_only/FOCUS_Z_files/accessible-code-block-0.0.1/empty-anchor.js b/docs/dev/articles/web_only/FOCUS_Z_files/accessible-code-block-0.0.1/empty-anchor.js deleted file mode 100644 index ca349fd6..00000000 --- a/docs/dev/articles/web_only/FOCUS_Z_files/accessible-code-block-0.0.1/empty-anchor.js +++ /dev/null @@ -1,15 +0,0 @@ -// Hide empty <a> tag within highlighted CodeBlock for screen reader accessibility (see https://github.com/jgm/pandoc/issues/6352#issuecomment-626106786) --> -// v0.0.1 -// Written by JooYoung Seo (jooyoung@psu.edu) and Atsushi Yasumoto on June 1st, 2020. - -document.addEventListener('DOMContentLoaded', function() { - const codeList = document.getElementsByClassName("sourceCode"); - for (var i = 0; i < codeList.length; i++) { - var linkList = codeList[i].getElementsByTagName('a'); - for (var j = 0; j < linkList.length; j++) { - if (linkList[j].innerHTML === "") { - linkList[j].setAttribute('aria-hidden', 'true'); - } - } - } -}); diff --git a/docs/dev/articles/web_only/FOCUS_Z_files/anchor-sections-1.0/anchor-sections.css b/docs/dev/articles/web_only/FOCUS_Z_files/anchor-sections-1.0/anchor-sections.css deleted file mode 100644 index 07aee5fc..00000000 --- a/docs/dev/articles/web_only/FOCUS_Z_files/anchor-sections-1.0/anchor-sections.css +++ /dev/null @@ -1,4 +0,0 @@ -/* Styles for section anchors */ -a.anchor-section {margin-left: 10px; visibility: hidden; color: inherit;} -a.anchor-section::before {content: '#';} -.hasAnchor:hover a.anchor-section {visibility: visible;} diff --git a/docs/dev/articles/web_only/FOCUS_Z_files/anchor-sections-1.0/anchor-sections.js b/docs/dev/articles/web_only/FOCUS_Z_files/anchor-sections-1.0/anchor-sections.js deleted file mode 100644 index 570f99a0..00000000 --- a/docs/dev/articles/web_only/FOCUS_Z_files/anchor-sections-1.0/anchor-sections.js +++ /dev/null @@ -1,33 +0,0 @@ -// Anchor sections v1.0 written by Atsushi Yasumoto on Oct 3rd, 2020. -document.addEventListener('DOMContentLoaded', function() { - // Do nothing if AnchorJS is used - if (typeof window.anchors === 'object' && anchors.hasOwnProperty('hasAnchorJSLink')) { - return; - } - - const h = document.querySelectorAll('h1, h2, h3, h4, h5, h6'); - - // Do nothing if sections are already anchored - if (Array.from(h).some(x => x.classList.contains('hasAnchor'))) { - return null; - } - - // Use section id when pandoc runs with --section-divs - const section_id = function(x) { - return ((x.classList.contains('section') || (x.tagName === 'SECTION')) - ? 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<div class="hidden name"><code>NAFTA_examples.rmd</code></div> - - </div> - - - -<div class="section level2"> -<h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#introduction"></a> -</h2> -<p>In this document, the example evaluations provided in Attachment 1 to -the SOP of US EPA for using the NAFTA guidance <span class="citation">(US EPA 2015)</span> are repeated using mkin. The -original evaluations reported in the attachment were performed using -PestDF in version 0.8.4. Note that PestDF 0.8.13 is the version -distributed at the US EPA website today (2019-02-26).</p> -<p>The datasets are now distributed with the mkin package.</p> -</div> -<div class="section level2"> -<h2 id="examples-where-dfop-did-not-converge-with-pestdf-0-8-4">Examples where DFOP did not converge with PestDF 0.8.4<a class="anchor" aria-label="anchor" href="#examples-where-dfop-did-not-converge-with-pestdf-0-8-4"></a> -</h2> -<p>In attachment 1, it is reported that the DFOP model does not converge -for these datasets when PestDF 0.8.4 was used. For all four datasets, -the DFOP model can be fitted with mkin (see below). The negative -half-life given by PestDF 0.8.4 for these fits appears to be the result -of a bug. The results for the other two models (SFO and IORE) are the -same.</p> -<div class="section level3"> -<h3 id="example-on-page-5-upper-panel">Example on page 5, upper panel<a class="anchor" aria-label="anchor" href="#example-on-page-5-upper-panel"></a> -</h3> -<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">p5a</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p5a"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre> -<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre> -<div class="sourceCode" id="cb4"><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">p5a</span><span class="op">)</span></span></code></pre></div> -<p><img src="NAFTA_examples_files/figure-html/p5a-1.png" width="700"></p> -<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p5a</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Sums of squares:</span></span> -<span><span class="co">## SFO IORE DFOP </span></span> -<span><span class="co">## 465.21753 56.27506 32.06401 </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span> -<span><span class="co">## [1] 64.4304</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Parameters:</span></span> -<span><span class="co">## $SFO</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 95.8401 4.67e-21 92.245 99.4357</span></span> -<span><span class="co">## k_parent 0.0102 3.92e-12 0.009 0.0117</span></span> -<span><span class="co">## sigma 4.8230 3.81e-06 3.214 6.4318</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $IORE</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 1.01e+02 NA 9.91e+01 1.02e+02</span></span> -<span><span class="co">## k__iore_parent 1.54e-05 NA 4.08e-06 5.84e-05</span></span> -<span><span class="co">## N_parent 2.57e+00 NA 2.25e+00 2.89e+00</span></span> -<span><span class="co">## sigma 1.68e+00 NA 1.12e+00 2.24e+00</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $DFOP</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 9.99e+01 1.41e-26 98.8116 101.0810</span></span> -<span><span class="co">## k1 2.67e-02 5.05e-06 0.0243 0.0295</span></span> -<span><span class="co">## k2 2.26e-12 5.00e-01 0.0000 Inf</span></span> -<span><span class="co">## g 6.47e-01 3.67e-06 0.6248 0.6677</span></span> -<span><span class="co">## sigma 1.27e+00 8.91e-06 0.8395 1.6929</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## DTx values:</span></span> -<span><span class="co">## DT50 DT90 DT50_rep</span></span> -<span><span class="co">## SFO 67.7 2.25e+02 6.77e+01</span></span> -<span><span class="co">## IORE 58.2 1.07e+03 3.22e+02</span></span> -<span><span class="co">## DFOP 55.5 5.59e+11 3.07e+11</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Representative half-life:</span></span> -<span><span class="co">## [1] 321.51</span></span></code></pre> -</div> -<div class="section level3"> -<h3 id="example-on-page-5-lower-panel">Example on page 5, lower panel<a class="anchor" aria-label="anchor" href="#example-on-page-5-lower-panel"></a> -</h3> -<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">p5b</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p5b"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre> -<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre> -<div class="sourceCode" id="cb10"><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">p5b</span><span class="op">)</span></span></code></pre></div> -<p><img src="NAFTA_examples_files/figure-html/p5b-1.png" width="700"></p> -<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p5b</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Sums of squares:</span></span> -<span><span class="co">## SFO IORE DFOP </span></span> -<span><span class="co">## 94.81123 10.10936 7.55871 </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span> -<span><span class="co">## [1] 11.77879</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Parameters:</span></span> -<span><span class="co">## $SFO</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 96.497 2.32e-24 94.85271 98.14155</span></span> -<span><span class="co">## k_parent 0.008 3.42e-14 0.00737 0.00869</span></span> -<span><span class="co">## sigma 2.295 1.22e-05 1.47976 3.11036</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $IORE</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 9.85e+01 1.17e-28 9.79e+01 9.92e+01</span></span> -<span><span class="co">## k__iore_parent 1.53e-04 6.50e-03 7.21e-05 3.26e-04</span></span> -<span><span class="co">## N_parent 1.94e+00 5.88e-13 1.76e+00 2.12e+00</span></span> -<span><span class="co">## sigma 7.49e-01 1.63e-05 4.82e-01 1.02e+00</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $DFOP</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 9.84e+01 1.24e-27 97.8078 98.9187</span></span> -<span><span class="co">## k1 1.55e-02 4.10e-04 0.0143 0.0167</span></span> -<span><span class="co">## k2 8.63e-12 5.00e-01 0.0000 Inf</span></span> -<span><span class="co">## g 6.89e-01 2.92e-03 0.6626 0.7142</span></span> -<span><span class="co">## sigma 6.48e-01 2.38e-05 0.4147 0.8813</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## DTx values:</span></span> -<span><span class="co">## DT50 DT90 DT50_rep</span></span> -<span><span class="co">## SFO 86.6 2.88e+02 8.66e+01</span></span> -<span><span class="co">## IORE 85.5 7.17e+02 2.16e+02</span></span> -<span><span class="co">## DFOP 83.6 1.32e+11 8.04e+10</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Representative half-life:</span></span> -<span><span class="co">## [1] 215.87</span></span></code></pre> -</div> -<div class="section level3"> -<h3 id="example-on-page-6">Example on page 6<a class="anchor" aria-label="anchor" href="#example-on-page-6"></a> -</h3> -<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">p6</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p6"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre> -<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre> -<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">p6</span><span class="op">)</span></span></code></pre></div> -<p><img src="NAFTA_examples_files/figure-html/p6-1.png" width="700"></p> -<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p6</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Sums of squares:</span></span> -<span><span class="co">## SFO IORE DFOP </span></span> -<span><span class="co">## 188.45361 51.00699 42.46931 </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span> -<span><span class="co">## [1] 58.39888</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Parameters:</span></span> -<span><span class="co">## $SFO</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 94.7759 7.29e-24 92.3478 97.2039</span></span> -<span><span class="co">## k_parent 0.0179 8.02e-16 0.0166 0.0194</span></span> -<span><span class="co">## sigma 3.0696 3.81e-06 2.0456 4.0936</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $IORE</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 97.12446 2.63e-26 95.62461 98.62431</span></span> -<span><span class="co">## k__iore_parent 0.00252 1.95e-03 0.00134 0.00472</span></span> -<span><span class="co">## N_parent 1.49587 4.07e-13 1.33896 1.65279</span></span> -<span><span class="co">## sigma 1.59698 5.05e-06 1.06169 2.13227</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $DFOP</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 9.66e+01 1.57e-25 95.3476 97.8979</span></span> -<span><span class="co">## k1 2.55e-02 7.33e-06 0.0233 0.0278</span></span> -<span><span class="co">## k2 3.22e-11 5.00e-01 0.0000 Inf</span></span> -<span><span class="co">## g 8.61e-01 7.55e-06 0.8314 0.8867</span></span> -<span><span class="co">## sigma 1.46e+00 6.93e-06 0.9661 1.9483</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## DTx values:</span></span> -<span><span class="co">## DT50 DT90 DT50_rep</span></span> -<span><span class="co">## SFO 38.6 1.28e+02 3.86e+01</span></span> -<span><span class="co">## IORE 34.0 1.77e+02 5.32e+01</span></span> -<span><span class="co">## DFOP 34.1 1.01e+10 2.15e+10</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Representative half-life:</span></span> -<span><span class="co">## [1] 53.17</span></span></code></pre> -</div> -<div class="section level3"> -<h3 id="example-on-page-7">Example on page 7<a class="anchor" aria-label="anchor" href="#example-on-page-7"></a> -</h3> -<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">p7</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p7"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre> -<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre> -<div class="sourceCode" id="cb22"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p7</span><span class="op">)</span></span></code></pre></div> -<p><img src="NAFTA_examples_files/figure-html/p7-1.png" width="700"></p> -<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p7</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Sums of squares:</span></span> -<span><span class="co">## SFO IORE DFOP </span></span> -<span><span class="co">## 3661.661 3195.030 3174.145 </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span> -<span><span class="co">## [1] 3334.194</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Parameters:</span></span> -<span><span class="co">## $SFO</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 96.41796 4.80e-53 93.32245 99.51347</span></span> -<span><span class="co">## k_parent 0.00735 7.64e-21 0.00641 0.00843</span></span> -<span><span class="co">## sigma 7.94557 1.83e-15 6.46713 9.42401</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $IORE</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 9.92e+01 NA 9.55e+01 1.03e+02</span></span> -<span><span class="co">## k__iore_parent 1.60e-05 NA 1.45e-07 1.77e-03</span></span> -<span><span class="co">## N_parent 2.45e+00 NA 1.35e+00 3.54e+00</span></span> -<span><span class="co">## sigma 7.42e+00 NA 6.04e+00 8.80e+00</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $DFOP</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 9.89e+01 9.44e-49 95.4640 102.2573</span></span> -<span><span class="co">## k1 1.81e-02 1.75e-01 0.0116 0.0281</span></span> -<span><span class="co">## k2 3.63e-10 5.00e-01 0.0000 Inf</span></span> -<span><span class="co">## g 6.06e-01 2.19e-01 0.4826 0.7178</span></span> -<span><span class="co">## sigma 7.40e+00 2.97e-15 6.0201 8.7754</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## DTx values:</span></span> -<span><span class="co">## DT50 DT90 DT50_rep</span></span> -<span><span class="co">## SFO 94.3 3.13e+02 9.43e+01</span></span> -<span><span class="co">## IORE 96.7 1.51e+03 4.55e+02</span></span> -<span><span class="co">## DFOP 96.4 3.77e+09 1.91e+09</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Representative half-life:</span></span> -<span><span class="co">## [1] 454.55</span></span></code></pre> -</div> -</div> -<div class="section level2"> -<h2 id="examples-where-the-representative-half-life-deviates-from-the-observed-dt50">Examples where the representative half-life deviates from the -observed DT50<a class="anchor" aria-label="anchor" href="#examples-where-the-representative-half-life-deviates-from-the-observed-dt50"></a> -</h2> -<div class="section level3"> -<h3 id="example-on-page-8">Example on page 8<a class="anchor" aria-label="anchor" href="#example-on-page-8"></a> -</h3> -<p>For this dataset, the IORE fit does not converge when the default -starting values used by mkin for the IORE model are used. Therefore, a -lower value for the rate constant is used here.</p> -<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">p8</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p8"</span><span class="op">]</span><span class="op">]</span>, parms.ini <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>k__iore_parent <span class="op">=</span> <span class="fl">1e-3</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre> -<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre> -<div class="sourceCode" id="cb28"><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">p8</span><span class="op">)</span></span></code></pre></div> -<p><img src="NAFTA_examples_files/figure-html/p8-1.png" width="700"></p> -<div class="sourceCode" id="cb29"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p8</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Sums of squares:</span></span> -<span><span class="co">## SFO IORE DFOP </span></span> -<span><span class="co">## 1996.9408 444.9237 547.5616 </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span> -<span><span class="co">## [1] 477.4924</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Parameters:</span></span> -<span><span class="co">## $SFO</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 88.16549 6.53e-29 83.37344 92.95754</span></span> -<span><span class="co">## k_parent 0.00803 1.67e-13 0.00674 0.00957</span></span> -<span><span class="co">## sigma 7.44786 4.17e-10 5.66209 9.23363</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $IORE</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 9.77e+01 7.03e-35 9.44e+01 1.01e+02</span></span> -<span><span class="co">## k__iore_parent 6.14e-05 3.20e-02 2.12e-05 1.78e-04</span></span> -<span><span class="co">## N_parent 2.27e+00 4.23e-18 2.00e+00 2.54e+00</span></span> -<span><span class="co">## sigma 3.52e+00 5.36e-10 2.67e+00 4.36e+00</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $DFOP</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 95.70619 8.99e-32 91.87941 99.53298</span></span> -<span><span class="co">## k1 0.02500 5.25e-04 0.01422 0.04394</span></span> -<span><span class="co">## k2 0.00273 6.84e-03 0.00125 0.00597</span></span> -<span><span class="co">## g 0.58835 2.84e-06 0.36595 0.77970</span></span> -<span><span class="co">## sigma 3.90001 6.94e-10 2.96260 4.83741</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## DTx values:</span></span> -<span><span class="co">## DT50 DT90 DT50_rep</span></span> -<span><span class="co">## SFO 86.3 287 86.3</span></span> -<span><span class="co">## IORE 53.4 668 201.0</span></span> -<span><span class="co">## DFOP 55.6 517 253.0</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Representative half-life:</span></span> -<span><span class="co">## [1] 201.03</span></span></code></pre> -</div> -</div> -<div class="section level2"> -<h2 id="examples-where-sfo-was-not-selected-for-an-abiotic-study">Examples where SFO was not selected for an abiotic study<a class="anchor" aria-label="anchor" href="#examples-where-sfo-was-not-selected-for-an-abiotic-study"></a> -</h2> -<div class="section level3"> -<h3 id="example-on-page-9-upper-panel">Example on page 9, upper panel<a class="anchor" aria-label="anchor" href="#example-on-page-9-upper-panel"></a> -</h3> -<div class="sourceCode" id="cb31"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">p9a</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p9a"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre> -<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre> -<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">p9a</span><span class="op">)</span></span></code></pre></div> -<p><img src="NAFTA_examples_files/figure-html/p9a-1.png" width="700"></p> -<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/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p9a</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Sums of squares:</span></span> -<span><span class="co">## SFO IORE DFOP </span></span> -<span><span class="co">## 839.35238 88.57064 9.93363 </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span> -<span><span class="co">## [1] 105.5678</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Parameters:</span></span> -<span><span class="co">## $SFO</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 88.1933 3.06e-12 79.9447 96.4419</span></span> -<span><span class="co">## k_parent 0.0409 2.07e-07 0.0324 0.0516</span></span> -<span><span class="co">## sigma 7.2429 3.92e-05 4.4768 10.0090</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $IORE</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 9.89e+01 1.12e-16 9.54e+01 1.02e+02</span></span> -<span><span class="co">## k__iore_parent 1.93e-05 1.13e-01 3.49e-06 1.06e-04</span></span> -<span><span class="co">## N_parent 2.91e+00 1.45e-09 2.50e+00 3.32e+00</span></span> -<span><span class="co">## sigma 2.35e+00 5.31e-05 1.45e+00 3.26e+00</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $DFOP</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 9.85e+01 2.54e-20 97.390 99.672</span></span> -<span><span class="co">## k1 1.38e-01 3.52e-05 0.131 0.146</span></span> -<span><span class="co">## k2 9.02e-13 5.00e-01 0.000 Inf</span></span> -<span><span class="co">## g 6.52e-01 8.13e-06 0.642 0.661</span></span> -<span><span class="co">## sigma 7.88e-01 6.13e-02 0.481 1.095</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## DTx values:</span></span> -<span><span class="co">## DT50 DT90 DT50_rep</span></span> -<span><span class="co">## SFO 16.9 5.63e+01 1.69e+01</span></span> -<span><span class="co">## IORE 11.6 3.37e+02 1.01e+02</span></span> -<span><span class="co">## DFOP 10.5 1.38e+12 7.69e+11</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Representative half-life:</span></span> -<span><span class="co">## [1] 101.43</span></span></code></pre> -<p>In this example, the residuals of the SFO indicate a lack of fit of -this model, so even if it was an abiotic experiment, the data do not -suggest a simple exponential decline.