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<h1>Testing covariate modelling in hierarchical parent degradation kinetics with residue data on mesotrione</h1>
<h4 data-toc-skip class="author">Johannes
Ranke</h4>
<h4 data-toc-skip class="date">Last change on 4 August 2023,
last compiled on 16 Februar 2025</h4>
<small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/prebuilt/2023_mesotrione_parent.rmd" class="external-link"><code>vignettes/prebuilt/2023_mesotrione_parent.rmd</code></a></small>
<div class="d-none name"><code>2023_mesotrione_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 test demonstrate how nonlinear
hierarchical models (NLHM) based on the parent degradation models SFO,
FOMC, DFOP and HS can be fitted with the mkin package, also considering
the influence of covariates like soil pH on different degradation
parameters. Because in some other case studies, the SFORB
parameterisation of biexponential decline has shown some advantages over
the DFOP parameterisation, SFORB was included in the list of tested
models as well.</p>
<p>The mkin package is used in version 1.2.10, which is contains the
functions that were used for 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="test-data">Test data<a class="anchor" aria-label="anchor" href="#test-data"></a>
</h3>
<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">"mesotrione_soil_efsa_2016.xlsx"</span>, package <span class="op">=</span> <span class="st">"mkin"</span><span class="op">)</span></span>
<span><span class="va">meso_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">TRUE</span><span class="op">)</span></span></code></pre></div>
<p>The following tables show the covariate data and the 18 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">meso_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">Richmond</td>
<td align="right">6.2</td>
</tr>
<tr class="even">
<td align="left">Richmond 2</td>
<td align="right">6.2</td>
</tr>
<tr class="odd">
<td align="left">ERTC</td>
<td align="right">6.4</td>
</tr>
<tr class="even">
<td align="left">Toulouse</td>
<td align="right">7.7</td>
</tr>
<tr class="odd">
<td align="left">Picket Piece</td>
<td align="right">7.1</td>
</tr>
<tr class="even">
<td align="left">721</td>
<td align="right">5.6</td>
</tr>
<tr class="odd">
<td align="left">722</td>
<td align="right">5.7</td>
</tr>
<tr class="even">
<td align="left">723</td>
<td align="right">5.4</td>
</tr>
<tr class="odd">
<td align="left">724</td>
<td align="right">4.8</td>
</tr>
<tr class="even">
<td align="left">725</td>
<td align="right">5.8</td>
</tr>
<tr class="odd">
<td align="left">727</td>
<td align="right">5.1</td>
</tr>
<tr class="even">
<td align="left">728</td>
<td align="right">5.9</td>
</tr>
<tr class="odd">
<td align="left">729</td>
<td align="right">5.6</td>
</tr>
<tr class="even">
<td align="left">730</td>
<td align="right">5.3</td>
</tr>
<tr class="odd">
<td align="left">731</td>
<td align="right">6.1</td>
</tr>
<tr class="even">
<td align="left">732</td>
<td align="right">5.0</td>
</tr>
<tr class="odd">
<td align="left">741</td>
<td align="right">5.7</td>
</tr>
<tr class="even">
<td align="left">742</td>
<td align="right">7.2</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">meso_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">meso_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="op">}</span></span></code></pre></div>
<table class="table">
<caption>Dataset Richmond</caption>
<thead><tr class="header">
<th align="right">time</th>
<th align="right">meso</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="right">0.000000</td>
<td align="right">91.00</td>
</tr>
<tr class="even">
<td align="right">1.179050</td>
<td align="right">86.70</td>
</tr>
<tr class="odd">
<td align="right">3.537149</td>
<td align="right">73.60</td>
</tr>
<tr class="even">
<td align="right">7.074299</td>
<td align="right">61.50</td>
</tr>
<tr class="odd">
<td align="right">10.611448</td>
<td align="right">55.70</td>
</tr>
<tr class="even">
<td align="right">15.327647</td>
<td align="right">47.70</td>
</tr>
<tr class="odd">
<td align="right">17.685747</td>
<td align="right">39.50</td>
</tr>
<tr class="even">
<td align="right">24.760046</td>
<td align="right">29.80</td>
</tr>
<tr class="odd">
<td align="right">35.371494</td>
<td align="right">19.60</td>
</tr>
<tr class="even">
<td align="right">68.384889</td>
<td align="right">5.67</td>
</tr>
<tr class="odd">
<td align="right">0.000000</td>
<td align="right">97.90</td>
</tr>
<tr class="even">
<td align="right">1.179050</td>
<td align="right">96.40</td>
</tr>
<tr class="odd">
<td align="right">3.537149</td>
<td align="right">89.10</td>
</tr>
<tr class="even">
<td align="right">7.074299</td>
<td align="right">74.40</td>
</tr>
<tr class="odd">
<td align="right">10.611448</td>
<td align="right">57.40</td>
</tr>
<tr class="even">
<td align="right">15.327647</td>
<td align="right">46.30</td>
</tr>
<tr class="odd">
<td align="right">18.864797</td>
<td align="right">35.50</td>
</tr>
<tr class="even">
<td align="right">27.118146</td>
<td align="right">27.20</td>
</tr>
<tr class="odd">
<td align="right">35.371494</td>
<td align="right">19.10</td>
</tr>
<tr class="even">
<td align="right">74.280138</td>
<td align="right">6.50</td>
</tr>
<tr class="odd">
<td align="right">108.472582</td>
<td align="right">3.40</td>
</tr>
<tr class="even">
<td align="right">142.665027</td>
<td align="right">2.20</td>
</tr>
</tbody>
</table>
<table class="table">
<caption>Dataset Richmond 2</caption>
<thead><tr class="header">
<th align="right">time</th>
<th align="right">meso</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="right">0.000000</td>
<td align="right">96.0</td>
</tr>
<tr class="even">
<td align="right">2.422004</td>
<td align="right">82.4</td>
</tr>
<tr class="odd">
<td align="right">5.651343</td>
<td align="right">71.2</td>
</tr>
<tr class="even">
<td align="right">8.073348</td>
<td align="right">53.1</td>
</tr>
<tr class="odd">
<td align="right">11.302687</td>
<td align="right">48.5</td>
</tr>
<tr class="even">
<td align="right">16.954030</td>
<td align="right">33.4</td>
</tr>
<tr class="odd">
<td align="right">22.605373</td>
<td align="right">24.2</td>
</tr>
<tr class="even">
<td align="right">45.210746</td>
<td align="right">11.9</td>
</tr>
</tbody>
</table>
<table class="table">
<caption>Dataset ERTC</caption>
<thead><tr class="header">
<th align="right">time</th>
<th align="right">meso</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="right">0.000000</td>
<td align="right">99.9</td>
</tr>
<tr class="even">
<td align="right">2.755193</td>
<td align="right">80.0</td>
</tr>
<tr class="odd">
<td align="right">6.428782</td>
<td align="right">42.1</td>
</tr>
<tr class="even">
<td align="right">9.183975</td>
<td align="right">50.1</td>
</tr>
<tr class="odd">
<td align="right">12.857565</td>
<td align="right">28.4</td>
</tr>
<tr class="even">
<td align="right">19.286347</td>
<td align="right">39.8</td>
</tr>
<tr class="odd">
<td align="right">25.715130</td>
<td align="right">29.9</td>
</tr>
<tr class="even">
<td align="right">51.430259</td>
<td align="right">2.5</td>
</tr>
</tbody>
</table>
<table class="table">
<caption>Dataset Toulouse</caption>
<thead><tr class="header">
<th align="right">time</th>
<th align="right">meso</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="right">0.000000</td>
<td align="right">96.8</td>
</tr>
<tr class="even">
<td align="right">2.897983</td>
<td align="right">63.3</td>
</tr>
<tr class="odd">
<td align="right">6.761960</td>
<td align="right">22.3</td>
</tr>
<tr class="even">
<td align="right">9.659942</td>
<td align="right">16.6</td>
</tr>
<tr class="odd">
<td align="right">13.523919</td>
<td align="right">16.1</td>
</tr>
<tr class="even">
<td align="right">20.285879</td>
<td align="right">17.2</td>
</tr>
<tr class="odd">
<td align="right">27.047838</td>
<td align="right">1.8</td>
</tr>
</tbody>
</table>
<table class="table">
<caption>Dataset Picket Piece</caption>
<thead><tr class="header">
<th align="right">time</th>
<th align="right">meso</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="right">0.000000</td>
<td align="right">102.0</td>
</tr>
<tr class="even">
<td align="right">2.841195</td>
<td align="right">73.7</td>
</tr>
<tr class="odd">
<td align="right">6.629454</td>
<td align="right">35.5</td>
</tr>
<tr class="even">
<td align="right">9.470649</td>
