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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"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/detectCores.html" class="external-link">detectCores</a></span><span class="op">(</span><span class="op">)</span></span> +<span><span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/Sys.info.html" class="external-link">Sys.info</a></span><span class="op">(</span><span class="op">)</span><span class="op">[</span><span class="st">"sysname"</span><span class="op">]</span> <span class="op">==</span> <span class="st">"Windows"</span><span class="op">)</span> <span class="op">{</span></span> +<span> <span class="va">cl</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makePSOCKcluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> +<span><span class="op">}</span> <span class="kw">else</span> <span class="op">{</span></span> +<span> <span class="va">cl</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makeForkCluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> +<span><span class="op">}</span></span></code></pre></div> +<div class="section level3"> +<h3 id="test-data">Test data<a class="anchor" aria-label="anchor" href="#test-data"></a> +</h3> +<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">data_file</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.file.html" class="external-link">system.file</a></span><span class="op">(</span></span> +<span> <span class="st">"testdata"</span>, <span class="st">"mesotrione_soil_efsa_2016.xlsx"</span>, package <span class="op">=</span> <span class="st">"mkin"</span><span class="op">)</span></span> +<span><span class="va">meso_ds</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/read_spreadsheet.html">read_spreadsheet</a></span><span class="op">(</span><span class="va">data_file</span>, parent_only <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<p>The following tables show the covariate data and the 18 datasets that +were read in from the spreadsheet file.</p> +<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">pH</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/attr.html" class="external-link">attr</a></span><span class="op">(</span><span class="va">meso_ds</span>, <span class="st">"covariates"</span><span class="op">)</span></span> +<span><span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="va">pH</span>, caption <span class="op">=</span> <span class="st">"Covariate data"</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<caption>Covariate data</caption> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">pH</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">Richmond</td> +<td align="right">6.2</td> +</tr> +<tr class="even"> +<td align="left">Richmond 2</td> +<td align="right">6.2</td> +</tr> +<tr class="odd"> +<td align="left">ERTC</td> +<td align="right">6.4</td> +</tr> +<tr class="even"> +<td align="left">Toulouse</td> +<td align="right">7.7</td> +</tr> +<tr class="odd"> +<td align="left">Picket Piece</td> +<td align="right">7.1</td> +</tr> +<tr class="even"> +<td align="left">721</td> +<td align="right">5.6</td> +</tr> +<tr class="odd"> +<td align="left">722</td> +<td align="right">5.7</td> +</tr> +<tr class="even"> +<td align="left">723</td> +<td align="right">5.4</td> +</tr> +<tr class="odd"> +<td align="left">724</td> +<td align="right">4.8</td> +</tr> +<tr class="even"> +<td align="left">725</td> +<td align="right">5.8</td> +</tr> +<tr class="odd"> +<td align="left">727</td> +<td align="right">5.1</td> +</tr> +<tr class="even"> +<td align="left">728</td> +<td align="right">5.9</td> +</tr> +<tr class="odd"> +<td align="left">729</td> +<td align="right">5.6</td> +</tr> +<tr class="even"> +<td align="left">730</td> +<td align="right">5.3</td> +</tr> +<tr class="odd"> +<td align="left">731</td> +<td align="right">6.1</td> +</tr> +<tr class="even"> +<td align="left">732</td> +<td align="right">5.0</td> +</tr> +<tr class="odd"> +<td align="left">741</td> +<td align="right">5.7</td> +</tr> +<tr class="even"> +<td align="left">742</td> +<td align="right">7.2</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="kw">for</span> <span class="op">(</span><span class="va">ds_name</span> <span class="kw">in</span> <span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">meso_ds</span><span class="op">)</span><span class="op">)</span> <span class="op">{</span></span> +<span> <span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span></span> +<span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="fu"><a href="../../reference/mkin_long_to_wide.html">mkin_long_to_wide</a></span><span class="op">(</span><span class="va">meso_ds</span><span class="op">[[</span><span class="va">ds_name</span><span class="op">]</span><span class="op">]</span><span class="op">)</span>,</span> +<span> caption <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste</a></span><span class="op">(</span><span class="st">"Dataset"</span>, <span class="va">ds_name</span><span class="op">)</span>,</span> +<span> booktabs <span class="op">=</span> <span class="cn">TRUE</span>, row.names <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="op">}</span></span></code></pre></div> +<table class="table"> +<caption>Dataset Richmond</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">91.00</td> +</tr> +<tr class="even"> +<td align="right">1.179050</td> +<td align="right">86.70</td> +</tr> +<tr class="odd"> +<td align="right">3.537149</td> +<td align="right">73.60</td> +</tr> +<tr class="even"> +<td align="right">7.074299</td> +<td align="right">61.50</td> +</tr> +<tr class="odd"> +<td align="right">10.611448</td> +<td align="right">55.70</td> +</tr> +<tr class="even"> +<td align="right">15.327647</td> +<td align="right">47.70</td> +</tr> +<tr class="odd"> +<td align="right">17.685747</td> +<td align="right">39.50</td> +</tr> +<tr class="even"> +<td align="right">24.760046</td> +<td align="right">29.80</td> +</tr> +<tr class="odd"> +<td align="right">35.371494</td> +<td align="right">19.60</td> +</tr> +<tr class="even"> +<td