</p> -</div> -<div class="section level3"> -<h3 id="example-on-page-9-lower-panel">Example on page 9, lower panel<a class="anchor" aria-label="anchor" href="#example-on-page-9-lower-panel"></a> -</h3> -<div class="sourceCode" id="cb37"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">p9b</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p9b"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Warning in sqrt(diag(covar)): NaNs produced</span></span></code></pre> -<pre><code><span><span class="co">## Warning in sqrt(diag(covar_notrans)): NaNs produced</span></span></code></pre> -<pre><code><span><span class="co">## Warning in sqrt(1/diag(V)): NaNs produced</span></span></code></pre> -<pre><code><span><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result</span></span> -<span><span class="co">## is doubtful</span></span></code></pre> -<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre> -<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre> -<div class="sourceCode" id="cb44"><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">p9b</span><span class="op">)</span></span></code></pre></div> -<p><img src="NAFTA_examples_files/figure-html/p9b-1.png" width="700"></p> -<div class="sourceCode" id="cb45"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p9b</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Sums of squares:</span></span> -<span><span class="co">## SFO IORE DFOP </span></span> -<span><span class="co">## 35.64867 23.22334 35.64867 </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span> -<span><span class="co">## [1] 28.54188</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Parameters:</span></span> -<span><span class="co">## $SFO</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 94.7123 2.15e-19 93.178 96.2464</span></span> -<span><span class="co">## k_parent 0.0389 4.47e-14 0.037 0.0408</span></span> -<span><span class="co">## sigma 1.5957 1.28e-04 0.932 2.2595</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $IORE</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 93.863 2.32e-18 92.4565 95.269</span></span> -<span><span class="co">## k__iore_parent 0.127 1.85e-02 0.0504 0.321</span></span> -<span><span class="co">## N_parent 0.711 1.88e-05 0.4843 0.937</span></span> -<span><span class="co">## sigma 1.288 1.76e-04 0.7456 1.830</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $DFOP</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 94.7123 1.61e-16 93.1355 96.2891</span></span> -<span><span class="co">## k1 0.0389 1.08e-04 0.0266 0.0569</span></span> -<span><span class="co">## k2 0.0389 2.23e-04 0.0255 0.0592</span></span> -<span><span class="co">## g 0.5256 NaN NA NA</span></span> -<span><span class="co">## sigma 1.5957 2.50e-04 0.9135 2.2779</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## DTx values:</span></span> -<span><span class="co">## DT50 DT90 DT50_rep</span></span> -<span><span class="co">## SFO 17.8 59.2 17.8</span></span> -<span><span class="co">## IORE 18.4 49.2 14.8</span></span> -<span><span class="co">## DFOP 17.8 59.2 17.8</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Representative half-life:</span></span> -<span><span class="co">## [1] 14.8</span></span></code></pre> -<p>Here, mkin gives a longer slow DT50 for the DFOP model (17.8 days) -than PestDF (13.5 days). Presumably, this is related to the fact that -PestDF gives a negative value for the proportion of the fast degradation -which should be between 0 and 1, inclusive. This parameter is called f -in PestDF and g in mkin. In mkin, it is restricted to the interval from -0 to 1.</p> -</div> -<div class="section level3"> -<h3 id="example-on-page-10">Example on page 10<a class="anchor" aria-label="anchor" href="#example-on-page-10"></a> -</h3> -<div class="sourceCode" id="cb47"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">p10</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p10"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Warning in sqrt(diag(covar)): NaNs produced</span></span></code></pre> -<pre><code><span><span class="co">## Warning in sqrt(1/diag(V)): NaNs produced</span></span></code></pre> -<pre><code><span><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result</span></span> -<span><span class="co">## is doubtful</span></span></code></pre> -<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre> -<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre> -<div class="sourceCode" id="cb53"><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">p10</span><span class="op">)</span></span></code></pre></div> -<p><img src="NAFTA_examples_files/figure-html/p10-1.png" width="700"></p> -<div class="sourceCode" id="cb54"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p10</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Sums of squares:</span></span> -<span><span class="co">## SFO IORE DFOP </span></span> -<span><span class="co">## 899.4089 336.4348 899.4089 </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span> -<span><span class="co">## [1] 413.4841</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Parameters:</span></span> -<span><span class="co">## $SFO</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 101.7315 6.42e-11 91.9259 111.5371</span></span> -<span><span class="co">## k_parent 0.0495 1.70e-07 0.0404 0.0607</span></span> -<span><span class="co">## sigma 8.0152 1.28e-04 4.6813 11.3491</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $IORE</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 96.86 3.32e-12 90.848 102.863</span></span> -<span><span class="co">## k__iore_parent 2.96 7.91e-02 0.687 12.761</span></span> -<span><span class="co">## N_parent 0.00 5.00e-01 -0.372 0.372</span></span> -<span><span class="co">## sigma 4.90 1.77e-04 2.837 6.968</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $DFOP</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 101.7315 1.41e-09 91.6534 111.8097</span></span> -<span><span class="co">## k1 0.0495 6.58e-03 0.0303 0.0809</span></span> -<span><span class="co">## k2 0.0495 2.60e-03 0.0410 0.0598</span></span> -<span><span class="co">## g 0.4487 5.00e-01 NA NA</span></span> -<span><span class="co">## sigma 8.0152 2.50e-04 4.5886 11.4418</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## DTx values:</span></span> -<span><span class="co">## DT50 DT90 DT50_rep</span></span> -<span><span class="co">## SFO 14.0 46.5 14.00</span></span> -<span><span class="co">## IORE 16.4 29.4 8.86</span></span> -<span><span class="co">## DFOP 14.0 46.5 14.00</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Representative half-life:</span></span> -<span><span class="co">## [1] 8.86</span></span></code></pre> -<p>Here, a value below N is given for the IORE model, because the data -suggests a faster decline towards the end of the experiment, which -appears physically rather unlikely in the case of a photolysis study. It -seems PestDF does not constrain N to values above zero, thus the slight -difference in IORE model parameters between PestDF and mkin.</p> -</div> -</div> -<div class="section level2"> -<h2 id="the-dt50-was-not-observed-during-the-study">The DT50 was not observed during the study<a class="anchor" aria-label="anchor" href="#the-dt50-was-not-observed-during-the-study"></a> -</h2> -<div class="section level3"> -<h3 id="example-on-page-11">Example on page 11<a class="anchor" aria-label="anchor" href="#example-on-page-11"></a> -</h3> -<div class="sourceCode" id="cb56"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">p11</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p11"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre> -<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre> -<div class="sourceCode" id="cb59"><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">p11</span><span class="op">)</span></span></code></pre></div> -<p><img src="NAFTA_examples_files/figure-html/p11-1.png" width="700"></p> -<div class="sourceCode" id="cb60"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p11</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Sums of squares:</span></span> -<span><span class="co">## SFO IORE DFOP </span></span> -<span><span class="co">## 579.6805 204.7932 144.7783 </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span> -<span><span class="co">## [1] 251.6944</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Parameters:</span></span> -<span><span class="co">## $SFO</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 96.15820 4.83e-13 90.24934 1.02e+02</span></span> -<span><span class="co">## k_parent 0.00321 4.71e-05 0.00222 4.64e-03</span></span> -<span><span class="co">## sigma 6.43473 1.28e-04 3.75822 9.11e+00</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $IORE</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 1.05e+02 NA 9.90e+01 1.10e+02</span></span> -<span><span class="co">## k__iore_parent 3.11e-17 NA 1.35e-20 7.18e-14</span></span> -<span><span class="co">## N_parent 8.36e+00 NA 6.62e+00 1.01e+01</span></span> -<span><span class="co">## sigma 3.82e+00 NA 2.21e+00 5.44e+00</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $DFOP</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 1.05e+02 9.47e-13 99.9990 109.1224</span></span> -<span><span class="co">## k1 4.41e-02 5.95e-03 0.0296 0.0658</span></span> -<span><span class="co">## k2 9.94e-13 5.00e-01 0.0000 Inf</span></span> -<span><span class="co">## g 3.22e-01 1.45e-03 0.2814 0.3650</span></span> -<span><span class="co">## sigma 3.22e+00 3.52e-04 1.8410 4.5906</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## DTx values:</span></span> -<span><span class="co">## DT50 DT90 DT50_rep</span></span> -<span><span class="co">## SFO 2.16e+02 7.18e+02 2.16e+02</span></span> -<span><span class="co">## IORE 9.73e+02 1.37e+08 4.11e+07</span></span> -<span><span class="co">## DFOP 3.07e+11 1.93e+12 6.98e+11</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Representative half-life:</span></span> -<span><span class="co">## [1] 41148170</span></span></code></pre> -<p>In this case, the DFOP fit reported for PestDF resulted in a negative -value for the slower rate constant, which is not possible in mkin. The -other results are in agreement.</p> -</div> -</div> -<div class="section level2"> -<h2 id="n-is-less-than-1-and-the-dfop-rate-constants-are-like-the-sfo-rate-constant">N is less than 1 and the DFOP rate constants are like the SFO rate -constant<a class="anchor" aria-label="anchor" href="#n-is-less-than-1-and-the-dfop-rate-constants-are-like-the-sfo-rate-constant"></a> -</h2> -<p>In the following three examples, the same results are obtained with -mkin as reported for PestDF. As in the case on page 10, the N values -below 1 are deemed unrealistic and appear to be the result of an -overparameterisation.</p> -<div class="section level3"> -<h3 id="example-on-page-12-upper-panel">Example on page 12, upper panel<a class="anchor" aria-label="anchor" href="#example-on-page-12-upper-panel"></a> -</h3> -<div class="sourceCode" id="cb62"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">p12a</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p12a"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Warning in summary.mkinfit(x): Could not calculate correlation; no covariance</span></span> -<span><span class="co">## matrix</span></span></code></pre> -<pre><code><span><span class="co">## Warning in sqrt(diag(covar)): NaNs produced</span></span></code></pre> -<pre><code><span><span class="co">## Warning in sqrt(diag(covar_notrans)): NaNs produced</span></span></code></pre> -<pre><code><span><span class="co">## Warning in sqrt(1/diag(V)): NaNs produced</span></span></code></pre> -<pre><code><span><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result</span></span> -<span><span class="co">## is doubtful</span></span></code></pre> -<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre> -<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre> -<div class="sourceCode" id="cb70"><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">p12a</span><span class="op">)</span></span></code></pre></div> -<p><img src="NAFTA_examples_files/figure-html/p12a-1.png" width="700"></p> -<div class="sourceCode" id="cb71"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p12a</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Sums of squares:</span></span> -<span><span class="co">## SFO IORE DFOP </span></span> -<span><span class="co">## 695.4440 220.0685 695.4440 </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span> -<span><span class="co">## [1] 270.4679</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Parameters:</span></span> -<span><span class="co">## $SFO</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 100.521 8.75e-12 92.461 108.581</span></span> -<span><span class="co">## k_parent 0.124 3.61e-08 0.104 0.148</span></span> -<span><span class="co">## sigma 7.048 1.28e-04 4.116 9.980</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $IORE</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 96.823 NA NA NA</span></span> -<span><span class="co">## k__iore_parent 2.436 NA NA NA</span></span> -<span><span class="co">## N_parent 0.263 NA NA NA</span></span> -<span><span class="co">## sigma 3.965 NA NA NA</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $DFOP</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 100.521 2.74e-10 92.2366 108.805</span></span> -<span><span class="co">## k1 0.124 2.53e-05 0.0908 0.170</span></span> -<span><span class="co">## k2 0.124 2.52e-02 0.0456 0.339</span></span> -<span><span class="co">## g 0.793 NaN NA NA</span></span> -<span><span class="co">## sigma 7.048 2.50e-04 4.0349 10.061</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## DTx values:</span></span> -<span><span class="co">## DT50 DT90 DT50_rep</span></span> -<span><span class="co">## SFO 5.58 18.5 5.58</span></span> -<span><span class="co">## IORE 6.49 13.2 3.99</span></span> -<span><span class="co">## DFOP 5.58 18.5 5.58</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Representative half-life:</span></span> -<span><span class="co">## [1] 3.99</span></span></code></pre> -</div> -<div class="section level3"> -<h3 id="example-on-page-12-lower-panel">Example on page 12, lower panel<a class="anchor" aria-label="anchor" href="#example-on-page-12-lower-panel"></a> -</h3> -<div class="sourceCode" id="cb73"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">p12b</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p12b"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Warning in qt(alpha/2, rdf): NaNs produced</span></span></code></pre> -<pre><code><span><span class="co">## Warning in qt(1 - alpha/2, rdf): NaNs produced</span></span></code></pre> -<pre><code><span><span class="co">## Warning in sqrt(diag(covar_notrans)): NaNs produced</span></span></code></pre> -<pre><code><span><span class="co">## Warning in pt(abs(tval), rdf, lower.tail = FALSE): NaNs produced</span></span></code></pre> -<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre> -<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre> -<div class="sourceCode" id="cb80"><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">p12b</span><span class="op">)</span></span></code></pre></div> -<p><img src="NAFTA_examples_files/figure-html/p12b-1.png" width="700"></p> -<div class="sourceCode" id="cb81"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p12b</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Sums of squares:</span></span> -<span><span class="co">## SFO IORE DFOP </span></span> -<span><span class="co">## 58.90242 19.06353 58.90242 </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span> -<span><span class="co">## [1] 51.51756</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Parameters:</span></span> -<span><span class="co">## $SFO</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 97.6840 0.00039 85.9388 109.4292</span></span> -<span><span class="co">## k_parent 0.0589 0.00261 0.0431 0.0805</span></span> -<span><span class="co">## sigma 3.4323 0.04356 -1.2377 8.1023</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $IORE</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 95.523 0.0055 74.539157 116.51</span></span> -<span><span class="co">## k__iore_parent 0.333 0.1433 0.000717 154.57</span></span> -<span><span class="co">## N_parent 0.568 0.0677 -0.989464 2.13</span></span> -<span><span class="co">## sigma 1.953 0.0975 -5.893100 9.80</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $DFOP</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 97.6840 NaN NaN NaN</span></span> -<span><span class="co">## k1 0.0589 NaN NA NA</span></span> -<span><span class="co">## k2 0.0589 NaN NA NA</span></span> -<span><span class="co">## g 0.6473 NaN NA NA</span></span> -<span><span class="co">## sigma 3.4323 NaN NaN NaN</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## DTx values:</span></span> -<span><span class="co">## DT50 DT90 DT50_rep</span></span> -<span><span class="co">## SFO 11.8 39.1 11.80</span></span> -<span><span class="co">## IORE 12.9 31.4 9.46</span></span> -<span><span class="co">## DFOP 11.8 39.1 11.80</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Representative half-life:</span></span> -<span><span class="co">## [1] 9.46</span></span></code></pre> -</div> -<div class="section level3"> -<h3 id="example-on-page-13">Example on page 13<a class="anchor" aria-label="anchor" href="#example-on-page-13"></a> -</h3> -<div class="sourceCode" id="cb83"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">p13</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p13"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre> -<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre> -<div class="sourceCode" id="cb86"><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">p13</span><span class="op">)</span></span></code></pre></div> -<p><img src="NAFTA_examples_files/figure-html/p13-1.png" width="700"></p> -<div class="sourceCode" id="cb87"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p13</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Sums of squares:</span></span> -<span><span class="co">## SFO IORE DFOP </span></span> -<span><span class="co">## 174.5971 142.3951 174.5971 </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span> -<span><span class="co">## [1] 172.131</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Parameters:</span></span> -<span><span class="co">## $SFO</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 92.73500 5.99e-17 89.61936 95.85065</span></span> -<span><span class="co">## k_parent 0.00258 2.42e-09 0.00223 0.00299</span></span> -<span><span class="co">## sigma 3.41172 7.07e-05 2.05455 4.76888</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $IORE</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 91.6016 6.34e-16 88.53086 94.672</span></span> -<span><span class="co">## k__iore_parent 0.0396 2.36e-01 0.00207 0.759</span></span> -<span><span class="co">## N_parent 0.3541 1.46e-01 -0.35153 1.060</span></span> -<span><span class="co">## sigma 3.0811 9.64e-05 1.84296 4.319</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $DFOP</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 92.73500 NA 8.95e+01 95.92118</span></span> -<span><span class="co">## k1 0.00258 NA 4.14e-04 0.01611</span></span> -<span><span class="co">## k2 0.00258 NA 1.74e-03 0.00383</span></span> -<span><span class="co">## g 0.16452 NA 0.00e+00 1.00000</span></span> -<span><span class="co">## sigma 3.41172 NA 2.02e+00 4.79960</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## DTx values:</span></span> -<span><span class="co">## DT50 DT90 DT50_rep</span></span> -<span><span class="co">## SFO 269 892 269</span></span> -<span><span class="co">## IORE 261 560 169</span></span> -<span><span class="co">## DFOP 269 892 269</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Representative half-life:</span></span> -<span><span class="co">## [1] 168.51</span></span></code></pre> -</div> -</div> -<div class="section level2"> -<h2 id="dt50-not-observed-in-the-study-and-dfop-problems-in-pestdf">DT50 not observed in the study and DFOP problems in PestDF<a class="anchor" aria-label="anchor" href="#dt50-not-observed-in-the-study-and-dfop-problems-in-pestdf"></a> -</h2> -<div class="sourceCode" id="cb89"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">p14</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p14"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Warning in sqrt(diag(covar)): NaNs produced</span></span></code></pre> -<pre><code><span><span class="co">## Warning in sqrt(1/diag(V)): NaNs produced</span></span></code></pre> -<pre><code><span><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result</span></span> -<span><span class="co">## is doubtful</span></span></code></pre> -<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre> -<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre> -<div class="sourceCode" id="cb95"><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">p14</span><span class="op">)</span></span></code></pre></div> -<p><img src="NAFTA_examples_files/figure-html/p14-1.png" width="700"></p> -<div class="sourceCode" id="cb96"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p14</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Sums of squares:</span></span> -<span><span class="co">## SFO IORE DFOP </span></span> -<span><span class="co">## 48.43249 28.67746 27.26248 </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span> -<span><span class="co">## [1] 32.83337</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Parameters:</span></span> -<span><span class="co">## $SFO</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 99.47124 2.06e-30 98.42254 1.01e+02</span></span> -<span><span class="co">## k_parent 0.00279 3.75e-15 0.00256 3.04e-03</span></span> -<span><span class="co">## sigma 1.55616 3.81e-06 1.03704 2.08e+00</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $IORE</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 1.00e+02 NA NaN NaN</span></span> -<span><span class="co">## k__iore_parent 9.44e-08 NA NaN NaN</span></span> -<span><span class="co">## N_parent 3.31e+00 NA NaN NaN</span></span> -<span><span class="co">## sigma 1.20e+00 NA 0.796 1.6</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $DFOP</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 1.00e+02 2.96e-28 99.40280 101.2768</span></span> -<span><span class="co">## k1 9.53e-03 1.20e-01 0.00638 0.0143</span></span> -<span><span class="co">## k2 6.08e-12 5.00e-01 0.00000 Inf</span></span> -<span><span class="co">## g 3.98e-01 2.19e-01 0.30481 0.4998</span></span> -<span><span class="co">## sigma 1.17e+00 7.68e-06 0.77406 1.5610</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## DTx values:</span></span> -<span><span class="co">## DT50 DT90 DT50_rep</span></span> -<span><span class="co">## SFO 2.48e+02 8.25e+02 2.48e+02</span></span> -<span><span class="co">## IORE 4.34e+02 2.22e+04 6.70e+03</span></span> -<span><span class="co">## DFOP 3.05e+10 2.95e+11 1.14e+11</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Representative half-life:</span></span> -<span><span class="co">## [1] 6697.44</span></span></code></pre> -<p>The slower rate constant reported by PestDF is negative, which is not -physically realistic, and not possible in mkin. The other fits give the -same results in mkin and PestDF.