<td align="right">31.8</td>
</tr>
<tr class="odd">
<td align="right">13.258909</td>
<td align="right">18.0</td>
</tr>
<tr class="even">
<td align="right">19.888364</td>
<td align="right">3.7</td>
</tr>
</tbody>
</table>
<table class="table">
<caption>Dataset 721</caption>
<thead><tr class="header">
<th align="right">time</th>
<th align="right">meso</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="right">0.00000</td>
<td align="right">86.4</td>
</tr>
<tr class="even">
<td align="right">11.24366</td>
<td align="right">61.4</td>
</tr>
<tr class="odd">
<td align="right">22.48733</td>
<td align="right">49.8</td>
</tr>
<tr class="even">
<td align="right">33.73099</td>
<td align="right">41.0</td>
</tr>
<tr class="odd">
<td align="right">44.97466</td>
<td align="right">35.1</td>
</tr>
</tbody>
</table>
<table class="table">
<caption>Dataset 722</caption>
<thead><tr class="header">
<th align="right">time</th>
<th align="right">meso</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="right">0.00000</td>
<td align="right">90.3</td>
</tr>
<tr class="even">
<td align="right">11.24366</td>
<td align="right">52.1</td>
</tr>
<tr class="odd">
<td align="right">22.48733</td>
<td align="right">37.4</td>
</tr>
<tr class="even">
<td align="right">33.73099</td>
<td align="right">21.2</td>
</tr>
<tr class="odd">
<td align="right">44.97466</td>
<td align="right">14.3</td>
</tr>
</tbody>
</table>
<table class="table">
<caption>Dataset 723</caption>
<thead><tr class="header">
<th align="right">time</th>
<th align="right">meso</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="right">0.00000</td>
<td align="right">89.3</td>
</tr>
<tr class="even">
<td align="right">11.24366</td>
<td align="right">70.8</td>
</tr>
<tr class="odd">
<td align="right">22.48733</td>
<td align="right">51.1</td>
</tr>
<tr class="even">
<td align="right">33.73099</td>
<td align="right">42.7</td>
</tr>
<tr class="odd">
<td align="right">44.97466</td>
<td align="right">26.7</td>
</tr>
</tbody>
</table>
<table class="table">
<caption>Dataset 724</caption>
<thead><tr class="header">
<th align="right">time</th>
<th align="right">meso</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="right">0.000000</td>
<td align="right">89.4</td>
</tr>
<tr class="even">
<td align="right">9.008208</td>
<td align="right">65.2</td>
</tr>
<tr class="odd">
<td align="right">18.016415</td>
<td align="right">55.8</td>
</tr>
<tr class="even">
<td align="right">27.024623</td>
<td align="right">46.0</td>
</tr>
<tr class="odd">
<td align="right">36.032831</td>
<td align="right">41.7</td>
</tr>
</tbody>
</table>
<table class="table">
<caption>Dataset 725</caption>
<thead><tr class="header">
<th align="right">time</th>
<th align="right">meso</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="right">0.00000</td>
<td align="right">89.0</td>
</tr>
<tr class="even">
<td align="right">10.99058</td>
<td align="right">35.4</td>
</tr>
<tr class="odd">
<td align="right">21.98116</td>
<td align="right">18.6</td>
</tr>
<tr class="even">
<td align="right">32.97174</td>
<td align="right">11.6</td>
</tr>
<tr class="odd">
<td align="right">43.96232</td>
<td align="right">7.6</td>
</tr>
</tbody>
</table>
<table class="table">
<caption>Dataset 727</caption>
<thead><tr class="header">
<th align="right">time</th>
<th align="right">meso</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="right">0.00000</td>
<td align="right">91.3</td>
</tr>
<tr class="even">
<td align="right">10.96104</td>
<td align="right">63.2</td>
</tr>
<tr class="odd">
<td align="right">21.92209</td>
<td align="right">51.1</td>
</tr>
<tr class="even">
<td align="right">32.88313</td>
<td align="right">42.0</td>
</tr>
<tr class="odd">
<td align="right">43.84417</td>
<td align="right">40.8</td>
</tr>
</tbody>
</table>
<table class="table">
<caption>Dataset 728</caption>
<thead><tr class="header">
<th align="right">time</th>
<th align="right">meso</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="right">0.00000</td>
<td align="right">91.8</td>
</tr>
<tr class="even">
<td align="right">11.24366</td>
<td align="right">43.6</td>
</tr>
<tr class="odd">
<td align="right">22.48733</td>
<td align="right">22.0</td>
</tr>
<tr class="even">
<td align="right">33.73099</td>
<td align="right">15.9</td>
</tr>
<tr class="odd">
<td align="right">44.97466</td>
<td align="right">8.8</td>
</tr>
</tbody>
</table>
<table class="table">
<caption>Dataset 729</caption>
<thead><tr class="header">
<th align="right">time</th>
<th align="right">meso</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="right">0.00000</td>
<td align="right">91.6</td>
</tr>
<tr class="even">
<td align="right">11.24366</td>
<td align="right">60.5</td>
</tr>
<tr class="odd">
<td align="right">22.48733</td>
<td align="right">43.5</td>
</tr>
<tr class="even">
<td align="right">33.73099</td>
<td align="right">28.4</td>
</tr>
<tr class="odd">
<td align="right">44.97466</td>
<td align="right">20.5</td>
</tr>
</tbody>
</table>
<table class="table">
<caption>Dataset 730</caption>
<thead><tr class="header">
<th align="right">time</th>
<th align="right">meso</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="right">0.00000</td>
<td align="right">92.7</td>
</tr>
<tr class="even">
<td align="right">11.07446</td>
<td align="right">58.9</td>
</tr>
<tr class="odd">
<td align="right">22.14893</td>
<td align="right">44.0</td>
</tr>
<tr class="even">
<td align="right">33.22339</td>
<td align="right">46.0</td>
</tr>
<tr class="odd">
<td align="right">44.29785</td>
<td align="right">29.3</td>
</tr>
</tbody>
</table>
<table class="table">
<caption>Dataset 731</caption>
<thead><tr class="header">
<th align="right">time</th>
<th align="right">meso</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="right">0.00000</td>
<td align="right">92.1</td>
</tr>
<tr class="even">
<td align="right">11.24366</td>
<td align="right">64.4</td>
</tr>
<tr class="odd">
<td align="right">22.48733</td>
<td align="right">45.3</td>
</tr>
<tr class="even">
<td align="right">33.73099</td>
<td align="right">33.6</td>
</tr>
<tr class="odd">
<td align="right">44.97466</td>
<td align="right">23.5</td>
</tr>
</tbody>
</table>
<table class="table">
<caption>Dataset 732</caption>
<thead><tr class="header">
<th align="right">time</th>
<th align="right">meso</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="right">0.00000</td>
<td align="right">90.3</td>
</tr>
<tr class="even">
<td align="right">11.24366</td>
<td align="right">58.2</td>
</tr>
<tr class="odd">
<td align="right">22.48733</td>
<td align="right">40.1</td>
</tr>
<tr class="even">
<td align="right">33.73099</td>
<td align="right">33.1</td>
</tr>
<tr class="odd">
<td align="right">44.97466</td>
<td align="right">25.8</td>
</tr>
</tbody>
</table>
<table class="table">
<caption>Dataset 741</caption>
<thead><tr class="header">
<th align="right">time</th>
<th align="right">meso</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="right">0.00000</td>
<td align="right">90.3</td>
</tr>
<tr class="even">
<td align="right">10.84712</td>
<td align="right">68.7</td>
</tr>
<tr class="odd">
<td align="right">21.69424</td>
<td align="right">58.0</td>
</tr>
<tr class="even">
<td align="right">32.54136</td>
<td align="right">52.2</td>
</tr>
<tr class="odd">
<td align="right">43.38848</td>
<td align="right">48.0</td>
</tr>
</tbody>
</table>
<table class="table">
<caption>Dataset 742</caption>
<thead><tr class="header">
<th align="right">time</th>
<th align="right">meso</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="right">0.00000</td>
<td align="right">92.0</td>
</tr>
<tr class="even">
<td align="right">11.24366</td>
<td align="right">60.9</td>
</tr>
<tr class="odd">
<td align="right">22.48733</td>
<td align="right">36.2</td>
</tr>
<tr class="even">
<td align="right">33.73099</td>
<td align="right">18.3</td>
</tr>
<tr class="odd">
<td align="right">44.97466</td>
<td align="right">8.7</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 five models to the data for each soil are generated
using the <code>mmkin</code> function from the mkin package. In a first
step, constant variance is assumed. Convergence is checked with the
<code>status</code> function.</p>
<div class="sourceCode" id="cb5"><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">"SFORB"</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">meso_ds</span>,</span>
