Update static docsv1.2.5

author: Johannes Ranke <jranke@uni-bremen.de> 2023-08-09 17:59:42 +0200
committer: Johannes Ranke <jranke@uni-bremen.de> 2023-08-09 17:59:42 +0200
commit: 9abab1e2d4385039b01ad3dc0d9c5966bbe94fee (patch)
tree: cc9f23c3abe70e289b40c2cb03a4cda4ed157122 /docs/articles/prebuilt
parent: f21373a16d368c56234246417a32bdfb95589cf9 (diff)
6 files changed, 2560 insertions, 0 deletions
diff --git a/docs/articles/prebuilt/2023_mesotrione_parent.html b/docs/articles/prebuilt/2023_mesotrione_parent.html
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+      <a href="../../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a>
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+      <a href="../../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a>
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+    <div class="page-header toc-ignore">
+      <h1 data-toc-skip>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 9 August 2023</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="hidden 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 1.2.5, 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">&lt;-</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">&lt;-</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">&lt;-</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">&lt;-</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">&lt;-</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">&lt;-</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">&lt;-</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">&lt;-</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">|&gt;</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">|&gt;</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">&lt;-</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">|&gt;</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">|&gt;</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">&lt;-</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">|&gt;</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">|&gt;</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">|&gt;</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">&lt;-</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">|&gt;</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">|&gt;</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"></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">&lt;-</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">|&gt;</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(&gt;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
+
+$distimes
+        DT50    DT90
+meso 8.89035 29.5331</code></pre>
+</div>
+<div class="section level3">
+<h3 id="fomc">FOMC<a class="anchor" aria-label="anchor" href="#fomc"></a>
+</h3>
+<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">fomc_pH</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"FOMC"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="st">"meso_0"</span>, covariates <span class="op">=</span> <span class="va">pH</span>,</span>
+<span>  covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_alpha</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<div class="sourceCode" id="cb28"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">fomc_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|&gt;</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">&lt;-</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(&gt;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">|&gt;</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">|&gt;</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">&lt;-</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">|&gt;</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">&lt;-</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">&lt;-</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">&lt;-</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(&gt;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
+
+$distimes
+         DT50     DT90 DT50back  DT50_k1  DT50_k2
+meso 8.346428 28.34437 8.532507 4.191901 8.753618</code></pre>
+</div>
+<div class="section level3">
+<h3 id="sforb">SFORB<a class="anchor" aria-label="anchor" href="#sforb"></a>
+</h3>
+<div class="sourceCode" id="cb59"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">sforb_pH</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"SFORB"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_free_0"</span>, <span class="st">"log_k_meso_free_bound"</span><span class="op">)</span>,</span>
+<span>  covariates <span class="op">=</span> <span class="va">pH</span>,</span>
+<span>  covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_k_meso_free</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">log_k_meso_bound_free</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<div class="sourceCode" id="cb60"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">sforb_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|&gt;</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">&lt;-</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(&gt;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">|&gt;</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 
+
+$distimes
+         DT50     DT90 DT50back DT50_meso_b1 DT50_meso_b2
+meso 7.932495 36.93311 11.11797     5.205671        18.26</code></pre>
+</div>
+<div class="section level3">
+<h3 id="hs">HS<a class="anchor" aria-label="anchor" href="#hs"></a>
+</h3>
+<div class="sourceCode" id="cb72"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">hs_pH</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"HS"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_0"</span><span class="op">)</span>,</span>
+<span>  covariates <span class="op">=</span> <span class="va">pH</span>,</span>
+<span>  covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_k1</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">log_k2</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">log_tb</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<div class="sourceCode" id="cb73"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">hs_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|&gt;</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">&lt;-</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(&gt;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">|&gt;</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 4.3.1 (2023-06-16)
+Platform: x86_64-pc-linux-gnu (64-bit)
+Running under: Debian GNU/Linux 12 (bookworm)
+
+Matrix products: default
+BLAS:   /usr/lib/x86_64-linux-gnu/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_3.2 npde_3.3   knitr_1.43 mkin_1.2.5
+
+loaded via a namespace (and not attached):
+ [1] sass_0.4.6        utf8_1.2.3        generics_0.1.3    stringi_1.7.12   
+ [5] lattice_0.20-45   digest_0.6.31     magrittr_2.0.3    evaluate_0.21    
+ [9] grid_4.3.1        fastmap_1.1.1     cellranger_1.1.0  rprojroot_2.0.3  
+[13] jsonlite_1.8.5    mclust_6.0.0      gridExtra_2.3     purrr_1.0.1      
+[17] fansi_1.0.4       scales_1.2.1      codetools_0.2-19  textshaping_0.3.6
+[21] jquerylib_0.1.4   cli_3.6.1         rlang_1.1.1       munsell_0.5.0    
+[25] cachem_1.0.8      yaml_2.3.7        tools_4.3.1       memoise_2.0.1    
+[29] dplyr_1.1.2       colorspace_2.1-0  ggplot2_3.4.2     vctrs_0.6.2      
+[33] R6_2.5.1          zoo_1.8-12        lifecycle_1.0.3   stringr_1.5.0    
+[37] fs_1.6.2          ragg_1.2.5        pkgconfig_2.0.3   desc_1.4.2       
+[41] pkgdown_2.0.7     bslib_0.4.2       pillar_1.9.0      gtable_0.3.3     
+[45] glue_1.6.2        systemfonts_1.0.4 highr_0.10        xfun_0.39        
+[49] tibble_3.2.1      lmtest_0.9-40     tidyselect_1.2.0  htmltools_0.5.5  
+[53] nlme_3.1-162      rmarkdown_2.22    compiler_4.3.1    readxl_1.4.2     </code></pre>
+</div>
+<div class="section level3">
+<h3 id="hardware-info">Hardware info<a class="anchor" aria-label="anchor" href="#hardware-info"></a>
+</h3>
+<pre><code>CPU model: Intel(R) Core(TM) i7-4710MQ CPU @ 2.50GHz</code></pre>
+<pre><code>MemTotal:       12165632 kB</code></pre>
+</div>
+</div>
+  </div>
+
+  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
+
+        <nav id="toc" data-toggle="toc"><h2 data-toc-skip>Contents</h2>
+    </nav>
+</div>
+
+</div>
+
+
+
+      <footer><div class="copyright">
+  <p></p>
+<p>Developed by Johannes Ranke.</p>
+</div>
+
+<div class="pkgdown">
+  <p></p>
+<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p>
+</div>
+
+      </footer>
+</div>
+
+  
+
+
+  
+
+  </body>
+</html>
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author	Johannes Ranke <jranke@uni-bremen.de>	2023-08-09 17:59:42 +0200
committer	Johannes Ranke <jranke@uni-bremen.de>	2023-08-09 17:59:42 +0200
commit	9abab1e2d4385039b01ad3dc0d9c5966bbe94fee (patch)
tree	cc9f23c3abe70e289b40c2cb03a4cda4ed157122 /docs/articles/prebuilt
parent	f21373a16d368c56234246417a32bdfb95589cf9 (diff)