</p> -</div> -<div class="section level2"> -<h2 id="n-is-less-than-1-and-dfop-fraction-parameter-is-below-zero">N is less than 1 and DFOP fraction parameter is below zero<a class="anchor" aria-label="anchor" href="#n-is-less-than-1-and-dfop-fraction-parameter-is-below-zero"></a> -</h2> -<div class="sourceCode" id="cb98"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">p15a</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p15a"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre> -<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre> -<div class="sourceCode" id="cb101"><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">p15a</span><span class="op">)</span></span></code></pre></div> -<p><img src="NAFTA_examples_files/figure-html/p15a-1.png" width="700"></p> -<div class="sourceCode" id="cb102"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p15a</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Sums of squares:</span></span> -<span><span class="co">## SFO IORE DFOP </span></span> -<span><span class="co">## 245.5248 135.0132 245.5248 </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span> -<span><span class="co">## [1] 165.9335</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Parameters:</span></span> -<span><span class="co">## $SFO</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 97.96751 2.00e-15 94.32049 101.615</span></span> -<span><span class="co">## k_parent 0.00952 4.93e-09 0.00824 0.011</span></span> -<span><span class="co">## sigma 4.18778 1.28e-04 2.44588 5.930</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $IORE</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 95.874 2.94e-15 92.937 98.811</span></span> -<span><span class="co">## k__iore_parent 0.629 2.11e-01 0.044 8.982</span></span> -<span><span class="co">## N_parent 0.000 5.00e-01 -0.642 0.642</span></span> -<span><span class="co">## sigma 3.105 1.78e-04 1.795 4.416</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $DFOP</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 97.96751 2.85e-13 94.21913 101.7159</span></span> -<span><span class="co">## k1 0.00952 6.28e-02 0.00250 0.0363</span></span> -<span><span class="co">## k2 0.00952 1.27e-04 0.00646 0.0140</span></span> -<span><span class="co">## g 0.21241 5.00e-01 0.00000 1.0000</span></span> -<span><span class="co">## sigma 4.18778 2.50e-04 2.39747 5.9781</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## DTx values:</span></span> -<span><span class="co">## DT50 DT90 DT50_rep</span></span> -<span><span class="co">## SFO 72.8 242 72.8</span></span> -<span><span class="co">## IORE 76.3 137 41.3</span></span> -<span><span class="co">## DFOP 72.8 242 72.8</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Representative half-life:</span></span> -<span><span class="co">## [1] 41.33</span></span></code></pre> -<div class="sourceCode" id="cb104"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">p15b</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p15b"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Warning in sqrt(diag(covar)): NaNs produced</span></span></code></pre> -<pre><code><span><span class="co">## Warning in sqrt(1/diag(V)): NaNs produced</span></span></code></pre> -<pre><code><span><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result</span></span> -<span><span class="co">## is doubtful</span></span></code></pre> -<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre> -<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre> -<div class="sourceCode" id="cb110"><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">p15b</span><span class="op">)</span></span></code></pre></div> -<p><img src="NAFTA_examples_files/figure-html/p15b-1.png" width="700"></p> -<div class="sourceCode" id="cb111"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p15b</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Sums of squares:</span></span> -<span><span class="co">## SFO IORE DFOP </span></span> -<span><span class="co">## 106.91629 68.55574 106.91629 </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span> -<span><span class="co">## [1] 84.25618</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Parameters:</span></span> -<span><span class="co">## $SFO</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 1.01e+02 3.06e-17 98.31594 1.03e+02</span></span> -<span><span class="co">## k_parent 4.86e-03 2.48e-10 0.00435 5.42e-03</span></span> -<span><span class="co">## sigma 2.76e+00 1.28e-04 1.61402 3.91e+00</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $IORE</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 99.83 1.81e-16 97.51349 102.14</span></span> -<span><span class="co">## k__iore_parent 0.38 3.22e-01 0.00352 41.05</span></span> -<span><span class="co">## N_parent 0.00 5.00e-01 -1.07696 1.08</span></span> -<span><span class="co">## sigma 2.21 2.57e-04 1.23245 3.19</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $DFOP</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 1.01e+02 NA 9.82e+01 1.04e+02</span></span> -<span><span class="co">## k1 4.86e-03 NA 8.63e-04 2.73e-02</span></span> -<span><span class="co">## k2 4.86e-03 NA 3.21e-03 7.35e-03</span></span> -<span><span class="co">## g 1.88e-01 NA NA NA</span></span> -<span><span class="co">## sigma 2.76e+00 NA 1.58e+00 3.94e+00</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## DTx values:</span></span> -<span><span class="co">## DT50 DT90 DT50_rep</span></span> -<span><span class="co">## SFO 143 474 143.0</span></span> -<span><span class="co">## IORE 131 236 71.2</span></span> -<span><span class="co">## DFOP 143 474 143.0</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Representative half-life:</span></span> -<span><span class="co">## [1] 71.18</span></span></code></pre> -<p>In mkin, only the IORE fit is affected (deemed unrealistic), as the -fraction parameter of the DFOP model is restricted to the interval -between 0 and 1 in mkin. The SFO fits give the same results for both -mkin and PestDF.</p> -</div> -<div class="section level2"> -<h2 id="the-dfop-fraction-parameter-is-greater-than-1">The DFOP fraction parameter is greater than 1<a class="anchor" aria-label="anchor" href="#the-dfop-fraction-parameter-is-greater-than-1"></a> -</h2> -<div class="sourceCode" id="cb113"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">p16</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p16"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre> -<pre><code><span><span class="co">## The representative half-life of the IORE model is longer than the one corresponding</span></span></code></pre> -<pre><code><span><span class="co">## to the terminal degradation rate found with the DFOP model.</span></span></code></pre> -<pre><code><span><span class="co">## The representative half-life obtained from the DFOP model may be used</span></span></code></pre> -<div class="sourceCode" id="cb118"><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">p16</span><span class="op">)</span></span></code></pre></div> -<p><img src="NAFTA_examples_files/figure-html/p16-1.png" width="700"></p> -<div class="sourceCode" id="cb119"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p16</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Sums of squares:</span></span> -<span><span class="co">## SFO IORE DFOP </span></span> -<span><span class="co">## 3831.804 2062.008 1550.980 </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span> -<span><span class="co">## [1] 2247.348</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Parameters:</span></span> -<span><span class="co">## $SFO</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 71.953 2.33e-13 60.509 83.40</span></span> -<span><span class="co">## k_parent 0.159 4.86e-05 0.102 0.25</span></span> -<span><span class="co">## sigma 11.302 1.25e-08 8.308 14.30</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $IORE</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 8.74e+01 2.48e-16 7.72e+01 97.52972</span></span> -<span><span class="co">## k__iore_parent 4.55e-04 2.16e-01 3.48e-05 0.00595</span></span> -<span><span class="co">## N_parent 2.70e+00 1.21e-08 1.99e+00 3.40046</span></span> -<span><span class="co">## sigma 8.29e+00 1.61e-08 6.09e+00 10.49062</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## $DFOP</span></span> -<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span> -<span><span class="co">## parent_0 88.5333 7.40e-18 79.9836 97.083</span></span> -<span><span class="co">## k1 18.8461 5.00e-01 0.0000 Inf</span></span> -<span><span class="co">## k2 0.0776 1.41e-05 0.0518 0.116</span></span> -<span><span class="co">## g 0.4733 1.41e-09 0.3674 0.582</span></span> -<span><span class="co">## sigma 7.1902 2.11e-08 5.2785 9.102</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## </span></span> -<span><span class="co">## DTx values:</span></span> -<span><span class="co">## DT50 DT90 DT50_rep</span></span> -<span><span class="co">## SFO 4.35 14.4 4.35</span></span> -<span><span class="co">## IORE 1.48 32.1 9.67</span></span> -<span><span class="co">## DFOP 0.67 21.4 8.93</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## Representative half-life:</span></span> -<span><span class="co">## [1] 8.93</span></span></code></pre> -<p>In PestDF, the DFOP fit seems to have stuck in a local minimum, as -mkin finds a solution with a much lower <span class="math inline">\(\chi^2\)</span> error level. As the half-life from -the slower rate constant of the DFOP model is larger than the IORE -derived half-life, the NAFTA recommendation obtained with mkin is to use -the DFOP representative half-life of 8.9 days.</p> -</div> -<div class="section level2"> -<h2 id="conclusions">Conclusions<a class="anchor" aria-label="anchor" href="#conclusions"></a> -</h2> -<p>The results obtained with mkin deviate from the results obtained with -PestDF either in cases where one of the interpretive rules would apply, -i.e. the IORE parameter N is less than one or the DFOP k values obtained -with PestDF are equal to the SFO k values, or in cases where the DFOP -model did not converge, which often lead to negative rate constants -returned by PestDF.</p> -<p>Therefore, mkin appears to suitable for kinetic evaluations according -to the NAFTA guidance.</p> -</div> -<div class="section level2"> -<h2 class="unnumbered" id="references">References<a class="anchor" aria-label="anchor" href="#references"></a> -</h2> -<div id="refs" class="references csl-bib-body hanging-indent"> -<div id="ref-usepa2015" class="csl-entry"> -US EPA. 2015. <span>“Standard Operating Procedure for Using the NAFTA -Guidance to Calculate Representative Half-Life Values and Characterizing -Pesticide Degradation.”</span> <a href="https://www.epa.gov/pesticide-science-and-assessing-pesticide-risks/standard-operating-procedure-using-nafta-guidance" class="external-link">https://www.epa.gov/pesticide-science-and-assessing-pesticide-risks/standard-operating-procedure-using-nafta-guidance</a>. -</div> -</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> 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</li> - <li> - <a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> - </li> - </ul> -</li> -<li> - <a href="../../news/index.html">News</a> -</li> - </ul> -<ul class="nav navbar-nav navbar-right"> -<li> - <a href="https://github.com/jranke/mkin/" class="external-link"> - <span class="fab fa-github fa-lg"></span> - - </a> -</li> - </ul> -</div> -<!--/.nav-collapse --> - </div> -<!--/.container --> -</div> -<!--/.navbar --> - - - - </header><div class="row"> - <div class="col-md-9 contents"> - <div class="page-header toc-ignore"> - <h1 data-toc-skip>Benchmark timings for mkin</h1> - <h4 data-toc-skip class="author">Johannes -Ranke</h4> - - <h4 data-toc-skip class="date">Last change 17 February 2023 -(rebuilt 2023-04-16)</h4> - - <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/benchmarks.rmd" class="external-link"><code>vignettes/web_only/benchmarks.rmd</code></a></small> - <div class="hidden name"><code>benchmarks.rmd</code></div> - - </div> - - - -<p>Each system is characterized by the operating system type, the CPU -type, the mkin version, and, as in June 2022 the current R version lead -to worse performance, the R version. A compiler was available, so if no -analytical solution was available, compiled ODE models are used.</p> -<p>Every fit is only performed once, so the accuracy of the benchmarks -is limited.</p> -<p>The following wrapper function for <code>mmkin</code> is used because -the way the error model is specified was changed in mkin version -0.9.49.1.</p> -<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/utils/packageDescription.html" class="external-link">packageVersion</a></span><span class="op">(</span><span class="st">"mkin"</span><span class="op">)</span> <span class="op">></span> <span class="st">"0.9.48.1"</span><span class="op">)</span> <span class="op">{</span></span> -<span> <span class="va">mmkin_bench</span> <span class="op"><-</span> <span class="kw">function</span><span class="op">(</span><span class="va">models</span>, <span class="va">datasets</span>, <span class="va">error_model</span> <span class="op">=</span> <span class="st">"const"</span><span class="op">)</span> <span class="op">{</span></span> -<span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span><span class="va">models</span>, <span class="va">datasets</span>, error_model <span class="op">=</span> <span class="va">error_model</span>, cores <span class="op">=</span> <span class="fl">1</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<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">mmkin_bench</span> <span class="op"><-</span> <span class="kw">function</span><span class="op">(</span><span class="va">models</span>, <span class="va">datasets</span>, <span class="va">error_model</span> <span class="op">=</span> <span class="cn">NULL</span><span class="op">)</span> <span class="op">{</span></span> -<span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span><span class="va">models</span>, <span class="va">datasets</span>, reweight.method <span class="op">=</span> <span class="va">error_model</span>, cores <span class="op">=</span> <span class="fl">1</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<span> <span class="op">}</span></span> -<span><span class="op">}</span></span></code></pre></div> -<div class="section level2"> -<h2 id="test-cases">Test cases<a class="anchor" aria-label="anchor" href="#test-cases"></a> -</h2> -<p>Parent only:</p> -<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">FOCUS_C</span> <span class="op"><-</span> <span class="va">FOCUS_2006_C</span></span> -<span><span class="va">FOCUS_D</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/subset.html" class="external-link">subset</a></span><span class="op">(</span><span class="va">FOCUS_2006_D</span>, <span class="va">value</span> <span class="op">!=</span> <span class="fl">0</span><span class="op">)</span></span> -<span><span class="va">parent_datasets</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">FOCUS_C</span>, <span class="va">FOCUS_D</span><span class="op">)</span></span> -<span></span> -<span></span> -<span><span class="va">t1</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>, <span class="st">"HS"</span><span class="op">)</span>, <span class="va">parent_datasets</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span> -<span><span class="va">t2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>, <span class="st">"HS"</span><span class="op">)</span>, <span class="va">parent_datasets</span>,</span> -<span> error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span></code></pre></div> -<p>One metabolite:</p> -<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">SFO_SFO</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> parent <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">"m1"</span><span class="op">)</span>,</span> -<span> m1 <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 class="op">)</span></span> -<span><span class="va">FOMC_SFO</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> parent <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="st">"m1"</span><span class="op">)</span>,</span> -<span> m1 <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 class="op">)</span></span> -<span><span class="va">DFOP_SFO</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> parent <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="st">"m1"</span><span class="op">)</span>, <span class="co"># erroneously used FOMC twice, not fixed for consistency</span></span> -<span> m1 <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 class="op">)</span></span> -<span><span class="va">t3</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</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">SFO_SFO</span>, <span class="va">FOMC_SFO</span>, <span class="va">DFOP_SFO</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">FOCUS_D</span><span class="op">)</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span> -<span><span class="va">t4</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</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">SFO_SFO</span>, <span class="va">FOMC_SFO</span>, <span class="va">DFOP_SFO</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">FOCUS_D</span><span class="op">)</span>,</span> -<span> error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span> -<span><span class="va">t5</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</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">SFO_SFO</span>, <span class="va">FOMC_SFO</span>, <span class="va">DFOP_SFO</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">FOCUS_D</span><span class="op">)</span>,</span> -<span> error_model <span class="op">=</span> <span class="st">"obs"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span></code></pre></div> -<p>Two metabolites, synthetic data:</p> -<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">m_synth_SFO_lin</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>parent <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">"M1"</span><span class="op">)</span>,</span> -<span> M1 <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">"M2"</span><span class="op">)</span>,</span> -<span> M2 <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> use_of_ff <span class="op">=</span> <span class="st">"max"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<span></span> -<span><span class="va">m_synth_DFOP_par</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>parent <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">"M1"</span>, <span class="st">"M2"</span><span class="op">)</span><span class="op">)</span>,</span> -<span> M1 <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> M2 <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> use_of_ff <span class="op">=</span> <span class="st">"max"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<span></span> -<span><span class="va">SFO_lin_a</span> <span class="op"><-</span> <span class="va">synthetic_data_for_UBA_2014</span><span class="op">[[</span><span class="fl">1</span><span class="op">]</span><span class="op">]</span><span class="op">$</span><span class="va">data</span></span> -<span></span> -<span><span class="va">DFOP_par_c</span> <span class="op"><-</span> <span class="va">synthetic_data_for_UBA_2014</span><span class="op">[[</span><span class="fl">12</span><span class="op">]</span><span class="op">]</span><span class="op">$</span><span class="va">data</span></span> -<span></span> -<span><span class="va">t6</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</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">m_synth_SFO_lin</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">SFO_lin_a</span><span class="op">)</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span> -<span><span class="va">t7</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</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">m_synth_DFOP_par</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">DFOP_par_c</span><span class="op">)</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span> -<span></span> -<span><span class="va">t8</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</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">m_synth_SFO_lin</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">SFO_lin_a</span><span class="op">)</span>,</span> -<span> error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span> -<span><span class="va">t9</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</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">m_synth_DFOP_par</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">DFOP_par_c</span><span class="op">)</span>,</span> -<span> error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span> -<span></span> -<span><span class="va">t10</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</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">m_synth_SFO_lin</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">SFO_lin_a</span><span class="op">)</span>,</span> -<span> error_model <span class="op">=</span> <span class="st">"obs"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span> -<span><span class="va">t11</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</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">m_synth_DFOP_par</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">DFOP_par_c</span><span class="op">)</span>,</span> -<span> error_model <span class="op">=</span> <span class="st">"obs"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span></code></pre></div> -</div> -<div class="section level2"> -<h2 id="results">Results<a class="anchor" aria-label="anchor" href="#results"></a> -</h2> -<p>Benchmarks for all available error models are shown. They are -intended for improving mkin, not for comparing CPUs or operating -systems. All trademarks belong to their respective owners.