<span> error_model <span class="op">=</span> <span class="st">"const"</span>,</span>
<span> cluster <span class="op">=</span> <span class="va">cl</span>,</span>
<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
<div class="sourceCode" id="cb6"><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_sep_const</span><span class="op">[</span>, <span class="fl">1</span><span class="op">:</span><span class="fl">5</span><span class="op">]</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">Richmond</th>
<th align="left">Richmond 2</th>
<th align="left">ERTC</th>
<th align="left">Toulouse</th>
<th align="left">Picket Piece</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>
</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>
</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>
</tr>
<tr class="even">
<td align="left">SFORB</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</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>
<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_sep_const</span><span class="op">[</span>, <span class="fl">6</span><span class="op">:</span><span class="fl">18</span><span class="op">]</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="10%">
<col width="6%">
<col width="6%">
<col width="6%">
<col width="6%">
<col width="6%">
<col width="6%">
<col width="6%">
<col width="6%">
<col width="6%">
<col width="6%">
<col width="6%">
<col width="6%">
<col width="6%">
</colgroup>
<thead><tr class="header">
<th align="left"></th>
<th align="left">721</th>
<th align="left">722</th>
<th align="left">723</th>
<th align="left">724</th>
<th align="left">725</th>
<th align="left">727</th>
<th align="left">728</th>
<th align="left">729</th>
<th align="left">730</th>
<th align="left">731</th>
<th align="left">732</th>
<th align="left">741</th>
<th align="left">742</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>
<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>
<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">C</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>
<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>
<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>
<td align="left">OK</td>
</tr>
<tr class="even">
<td align="left">SFORB</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>
<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>
<td align="left">OK</td>
</tr>
<tr class="odd">
<td align="left">HS</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>
<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>
<td align="left">OK</td>
</tr>
</tbody>
</table>
<p>In the tables above, OK indicates convergence and C indicates failure
to converge. Most separate fits with constant variance converged, with
the exception of two FOMC fits, one SFORB fit and one HS fit.</p>
<div class="sourceCode" id="cb8"><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></code></pre></div>
<div class="sourceCode" id="cb9"><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_sep_tc</span><span class="op">[</span>, <span class="fl">1</span><span class="op">:</span><span class="fl">5</span><span class="op">]</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">Richmond</th>
<th align="left">Richmond 2</th>
<th align="left">ERTC</th>
<th align="left">Toulouse</th>
<th align="left">Picket Piece</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>
</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>
</tr>
<tr class="odd">
<td align="left">DFOP</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</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</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>
<div class="sourceCode" id="cb10"><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_sep_tc</span><span class="op">[</span>, <span class="fl">6</span><span class="op">:</span><span class="fl">18</span><span class="op">]</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="10%">
<col width="6%">
<col width="6%">
<col width="6%">
<col width="6%">
<col width="6%">
<col width="6%">
<col width="6%">
<col width="6%">
<col width="6%">
<col width="6%">
<col width="6%">
<col width="6%">
<col width="6%">
</colgroup>
<thead><tr class="header">
<th align="left"></th>
<th align="left">721</th>
<th align="left">722</th>
<th align="left">723</th>
<th align="left">724</th>
<th align="left">725</th>
<th align="left">727</th>
<th align="left">728</th>
<th align="left">729</th>
<th align="left">730</th>
<th align="left">731</th>
<th align="left">732</th>
<th align="left">741</th>
<th align="left">742</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>
<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>
<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">C</td>
<td align="left">OK</td>
<td align="left">C</td>
<td align="left">C</td>
<td align="left">OK</td>
<td align="left">C</td>
<td align="left">OK</td>
<td align="left">C</td>
<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">C</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>
<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">SFORB</td>
<td align="left">C</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>
<td align="left">C</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">HS</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>
<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>
<td align="left">OK</td>
</tr>
</tbody>
</table>
<p>With the two-component error model, the set of fits that did not
converge is larger, with convergence problems appearing for a number of
non-SFO fits.</p>
</div>
<div class="section level2">
<h2 id="hierarchical-model-fits-without-covariate-effect">Hierarchical model fits without covariate effect<a class="anchor" aria-label="anchor" href="#hierarchical-model-fits-without-covariate-effect"></a>
</h2>
<p>The following code fits hierarchical kinetic models for the ten
combinations of the five different degradation models with the two
different error models in parallel.</p>
<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">f_saem_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mhmkin.html">mhmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">f_sep_const</span>, <span class="va">f_sep_tc</span><span class="op">)</span>, cluster <span class="op">=</span> <span class="va">cl</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_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</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 terminate without errors (status OK).</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_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 const</td>
<td align="right">5</td>
<td align="right">800.0</td>
<td align="right">804.5</td>
<td align="right">-395.0</td>
</tr>
<tr class="even">
<td align="left">SFO tc</td>
<td align="right">6</td>
<td align="right">801.9</td>
<td align="right">807.2</td>
<td align="right">-394.9</td>
</tr>
<tr class="odd">
<td align="left">FOMC const</td>
<td align="right">7</td>
<td align="right">787.4</td>
<td align="right">793.6</td>
<td align="right">-386.7</td>
</tr>
<tr class="even">
<td align="left">FOMC tc</td>
<td align="right">8</td>
<td align="right">788.9</td>
<td align="right">796.1</td>
<td align="right">-386.5</td>
</tr>
<tr class="odd">
<td align="left">DFOP const</td>
<td align="right">9</td>
<td align="right">787.6</td>
<td align="right">795.6</td>
<td align="right">-384.8</td>
</tr>
<tr class="even">
<td align="left">SFORB const</td>
<td align="right">9</td>
<td align="right">787.4</td>
<td align="right">795.4</td>
<td align="right">-384.7</td>
</tr>
<tr class="odd">
<td align="left">HS const</td>
<td align="right">9</td>
<td align="right">781.9</td>
<td align="right">789.9</td>
<td align="right">-382.0</td>
</tr>
<tr class="even">
<td align="left">DFOP tc</td>
<td align="right">10</td>
<td align="right">787.4</td>
<td align="right">796.3</td>
<td align="right">-383.7</td>
</tr>
<tr class="odd">
<td align="left">SFORB tc</td>
<td align="right">10</td>
<td align="right">795.8</td>
<td align="right">804.7</td>
<td align="right">-387.9</td>
</tr>
<tr class="even">
<td align="left">HS tc</td>
<td align="right">10</td>
<td align="right">783.7</td>
<td align="right">792.7</td>
<td align="right">-381.9</td>
</tr>
</tbody>
</table>
<p>The model comparisons show that the fits with constant variance are
consistently preferable to the corresponding fits with two-component
error for these data. This is confirmed by the fact that the parameter
<code>b.1</code> (the relative standard deviation in the fits obtained
with the saemix package), is ill-defined in all fits.</p>
<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
<table class="table">
<colgroup>
<col width="6%">
<col width="44%">
<col width="49%">
</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</td>
<td align="left">sd(meso_0)</td>
<td align="left">sd(meso_0), b.1</td>
</tr>
<tr class="even">
<td align="left">FOMC</td>
<td align="left">sd(meso_0), sd(log_beta)</td>
<td align="left">sd(meso_0), sd(log_beta), b.1</td>
</tr>
<tr class="odd">
<td align="left">DFOP</td>
<td align="left">sd(meso_0), sd(log_k1)</td>
<td align="left">sd(meso_0), sd(g_qlogis), b.1</td>
</tr>
<tr class="even">
<td align="left">SFORB</td>
<td align="left">sd(meso_free_0), sd(log_k_meso_free_bound)</td>
<td align="left">sd(meso_free_0), sd(log_k_meso_free_bound), b.1</td>
</tr>
<tr class="odd">
<td align="left">HS</td>
<td align="left">sd(meso_0)</td>
<td align="left">sd(meso_0), b.1</td>
</tr>
</tbody>
</table>
<p>For obtaining fits with only well-defined random effects, we update
the set of fits, excluding random effects that were ill-defined
according to the <code>illparms</code> function.</p>
<div class="sourceCode" id="cb14"><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="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_saem_1</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">f_saem_1</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">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">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>The updated fits terminate without errors.</p>
<div class="sourceCode" id="cb15"><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">
<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">b.1</td>
</tr>
<tr class="odd">
<td align="left">DFOP</td>
<td align="left"></td>
<td align="left">b.1</td>
</tr>
<tr class="even">
<td align="left">SFORB</td>
<td align="left"></td>
<td align="left">b.1</td>
</tr>
<tr class="odd">
<td align="left">HS</td>
<td align="left"></td>
<td align="left">b.1</td>
</tr>
</tbody>
</table>
<p>No ill-defined errors remain in the fits with constant variance.</p>
</div>
<div class="section level2">
<h2 id="hierarchical-model-fits-with-covariate-effect">Hierarchical model fits with covariate effect<a class="anchor" aria-label="anchor" href="#hierarchical-model-fits-with-covariate-effect"></a>
</h2>
<p>In the following sections, hierarchical fits including a model for
the influence of pH on selected degradation parameters are shown for all
parent models. Constant variance is selected as the error model based on
the fits without covariate effects. Random effects that were ill-defined
in the fits without pH influence are excluded. A potential influence of
the soil pH is only included for parameters with a well-defined random
effect, because experience has shown that only for such parameters a
significant pH effect could be found.</p>
<div class="section level3">
<h3 id="sfo">SFO<a class="anchor" aria-label="anchor" href="#sfo"></a>
</h3>
<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">sfo_pH</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="st">"meso_0"</span>, covariates <span class="op">=</span> <span class="va">pH</span>,</span>
<span> covariate_models <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">log_k_meso</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</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/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">sfo_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</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">2</span><span class="op">)</span></span></code></pre></div>
<table class="table">
<thead><tr class="header">
<th align="left"></th>
<th align="right">est.</th>
<th align="right">lower</th>
<th align="right">upper</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="left">meso_0</td>
<td align="right">91.35</td>
<td align="right">89.27</td>
<td align="right">93.43</td>
</tr>
<tr class="even">
<td align="left">log_k_meso</td>
<td align="right">-6.66</td>
<td align="right">-7.97</td>
<td align="right">-5.35</td>
</tr>
<tr class="odd">
<td align="left">beta_pH(log_k_meso)</td>
<td align="right">0.59</td>
<td align="right">0.37</td>
<td align="right">0.81</td>
</tr>
<tr class="even">
<td align="left">a.1</td>
<td align="right">5.48</td>
<td align="right">4.71</td>
<td align="right">6.24</td>
</tr>
<tr class="odd">
<td align="left">SD.log_k_meso</td>
<td align="right">0.35</td>
<td align="right">0.23</td>
<td align="right">0.47</td>
</tr>
</tbody>
</table>
<p>The parameter showing the pH influence in the above table is
<code>beta_pH(log_k_meso)</code>. Its confidence interval does not
include zero, indicating that the influence of soil pH on the log of the
degradation rate constant is significantly greater than zero.</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/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="st">"SFO"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span>, <span class="va">sfo_pH</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets
npar AIC BIC Lik Chisq Df Pr(>Chisq)
f_saem_2[["SFO", "const"]] 4 797.56 801.12 -394.78
sfo_pH 5 783.09 787.54 -386.54 16.473 1 4.934e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre>
<p>The comparison with the SFO fit without covariate effect confirms
that considering the soil pH improves the model, both by comparison of
AIC and BIC and by the likelihood ratio test.</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/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">sfo_pH</span><span class="op">)</span></span></code></pre></div>
<p><img src="2023_mesotrione_parent_files/figure-html/unnamed-chunk-8-1.png" width="700" style="display: block; margin: auto;"></p>
<p>Endpoints for a model with covariates are by default calculated for
the median of the covariate values. This quantile can be adapted, or a
specific covariate value can be given as shown below.</p>
<div class="sourceCode" id="cb21"><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">sfo_pH</span><span class="op">)</span></span></code></pre></div>
<pre><code>$covariates
pH
50% 5.75
$distimes
DT50 DT90
meso 18.52069 61.52441</code></pre>
<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">sfo_pH</span>, covariate_quantile <span class="op">=</span> <span class="fl">0.9</span><span class="op">)</span></span></code></pre></div>
<pre><code>$covariates
pH
90% 7.13
$distimes
DT50 DT90
meso 8.237019 27.36278</code></pre>
<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">sfo_pH</span>, covariates <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>pH <span class="op">=</span> <span class="fl">7.0</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
<pre><code>$covariates
pH
User 7
$distimes
DT50 DT90
meso 8.89035 29.5331</code></pre>
</div>
<div class="section level3">
<h3 id="fomc">FOMC<a class="anchor" aria-label="anchor" href="#fomc"></a>
</h3>
<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">fomc_pH</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"FOMC"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="st">"meso_0"</span>, covariates <span class="op">=</span> <span class="va">pH</span>,</span>
<span> covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_alpha</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
<div class="sourceCode" id="cb28"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">fomc_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</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">2</span><span class="op">)</span></span></code></pre></div>
<table class="table">
<thead><tr class="header">
<th align="left"></th>
<th align="right">est.</th>
<th align="right">lower</th>
<th align="right">upper</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="left">meso_0</td>
<td align="right">92.84</td>
<td align="right">90.75</td>
<td align="right">94.93</td>
</tr>
<tr class="even">
<td align="left">log_alpha</td>
<td align="right">-2.21</td>
<td align="right">-3.49</td>
<td align="right">-0.92</td>
</tr>
<tr class="odd">
<td align="left">beta_pH(log_alpha)</td>
<td align="right">0.58</td>
<td align="right">0.37</td>
<td align="right">0.79</td>
</tr>
<tr class="even">
<td align="left">log_beta</td>