</p> -<div class="section level3"> -<h3 id="parent-only">Parent only<a class="anchor" aria-label="anchor" href="#parent-only"></a> -</h3> -<p>Constant variance (t1) and two-component error model (t2) for four -models fitted to two datasets, i.e. eight fits for each test.</p> -<table class="table"> -<thead><tr class="header"> -<th align="left">OS</th> -<th align="left">CPU</th> -<th align="left">R</th> -<th align="left">mkin</th> -<th align="right">t1</th> -<th align="right">t2</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">NA</td> -<td align="left">0.9.48.1</td> -<td align="right">3.610</td> -<td align="right">11.019</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">NA</td> -<td align="left">0.9.49.1</td> -<td align="right">8.184</td> -<td align="right">22.889</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">NA</td> -<td align="left">0.9.49.2</td> -<td align="right">7.064</td> -<td align="right">12.558</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">NA</td> -<td align="left">0.9.49.3</td> -<td align="right">7.296</td> -<td align="right">21.239</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">NA</td> -<td align="left">0.9.49.4</td> -<td align="right">5.936</td> -<td align="right">20.545</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">NA</td> -<td align="left">0.9.50.2</td> -<td align="right">1.714</td> -<td align="right">3.971</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">NA</td> -<td align="left">0.9.50.3</td> -<td align="right">1.752</td> -<td align="right">4.156</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">NA</td> -<td align="left">0.9.50.4</td> -<td align="right">1.786</td> -<td align="right">3.729</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">NA</td> -<td align="left">1.0.3</td> -<td align="right">1.881</td> -<td align="right">3.504</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">NA</td> -<td align="left">1.0.4</td> -<td align="right">1.867</td> -<td align="right">3.450</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">4.1.3</td> -<td align="left">1.1.0</td> -<td align="right">1.791</td> -<td align="right">3.289</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">4.2.1</td> -<td align="left">1.1.0</td> -<td align="right">1.842</td> -<td align="right">3.453</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">i7-4710MQ</td> -<td align="left">4.2.1</td> -<td align="left">1.1.0</td> -<td align="right">1.959</td> -<td align="right">4.116</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">i7-4710MQ</td> -<td align="left">4.1.3</td> -<td align="left">1.1.0</td> -<td align="right">1.877</td> -<td align="right">3.906</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">i7-4710MQ</td> -<td align="left">4.2.1</td> -<td align="left">1.1.1</td> -<td align="right">1.644</td> -<td align="right">3.172</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">4.2.1</td> -<td align="left">1.1.1</td> -<td align="right">1.770</td> -<td align="right">3.377</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">4.2.1</td> -<td align="left">1.1.2</td> -<td align="right">1.957</td> -<td align="right">3.633</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">4.2.2</td> -<td align="left">1.2.0</td> -<td align="right">2.140</td> -<td align="right">3.774</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">4.2.2</td> -<td align="left">1.2.2</td> -<td align="right">2.187</td> -<td align="right">3.851</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">Ryzen 9 7950X</td> -<td align="left">4.2.2</td> -<td align="left">1.2.0</td> -<td align="right">1.288</td> -<td align="right">1.794</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">Ryzen 9 7950X</td> -<td align="left">4.2.2</td> -<td align="left">1.2.2</td> -<td align="right">1.276</td> -<td align="right">1.804</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">Ryzen 9 7950X</td> -<td align="left">4.2.2</td> -<td align="left">1.2.3</td> -<td align="right">1.370</td> -<td align="right">1.883</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">Ryzen 9 7950X</td> -<td align="left">4.2.3</td> -<td align="left">1.2.3</td> -<td align="right">1.404</td> -<td align="right">1.933</td> -</tr> -</tbody> -</table> -</div> -<div class="section level3"> -<h3 id="one-metabolite">One metabolite<a class="anchor" aria-label="anchor" href="#one-metabolite"></a> -</h3> -<p>Constant variance (t3), two-component error model (t4), and variance -by variable (t5) for three models fitted to one dataset, i.e. three fits -for each test.</p> -<table class="table"> -<thead><tr class="header"> -<th align="left">OS</th> -<th align="left">CPU</th> -<th align="left">R</th> -<th align="left">mkin</th> -<th align="right">t3</th> -<th align="right">t4</th> -<th align="right">t5</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">NA</td> -<td align="left">0.9.48.1</td> -<td align="right">3.764</td> -<td align="right">14.347</td> -<td align="right">9.495</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">NA</td> -<td align="left">0.9.49.1</td> -<td align="right">4.649</td> -<td align="right">13.789</td> -<td align="right">6.395</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">NA</td> -<td align="left">0.9.49.2</td> -<td align="right">4.786</td> -<td align="right">8.461</td> -<td align="right">5.675</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">NA</td> -<td align="left">0.9.49.3</td> -<td align="right">4.510</td> -<td align="right">13.805</td> -<td align="right">7.386</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">NA</td> -<td align="left">0.9.49.4</td> -<td align="right">4.446</td> -<td align="right">15.335</td> -<td align="right">6.002</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">NA</td> -<td align="left">0.9.50.2</td> -<td align="right">1.402</td> -<td align="right">6.174</td> -<td align="right">2.764</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">NA</td> -<td align="left">0.9.50.3</td> -<td align="right">1.430</td> -<td align="right">6.615</td> -<td align="right">2.878</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">NA</td> -<td align="left">0.9.50.4</td> -<td align="right">1.397</td> -<td align="right">7.251</td> -<td align="right">2.810</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">NA</td> -<td align="left">1.0.3</td> -<td align="right">1.430</td> -<td align="right">6.344</td> -<td align="right">2.798</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">NA</td> -<td align="left">1.0.4</td> -<td align="right">1.415</td> -<td align="right">6.364</td> -<td align="right">2.820</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">4.1.3</td> -<td align="left">1.1.0</td> -<td align="right">1.310</td> -<td align="right">6.279</td> -<td align="right">2.681</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">4.2.1</td> -<td align="left">1.1.0</td> -<td align="right">3.802</td> -<td align="right">21.247</td> -<td align="right">8.461</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">i7-4710MQ</td> -<td align="left">4.2.1</td> -<td align="left">1.1.0</td> -<td align="right">3.334</td> -<td align="right">19.521</td> -<td align="right">7.565</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">i7-4710MQ</td> -<td align="left">4.1.3</td> -<td align="left">1.1.0</td> -<td align="right">1.578</td> -<td align="right">8.058</td> -<td align="right">3.339</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">i7-4710MQ</td> -<td align="left">4.2.1</td> -<td align="left">1.1.1</td> -<td align="right">1.230</td> -<td align="right">5.839</td> -<td align="right">2.444</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">4.2.1</td> -<td align="left">1.1.1</td> -<td align="right">1.308</td> -<td align="right">5.758</td> -<td align="right">2.558</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">4.2.1</td> -<td align="left">1.1.2</td> -<td align="right">1.503</td> -<td align="right">6.147</td> -<td align="right">2.803</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">4.2.2</td> -<td align="left">1.2.0</td> -<td align="right">1.554</td> -<td align="right">6.193</td> -<td align="right">2.843</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">4.2.2</td> -<td align="left">1.2.2</td> -<td align="right">1.585</td> -<td align="right">6.335</td> -<td align="right">3.003</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">Ryzen 9 7950X</td> -<td align="left">4.2.2</td> -<td align="left">1.2.0</td> -<td align="right">0.792</td> -<td align="right">2.378</td> -<td align="right">1.245</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">Ryzen 9 7950X</td> -<td align="left">4.2.2</td> -<td align="left">1.2.2</td> -<td align="right">0.784</td> -<td align="right">2.355</td> -<td align="right">1.233</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">Ryzen 9 7950X</td> -<td align="left">4.2.2</td> -<td align="left">1.2.3</td> -<td align="right">0.770</td> -<td align="right">2.011</td> -<td align="right">1.123</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">Ryzen 9 7950X</td> -<td align="left">4.2.3</td> -<td align="left">1.2.3</td> -<td align="right">0.797</td> -<td align="right">2.124</td> -<td align="right">1.182</td> -</tr> -</tbody> -</table> -</div> -<div class="section level3"> -<h3 id="two-metabolites">Two metabolites<a class="anchor" aria-label="anchor" href="#two-metabolites"></a> -</h3> -<p>Constant variance (t6 and t7), two-component error model (t8 and t9), -and variance by variable (t10 and t11) for one model fitted to one -dataset, i.e. one fit for each test.</p> -<table class="table"> -<colgroup> -<col width="8%"> -<col width="19%"> -<col width="8%"> -<col width="12%"> -<col width="8%"> -<col width="8%"> -<col width="8%"> -<col width="9%"> -<col width="8%"> -<col width="9%"> -</colgroup> -<thead><tr class="header"> -<th align="left">OS</th> -<th align="left">CPU</th> -<th align="left">R</th> -<th align="left">mkin</th> -<th align="right">t6</th> -<th align="right">t7</th> -<th align="right">t8</th> -<th align="right">t9</th> -<th align="right">t10</th> -<th align="right">t11</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">NA</td> -<td align="left">0.9.48.1</td> -<td align="right">2.623</td> -<td align="right">4.587</td> -<td align="right">7.525</td> -<td align="right">16.621</td> -<td align="right">8.576</td> -<td align="right">31.267</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">NA</td> -<td align="left">0.9.49.1</td> -<td align="right">2.542</td> -<td align="right">4.128</td> -<td align="right">4.632</td> -<td align="right">8.171</td> -<td align="right">3.676</td> -<td align="right">5.636</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">NA</td> -<td align="left">0.9.49.2</td> -<td align="right">2.723</td> -<td align="right">4.478</td> -<td align="right">4.862</td> -<td align="right">7.618</td> -<td align="right">3.579</td> -<td align="right">5.574</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">NA</td> -<td align="left">0.9.49.3</td> -<td align="right">2.643</td> -<td align="right">4.374</td> -<td align="right">7.020</td> -<td align="right">11.124</td> -<td align="right">5.388</td> -<td align="right">7.365</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">NA</td> -<td align="left">0.9.49.4</td> -<td align="right">2.635</td> -<td align="right">4.259</td> -<td align="right">4.737</td> -<td align="right">7.763</td> -<td align="right">3.427</td> -<td align="right">5.626</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">NA</td> -<td align="left">0.9.50.2</td> -<td align="right">0.777</td> -<td align="right">1.236</td> -<td align="right">1.332</td> -<td align="right">2.872</td> -<td align="right">2.069</td> -<td align="right">2.987</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">NA</td> -<td align="left">0.9.50.3</td> -<td align="right">0.858</td> -<td align="right">1.264</td> -<td align="right">1.333</td> -<td align="right">2.984</td> -<td align="right">2.113</td> -<td align="right">3.073</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">NA</td> -<td align="left">0.9.50.4</td> -<td align="right">0.783</td> -<td align="right">1.282</td> -<td align="right">1.486</td> -<td align="right">3.815</td> -<td align="right">1.958</td> -<td align="right">3.105</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">NA</td> -<td align="left">1.0.3</td> -<td align="right">0.763</td> -<td align="right">1.244</td> -<td align="right">1.457</td> -<td align="right">3.054</td> -<td align="right">1.923</td> -<td align="right">2.839</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">NA</td> -<td align="left">1.0.4</td> -<td align="right">0.785</td> -<td align="right">1.252</td> -<td align="right">1.466</td> -<td align="right">3.091</td> -<td align="right">1.936</td> -<td align="right">2.826</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">4.1.3</td> -<td align="left">1.1.0</td> -<td align="right">0.744</td> -<td align="right">1.227</td> -<td align="right">1.288</td> -<td align="right">3.553</td> -<td align="right">1.895</td> -<td align="right">2.738</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">4.2.1</td> -<td align="left">1.1.0</td> -<td align="right">3.018</td> -<td align="right">4.165</td> -<td align="right">5.036</td> -<td align="right">10.844</td> -<td align="right">6.623</td> -<td align="right">9.722</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">i7-4710MQ</td> -<td align="left">4.2.1</td> -<td align="left">1.1.0</td> -<td align="right">2.522</td> -<td align="right">3.792</td> -<td align="right">4.143</td> -<td align="right">11.268</td> -<td align="right">5.935</td> -<td align="right">8.728</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">i7-4710MQ</td> -<td align="left">4.1.3</td> -<td align="left">1.1.0</td> -<td align="right">0.907</td> -<td align="right">1.535</td> -<td align="right">1.589</td> -<td align="right">4.544</td> -<td align="right">2.302</td> -<td align="right">3.463</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">i7-4710MQ</td> -<td align="left">4.2.1</td> -<td align="left">1.1.1</td> -<td align="right">0.678</td> -<td align="right">1.095</td> -<td align="right">1.149</td> -<td align="right">3.247</td> -<td align="right">1.658</td> -<td align="right">2.472</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">4.2.1</td> -<td align="left">1.1.1</td> -<td align="right">0.696</td> -<td align="right">1.124</td> -<td align="right">1.321</td> -<td align="right">2.786</td> -<td align="right">1.744</td> -<td align="right">2.566</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">4.2.1</td> -<td align="left">1.1.2</td> -<td align="right">0.861</td> -<td align="right">1.295</td> -<td align="right">1.507</td> -<td align="right">3.102</td> -<td align="right">1.961</td> -<td align="right">2.852</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">4.2.2</td> -<td align="left">1.2.0</td> -<td align="right">0.913</td> -<td align="right">1.345</td> -<td align="right">1.539</td> -<td align="right">3.011</td> -<td align="right">1.987</td> -<td align="right">2.802</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">Ryzen 7 1700</td> -<td align="left">4.2.2</td> -<td align="left">1.2.2</td> -<td align="right">0.935</td> -<td align="right">1.381</td> -<td align="right">1.551</td> -<td align="right">3.209</td> -<td align="right">1.976</td> -<td align="right">3.013</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">Ryzen 9 7950X</td> -<td align="left">4.2.2</td> -<td align="left">1.2.0</td> -<td align="right">0.445</td> -<td align="right">0.591</td> -<td align="right">0.660</td> -<td align="right">1.190</td> -<td align="right">0.814</td> -<td align="right">1.100</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">Ryzen 9 7950X</td> -<td align="left">4.2.2</td> -<td align="left">1.2.2</td> -<td align="right">0.443</td> -<td align="right">0.586</td> -<td align="right">0.661</td> -<td align="right">1.176</td> -<td align="right">0.803</td> -<td align="right">1.097</td> -</tr> -<tr class="even"> -<td align="left">Linux</td> -<td align="left">Ryzen 9 7950X</td> -<td align="left">4.2.2</td> -<td align="left">1.2.3</td> -<td align="right">0.418</td> -<td align="right">0.530</td> -<td align="right">0.591</td> -<td align="right">1.006</td> -<td align="right">0.716</td> -<td align="right">0.949</td> -</tr> -<tr class="odd"> -<td align="left">Linux</td> -<td align="left">Ryzen 9 7950X</td> -<td align="left">4.2.3</td> -<td align="left">1.2.3</td> -<td align="right">0.432</td> -<td align="right">0.551</td> -<td align="right">0.616</td> -<td align="right">1.039</td> -<td align="right">0.734</td> -<td align="right">0.981</td> -</tr> -</tbody> -</table> -</div> -</div> - </div> - - <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar"> - - <nav id="toc" data-toggle="toc"><h2 data-toc-skip>Contents</h2> - </nav> -</div> - -</div> - - - - <footer><div class="copyright"> - <p></p> -<p>Developed by Johannes Ranke.</p> -</div> - -<div class="pkgdown"> - <p></p> -<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p> -</div> - - </footer> -</div> - - - - - - - </body> -</html> diff --git a/docs/dev/articles/web_only/benchmarks_files/accessible-code-block-0.0.1/empty-anchor.js b/docs/dev/articles/web_only/benchmarks_files/accessible-code-block-0.0.1/empty-anchor.js deleted file mode 100644 index ca349fd6..00000000 --- a/docs/dev/articles/web_only/benchmarks_files/accessible-code-block-0.0.1/empty-anchor.js +++ /dev/null @@ -1,15 +0,0 @@ -// Hide empty <a> tag within highlighted 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</li> - <li> - <a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> - </li> - </ul> -</li> -<li> - <a href="../../news/index.html">News</a> -</li> - </ul> -<ul class="nav navbar-nav navbar-right"> -<li> - <a href="https://github.com/jranke/mkin/" class="external-link"> - <span class="fab fa-github fa-lg"></span> - - </a> -</li> - </ul> -</div> -<!--/.nav-collapse --> - </div> -<!--/.container --> -</div> -<!--/.navbar --> - - - - </header><div class="row"> - <div class="col-md-9 contents"> - <div class="page-header toc-ignore"> - <h1 data-toc-skip>Performance benefit by using compiled model -definitions in mkin</h1> - <h4 data-toc-skip class="author">Johannes -Ranke</h4> - - <h4 data-toc-skip class="date">2023-04-16</h4> - - <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/compiled_models.rmd" class="external-link"><code>vignettes/web_only/compiled_models.rmd</code></a></small> - <div class="hidden name"><code>compiled_models.rmd</code></div> - - </div> - - - -<div class="section level2"> -<h2 id="how-to-benefit-from-compiled-models">How to benefit from compiled models<a class="anchor" aria-label="anchor" href="#how-to-benefit-from-compiled-models"></a> -</h2> -<p>When using an mkin version equal to or greater than 0.9-36 and a C -compiler is available, you will see a message that the model is being -compiled from autogenerated C code when defining a model using mkinmod. -Starting from version 0.9.49.9, the <code><a href="../../reference/mkinmod.html">mkinmod()</a></code> function -checks for presence of a compiler using</p> -<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu">pkgbuild</span><span class="fu">::</span><span class="fu"><a href="https://r-lib.github.io/pkgbuild/reference/has_compiler.html" class="external-link">has_compiler</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<p>In previous versions, it used <code>Sys.which("gcc")</code> for this -check.</p> -<p>On Linux, you need to have the essential build tools like make and -gcc or clang installed. On Debian based linux distributions, these will -be pulled in by installing the build-essential package.