<td align="right">4.21</td>
<td align="right">3.44</td>
<td align="right">4.99</td>
</tr>
<tr class="odd">
<td align="left">a.1</td>
<td align="right">5.03</td>
<td align="right">4.32</td>
<td align="right">5.73</td>
</tr>
<tr class="even">
<td align="left">SD.log_alpha</td>
<td align="right">0.00</td>
<td align="right">-23.77</td>
<td align="right">23.78</td>
</tr>
<tr class="odd">
<td align="left">SD.log_beta</td>
<td align="right">0.37</td>
<td align="right">0.01</td>
<td align="right">0.74</td>
</tr>
</tbody>
</table>
<p>As in the case of SFO, the confidence interval of the slope parameter
(here <code>beta_pH(log_alpha)</code>) quantifying the influence of soil
pH does not include zero, and the model comparison clearly indicates
that the model with covariate influence is preferable. However, the
random effect for <code>alpha</code> is not well-defined any more after
inclusion of the covariate effect (the confidence interval of
<code>SD.log_alpha</code> includes zero).</p>
<div class="sourceCode" id="cb29"><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">fomc_pH</span><span class="op">)</span></span></code></pre></div>
<pre><code>[1] "sd(log_alpha)"</code></pre>
<p>Therefore, the model is updated without this random effect, and no
ill-defined parameters remain.</p>
<div class="sourceCode" id="cb31"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">fomc_pH_2</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">fomc_pH</span>, no_random_effect <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">"meso_0"</span>, <span class="st">"log_alpha"</span><span class="op">)</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">fomc_pH_2</span><span class="op">)</span></span></code></pre></div>
<div class="sourceCode" id="cb32"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/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="st">"FOMC"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span>, <span class="va">fomc_pH</span>, <span class="va">fomc_pH_2</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets
npar AIC BIC Lik Chisq Df Pr(>Chisq)
f_saem_2[["FOMC", "const"]] 5 783.25 787.71 -386.63
fomc_pH_2 6 767.49 772.83 -377.75 17.762 1 2.503e-05 ***
fomc_pH 7 770.07 776.30 -378.04 0.000 1 1
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre>
<p>Model comparison indicates that including pH dependence significantly
improves the fit, and that the reduced model with covariate influence
results in the most preferable FOMC fit.</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">fomc_pH_2</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</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">2</span><span class="op">)</span></span></code></pre></div>
<table class="table">
<thead><tr class="header">
<th align="left"></th>
<th align="right">est.</th>
<th align="right">lower</th>
<th align="right">upper</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="left">meso_0</td>
<td align="right">93.05</td>
<td align="right">90.98</td>
<td align="right">95.13</td>
</tr>
<tr class="even">
<td align="left">log_alpha</td>
<td align="right">-2.91</td>
<td align="right">-4.18</td>
<td align="right">-1.63</td>
</tr>
<tr class="odd">
<td align="left">beta_pH(log_alpha)</td>
<td align="right">0.66</td>
<td align="right">0.44</td>
<td align="right">0.87</td>
</tr>
<tr class="even">
<td align="left">log_beta</td>
<td align="right">3.95</td>
<td align="right">3.29</td>
<td align="right">4.62</td>
</tr>
<tr class="odd">
<td align="left">a.1</td>
<td align="right">4.98</td>
<td align="right">4.28</td>
<td align="right">5.68</td>
</tr>
<tr class="even">
<td align="left">SD.log_beta</td>
<td align="right">0.40</td>
<td align="right">0.26</td>
<td align="right">0.54</td>
</tr>
</tbody>
</table>
<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">fomc_pH_2</span><span class="op">)</span></span></code></pre></div>
<p><img src="2023_mesotrione_parent_files/figure-html/unnamed-chunk-14-1.png" width="700" style="display: block; margin: auto;"></p>
<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">fomc_pH_2</span><span class="op">)</span></span></code></pre></div>
<pre><code>$covariates
pH
50% 5.75
$distimes
DT50 DT90 DT50back
meso 17.30248 82.91343 24.95943</code></pre>
<div class="sourceCode" id="cb38"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">fomc_pH_2</span>, covariates <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>pH <span class="op">=</span> <span class="fl">7</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
<pre><code>$covariates
pH
User 7
$distimes
DT50 DT90 DT50back
meso 6.986239 27.02927 8.136621</code></pre>
</div>
<div class="section level3">
<h3 id="dfop">DFOP<a class="anchor" aria-label="anchor" href="#dfop"></a>
</h3>
<p>In the DFOP fits without covariate effects, random effects for two
degradation parameters (<code>k2</code> and <code>g</code>) were
identifiable.</p>
<div class="sourceCode" id="cb40"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</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">2</span><span class="op">)</span></span></code></pre></div>
<table class="table">
<thead><tr class="header">
<th align="left"></th>
<th align="right">est.</th>
<th align="right">lower</th>
<th align="right">upper</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="left">meso_0</td>
<td align="right">93.61</td>
<td align="right">91.58</td>
<td align="right">95.63</td>
</tr>
<tr class="even">
<td align="left">log_k1</td>
<td align="right">-1.53</td>
<td align="right">-2.27</td>
<td align="right">-0.79</td>
</tr>
<tr class="odd">
<td align="left">log_k2</td>
<td align="right">-3.42</td>
<td align="right">-3.73</td>
<td align="right">-3.11</td>
</tr>
<tr class="even">
<td align="left">g_qlogis</td>
<td align="right">-1.67</td>
<td align="right">-2.57</td>
<td align="right">-0.77</td>
</tr>
<tr class="odd">
<td align="left">a.1</td>
<td align="right">4.74</td>
<td align="right">4.02</td>
<td align="right">5.45</td>
</tr>
<tr class="even">
<td align="left">SD.log_k2</td>
<td align="right">0.60</td>
<td align="right">0.38</td>
<td align="right">0.81</td>
</tr>
<tr class="odd">
<td align="left">SD.g_qlogis</td>
<td align="right">0.94</td>
<td align="right">0.33</td>
<td align="right">1.54</td>
</tr>
</tbody>
</table>
<p>A fit with pH dependent degradation parameters was obtained by
excluding the same random effects as in the refined DFOP fit without
covariate influence, and including covariate models for the two
identifiable parameters <code>k2</code> and <code>g</code>.</p>
<div class="sourceCode" id="cb41"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">dfop_pH</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, no_random_effect <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">"meso_0"</span>, <span class="st">"log_k1"</span><span class="op">)</span>,</span>
<span> covariates <span class="op">=</span> <span class="va">pH</span>,</span>
<span> covariate_models <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">log_k2</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">g_qlogis</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
<p>The corresponding parameters for the influence of soil pH are
<code>beta_pH(log_k2)</code> for the influence of soil pH on
<code>k2</code>, and <code>beta_pH(g_qlogis)</code> for its influence on
<code>g</code>.</p>
<div class="sourceCode" id="cb42"><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">dfop_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</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">2</span><span class="op">)</span></span></code></pre></div>
<table class="table">
<thead><tr class="header">
<th align="left"></th>
<th align="right">est.</th>
<th align="right">lower</th>
<th align="right">upper</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="left">meso_0</td>
<td align="right">92.84</td>
<td align="right">90.85</td>
<td align="right">94.84</td>
</tr>
<tr class="even">
<td align="left">log_k1</td>
<td align="right">-2.82</td>
<td align="right">-3.09</td>
<td align="right">-2.54</td>
</tr>
<tr class="odd">
<td align="left">log_k2</td>
<td align="right">-11.48</td>
<td align="right">-15.32</td>
<td align="right">-7.64</td>
</tr>
<tr class="even">
<td align="left">beta_pH(log_k2)</td>
<td align="right">1.31</td>
<td align="right">0.69</td>
<td align="right">1.92</td>
</tr>
<tr class="odd">