</p> -<p>On MacOS, which I do not use personally, I have had reports that a -compiler is available by default.</p> -<p>On Windows, you need to install Rtools and have the path to its bin -directory in your PATH variable. You do not need to modify the PATH -variable when installing Rtools. Instead, I would recommend to put the -line</p> -<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/Sys.setenv.html" class="external-link">Sys.setenv</a></span><span class="op">(</span>PATH <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">"C:/Rtools/bin"</span>, <span class="fu"><a href="https://rdrr.io/r/base/Sys.getenv.html" class="external-link">Sys.getenv</a></span><span class="op">(</span><span class="st">"PATH"</span><span class="op">)</span>, sep<span class="op">=</span><span class="st">";"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> -<p>into your .Rprofile startup file. This is just a text file with some -R code that is executed when your R session starts. It has to be named -.Rprofile and has to be located in your home directory, which will -generally be your Documents folder. You can check the location of the -home directory used by R by issuing</p> -<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/Sys.getenv.html" class="external-link">Sys.getenv</a></span><span class="op">(</span><span class="st">"HOME"</span><span class="op">)</span></span></code></pre></div> -</div> -<div class="section level2"> -<h2 id="comparison-with-other-solution-methods">Comparison with other solution methods<a class="anchor" aria-label="anchor" href="#comparison-with-other-solution-methods"></a> -</h2> -<p>First, we build a simple degradation model for a parent compound with -one metabolite, and we remove zero values from the dataset.</p> -<div class="sourceCode" id="cb4"><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="st"><a href="https://pkgdown.jrwb.de/mkin/">"mkin"</a></span>, quietly <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<span><span class="va">SFO_SFO</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> parent <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">"m1"</span><span class="op">)</span>,</span> -<span> m1 <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 class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre> -<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">FOCUS_D</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/subset.html" class="external-link">subset</a></span><span class="op">(</span><span class="va">FOCUS_2006_D</span>, <span class="va">value</span> <span class="op">!=</span> <span class="fl">0</span><span class="op">)</span></span></code></pre></div> -<p>We can compare the performance of the Eigenvalue based solution -against the compiled version and the R implementation of the -differential equations using the benchmark package. In the output of -below code, the warnings about zero being removed from the FOCUS D -dataset are suppressed. Since mkin version 0.9.49.11, an analytical -solution is also implemented, which is included in the tests below.</p> -<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="kw">if</span> <span class="op">(</span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">require</a></span><span class="op">(</span><span class="va"><a href="http://rbenchmark.googlecode.com" class="external-link">rbenchmark</a></span><span class="op">)</span><span class="op">)</span> <span class="op">{</span></span> -<span> <span class="va">b.1</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/rbenchmark/man/benchmark.html" class="external-link">benchmark</a></span><span class="op">(</span></span> -<span> <span class="st">"deSolve, not compiled"</span> <span class="op">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOCUS_D</span>,</span> -<span> solution_type <span class="op">=</span> <span class="st">"deSolve"</span>,</span> -<span> use_compiled <span class="op">=</span> <span class="cn">FALSE</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,</span> -<span> <span class="st">"Eigenvalue based"</span> <span class="op">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOCUS_D</span>,</span> -<span> solution_type <span class="op">=</span> <span class="st">"eigen"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,</span> -<span> <span class="st">"deSolve, compiled"</span> <span class="op">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOCUS_D</span>,</span> -<span> solution_type <span class="op">=</span> <span class="st">"deSolve"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,</span> -<span> <span class="st">"analytical"</span> <span class="op">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOCUS_D</span>,</span> -<span> solution_type <span class="op">=</span> <span class="st">"analytical"</span>,</span> -<span> use_compiled <span class="op">=</span> <span class="cn">FALSE</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,</span> -<span> replications <span class="op">=</span> <span class="fl">1</span>, order <span class="op">=</span> <span class="st">"relative"</span>,</span> -<span> columns <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">"test"</span>, <span class="st">"replications"</span>, <span class="st">"relative"</span>, <span class="st">"elapsed"</span><span class="op">)</span><span class="op">)</span></span> -<span> <span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">b.1</span><span class="op">)</span></span> -<span><span class="op">}</span> <span class="kw">else</span> <span class="op">{</span></span> -<span> <span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="st">"R package rbenchmark is not available"</span><span class="op">)</span></span> -<span><span class="op">}</span></span></code></pre></div> -<pre><code><span><span class="co">## test replications relative elapsed</span></span> -<span><span class="co">## 4 analytical 1 1.000 0.105</span></span> -<span><span class="co">## 3 deSolve, compiled 1 1.276 0.134</span></span> -<span><span class="co">## 2 Eigenvalue based 1 1.762 0.185</span></span> -<span><span class="co">## 1 deSolve, not compiled 1 21.914 2.301</span></span></code></pre> -<p>We see that using the compiled model is by more than a factor of 10 -faster than using deSolve without compiled code.</p> -</div> -<div class="section level2"> -<h2 id="model-without-analytical-solution">Model without analytical solution<a class="anchor" aria-label="anchor" href="#model-without-analytical-solution"></a> -</h2> -<p>This evaluation is also taken from the example section of mkinfit. No -analytical solution is available for this system, and now Eigenvalue -based solution is possible, so only deSolve using with or without -compiled code is available.</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="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">require</a></span><span class="op">(</span><span class="va"><a href="http://rbenchmark.googlecode.com" class="external-link">rbenchmark</a></span><span class="op">)</span><span class="op">)</span> <span class="op">{</span></span> -<span> <span class="va">FOMC_SFO</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> parent <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="st">"m1"</span><span class="op">)</span>,</span> -<span> m1 <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 class="op">)</span></span> -<span></span> -<span> <span class="va">b.2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/rbenchmark/man/benchmark.html" class="external-link">benchmark</a></span><span class="op">(</span></span> -<span> <span class="st">"deSolve, not compiled"</span> <span class="op">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">FOMC_SFO</span>, <span class="va">FOCUS_D</span>,</span> -<span> use_compiled <span class="op">=</span> <span class="cn">FALSE</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,</span> -<span> <span class="st">"deSolve, compiled"</span> <span class="op">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">FOMC_SFO</span>, <span class="va">FOCUS_D</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,</span> -<span> replications <span class="op">=</span> <span class="fl">1</span>, order <span class="op">=</span> <span class="st">"relative"</span>,</span> -<span> columns <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">"test"</span>, <span class="st">"replications"</span>, <span class="st">"relative"</span>, <span class="st">"elapsed"</span><span class="op">)</span><span class="op">)</span></span> -<span> <span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">b.2</span><span class="op">)</span></span> -<span> <span class="va">factor_FOMC_SFO</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/Round.html" class="external-link">round</a></span><span class="op">(</span><span class="va">b.2</span><span class="op">[</span><span class="st">"1"</span>, <span class="st">"relative"</span><span class="op">]</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">factor_FOMC_SFO</span> <span class="op"><-</span> <span class="cn">NA</span></span> -<span> <span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="st">"R package benchmark is not available"</span><span class="op">)</span></span> -<span><span class="op">}</span></span></code></pre></div> -<pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre> -<pre><code><span><span class="co">## test replications relative elapsed</span></span> -<span><span class="co">## 2 deSolve, compiled 1 1.000 0.176</span></span> -<span><span class="co">## 1 deSolve, not compiled 1 23.938 4.213</span></span></code></pre> -<p>Here we get a performance benefit of a factor of 24 using the version -of the differential equation model compiled from C code!</p> -<p>This vignette was built with mkin 1.2.3 on</p> -<pre><code><span><span class="co">## R version 4.2.3 (2023-03-15)</span></span> -<span><span class="co">## Platform: x86_64-pc-linux-gnu (64-bit)</span></span> -<span><span class="co">## Running under: Debian GNU/Linux 12 (bookworm)</span></span></code></pre> -<pre><code><span><span class="co">## CPU model: AMD Ryzen 9 7950X 16-Core Processor</span></span></code></pre> -</div> - 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</li> - <li> - <a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> - </li> - </ul> -</li> -<li> - <a href="../../news/index.html">News</a> -</li> - </ul> -<ul class="nav navbar-nav navbar-right"> -<li> - <a href="https://github.com/jranke/mkin/" class="external-link"> - <span class="fab fa-github fa-lg"></span> - - </a> -</li> - </ul> -</div> -<!--/.nav-collapse --> - </div> -<!--/.container --> -</div> -<!--/.navbar --> - - - - </header><div class="row"> - <div class="col-md-9 contents"> - <div class="page-header toc-ignore"> - <h1 data-toc-skip>Example evaluations of the dimethenamid data -from 2018</h1> - <h4 data-toc-skip class="author">Johannes -Ranke</h4> - - <h4 data-toc-skip class="date">Last change 1 July 2022, -built on 16 Apr 2023</h4> - - <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/dimethenamid_2018.rmd" class="external-link"><code>vignettes/web_only/dimethenamid_2018.rmd</code></a></small> - <div class="hidden name"><code>dimethenamid_2018.rmd</code></div> - - </div> - - - -<p><a href="http://www.jrwb.de" class="external-link">Wissenschaftlicher Berater, Kronacher -Str. 12, 79639 Grenzach-Wyhlen, Germany</a></p> -<div class="section level2"> -<h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#introduction"></a> -</h2> -<p>A first analysis of the data analysed here was presented in a recent -journal article on nonlinear mixed-effects models in degradation -kinetics <span class="citation">(Ranke et al. 2021)</span>. That -analysis was based on the <code>nlme</code> package and a development -version of the <code>saemix</code> package that was unpublished at the -time. Meanwhile, version 3.0 of the <code>saemix</code> package is -available from the CRAN repository. Also, it turned out that there was -an error in the handling of the Borstel data in the mkin package at the -time, leading to the duplication of a few data points from that soil. -The dataset in the mkin package has been corrected, and the interface to -<code>saemix</code> in the mkin package has been updated to use the -released version.</p> -<p>This vignette is intended to present an up to date analysis of the -data, using the corrected dataset and released versions of -<code>mkin</code> and <code>saemix</code>.</p> -</div> -<div class="section level2"> -<h2 id="data">Data<a class="anchor" aria-label="anchor" href="#data"></a> -</h2> -<p>Residue data forming the basis for the endpoints derived in the -conclusion on the peer review of the pesticide risk assessment of -dimethenamid-P published by the European Food Safety Authority (EFSA) in -2018 <span class="citation">(EFSA 2018)</span> were transcribed from the -risk assessment report <span class="citation">(Rapporteur Member State -Germany, Co-Rapporteur Member State Bulgaria 2018)</span> which can be -downloaded from the Open EFSA repository <a href="https://open.efsa.europa.eu" class="external-link">https://open.efsa.europa.eu/study-inventory/EFSA-Q-2014-00716</a>.</p> -<p>The data are <a href="https://pkgdown.jrwb.de/mkin/reference/dimethenamid_2018.html">available -in the mkin package</a>. The following code (hidden by default, please -use the button to the right to show it) treats the data available for -the racemic mixture dimethenamid (DMTA) and its enantiomer -dimethenamid-P (DMTAP) in the same way, as no difference between their -degradation behaviour was identified in the EU risk assessment. The -observation times of each dataset are multiplied with the corresponding -normalisation factor also available in the dataset, in order to make it -possible to describe all datasets with a single set of parameters.</p> -<p>Also, datasets observed in the same soil are merged, resulting in -dimethenamid (DMTA) data from six soils.</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>, quietly <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<span><span class="va">dmta_ds</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">lapply</a></span><span class="op">(</span><span class="fl">1</span><span class="op">:</span><span class="fl">7</span>, <span class="kw">function</span><span class="op">(</span><span class="va">i</span><span class="op">)</span> <span class="op">{</span></span> -<span> <span class="va">ds_i</span> <span class="op"><-</span> <span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">ds</span><span class="op">[[</span><span class="va">i</span><span class="op">]</span><span class="op">]</span><span class="op">$</span><span class="va">data</span></span> -<span> <span class="va">ds_i</span><span class="op">[</span><span class="va">ds_i</span><span class="op">$</span><span class="va">name</span> <span class="op">==</span> <span class="st">"DMTAP"</span>, <span class="st">"name"</span><span class="op">]</span> <span class="op"><-</span> <span class="st">"DMTA"</span></span> -<span> <span class="va">ds_i</span><span class="op">$</span><span class="va">time</span> <span class="op"><-</span> <span class="va">ds_i</span><span class="op">$</span><span class="va">time</span> <span class="op">*</span> <span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">f_time_norm</span><span class="op">[</span><span class="va">i</span><span class="op">]</span></span> -<span> <span class="va">ds_i</span></span> -<span><span class="op">}</span><span class="op">)</span></span> -<span><span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">)</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</span><span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">ds</span>, <span class="kw">function</span><span class="op">(</span><span class="va">ds</span><span class="op">)</span> <span class="va">ds</span><span class="op">$</span><span class="va">title</span><span class="op">)</span></span> -<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/cbind.html" class="external-link">rbind</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 1"</span><span class="op">]</span><span class="op">]</span>, <span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 2"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span> -<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 1"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="cn">NULL</span></span> -<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 2"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="cn">NULL</span></span></code></pre></div> -</div> -<div class="section level2"> -<h2 id="parent-degradation">Parent degradation<a class="anchor" aria-label="anchor" href="#parent-degradation"></a> -</h2> -<p>We evaluate the observed degradation of the parent compound using -simple exponential decline (SFO) and biexponential decline (DFOP), using -constant variance (const) and a two-component variance (tc) as error -models.</p> -<div class="section level3"> -<h3 id="separate-evaluations">Separate evaluations<a class="anchor" aria-label="anchor" href="#separate-evaluations"></a> -</h3> -<p>As a first step, to get a visual impression of the fit of the -different models, we do separate evaluations for each soil using the -mmkin function from the mkin package:</p> -<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_parent_mkin_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">"DFOP"</span><span class="op">)</span>, <span class="va">dmta_ds</span>,</span> -<span> error_model <span class="op">=</span> <span class="st">"const"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<span><span class="va">f_parent_mkin_tc</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">"DFOP"</span><span class="op">)</span>, <span class="va">dmta_ds</span>,</span> -<span> error_model <span class="op">=</span> <span class="st">"tc"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> -<p>The plot of the individual SFO fits shown below suggests that at -least in some datasets the degradation slows down towards later time -points, and that the scatter of the residuals error is smaller for -smaller values (panel to the right):</p> -<div class="sourceCode" id="cb3"><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="fu"><a href="../../reference/mixed.html">mixed</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> -<p><img src="dimethenamid_2018_files/figure-html/f_parent_mkin_sfo_const-1.png" width="700"></p> -<p>Using biexponential decline (DFOP) results in a slightly more random -scatter of the residuals:</p> -<div class="sourceCode" id="cb4"><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="fu"><a href="../../reference/mixed.html">mixed</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> -<p><img src="dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const-1.png" width="700"></p> -<p>The population curve (bold line) in the above plot results from -taking the mean of the individual transformed parameters, i.e. of log k1 -and log k2, as well as of the logit of the g parameter of the DFOP -model). Here, this procedure does not result in parameters that -represent the degradation well, because in some datasets the fitted -value for k2 is extremely close to zero, leading to a log k2 value that -dominates the average. This is alleviated if only rate constants that -pass the t-test for significant difference from zero (on the -untransformed scale) are considered in the averaging:</p> -<div class="sourceCode" id="cb5"><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="fu"><a href="../../reference/mixed.html">mixed</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span><span class="op">)</span>, test_log_parms <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> -<p><img src="dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const_test-1.png" width="700"></p> -<p>While this is visually much more satisfactory, such an average -procedure could introduce a bias, as not all results from the individual -fits enter the population curve with the same weight. This is where -nonlinear mixed-effects models can help out by treating all datasets -with equally by fitting a parameter distribution model together with the -degradation model and the error model (see below).</p> -<p>The remaining trend of the residuals to be higher for higher -predicted residues is reduced by using the two-component error -model:</p> -<div class="sourceCode" id="cb6"><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="fu"><a href="../../reference/mixed.html">mixed</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span><span class="op">)</span>, test_log_parms <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> -<p><img src="dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_tc_test-1.png" width="700"></p> -<p>However, note that in the case of using this error model, the fits to -the Flaach and BBA 2.3 datasets appear to be ill-defined, indicated by -the fact that they did not converge:</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/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span><span class="op">)</span></span></code></pre></div> -<pre><code><mmkin> object -Status of individual fits: - - dataset -model Calke Borstel Flaach BBA 2.2 BBA 2.3 Elliot - DFOP OK OK C OK C OK - -C: Optimisation did not converge: -iteration limit reached without convergence (10) -OK: No warnings</code></pre> -</div> -<div class="section level3"> -<h3 id="nonlinear-mixed-effects-models">Nonlinear mixed-effects models<a class="anchor" aria-label="anchor" href="#nonlinear-mixed-effects-models"></a> -</h3> -<p>Instead of taking a model selection decision for each of the -individual fits, we fit nonlinear mixed-effects models (using different -fitting algorithms as implemented in different packages) and do model -selection using all available data at the same time. In order to make -sure that these decisions are not unduly influenced by the type of -algorithm used, by implementation details or by the use of wrong control -parameters, we compare the model selection results obtained with -different R packages, with different algorithms and checking control -parameters.</p> -<div class="section level4"> -<h4 id="nlme">nlme<a class="anchor" aria-label="anchor" href="#nlme"></a> -</h4> -<p>The nlme package was the first R extension providing facilities to -fit nonlinear mixed-effects models. We would like to do model selection -from all four combinations of degradation models and error models based -on the AIC. However, fitting the DFOP model with constant variance and -using default control parameters results in an error, signalling that -the maximum number of 50 iterations was reached, potentially indicating -overparameterisation. Nevertheless, the algorithm converges when the -two-component error model is used in combination with the DFOP model. -This can be explained by the fact that the smaller residues observed at -later sampling times get more weight when using the two-component error -model which will counteract the tendency of the algorithm to try -parameter combinations unsuitable for fitting these data.</p> -<div class="sourceCode" id="cb9"><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://svn.r-project.org/R-packages/trunk/nlme/" class="external-link">nlme</a></span><span class="op">)</span></span> -<span><span class="va">f_parent_nlme_sfo_const</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlme/man/nlme.html" class="external-link">nlme</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span><span class="op">)</span></span> -<span><span class="co"># f_parent_nlme_dfop_const <- nlme(f_parent_mkin_const["DFOP", ])</span></span> -<span><span class="va">f_parent_nlme_sfo_tc</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlme/man/nlme.html" class="external-link">nlme</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span><span class="op">)</span></span> -<span><span class="va">f_parent_nlme_dfop_tc</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlme/man/nlme.html" class="external-link">nlme</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span><span class="op">)</span></span></code></pre></div> -<p>Note that a certain degree of overparameterisation is also indicated -by a warning obtained when fitting DFOP with the two-component error -model (‘false convergence’ in the ‘LME step’ in iteration 3). However, -as this warning does not occur in later iterations, and specifically not -in the last of the 5 iterations, we can ignore this warning.</p> -<p>The model comparison function of the nlme package can directly be -applied to these fits showing a much lower AIC for the DFOP model fitted -with the two-component error model. Also, the likelihood ratio test -indicates that this difference is significant as the p-value is below -0.0001.</p> -<div class="sourceCode" id="cb10"><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> -<span> <span class="va">f_parent_nlme_sfo_const</span>, <span class="va">f_parent_nlme_sfo_tc</span>, <span class="va">f_parent_nlme_dfop_tc</span></span> -<span><span class="op">)</span></span></code></pre></div> -<pre><code> Model df AIC BIC logLik Test L.Ratio p-value -f_parent_nlme_sfo_const 1 5 796.60 811.82 -393.30 -f_parent_nlme_sfo_tc 2 6 798.60 816.86 -393.30 1 vs 2 0.00 0.998 -f_parent_nlme_dfop_tc 3 10 671.91 702.34 -325.96 2 vs 3 134.69 <.0001</code></pre> -<p>In addition to these fits, attempts were also made to include -correlations between random effects by using the log Cholesky -parameterisation of the matrix specifying them. The code used for these -attempts can be made visible below.</p> -<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_parent_nlme_sfo_const_logchol</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlme/man/nlme.html" class="external-link">nlme</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span>,</span> -<span> random <span class="op">=</span> <span class="fu">nlme</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/nlme/man/pdLogChol.html" class="external-link">pdLogChol</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">DMTA_0</span> <span class="op">~</span> <span class="fl">1</span>, <span class="va">log_k_DMTA</span> <span class="op">~</span> <span class="fl">1</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span> -<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_parent_nlme_sfo_const</span>, <span class="va">f_parent_nlme_sfo_const_logchol</span><span class="op">)</span></span> -<span><span class="va">f_parent_nlme_sfo_tc_logchol</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlme/man/nlme.html" class="external-link">nlme</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span>,</span> -<span> random <span class="op">=</span> <span class="fu">nlme</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/nlme/man/pdLogChol.html" class="external-link">pdLogChol</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">DMTA_0</span> <span class="op">~</span> <span class="fl">1</span>, <span class="va">log_k_DMTA</span> <span class="op">~</span> <span class="fl">1</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span> -<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_parent_nlme_sfo_tc</span>, <span class="va">f_parent_nlme_sfo_tc_logchol</span><span class="op">)</span></span> -<span><span class="va">f_parent_nlme_dfop_tc_logchol</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlme/man/nlme.html" class="external-link">nlme</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>,</span> -<span> random <span class="op">=</span> <span class="fu">nlme</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/nlme/man/pdLogChol.html" class="external-link">pdLogChol</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">DMTA_0</span> <span class="op">~</span> <span class="fl">1</span>, <span class="va">log_k1</span> <span class="op">~</span> <span class="fl">1</span>, <span class="va">log_k2</span> <span class="op">~</span> <span class="fl">1</span>, <span class="va">g_qlogis</span> <span class="op">~</span> <span class="fl">1</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span> -<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_parent_nlme_dfop_tc</span>, <span class="va">f_parent_nlme_dfop_tc_logchol</span><span class="op">)</span></span></code></pre></div> -<p>While the SFO variants converge fast, the additional parameters -introduced by this lead to convergence warnings for the DFOP model. The -model comparison clearly show that adding correlations between random -effects does not improve the fits.</p> -<p>The selected model (DFOP with two-component error) fitted to the data -assuming no correlations between random effects is shown below.</p> -<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_parent_nlme_dfop_tc</span><span class="op">)</span></span></code></pre></div> -<p><img src="dimethenamid_2018_files/figure-html/plot_parent_nlme-1.png" width="700"></p> -</div> -<div class="section level4"> -<h4 id="saemix">saemix<a class="anchor" aria-label="anchor" href="#saemix"></a> -</h4> -<p>The saemix package provided the first Open Source implementation of -the Stochastic Approximation to the Expectation Maximisation (SAEM) -algorithm. SAEM fits of degradation models can be conveniently performed -using an interface to the saemix package available in current -development versions of the mkin package.</p> -<p>The corresponding SAEM fits of the four combinations of degradation -and error models are fitted below. As there is no convergence criterion -implemented in the saemix package, the convergence plots need to be -manually checked for every fit. We define control settings that work -well for all the parent data fits shown in this vignette.</p> -<div class="sourceCode" id="cb14"><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">saemix</span><span class="op">)</span></span> -<span><span class="va">saemix_control</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/saemix/man/saemixControl.html" class="external-link">saemixControl</a></span><span class="op">(</span>nbiter.saemix <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">800</span>, <span class="fl">300</span><span class="op">)</span>, nb.chains <span class="op">=</span> <span class="fl">15</span>,</span> -<span> print <span class="op">=</span> <span class="cn">FALSE</span>, save <span class="op">=</span> <span class="cn">FALSE</span>, save.graphs <span class="op">=</span> <span class="cn">FALSE</span>, displayProgress <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span> -<span><span class="va">saemix_control_moreiter</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/saemix/man/saemixControl.html" class="external-link">saemixControl</a></span><span class="op">(</span>nbiter.saemix <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">1600</span>, <span class="fl">300</span><span class="op">)</span>, nb.chains <span class="op">=</span> <span class="fl">15</span>,</span> -<span> print <span class="op">=</span> <span class="cn">FALSE</span>, save <span class="op">=</span> <span class="cn">FALSE</span>, save.graphs <span class="op">=</span> <span class="cn">FALSE</span>, displayProgress <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span> -<span><span class="va">saemix_control_10k</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/saemix/man/saemixControl.html" class="external-link">saemixControl</a></span><span class="op">(</span>nbiter.saemix <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">10000</span>, <span class="fl">300</span><span class="op">)</span>, nb.chains <span class="op">=</span> <span class="fl">15</span>,</span> -<span> print <span class="op">=</span> <span class="cn">FALSE</span>, save <span class="op">=</span> <span class="cn">FALSE</span>, save.graphs <span class="op">=</span> <span class="cn">FALSE</span>, displayProgress <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div> -<p>The convergence plot for the SFO model using constant variance is -shown below.</p> -<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_parent_saemix_sfo_const</span> <span class="op"><-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</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> control <span class="op">=</span> <span class="va">saemix_control</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span></span> -<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_parent_saemix_sfo_const</span><span class="op">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></span></code></pre></div> -<p><img src="dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_const-1.png" width="700"></p> -<p>Obviously the selected number of iterations is sufficient to reach -convergence. This can also be said for the SFO fit using the -two-component error model.</p> -<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_parent_saemix_sfo_tc</span> <span class="op"><-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> control <span class="op">=</span> <span class="va">saemix_control</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span></span> -<span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_parent_saemix_sfo_tc</span><span class="op">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></span></code></pre></div> -<p><img src="dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_tc-1.png" width="700"></p> -<p>When fitting the DFOP model with constant variance (see below), -parameter convergence is not as unambiguous.</p> -<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_parent_saemix_dfop_const</span> <span class="op"><-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> control <span class="op">=</span> <span class="va">saemix_control</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span></span> -<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_parent_saemix_dfop_const</span><span class="op">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></span></code></pre></div> -<p><img src="dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_const-1.png" width="700"></p> -<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_const</span><span class="op">)</span></span></code></pre></div> -<pre><code>Kinetic nonlinear mixed-effects model fit by SAEM -Structural model: -d_DMTA/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * - time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) - * DMTA - -Data: -155 observations of 1 variable(s) grouped in 6 datasets - -Likelihood computed by importance sampling - AIC BIC logLik - 706 704 -344 - -Fitted parameters: - estimate lower upper -DMTA_0 97.99583 96.50079 99.4909 -k1 0.06377 0.03432 0.0932 -k2 0.00848 0.00444 0.0125 -g 0.95701 0.91313 1.0009 -a.1 1.82141 1.65122 1.9916 -SD.DMTA_0 1.64787 0.45772 2.8380 -SD.k1 0.57439 0.24731 0.9015 -SD.k2 0.03296 -2.50195 2.5679 -SD.g 1.10266 0.32369 1.8816</code></pre> -<p>While the other parameters converge to credible values, the variance -of k2 (<code>omega2.k2</code>) converges to a very small value. The -printout of the <code>saem.mmkin</code> model shows that the estimated -standard deviation of k2 across the population of soils -(<code>SD.k2</code>) is ill-defined, indicating overparameterisation of -this model.</p> -<p>When the DFOP model is fitted with the two-component error model, we -also observe that the estimated variance of k2 becomes very small, while -being ill-defined, as illustrated by the excessive confidence interval -of <code>SD.k2</code>.</p> -<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_parent_saemix_dfop_tc</span> <span class="op"><-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> control <span class="op">=</span> <span class="va">saemix_control</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span></span> -<span><span class="va">f_parent_saemix_dfop_tc_moreiter</span> <span class="op"><-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span> -<span> control <span class="op">=</span> <span class="va">saemix_control_moreiter</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span></span> -<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_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></span></code></pre></div> -<p><img src="dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc-1.png" width="700"></p> -<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc</span><span class="op">)</span></span></code></pre></div> -<pre><code>Kinetic nonlinear mixed-effects model fit by SAEM -Structural model: -d_DMTA/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * - time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) - * DMTA - -Data: -155 observations of 1 variable(s) grouped in 6 datasets - -Likelihood computed by importance sampling - AIC BIC logLik - 666 664 -323 - -Fitted parameters: - estimate lower upper -DMTA_0 98.27617 96.3088 100.2436 -k1 0.06437 0.0337 0.0950 -k2 0.00880 0.0063 0.0113 -g 0.95249 0.9100 0.9949 -a.1 1.06161 0.8625 1.2607 -b.1 0.02967 0.0226 0.0367 -SD.DMTA_0 2.06075 0.4187 3.7028 -SD.k1 0.59357 0.2561 0.9310 -SD.k2 0.00292 -10.2960 10.3019 -SD.g 1.05725 0.3808 1.7337</code></pre> -<p>Doubling the number of iterations in the first phase of the algorithm -leads to a slightly lower likelihood, and therefore to slightly higher -AIC and BIC values. With even more iterations, the algorithm stops with -an error message. This is related to the variance of k2 approximating -zero and has been submitted as a <a href="https://github.com/saemixdevelopment/saemixextension/issues/29" class="external-link">bug -to the saemix package</a>, as the algorithm does not converge in this -case.</p> -<p>An alternative way to fit DFOP in combination with the two-component -error model is to use the model formulation with transformed parameters -as used per default in mkin. When using this option, convergence is -slower, but eventually the algorithm stops as well with the same error -message.</p> -<p>The four combinations (SFO/const, SFO/tc, DFOP/const and DFOP/tc) and -the version with increased iterations can be compared using the model -comparison function of the saemix package:</p> -<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">AIC_parent_saemix</span> <span class="op"><-</span> <span class="fu">saemix</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/compare.saemix.html" class="external-link">compare.saemix</a></span><span class="op">(</span></span> -<span> <span class="va">f_parent_saemix_sfo_const</span><span class="op">$</span><span class="va">so</span>,</span> -<span> <span class="va">f_parent_saemix_sfo_tc</span><span class="op">$</span><span class="va">so</span>,</span> -<span> <span class="va">f_parent_saemix_dfop_const</span><span class="op">$</span><span class="va">so</span>,</span> -<span> <span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span>,</span> -<span> <span class="va">f_parent_saemix_dfop_tc_moreiter</span><span class="op">$</span><span class="va">so</span><span class="op">)</span></span></code></pre></div> -<pre><code>Likelihoods calculated by importance sampling</code></pre> -<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/colnames.html" class="external-link">rownames</a></span><span class="op">(</span><span class="va">AIC_parent_saemix</span><span class="op">)</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span></span> -<span> <span class="st">"SFO const"</span>, <span class="st">"SFO tc"</span>, <span class="st">"DFOP const"</span>, <span class="st">"DFOP tc"</span>, <span class="st">"DFOP tc more iterations"</span><span class="op">)</span></span> -<span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">AIC_parent_saemix</span><span class="op">)</span></span></code></pre></div> -<pre><code> AIC BIC -SFO const 796.38 795.34 -SFO tc 798.38 797.13 -DFOP const 705.75 703.88 -DFOP tc 665.65 663.57 -DFOP tc more iterations 665.88 663.80</code></pre> -<p>In order to check the influence of the likelihood calculation -algorithms implemented in saemix, the likelihood from Gaussian -quadrature is added to the best fit, and the AIC values obtained from -the three methods are compared.</p> -<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span> <span class="op"><-</span></span> -<span> <span class="fu">saemix</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/llgq.saemix.html" class="external-link">llgq.saemix</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span><span class="op">)</span></span> -<span><span class="va">AIC_parent_saemix_methods</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span></span> -<span> is <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/AIC.html" class="external-link">AIC</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span>, method <span class="op">=</span> <span class="st">"is"</span><span class="op">)</span>,</span> -<span> gq <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/AIC.html" class="external-link">AIC</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span>, method <span class="op">=</span> <span class="st">"gq"</span><span class="op">)</span>,</span> -<span> lin <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/AIC.html" class="external-link">AIC</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span>, method <span class="op">=</span> <span class="st">"lin"</span><span class="op">)</span></span> -<span><span class="op">)</span></span> -<span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">AIC_parent_saemix_methods</span><span class="op">)</span></span></code></pre></div> -<pre><code> is gq lin -665.65 665.68 665.11 </code></pre> -<p>The AIC values based on importance sampling and Gaussian quadrature -are very similar. Using linearisation is known to be less accurate, but -still gives a similar value.</p> -<p>In order to illustrate that the comparison of the three method -depends on the degree of convergence obtained in the fit, the same -comparison is shown below for the fit using the defaults for the number -of iterations and the number of MCMC chains.</p> -<p>When using OpenBlas for linear algebra, there is a large difference -in the values obtained with Gaussian quadrature, so the larger number of -iterations makes a lot of difference. When using the LAPACK version -coming with Debian Bullseye, the AIC based on Gaussian quadrature is -almost the same as the one obtained with the other methods, also when -using defaults for the fit.