<td align="left">g_qlogis</td>
<td align="right">3.13</td>
<td align="right">0.47</td>
<td align="right">5.80</td>
</tr>
<tr class="even">
<td align="left">beta_pH(g_qlogis)</td>
<td align="right">-0.57</td>
<td align="right">-1.04</td>
<td align="right">-0.09</td>
</tr>
<tr class="odd">
<td align="left">a.1</td>
<td align="right">4.96</td>
<td align="right">4.26</td>
<td align="right">5.65</td>
</tr>
<tr class="even">
<td align="left">SD.log_k2</td>
<td align="right">0.76</td>
<td align="right">0.47</td>
<td align="right">1.05</td>
</tr>
<tr class="odd">
<td align="left">SD.g_qlogis</td>
<td align="right">0.01</td>
<td align="right">-9.96</td>
<td align="right">9.97</td>
</tr>
</tbody>
</table>
<div class="sourceCode" id="cb43"><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_pH</span><span class="op">)</span></span></code></pre></div>
<pre><code>[1] "sd(g_qlogis)"</code></pre>
<p>Confidence intervals for neither of them include zero, indicating a
significant difference from zero. However, the random effect for
<code>g</code> is now ill-defined. The fit is updated without this
ill-defined random effect.</p>
<div class="sourceCode" id="cb45"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">dfop_pH_2</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">dfop_pH</span>,</span>
<span> no_random_effect <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">"meso_0"</span>, <span class="st">"log_k1"</span>, <span class="st">"g_qlogis"</span><span class="op">)</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">dfop_pH_2</span><span class="op">)</span></span></code></pre></div>
<pre><code>[1] "beta_pH(g_qlogis)"</code></pre>
<p>Now, the slope parameter for the pH effect on <code>g</code> is
ill-defined. Therefore, another attempt is made without the
corresponding covariate model.</p>
<div class="sourceCode" id="cb47"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">dfop_pH_3</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, no_random_effect <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">"meso_0"</span>, <span class="st">"log_k1"</span><span class="op">)</span>,</span>
<span> covariates <span class="op">=</span> <span class="va">pH</span>,</span>
<span> covariate_models <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">log_k2</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</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">dfop_pH_3</span><span class="op">)</span></span></code></pre></div>
<pre><code>[1] "sd(g_qlogis)"</code></pre>
<p>As the random effect for <code>g</code> is again ill-defined, the fit
is repeated without it.</p>
<div class="sourceCode" id="cb49"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">dfop_pH_4</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">dfop_pH_3</span>, no_random_effect <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">"meso_0"</span>, <span class="st">"log_k1"</span>, <span class="st">"g_qlogis"</span><span class="op">)</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">dfop_pH_4</span><span class="op">)</span></span></code></pre></div>
<p>While no ill-defined parameters remain, model comparison suggests
that the previous model <code>dfop_pH_2</code> with two pH dependent
parameters is preferable, based on information criteria as well as based
on the likelihood ratio test.</p>
<div class="sourceCode" id="cb50"><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="st">"DFOP"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span>, <span class="va">dfop_pH</span>, <span class="va">dfop_pH_2</span>, <span class="va">dfop_pH_3</span>, <span class="va">dfop_pH_4</span><span class="op">)</span></span></code></pre></div>
<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets
npar AIC BIC Lik
f_saem_2[["DFOP", "const"]] 7 782.94 789.18 -384.47
dfop_pH_4 7 767.35 773.58 -376.68
dfop_pH_2 8 765.14 772.26 -374.57
dfop_pH_3 8 769.00 776.12 -376.50
dfop_pH 9 769.10 777.11 -375.55</code></pre>
<div class="sourceCode" id="cb52"><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">dfop_pH_2</span>, <span class="va">dfop_pH_4</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets
npar AIC BIC Lik Chisq Df Pr(>Chisq)
dfop_pH_4 7 767.35 773.58 -376.68
dfop_pH_2 8 765.14 772.26 -374.57 4.2153 1 0.04006 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre>
<p>When focussing on parameter identifiability using the test if the
confidence interval includes zero, <code>dfop_pH_4</code> would still be
the preferred model. However, it should be kept in mind that parameter
confidence intervals are constructed using a simple linearisation of the
likelihood. As the confidence interval of the random effect for
<code>g</code> only marginally includes zero, it is suggested that this
is acceptable, and that <code>dfop_pH_2</code> can be considered the
most preferable model.</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/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">dfop_pH_2</span><span class="op">)</span></span></code></pre></div>
<p><img src="2023_mesotrione_parent_files/figure-html/unnamed-chunk-19-1.png" width="700" style="display: block; margin: auto;"></p>
<div class="sourceCode" id="cb55"><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">dfop_pH_2</span><span class="op">)</span></span></code></pre></div>
<pre><code>$covariates
pH
50% 5.75
$distimes
DT50 DT90 DT50back DT50_k1 DT50_k2
meso 18.36876 73.51841 22.13125 4.191901 23.98672</code></pre>
<div class="sourceCode" id="cb57"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">dfop_pH_2</span>, covariates <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>pH <span class="op">=</span> <span class="fl">7</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
<pre><code>$covariates
pH
User 7
$distimes
DT50 DT90 DT50back DT50_k1 DT50_k2
meso 8.346428 28.34437 8.532507 4.191901 8.753618</code></pre>
</div>
<div class="section level3">
<h3 id="sforb">SFORB<a class="anchor" aria-label="anchor" href="#sforb"></a>
</h3>
<div class="sourceCode" id="cb59"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">sforb_pH</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"SFORB"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_free_0"</span>, <span class="st">"log_k_meso_free_bound"</span><span class="op">)</span>,</span>
<span> covariates <span class="op">=</span> <span class="va">pH</span>,</span>
<span> covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_k_meso_free</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">log_k_meso_bound_free</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
<div class="sourceCode" id="cb60"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">sforb_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</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">2</span><span class="op">)</span></span></code></pre></div>
<table class="table">
<thead><tr class="header">
<th align="left"></th>
<th align="right">est.</th>
<th align="right">lower</th>
<th align="right">upper</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="left">meso_free_0</td>
<td align="right">93.42</td>
<td align="right">91.32</td>
<td align="right">95.52</td>
</tr>
<tr class="even">
<td align="left">log_k_meso_free</td>
<td align="right">-5.37</td>
<td align="right">-6.94</td>
<td align="right">-3.81</td>
</tr>
<tr class="odd">
<td align="left">beta_pH(log_k_meso_free)</td>
<td align="right">0.42</td>
<td align="right">0.18</td>
<td align="right">0.67</td>
</tr>
<tr class="even">
<td align="left">log_k_meso_free_bound</td>
<td align="right">-3.49</td>
<td align="right">-4.92</td>
<td align="right">-2.05</td>
</tr>
<tr class="odd">
<td align="left">log_k_meso_bound_free</td>
<td align="right">-9.98</td>
<td align="right">-19.22</td>
<td align="right">-0.74</td>
</tr>
<tr class="even">
<td align="left">beta_pH(log_k_meso_bound_free)</td>
<td align="right">1.23</td>
<td align="right">-0.21</td>
<td align="right">2.67</td>
</tr>
<tr class="odd">
<td align="left">a.1</td>
<td align="right">4.90</td>
<td align="right">4.18</td>
<td align="right">5.63</td>
</tr>
<tr class="even">
<td align="left">SD.log_k_meso_free</td>
<td align="right">0.35</td>
<td align="right">0.23</td>
<td align="right">0.47</td>
</tr>
<tr class="odd">
<td align="left">SD.log_k_meso_bound_free</td>
<td align="right">0.13</td>
<td align="right">-1.95</td>
<td align="right">2.20</td>