</p> -<div class="sourceCode" id="cb29"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_parent_saemix_dfop_tc_defaults</span> <span class="op"><-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span><span class="op">)</span></span> -<span><span class="va">f_parent_saemix_dfop_tc_defaults</span><span class="op">$</span><span class="va">so</span> <span class="op"><-</span></span> -<span> <span class="fu">saemix</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/llgq.saemix.html" class="external-link">llgq.saemix</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc_defaults</span><span class="op">$</span><span class="va">so</span><span class="op">)</span></span> -<span><span class="va">AIC_parent_saemix_methods_defaults</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> -<span> is <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/AIC.html" class="external-link">AIC</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc_defaults</span><span class="op">$</span><span class="va">so</span>, method <span class="op">=</span> <span class="st">"is"</span><span class="op">)</span>,</span> -<span> gq <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/AIC.html" class="external-link">AIC</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc_defaults</span><span class="op">$</span><span class="va">so</span>, method <span class="op">=</span> <span class="st">"gq"</span><span class="op">)</span>,</span> -<span> lin <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/AIC.html" class="external-link">AIC</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc_defaults</span><span class="op">$</span><span class="va">so</span>, method <span class="op">=</span> <span class="st">"lin"</span><span class="op">)</span></span> -<span><span class="op">)</span></span> -<span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">AIC_parent_saemix_methods_defaults</span><span class="op">)</span></span></code></pre></div> -<pre><code> is gq lin -669.77 669.36 670.95 </code></pre> -</div> -</div> -<div class="section level3"> -<h3 id="comparison">Comparison<a class="anchor" aria-label="anchor" href="#comparison"></a> -</h3> -<p>The following table gives the AIC values obtained with both backend -packages using the same control parameters (800 iterations burn-in, 300 -iterations second phase, 15 chains).</p> -<div class="sourceCode" id="cb31"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">AIC_all</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span></span> -<span> check.names <span class="op">=</span> <span class="cn">FALSE</span>,</span> -<span> <span class="st">"Degradation model"</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">"SFO"</span>, <span class="st">"DFOP"</span>, <span class="st">"DFOP"</span><span class="op">)</span>,</span> -<span> <span class="st">"Error model"</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">"const"</span>, <span class="st">"tc"</span>, <span class="st">"const"</span>, <span class="st">"tc"</span><span class="op">)</span>,</span> -<span> nlme <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="fu"><a href="https://rdrr.io/r/stats/AIC.html" class="external-link">AIC</a></span><span class="op">(</span><span class="va">f_parent_nlme_sfo_const</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/stats/AIC.html" class="external-link">AIC</a></span><span class="op">(</span><span class="va">f_parent_nlme_sfo_tc</span><span class="op">)</span>, <span class="cn">NA</span>, <span class="fu"><a href="https://rdrr.io/r/stats/AIC.html" class="external-link">AIC</a></span><span class="op">(</span><span class="va">f_parent_nlme_dfop_tc</span><span class="op">)</span><span class="op">)</span>,</span> -<span> saemix_lin <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">f_parent_saemix_sfo_const</span><span class="op">$</span><span class="va">so</span>, <span class="va">f_parent_saemix_sfo_tc</span><span class="op">$</span><span class="va">so</span>,</span> -<span> <span class="va">f_parent_saemix_dfop_const</span><span class="op">$</span><span class="va">so</span>, <span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span><span class="op">)</span>, <span class="va">AIC</span>, method <span class="op">=</span> <span class="st">"lin"</span><span class="op">)</span>,</span> -<span> saemix_is <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">f_parent_saemix_sfo_const</span><span class="op">$</span><span class="va">so</span>, <span class="va">f_parent_saemix_sfo_tc</span><span class="op">$</span><span class="va">so</span>,</span> -<span> <span class="va">f_parent_saemix_dfop_const</span><span class="op">$</span><span class="va">so</span>, <span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span><span class="op">)</span>, <span class="va">AIC</span>, method <span class="op">=</span> <span class="st">"is"</span><span class="op">)</span></span> -<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">AIC_all</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left">Degradation model</th> -<th align="left">Error model</th> -<th align="right">nlme</th> -<th align="right">saemix_lin</th> -<th align="right">saemix_is</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">SFO</td> -<td align="left">const</td> -<td align="right">796.60</td> -<td align="right">796.60</td> -<td align="right">796.38</td> -</tr> -<tr class="even"> -<td align="left">SFO</td> -<td align="left">tc</td> -<td align="right">798.60</td> -<td align="right">798.60</td> -<td align="right">798.38</td> -</tr> -<tr class="odd"> -<td align="left">DFOP</td> -<td align="left">const</td> -<td align="right">NA</td> -<td align="right">709.26</td> -<td align="right">705.75</td> -</tr> -<tr class="even"> -<td align="left">DFOP</td> -<td align="left">tc</td> -<td align="right">671.91</td> -<td align="right">665.11</td> -<td align="right">665.65</td> -</tr> -</tbody> -</table> -</div> -</div> -<div class="section level2"> -<h2 id="conclusion">Conclusion<a class="anchor" aria-label="anchor" href="#conclusion"></a> -</h2> -<p>A more detailed analysis of the dimethenamid dataset confirmed that -the DFOP model provides the most appropriate description of the decline -of the parent compound in these data. On the other hand, closer -inspection of the results revealed that the variability of the k2 -parameter across the population of soils is ill-defined. This coincides -with the observation that this parameter cannot robustly be quantified -for some of the soils.</p> -<p>Regarding the regulatory use of these data, it is claimed that an -improved characterisation of the mean parameter values across the -population is obtained using the nonlinear mixed-effects models -presented here. However, attempts to quantify the variability of the -slower rate constant of the biphasic decline of dimethenamid indicate -that the data are not sufficient to characterise this variability to a -satisfactory precision.</p> -</div> -<div class="section level2"> -<h2 id="session-info">Session Info<a class="anchor" aria-label="anchor" href="#session-info"></a> -</h2> -<div class="sourceCode" id="cb32"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/utils/sessionInfo.html" class="external-link">sessionInfo</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<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=C 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] stats graphics grDevices utils datasets methods base - -other attached packages: -[1] saemix_3.2 npde_3.3 nlme_3.1-162 mkin_1.2.3 knitr_1.42 - -loaded via a namespace (and not attached): - [1] highr_0.10 pillar_1.9.0 bslib_0.4.2 compiler_4.2.3 - [5] jquerylib_0.1.4 tools_4.2.3 mclust_6.0.0 digest_0.6.31 - [9] tibble_3.2.1 jsonlite_1.8.4 evaluate_0.20 memoise_2.0.1 -[13] lifecycle_1.0.3 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] parallel_4.2.3 pkgdown_2.0.7 xfun_0.38 fastmap_1.1.1 -[25] gridExtra_2.3 dplyr_1.1.1 stringr_1.5.0 generics_0.1.3 -[29] desc_1.4.2 fs_1.6.1 vctrs_0.6.1 sass_0.4.5 -[33] systemfonts_1.0.4 tidyselect_1.2.0 rprojroot_2.0.3 lmtest_0.9-40 -[37] grid_4.2.3 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 codetools_0.2-19 scales_1.2.1 htmltools_0.5.5 -[49] colorspace_2.1-0 ragg_1.2.5 utf8_1.2.3 stringi_1.7.12 -[53] munsell_0.5.0 cachem_1.0.7 zoo_1.8-12 </code></pre> -</div> -<div class="section level2"> -<h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a> -</h2> -<!-- vim: set foldmethod=syntax: --> -<div id="refs" class="references csl-bib-body hanging-indent"> -<div id="ref-efsa_2018_dimethenamid" class="csl-entry"> -EFSA. 2018. <span>“Peer Review of the Pesticide Risk Assessment of the -Active Substance Dimethenamid-p.”</span> <em>EFSA Journal</em> 16: 5211. -</div> -<div id="ref-ranke2021" class="csl-entry"> -Ranke, Johannes, Janina Wöltjen, Jana Schmidt, and Emmanuelle Comets. -2021. <span>“Taking Kinetic Evaluations of Degradation Data to the Next -Level with Nonlinear Mixed-Effects Models.”</span> <em>Environments</em> -8 (8). <a href="https://doi.org/10.3390/environments8080071" class="external-link">https://doi.org/10.3390/environments8080071</a>. -</div> -<div id="ref-dimethenamid_rar_2018_b8" class="csl-entry"> -Rapporteur Member State Germany, Co-Rapporteur Member State Bulgaria. -2018. <span>“<span class="nocase">Renewal Assessment Report -Dimethenamid-P Volume 3 - B.8 Environmental fate and behaviour, Rev. 2 - -November 2017</span>.”</span> <a href="https://open.efsa.europa.eu/study-inventory/EFSA-Q-2014-00716" class="external-link">https://open.efsa.europa.eu/study-inventory/EFSA-Q-2014-00716</a>. -</div> -</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/" 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We remove the former (to -// be compatible with the behavior of Pandoc < 2.8). -document.addEventListener('DOMContentLoaded', function(e) { - var hs = document.querySelectorAll("div.section[class*='level'] > :first-child"); - var i, h, a; - for (i = 0; i < hs.length; i++) { - h = hs[i]; - if (!/^h[1-6]$/i.test(h.tagName)) continue; // it should be a header h1-h6 - a = h.attributes; - while (a.length > 0) h.removeAttribute(a[0].name); - } -}); diff --git a/docs/dev/articles/web_only/dimethenamid_2018_files/header-attrs-2.9/header-attrs.js b/docs/dev/articles/web_only/dimethenamid_2018_files/header-attrs-2.9/header-attrs.js deleted file mode 100644 index dd57d92e..00000000 --- a/docs/dev/articles/web_only/dimethenamid_2018_files/header-attrs-2.9/header-attrs.js +++ /dev/null @@ -1,12 +0,0 @@ -// Pandoc 2.9 adds attributes on both header and div. 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</li> - <li> - <a href="../../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a> - </li> - <li> - <a href="../../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a> - </li> - <li> - <a href="../../articles/web_only/multistart.html">Short demo of the multistart method</a> - </li> - <li class="divider"> - </li> -<li class="dropdown-header">Performance</li> - <li> - <a href="../../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> - </li> - <li> - <a href="../../articles/web_only/benchmarks.html">Benchmark timings for mkin</a> - </li> - <li> - <a href="../../articles/web_only/saem_benchmarks.html">Benchmark timings for saem.mmkin</a> - </li> - <li class="divider"> - </li> -<li class="dropdown-header">Miscellaneous</li> - <li> - <a href="../../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> - </li> - <li> - <a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> - </li> - </ul> -</li> -<li> - <a href="../../news/index.html">News</a> -</li> - </ul> -<ul class="nav navbar-nav navbar-right"> -<li> - <a href="https://github.com/jranke/mkin/" class="external-link"> - <span class="fab fa-github fa-lg"></span> - - </a> -</li> - </ul> -</div> -<!--/.nav-collapse --> - </div> -<!--/.container --> -</div> -<!--/.navbar --> - - - - </header><div class="row"> - <div class="col-md-9 contents"> - <div class="page-header toc-ignore"> - <h1 data-toc-skip>Short demo of the multistart method</h1> - <h4 data-toc-skip class="author">Johannes -Ranke</h4> - - <h4 data-toc-skip class="date">Last change 20 April 2023 -(rebuilt 2023-04-20)</h4> - - <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/multistart.rmd" class="external-link"><code>vignettes/web_only/multistart.rmd</code></a></small> - <div class="hidden name"><code>multistart.rmd</code></div> - - </div> - - - -<p>The dimethenamid data from 2018 from seven soils is used as example -data in this vignette.</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="va">dmta_ds</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">lapply</a></span><span class="op">(</span><span class="fl">1</span><span class="op">:</span><span class="fl">7</span>, <span class="kw">function</span><span class="op">(</span><span class="va">i</span><span class="op">)</span> <span class="op">{</span></span> -<span> <span class="va">ds_i</span> <span class="op"><-</span> <span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">ds</span><span class="op">[[</span><span class="va">i</span><span class="op">]</span><span class="op">]</span><span class="op">$</span><span class="va">data</span></span> -<span> <span class="va">ds_i</span><span class="op">[</span><span class="va">ds_i</span><span class="op">$</span><span class="va">name</span> <span class="op">==</span> <span class="st">"DMTAP"</span>, <span class="st">"name"</span><span class="op">]</span> <span class="op"><-</span> <span class="st">"DMTA"</span></span> -<span> <span class="va">ds_i</span><span class="op">$</span><span class="va">time</span> <span class="op"><-</span> <span class="va">ds_i</span><span class="op">$</span><span class="va">time</span> <span class="op">*</span> <span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">f_time_norm</span><span class="op">[</span><span class="va">i</span><span class="op">]</span></span> -<span> <span class="va">ds_i</span></span> -<span><span class="op">}</span><span class="op">)</span></span> -<span><span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">)</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</span><span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">ds</span>, <span class="kw">function</span><span class="op">(</span><span class="va">ds</span><span class="op">)</span> <span class="va">ds</span><span class="op">$</span><span class="va">title</span><span class="op">)</span></span> -<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/cbind.html" class="external-link">rbind</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 1"</span><span class="op">]</span><span class="op">]</span>, <span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 2"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span> -<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 1"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 2"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="cn">NULL</span></span></code></pre></div> -<p>First, we check the DFOP model with the two-component error model and -random effects for all degradation parameters.</p> -<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_mmkin</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span><span class="st">"DFOP"</span>, <span class="va">dmta_ds</span>, error_model <span class="op">=</span> <span class="st">"tc"</span>, cores <span class="op">=</span> <span class="fl">7</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<span><span class="va">f_saem_full</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_mmkin</span><span class="op">)</span></span> -<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_full</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## [1] "sd(log_k2)"</span></span></code></pre> -<p>We see that not all variability parameters are identifiable. The -<code>illparms</code> function tells us that the confidence interval for -the standard deviation of ‘log_k2’ includes zero. We check this -assessment using multiple runs with different starting values.</p> -<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_saem_full_multi</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/multistart.html">multistart</a></span><span class="op">(</span><span class="va">f_saem_full</span>, n <span class="op">=</span> <span class="fl">16</span>, cores <span class="op">=</span> <span class="fl">16</span><span class="op">)</span></span> -<span><span class="fu"><a href="../../reference/parplot.html">parplot</a></span><span class="op">(</span><span class="va">f_saem_full_multi</span>, lpos <span class="op">=</span> <span class="st">"topleft"</span><span class="op">)</span></span></code></pre></div> -<p><img src="multistart_files/figure-html/unnamed-chunk-3-1.png" width="700"></p> -<p>This confirms that the variance of k2 is the most problematic -parameter, so we reduce the parameter distribution model by removing the -intersoil variability for k2.</p> -<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">f_saem_reduced</span> <span class="op"><-</span> <span class="fu">stats</span><span class="fu">::</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_full</span>, no_random_effect <span class="op">=</span> <span class="st">"log_k2"</span><span class="op">)</span></span> -<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_reduced</span><span class="op">)</span></span> -<span><span class="va">f_saem_reduced_multi</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/multistart.html">multistart</a></span><span class="op">(</span><span class="va">f_saem_reduced</span>, n <span class="op">=</span> <span class="fl">16</span>, cores <span class="op">=</span> <span class="fl">16</span><span class="op">)</span></span> -<span><span class="fu"><a href="../../reference/parplot.html">parplot</a></span><span class="op">(</span><span class="va">f_saem_reduced_multi</span>, lpos <span class="op">=</span> <span class="st">"topright"</span>, ylim <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.5</span>, <span class="fl">2</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> -<p><img src="multistart_files/figure-html/unnamed-chunk-4-1.png" width="700"></p> -<p>The results confirm that all remaining parameters can be determined -with sufficient certainty.</p> -<p>We can also analyse the log-likelihoods obtained in the multiple -runs:</p> -<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/llhist.html">llhist</a></span><span class="op">(</span><span class="va">f_saem_reduced_multi</span><span class="op">)</span></span></code></pre></div> -<p><img src="multistart_files/figure-html/unnamed-chunk-5-1.png" width="700"></p> -<p>We can use the <code>anova</code> method to compare the models.</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">f_saem_full</span>, <span class="fu"><a href="../../reference/multistart.html">best</a></span><span class="op">(</span><span class="va">f_saem_full_multi</span><span class="op">)</span>,</span> -<span> <span class="va">f_saem_reduced</span>, <span class="fu"><a href="../../reference/multistart.html">best</a></span><span class="op">(</span><span class="va">f_saem_reduced_multi</span><span class="op">)</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Data: 155 observations of 1 variable(s) grouped in 6 datasets</span></span> -<span><span class="co">## </span></span> -<span><span class="co">## npar AIC BIC Lik Chisq Df Pr(>Chisq)</span></span> -<span><span class="co">## f_saem_reduced 9 663.73 661.86 -322.86 </span></span> -<span><span class="co">## best(f_saem_reduced_multi) 9 663.69 661.82 -322.85 0.0361 0 </span></span> -<span><span class="co">## f_saem_full 10 669.77 667.69 -324.89 0.0000 1 1</span></span> -<span><span class="co">## best(f_saem_full_multi) 10 665.56 663.48 -322.78 4.2060 0</span></span></code></pre> -<p>The reduced model results in lower AIC and BIC values, so it is -clearly preferable. Using multiple starting values gives a large -improvement in case of the full model, because it is less well-defined, -which impedes convergence. For the reduced model, using multiple -starting values only results in a small improvement of the model -fit.</p> - </div> - - <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar"> - - </div> - -</div> - - - - <footer><div class="copyright"> - <p></p> -<p>Developed by Johannes Ranke.</p> -</div> - -<div class="pkgdown"> - <p></p> -<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p> -</div> - - </footer> -</div> - - - - - - - </body> -</html> diff --git a/docs/dev/articles/web_only/multistart_files/accessible-code-block-0.0.1/empty-anchor.js b/docs/dev/articles/web_only/multistart_files/accessible-code-block-0.0.1/empty-anchor.js deleted file mode 100644 index ca349fd6..00000000 --- a/docs/dev/articles/web_only/multistart_files/accessible-code-block-0.0.1/empty-anchor.js +++ /dev/null @@ -1,15 +0,0 @@ -// Hide empty <a> tag within highlighted CodeBlock for screen reader accessibility (see 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-</li> -<li> - <a href="../../news/index.html">News</a> -</li> - </ul> -<ul class="nav navbar-nav navbar-right"> -<li> - <a href="https://github.com/jranke/mkin/" class="external-link"> - <span class="fab fa-github fa-lg"></span> - - </a> -</li> - </ul> -</div> -<!--/.nav-collapse --> - </div> -<!--/.container --> -</div> -<!--/.navbar --> - - - - </header><div class="row"> - <div class="col-md-9 contents"> - <div class="page-header toc-ignore"> - <h1 data-toc-skip>Benchmark timings for saem.mmkin</h1> - <h4 data-toc-skip class="author">Johannes -Ranke</h4> - - <h4 data-toc-skip class="date">Last change 17 February 2023 -(rebuilt 2023-04-16)</h4> - - <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/saem_benchmarks.rmd" class="external-link"><code>vignettes/web_only/saem_benchmarks.rmd</code></a></small> - <div class="hidden name"><code>saem_benchmarks.rmd</code></div> - - </div> - - - -<p>Each system is characterized by operating system type, CPU type, mkin -version, saemix version and R version. A compiler was available, so if -no analytical solution was available, compiled ODE models are used.</p> -<p>Every fit is only performed once, so the accuracy of the benchmarks -is limited.</p> -<p>For the initial mmkin fits, we use all available cores.