</tr>
</tbody>
</table>
<p>The confidence interval of
<code>beta_pH(log_k_meso_bound_free)</code> includes zero, indicating
that the influence of soil pH on <code>k_meso_bound_free</code> cannot
reliably be quantified. Also, the confidence interval for the random
effect on this parameter (<code>SD.log_k_meso_bound_free</code>)
includes zero.</p>
<p>Using the <code>illparms</code> function, these ill-defined
parameters can be found more conveniently.</p>
<div class="sourceCode" id="cb61"><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_pH</span><span class="op">)</span></span></code></pre></div>
<pre><code>[1] "sd(log_k_meso_bound_free)" "beta_pH(log_k_meso_bound_free)"</code></pre>
<p>To remove the ill-defined parameters, a second variant of the SFORB
model with pH influence is fitted. No ill-defined parameters remain.</p>
<div class="sourceCode" id="cb63"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">sforb_pH_2</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">sforb_pH</span>,</span>
<span> no_random_effect <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">"meso_free_0"</span>, <span class="st">"log_k_meso_free_bound"</span>, <span class="st">"log_k_meso_bound_free"</span><span class="op">)</span>,</span>
<span> covariate_models <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">log_k_meso_free</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</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">sforb_pH_2</span><span class="op">)</span></span></code></pre></div>
<p>The model comparison of the SFORB fits includes the refined model
without covariate effect, and both versions of the SFORB fit with
covariate effect.</p>
<div class="sourceCode" id="cb64"><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="st">"SFORB"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span>, <span class="va">sforb_pH</span>, <span class="va">sforb_pH_2</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets
npar AIC BIC Lik Chisq Df Pr(>Chisq)
f_saem_2[["SFORB", "const"]] 7 783.40 789.63 -384.70
sforb_pH_2 7 770.94 777.17 -378.47 12.4616 0
sforb_pH 9 768.81 776.83 -375.41 6.1258 2 0.04675 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre>
<p>The first model including pH influence is preferable based on
information criteria and the likelihood ratio test. However, as it is
not fully identifiable, the second model is selected.</p>
<div class="sourceCode" id="cb66"><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">sforb_pH_2</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</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">2</span><span class="op">)</span></span></code></pre></div>
<table class="table">
<thead><tr class="header">
<th align="left"></th>
<th align="right">est.</th>
<th align="right">lower</th>
<th align="right">upper</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="left">meso_free_0</td>
<td align="right">93.32</td>
<td align="right">91.16</td>
<td align="right">95.48</td>
</tr>
<tr class="even">
<td align="left">log_k_meso_free</td>
<td align="right">-6.15</td>
<td align="right">-7.43</td>
<td align="right">-4.86</td>
</tr>
<tr class="odd">
<td align="left">beta_pH(log_k_meso_free)</td>
<td align="right">0.54</td>
<td align="right">0.33</td>
<td align="right">0.75</td>
</tr>
<tr class="even">
<td align="left">log_k_meso_free_bound</td>
<td align="right">-3.80</td>
<td align="right">-5.20</td>
<td align="right">-2.40</td>
</tr>
<tr class="odd">
<td align="left">log_k_meso_bound_free</td>
<td align="right">-2.95</td>
<td align="right">-4.26</td>
<td align="right">-1.64</td>
</tr>
<tr class="even">
<td align="left">a.1</td>
<td align="right">5.08</td>
<td align="right">4.38</td>
<td align="right">5.79</td>
</tr>
<tr class="odd">
<td align="left">SD.log_k_meso_free</td>
<td align="right">0.33</td>
<td align="right">0.22</td>
<td align="right">0.45</td>
</tr>
</tbody>
</table>
<div class="sourceCode" id="cb67"><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">sforb_pH_2</span><span class="op">)</span></span></code></pre></div>
<p><img src="2023_mesotrione_parent_files/figure-html/unnamed-chunk-25-1.png" width="700" style="display: block; margin: auto;"></p>
<div class="sourceCode" id="cb68"><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">sforb_pH_2</span><span class="op">)</span></span></code></pre></div>
<pre><code>$covariates
pH
50% 5.75
$ff
meso_free
1
$SFORB
meso_b1 meso_b2 meso_g
0.09735824 0.02631699 0.31602120
$distimes
DT50 DT90 DT50back DT50_meso_b1 DT50_meso_b2
meso 16.86549 73.15824 22.02282 7.119554 26.33839</code></pre>
<div class="sourceCode" id="cb70"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">sforb_pH_2</span>, covariates <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>pH <span class="op">=</span> <span class="fl">7</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
<pre><code>$covariates
pH
User 7
$ff
meso_free
1
$SFORB
meso_b1 meso_b2 meso_g
0.13315233 0.03795988 0.61186191
$distimes
DT50 DT90 DT50back DT50_meso_b1 DT50_meso_b2
meso 7.932495 36.93311 11.11797 5.205671 18.26</code></pre>
</div>
<div class="section level3">
<h3 id="hs">HS<a class="anchor" aria-label="anchor" href="#hs"></a>
</h3>
<div class="sourceCode" id="cb72"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">hs_pH</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"HS"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_0"</span><span class="op">)</span>,</span>
<span> covariates <span class="op">=</span> <span class="va">pH</span>,</span>
<span> covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_k1</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">log_k2</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">log_tb</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
<div class="sourceCode" id="cb73"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">hs_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</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">2</span><span class="op">)</span></span></code></pre></div>
<table class="table">
<thead><tr class="header">
<th align="left"></th>
<th align="right">est.</th>
<th align="right">lower</th>
<th align="right">upper</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="left">meso_0</td>
<td align="right">93.33</td>
<td align="right">91.47</td>
<td align="right">95.19</td>
</tr>
<tr class="even">
<td align="left">log_k1</td>
<td align="right">-5.81</td>
<td align="right">-7.27</td>
<td align="right">-4.36</td>
</tr>
<tr class="odd">
<td align="left">beta_pH(log_k1)</td>
<td align="right">0.47</td>
<td align="right">0.23</td>
<td align="right">0.72</td>
</tr>
<tr class="even">
<td align="left">log_k2</td>
<td align="right">-6.80</td>
<td align="right">-8.76</td>
<td align="right">-4.83</td>
</tr>
<tr class="odd">
<td align="left">beta_pH(log_k2)</td>
<td align="right">0.54</td>
<td align="right">0.21</td>
<td align="right">0.87</td>
</tr>
<tr class="even">
<td align="left">log_tb</td>
<td align="right">3.25</td>
<td align="right">1.25</td>
<td align="right">5.25</td>
</tr>
<tr class="odd">
<td align="left">beta_pH(log_tb)</td>
<td align="right">-0.10</td>
<td align="right">-0.43</td>
<td align="right">0.23</td>
</tr>
<tr class="even">
<td align="left">a.1</td>
<td align="right">4.49</td>
<td align="right">3.78</td>
<td align="right">5.21</td>
</tr>
<tr class="odd">
<td align="left">SD.log_k1</td>
<td align="right">0.37</td>
<td align="right">0.24</td>
<td align="right">0.51</td>
</tr>
<tr class="even">
<td align="left">SD.log_k2</td>
<td align="right">0.29</td>
<td align="right">0.10</td>
<td align="right">0.48</td>
</tr>
<tr class="odd">
<td align="left">SD.log_tb</td>
<td align="right">0.25</td>
<td align="right">-0.07</td>
<td align="right">0.57</td>
</tr>
</tbody>
</table>
<div class="sourceCode" id="cb74"><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">hs_pH</span><span class="op">)</span></span></code></pre></div>
<pre><code>[1] "sd(log_tb)" "beta_pH(log_tb)"</code></pre>
<p>According to the output of the <code>illparms</code> function, the
random effect on the break time <code>tb</code> cannot reliably be
quantified, neither can the influence of soil pH on <code>tb</code>. The
fit is repeated without the corresponding covariate model, and no
ill-defined parameters remain.</p>
<div class="sourceCode" id="cb76"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">hs_pH_2</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">hs_pH</span>, covariate_models <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">log_k1</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">log_k2</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</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">hs_pH_2</span><span class="op">)</span></span></code></pre></div>
<p>Model comparison confirms that this model is preferable to the fit
without covariate influence, and also to the first version with
covariate influence.</p>
<div class="sourceCode" id="cb77"><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="st">"HS"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span>, <span class="va">hs_pH</span>, <span class="va">hs_pH_2</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets
npar AIC BIC Lik Chisq Df Pr(>Chisq)
f_saem_2[["HS", "const"]] 8 780.08 787.20 -382.04
hs_pH_2 10 766.47 775.37 -373.23 17.606 2 0.0001503 ***
hs_pH 11 769.80 779.59 -373.90 0.000 1 1.0000000
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre>
<div class="sourceCode" id="cb79"><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">hs_pH_2</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</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">2</span><span class="op">)</span></span></code></pre></div>
<table class="table">
<thead><tr class="header">
<th align="left"></th>
<th align="right">est.</th>
<th align="right">lower</th>
<th align="right">upper</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="left">meso_0</td>
<td align="right">93.33</td>
<td align="right">91.50</td>
<td align="right">95.15</td>
</tr>
<tr class="even">
<td align="left">log_k1</td>
<td align="right">-5.68</td>
<td align="right">-7.09</td>
<td align="right">-4.27</td>
</tr>
<tr class="odd">
<td align="left">beta_pH(log_k1)</td>
<td align="right">0.46</td>
<td align="right">0.22</td>
<td align="right">0.69</td>
</tr>
<tr class="even">
<td align="left">log_k2</td>
<td align="right">-6.61</td>
<td align="right">-8.34</td>
<td align="right">-4.88</td>
</tr>
<tr class="odd">
<td align="left">beta_pH(log_k2)</td>
<td align="right">0.50</td>
<td align="right">0.21</td>
<td align="right">0.79</td>
</tr>
<tr class="even">
<td align="left">log_tb</td>
<td align="right">2.70</td>
<td align="right">2.33</td>
<td align="right">3.08</td>
</tr>
<tr class="odd">
<td align="left">a.1</td>
<td align="right">4.45</td>
<td align="right">3.74</td>
<td align="right">5.16</td>
</tr>
<tr class="even">
<td align="left">SD.log_k1</td>
<td align="right">0.36</td>
<td align="right">0.22</td>
<td align="right">0.49</td>
</tr>
<tr class="odd">
<td align="left">SD.log_k2</td>
<td align="right">0.23</td>
<td align="right">0.02</td>
<td align="right">0.43</td>
</tr>
<tr class="even">
<td align="left">SD.log_tb</td>
<td align="right">0.55</td>
<td align="right">0.25</td>
<td align="right">0.85</td>
</tr>
</tbody>
</table>
<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">hs_pH_2</span><span class="op">)</span></span></code></pre></div>
<p><img src="2023_mesotrione_parent_files/figure-html/unnamed-chunk-30-1.png" width="700" style="display: block; margin: auto;"></p>
<div class="sourceCode" id="cb81"><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">hs_pH_2</span><span class="op">)</span></span></code></pre></div>
<pre><code>$covariates
pH
50% 5.75
$distimes
DT50 DT90 DT50back DT50_k1 DT50_k2
meso 14.68725 82.45287 24.82079 14.68725 29.29299</code></pre>
<div class="sourceCode" id="cb83"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">hs_pH_2</span>, covariates <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>pH <span class="op">=</span> <span class="fl">7</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
<pre><code>$covariates
pH
User 7
$distimes
DT50 DT90 DT50back DT50_k1 DT50_k2
meso 8.298536 38.85371 11.69613 8.298536 15.71561</code></pre>
</div>
<div class="section level3">
<h3 id="comparison-across-parent-models">Comparison across parent models<a class="anchor" aria-label="anchor" href="#comparison-across-parent-models"></a>
</h3>
<p>After model reduction for all models with pH influence, they are
compared with each other.</p>
<div class="sourceCode" id="cb85"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">sfo_pH</span>, <span class="va">fomc_pH_2</span>, <span class="va">dfop_pH_2</span>, <span class="va">dfop_pH_4</span>, <span class="va">sforb_pH_2</span>, <span class="va">hs_pH_2</span><span class="op">)</span></span></code></pre></div>
<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets
npar AIC BIC Lik
sfo_pH 5 783.09 787.54 -386.54
fomc_pH_2 6 767.49 772.83 -377.75
dfop_pH_4 7 767.35 773.58 -376.68
sforb_pH_2 7 770.94 777.17 -378.47
dfop_pH_2 8 765.14 772.26 -374.57
hs_pH_2 10 766.47 775.37 -373.23</code></pre>
<p>The DFOP model with pH influence on <code>k2</code> and
<code>g</code> and a random effect only on <code>k2</code> is finally
selected as the best fit.</p>
<p>The endpoints resulting from this model are listed below. Please
refer to the Appendix for a detailed listing.</p>
<div class="sourceCode" id="cb87"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">dfop_pH_2</span><span class="op">)</span></span></code></pre></div>
<pre><code>$covariates
pH
50% 5.75
$distimes
DT50 DT90 DT50back DT50_k1 DT50_k2
meso 18.36876 73.51841 22.13125 4.191901 23.98672</code></pre>
<div class="sourceCode" id="cb89"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">dfop_pH_2</span>, covariates <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>pH <span class="op">=</span> <span class="fl">7</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
<pre><code>$covariates
pH
User 7
$distimes
DT50 DT90 DT50back DT50_k1 DT50_k2
meso 8.346428 28.34437 8.532507 4.191901 8.753618</code></pre>
</div>
</div>
<div class="section level2">
<h2 id="conclusions">Conclusions<a class="anchor" aria-label="anchor" href="#conclusions"></a>
</h2>
<p>These evaluations demonstrate that covariate effects can be included
for all types of parent degradation models. These models can then be
further refined to make them fully identifiable.</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-fit-listings">Hierarchical fit listings<a class="anchor" aria-label="anchor" href="#hierarchical-fit-listings"></a>
</h3>
<div class="section level4">
<h4 id="fits-without-covariate-effects">Fits without covariate effects<a class="anchor" aria-label="anchor" href="#fits-without-covariate-effects"></a>
</h4>
</div>
<div class="section level4">
<h4 id="fits-with-covariate-effects">Fits with covariate effects<a class="anchor" aria-label="anchor" href="#fits-with-covariate-effects"></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 4.4.2 (2024-10-31)
Platform: x86_64-pc-linux-gnu
Running under: Debian GNU/Linux 12 (bookworm)
Matrix products: default
BLAS: /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.11.0
LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.11.0
locale:
[1] LC_CTYPE=de_DE.UTF-8 LC_NUMERIC=C
[3] LC_TIME=de_DE.UTF-8 LC_COLLATE=de_DE.UTF-8
[5] LC_MONETARY=de_DE.UTF-8 LC_MESSAGES=de_DE.UTF-8
[7] LC_PAPER=de_DE.UTF-8 LC_NAME=C
[9] LC_ADDRESS=C LC_TELEPHONE=C
[11] LC_MEASUREMENT=de_DE.UTF-8 LC_IDENTIFICATION=C
time zone: Europe/Berlin
tzcode source: system (glibc)
attached base packages:
[1] parallel stats graphics grDevices utils datasets methods
[8] base
other attached packages:
[1] saemix_3.3 npde_3.5 knitr_1.49 mkin_1.2.10
loaded via a namespace (and not attached):
[1] gtable_0.3.6 jsonlite_1.8.9 dplyr_1.1.4 compiler_4.4.2
[5] tidyselect_1.2.1 gridExtra_2.3 jquerylib_0.1.4 systemfonts_1.1.0
[9] scales_1.3.0 textshaping_0.4.1 yaml_2.3.10 fastmap_1.2.0
[13] lattice_0.22-6 ggplot2_3.5.1 R6_2.5.1 generics_0.1.3
[17] lmtest_0.9-40 MASS_7.3-61 htmlwidgets_1.6.4 tibble_3.2.1
[21] desc_1.4.3 munsell_0.5.1 bslib_0.8.0 pillar_1.9.0
[25] rlang_1.1.4 utf8_1.2.4 cachem_1.1.0 xfun_0.49
[29] fs_1.6.5 sass_0.4.9 cli_3.6.3 pkgdown_2.1.1
[33] magrittr_2.0.3 digest_0.6.37 grid_4.4.2 mclust_6.1.1
[37] lifecycle_1.0.4 nlme_3.1-166 vctrs_0.6.5 evaluate_1.0.1
[41] glue_1.8.0 ragg_1.3.3 zoo_1.8-12 fansi_1.0.6
[45] colorspace_2.1-1 rmarkdown_2.29 pkgconfig_2.0.3 tools_4.4.2
[49] htmltools_0.5.8.1</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: 64927788 kB</code></pre>
</div>
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