</p> -<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">n_cores</span> <span class="op"><-</span> <span class="fu">parallel</span><span class="fu">::</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></code></pre></div> -<div class="section level2"> -<h2 id="test-data">Test data<a class="anchor" aria-label="anchor" href="#test-data"></a> -</h2> -<p>Please refer to the vignette <code>dimethenamid_2018</code> for an -explanation of the following preprocessing.</p> -<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">dmta_ds</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">lapply</a></span><span class="op">(</span><span class="fl">1</span><span class="op">:</span><span class="fl">7</span>, <span class="kw">function</span><span class="op">(</span><span class="va">i</span><span class="op">)</span> <span class="op">{</span></span> -<span> <span class="va">ds_i</span> <span class="op"><-</span> <span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">ds</span><span class="op">[[</span><span class="va">i</span><span class="op">]</span><span class="op">]</span><span class="op">$</span><span class="va">data</span></span> -<span> <span class="va">ds_i</span><span class="op">[</span><span class="va">ds_i</span><span class="op">$</span><span class="va">name</span> <span class="op">==</span> <span class="st">"DMTAP"</span>, <span class="st">"name"</span><span class="op">]</span> <span class="op"><-</span> <span class="st">"DMTA"</span></span> -<span> <span class="va">ds_i</span><span class="op">$</span><span class="va">time</span> <span class="op"><-</span> <span class="va">ds_i</span><span class="op">$</span><span class="va">time</span> <span class="op">*</span> <span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">f_time_norm</span><span class="op">[</span><span class="va">i</span><span class="op">]</span></span> -<span> <span class="va">ds_i</span></span> -<span><span class="op">}</span><span class="op">)</span></span> -<span><span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">)</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</span><span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">ds</span>, <span class="kw">function</span><span class="op">(</span><span class="va">ds</span><span class="op">)</span> <span class="va">ds</span><span class="op">$</span><span class="va">title</span><span class="op">)</span></span> -<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/cbind.html" class="external-link">rbind</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 1"</span><span class="op">]</span><span class="op">]</span>, <span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 2"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span> -<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 1"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="cn">NULL</span></span> -<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 2"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="cn">NULL</span></span></code></pre></div> -</div> -<div class="section level2"> -<h2 id="test-cases">Test cases<a class="anchor" aria-label="anchor" href="#test-cases"></a> -</h2> -<div class="section level3"> -<h3 id="parent-only">Parent only<a class="anchor" aria-label="anchor" href="#parent-only"></a> -</h3> -<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">parent_mods</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"DFOP"</span>, <span class="st">"SFORB"</span>, <span class="st">"HS"</span><span class="op">)</span></span> -<span><span class="va">parent_sep_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span><span class="va">parent_mods</span>, <span class="va">dmta_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">parent_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">parent_sep_const</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span> -<span></span> -<span><span class="va">t1</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">sfo_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">parent_sep_const</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span> -<span><span class="va">t2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">dfop_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">parent_sep_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span> -<span><span class="va">t3</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">sforb_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">parent_sep_const</span><span class="op">[</span><span class="st">"SFORB"</span>, <span class="op">]</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span> -<span><span class="va">t4</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">hs_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">parent_sep_const</span><span class="op">[</span><span class="st">"HS"</span>, <span class="op">]</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span> -<span><span class="va">t5</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">sfo_tc</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">parent_sep_tc</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span> -<span><span class="va">t6</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">dfop_tc</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">parent_sep_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span> -<span><span class="va">t7</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">sforb_tc</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">parent_sep_tc</span><span class="op">[</span><span class="st">"SFORB"</span>, <span class="op">]</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span> -<span><span class="va">t8</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">hs_tc</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">parent_sep_tc</span><span class="op">[</span><span class="st">"HS"</span>, <span class="op">]</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span></code></pre></div> -<div class="sourceCode" id="cb4"><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> -<span> <span class="va">sfo_const</span>, <span class="va">dfop_const</span>, <span class="va">sforb_const</span>, <span class="va">hs_const</span>,</span> -<span> <span class="va">sfo_tc</span>, <span class="va">dfop_tc</span>, <span class="va">sforb_tc</span>, <span class="va">hs_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>, digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> -<table class="table"> -<thead><tr class="header"> -<th align="left"></th> -<th align="right">npar</th> -<th align="right">AIC</th> -<th align="right">BIC</th> -<th align="right">Lik</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">sfo_const</td> -<td align="right">5</td> -<td align="right">796.3</td> -<td align="right">795.3</td> -<td align="right">-393.2</td> -</tr> -<tr class="even"> -<td align="left">sfo_tc</td> -<td align="right">6</td> -<td align="right">798.3</td> -<td align="right">797.1</td> -<td align="right">-393.2</td> -</tr> -<tr class="odd"> -<td align="left">dfop_const</td> -<td align="right">9</td> -<td align="right">709.4</td> -<td align="right">707.5</td> -<td align="right">-345.7</td> -</tr> -<tr class="even"> -<td align="left">sforb_const</td> -<td align="right">9</td> -<td align="right">710.0</td> -<td align="right">708.1</td> -<td align="right">-346.0</td> -</tr> -<tr class="odd"> -<td align="left">hs_const</td> -<td align="right">9</td> -<td align="right">713.7</td> -<td align="right">711.8</td> -<td align="right">-347.8</td> -</tr> -<tr class="even"> -<td align="left">dfop_tc</td> -<td align="right">10</td> -<td align="right">669.8</td> -<td align="right">667.7</td> -<td align="right">-324.9</td> -</tr> -<tr class="odd"> -<td align="left">sforb_tc</td> -<td align="right">10</td> -<td align="right">662.8</td> -<td align="right">660.7</td> -<td align="right">-321.4</td> -</tr> -<tr class="even"> -<td align="left">hs_tc</td> -<td align="right">10</td> -<td align="right">667.3</td> -<td align="right">665.2</td> -<td align="right">-323.6</td> -</tr> -</tbody> -</table> -<p>The above model comparison suggests to use the SFORB model with -two-component error. For comparison, we keep the DFOP model with -two-component error, as it competes with SFORB for biphasic curves.</p> -<div class="sourceCode" id="cb5"><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">dfop_tc</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## [1] "sd(log_k2)"</span></span></code></pre> -<div class="sourceCode" id="cb7"><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">sforb_tc</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## [1] "sd(log_k_DMTA_bound_free)"</span></span></code></pre> -<p>For these two models, random effects for the transformed parameters -<code>k2</code> and <code>k_DMTA_bound_free</code> could not be -quantified.</p> -</div> -<div class="section level3"> -<h3 id="one-metabolite">One metabolite<a class="anchor" aria-label="anchor" href="#one-metabolite"></a> -</h3> -<p>We remove parameters that were found to be ill-defined in the parent -only fits.</p> -<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">one_met_mods</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> DFOP_SFO <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> DMTA <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"DFOP"</span>, <span class="st">"M23"</span><span class="op">)</span>,</span> -<span> M23 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span><span class="op">)</span>,</span> -<span> SFORB_SFO <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> DMTA <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span>, <span class="st">"M23"</span><span class="op">)</span>,</span> -<span> M23 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span> -<span></span> -<span><span class="va">one_met_sep_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span><span class="va">one_met_mods</span>, <span class="va">dmta_ds</span>, error_model <span class="op">=</span> <span class="st">"const"</span>,</span> -<span> cores <span class="op">=</span> <span class="va">n_cores</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<span><span class="va">one_met_sep_tc</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span><span class="va">one_met_mods</span>, <span class="va">dmta_ds</span>, error_model <span class="op">=</span> <span class="st">"tc"</span>,</span> -<span> cores <span class="op">=</span> <span class="va">n_cores</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<span></span> -<span><span class="va">t9</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">dfop_sfo_tc</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">one_met_sep_tc</span><span class="op">[</span><span class="st">"DFOP_SFO"</span>, <span class="op">]</span>,</span> -<span> no_random_effect <span class="op">=</span> <span class="st">"log_k2"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span> -<span><span class="va">t10</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">sforb_sfo_tc</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">one_met_sep_tc</span><span class="op">[</span><span class="st">"SFORB_SFO"</span>, <span class="op">]</span>,</span> -<span> no_random_effect <span class="op">=</span> <span class="st">"log_k_DMTA_bound_free"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span></code></pre></div> -</div> -<div class="section level3"> -<h3 id="three-metabolites">Three metabolites<a class="anchor" aria-label="anchor" href="#three-metabolites"></a> -</h3> -<p>For the case of three metabolites, we only keep the SFORB model in -order to limit the time for compiling this vignette, and as fitting in -parallel may disturb the benchmark. Again, we do not include random -effects that were ill-defined in previous fits of subsets of the -degradation model.</p> -<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">sforb_sfo_tc</span><span class="op">)</span></span></code></pre></div> -<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="va">three_met_mods</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> SFORB_SFO3_plus <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> -<span> DMTA <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"M23"</span>, <span class="st">"M27"</span>, <span class="st">"M31"</span><span class="op">)</span><span class="op">)</span>,</span> -<span> M23 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> M27 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> -<span> M31 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M27"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span> -<span></span> -<span><span class="va">three_met_sep_tc</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span><span class="va">three_met_mods</span>, <span class="va">dmta_ds</span>, error_model <span class="op">=</span> <span class="st">"tc"</span>,</span> -<span> cores <span class="op">=</span> <span class="va">n_cores</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> -<span></span> -<span><span class="va">t11</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">sforb_sfo3_plus_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">three_met_sep_tc</span><span class="op">[</span><span class="st">"SFORB_SFO3_plus"</span>, <span class="op">]</span>,</span> -<span> no_random_effect <span class="op">=</span> <span class="st">"log_k_DMTA_bound_free"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span></code></pre></div> -</div> -</div> -<div class="section level2"> -<h2 id="results">Results<a class="anchor" aria-label="anchor" href="#results"></a> -</h2> -<p>Benchmarks for all available error models are shown. They are -intended for improving mkin, not for comparing CPUs or operating -systems. All trademarks belong to their respective owners.</p> -<div class="section level3"> -<h3 id="parent-only-1">Parent only<a class="anchor" aria-label="anchor" href="#parent-only-1"></a> -</h3> -<p>Constant variance for SFO, DFOP, SFORB and HS.</p> -<table class="table"> -<thead><tr class="header"> -<th align="left">CPU</th> -<th align="left">OS</th> -<th align="left">mkin</th> -<th align="left">saemix</th> -<th align="right">t1</th> -<th align="right">t2</th> -<th align="right">t3</th> -<th align="right">t4</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">Ryzen 7 1700</td> -<td align="left">Linux</td> -<td align="left">1.2.0</td> -<td align="left">3.2</td> -<td align="right">2.140</td> -<td align="right">4.626</td> -<td align="right">4.328</td> -<td align="right">4.998</td> -</tr> -<tr class="even"> -<td align="left">Ryzen 7 1700</td> -<td align="left">Linux</td> -<td align="left">1.2.2</td> -<td align="left">3.2</td> -<td align="right">2.427</td> -<td align="right">4.550</td> -<td align="right">4.217</td> -<td align="right">4.851</td> -</tr> -<tr class="odd"> -<td align="left">Ryzen 9 7950X</td> -<td align="left">Linux</td> -<td align="left">1.2.1</td> -<td align="left">3.2</td> -<td align="right">1.352</td> -<td align="right">2.813</td> -<td align="right">2.401</td> -<td align="right">2.074</td> -</tr> -<tr class="even"> -<td align="left">Ryzen 9 7950X</td> -<td align="left">Linux</td> -<td align="left">1.2.2</td> -<td align="left">3.2</td> -<td align="right">1.328</td> -<td align="right">2.738</td> -<td align="right">2.336</td> -<td align="right">2.023</td> -</tr> -<tr class="odd"> -<td align="left">Ryzen 9 7950X</td> -<td align="left">Linux</td> -<td align="left">1.2.3</td> -<td align="left">3.2</td> -<td align="right">1.118</td> -<td align="right">2.036</td> -<td align="right">2.010</td> -<td align="right">2.088</td> -</tr> -<tr class="even"> -<td align="left">Ryzen 9 7950X</td> -<td align="left">Linux</td> -<td align="left">1.2.3</td> -<td align="left">3.2</td> -<td align="right">1.389</td> -<td align="right">2.300</td> -<td align="right">1.880</td> -<td align="right">2.355</td> -</tr> -</tbody> -</table> -<p>Two-component error fits for SFO, DFOP, SFORB and HS.</p> -<table class="table"> -<thead><tr class="header"> -<th align="left">CPU</th> -<th align="left">OS</th> -<th align="left">mkin</th> -<th align="left">saemix</th> -<th align="right">t5</th> -<th align="right">t6</th> -<th align="right">t7</th> -<th align="right">t8</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">Ryzen 7 1700</td> -<td align="left">Linux</td> -<td align="left">1.2.0</td> -<td align="left">3.2</td> -<td align="right">5.678</td> -<td align="right">7.441</td> -<td align="right">8.000</td> -<td align="right">7.980</td> -</tr> -<tr class="even"> -<td align="left">Ryzen 7 1700</td> -<td align="left">Linux</td> -<td align="left">1.2.2</td> -<td align="left">3.2</td> -<td align="right">5.352</td> -<td align="right">7.201</td> -<td align="right">8.174</td> -<td align="right">8.401</td> -</tr> -<tr class="odd"> -<td align="left">Ryzen 9 7950X</td> -<td align="left">Linux</td> -<td align="left">1.2.1</td> -<td align="left">3.2</td> -<td align="right">2.388</td> -<td align="right">3.033</td> -<td align="right">3.532</td> -<td align="right">3.310</td> -</tr> -<tr class="even"> -<td align="left">Ryzen 9 7950X</td> -<td align="left">Linux</td> -<td align="left">1.2.2</td> -<td align="left">3.2</td> -<td align="right">2.341</td> -<td align="right">2.968</td> -<td align="right">3.465</td> -<td align="right">3.341</td> -</tr> -<tr class="odd"> -<td align="left">Ryzen 9 7950X</td> -<td align="left">Linux</td> -<td align="left">1.2.3</td> -<td align="left">3.2</td> -<td align="right">2.159</td> -<td align="right">3.584</td> -<td align="right">3.307</td> -<td align="right">3.460</td> -</tr> -<tr class="even"> -<td align="left">Ryzen 9 7950X</td> -<td align="left">Linux</td> -<td align="left">1.2.3</td> -<td align="left">3.2</td> -<td align="right">2.300</td> -<td align="right">3.075</td> -<td align="right">3.206</td> -<td align="right">3.471</td> -</tr> -</tbody> -</table> -</div> -<div class="section level3"> -<h3 id="one-metabolite-1">One metabolite<a class="anchor" aria-label="anchor" href="#one-metabolite-1"></a> -</h3> -<p>Two-component error for DFOP-SFO and SFORB-SFO.</p> -<table class="table"> -<thead><tr class="header"> -<th align="left">CPU</th> -<th align="left">OS</th> -<th align="left">mkin</th> -<th align="left">saemix</th> -<th align="right">t9</th> -<th align="right">t10</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">Ryzen 7 1700</td> -<td align="left">Linux</td> -<td align="left">1.2.0</td> -<td align="left">3.2</td> -<td align="right">24.465</td> -<td align="right">800.266</td> -</tr> -<tr class="even"> -<td align="left">Ryzen 7 1700</td> -<td align="left">Linux</td> -<td align="left">1.2.2</td> -<td align="left">3.2</td> -<td align="right">25.193</td> -<td align="right">798.580</td> -</tr> -<tr class="odd"> -<td align="left">Ryzen 9 7950X</td> -<td align="left">Linux</td> -<td align="left">1.2.1</td> -<td align="left">3.2</td> -<td align="right">11.247</td> -<td align="right">285.216</td> -</tr> -<tr class="even"> -<td align="left">Ryzen 9 7950X</td> -<td align="left">Linux</td> -<td align="left">1.2.2</td> -<td align="left">3.2</td> -<td align="right">11.242</td> -<td align="right">284.258</td> -</tr> -<tr class="odd"> -<td align="left">Ryzen 9 7950X</td> -<td align="left">Linux</td> -<td align="left">1.2.3</td> -<td align="left">3.2</td> -<td align="right">11.796</td> -<td align="right">216.012</td> -</tr> -<tr class="even"> -<td align="left">Ryzen 9 7950X</td> -<td align="left">Linux</td> -<td align="left">1.2.3</td> -<td align="left">3.2</td> -<td align="right">12.951</td> -<td align="right">294.082</td> -</tr> -</tbody> -</table> -</div> -<div class="section level3"> -<h3 id="three-metabolites-1">Three metabolites<a class="anchor" aria-label="anchor" href="#three-metabolites-1"></a> -</h3> -<p>Two-component error for SFORB-SFO3-plus</p> -<table class="table"> -<thead><tr class="header"> -<th align="left">CPU</th> -<th align="left">OS</th> -<th align="left">mkin</th> -<th align="left">saemix</th> -<th align="right">t11</th> -</tr></thead> -<tbody> -<tr class="odd"> -<td align="left">Ryzen 7 1700</td> -<td align="left">Linux</td> -<td align="left">1.2.0</td> -<td align="left">3.2</td> -<td align="right">1289.198</td> -</tr> -<tr class="even"> -<td align="left">Ryzen 7 1700</td> -<td align="left">Linux</td> -<td align="left">1.2.2</td> -<td align="left">3.2</td> -<td align="right">1312.445</td> -</tr> -<tr class="odd"> -<td align="left">Ryzen 9 7950X</td> -<td align="left">Linux</td> -<td align="left">1.2.1</td> -<td align="left">3.2</td> -<td align="right">489.939</td> -</tr> -<tr class="even"> -<td align="left">Ryzen 9 7950X</td> -<td align="left">Linux</td> -<td align="left">1.2.2</td> -<td align="left">3.2</td> -<td align="right">482.970</td> -</tr> -<tr class="odd"> -<td align="left">Ryzen 9 7950X</td> -<td align="left">Linux</td> -<td align="left">1.2.3</td> -<td align="left">3.2</td> -<td align="right">392.364</td> -</tr> -<tr class="even"> -<td align="left">Ryzen 9 7950X</td> -<td align="left">Linux</td> -<td align="left">1.2.3</td> -<td align="left">3.2</td> -<td align="right">477.297</td> -</tr> -</tbody> -</table> -</div> -</div> - </div> - - <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar"> - - <nav id="toc" data-toggle="toc"><h2 data-toc-skip>Contents</h2> - </nav> -</div> - -</div> - - - - <footer><div class="copyright"> - <p></p> -<p>Developed by Johannes Ranke.</p> -</div> - -<div class="pkgdown"> - <p></p> -<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p> -</div> - - </footer> -</div> - - - - - - - </body> -</html> diff --git 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