align="right">68.384889</td> +<td align="right">5.67</td> +</tr> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">97.90</td> +</tr> +<tr class="even"> +<td align="right">1.179050</td> +<td align="right">96.40</td> +</tr> +<tr class="odd"> +<td align="right">3.537149</td> +<td align="right">89.10</td> +</tr> +<tr class="even"> +<td align="right">7.074299</td> +<td align="right">74.40</td> +</tr> +<tr class="odd"> +<td align="right">10.611448</td> +<td align="right">57.40</td> +</tr> +<tr class="even"> +<td align="right">15.327647</td> +<td align="right">46.30</td> +</tr> +<tr class="odd"> +<td align="right">18.864797</td> +<td align="right">35.50</td> +</tr> +<tr class="even"> +<td align="right">27.118146</td> +<td align="right">27.20</td> +</tr> +<tr class="odd"> +<td align="right">35.371494</td> +<td align="right">19.10</td> +</tr> +<tr class="even"> +<td align="right">74.280138</td> +<td align="right">6.50</td> +</tr> +<tr class="odd"> +<td align="right">108.472582</td> +<td align="right">3.40</td> +</tr> +<tr class="even"> +<td align="right">142.665027</td> +<td align="right">2.20</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset Richmond 2</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">96.0</td> +</tr> +<tr class="even"> +<td align="right">2.422004</td> +<td align="right">82.4</td> +</tr> +<tr class="odd"> +<td align="right">5.651343</td> +<td align="right">71.2</td> +</tr> +<tr class="even"> +<td align="right">8.073348</td> +<td align="right">53.1</td> +</tr> +<tr class="odd"> +<td align="right">11.302687</td> +<td align="right">48.5</td> +</tr> +<tr class="even"> +<td align="right">16.954030</td> +<td align="right">33.4</td> +</tr> +<tr class="odd"> +<td align="right">22.605373</td> +<td align="right">24.2</td> +</tr> +<tr class="even"> +<td align="right">45.210746</td> +<td align="right">11.9</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset ERTC</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">99.9</td> +</tr> +<tr class="even"> +<td align="right">2.755193</td> +<td align="right">80.0</td> +</tr> +<tr class="odd"> +<td align="right">6.428782</td> +<td align="right">42.1</td> +</tr> +<tr class="even"> +<td align="right">9.183975</td> +<td align="right">50.1</td> +</tr> +<tr class="odd"> +<td align="right">12.857565</td> +<td align="right">28.4</td> +</tr> +<tr class="even"> +<td align="right">19.286347</td> +<td align="right">39.8</td> +</tr> +<tr class="odd"> +<td align="right">25.715130</td> +<td align="right">29.9</td> +</tr> +<tr class="even"> +<td align="right">51.430259</td> +<td align="right">2.5</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset Toulouse</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">96.8</td> +</tr> +<tr class="even"> +<td align="right">2.897983</td> +<td align="right">63.3</td> +</tr> +<tr class="odd"> +<td align="right">6.761960</td> +<td align="right">22.3</td> +</tr> +<tr class="even"> +<td align="right">9.659942</td> +<td align="right">16.6</td> +</tr> +<tr class="odd"> +<td align="right">13.523919</td> +<td align="right">16.1</td> +</tr> +<tr class="even"> +<td align="right">20.285879</td> +<td align="right">17.2</td> +</tr> +<tr class="odd"> +<td align="right">27.047838</td> +<td align="right">1.8</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset Picket Piece</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">102.0</td> +</tr> +<tr class="even"> +<td align="right">2.841195</td> +<td align="right">73.7</td> +</tr> +<tr class="odd"> +<td align="right">6.629454</td> +<td align="right">35.5</td> +</tr> +<tr class="even"> +<td align="right">9.470649</td> +<td align="right">31.8</td> +</tr> +<tr class="odd"> +<td align="right">13.258909</td> +<td align="right">18.0</td> +</tr> +<tr class="even"> +<td align="right">19.888364</td> +<td align="right">3.7</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 721</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">86.4</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">61.4</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">49.8</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">41.0</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">35.1</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 722</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">90.3</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">52.1</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">37.4</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">21.2</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">14.3</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 723</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">89.3</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">70.8</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">51.1</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">42.7</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">26.7</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 724</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">89.4</td> +</tr> +<tr class="even"> +<td align="right">9.008208</td> +<td align="right">65.2</td> +</tr> +<tr class="odd"> +<td align="right">18.016415</td> +<td align="right">55.8</td> +</tr> +<tr class="even"> +<td align="right">27.024623</td> +<td align="right">46.0</td> +</tr> +<tr class="odd"> +<td align="right">36.032831</td> +<td align="right">41.7</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 725</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">89.0</td> +</tr> +<tr class="even"> +<td align="right">10.99058</td> +<td align="right">35.4</td> +</tr> +<tr class="odd"> +<td align="right">21.98116</td> +<td align="right">18.6</td> +</tr> +<tr class="even"> +<td align="right">32.97174</td> +<td align="right">11.6</td> +</tr> +<tr class="odd"> +<td align="right">43.96232</td> +<td align="right">7.6</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 727</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">91.3</td> +</tr> +<tr class="even"> +<td align="right">10.96104</td> +<td align="right">63.2</td> +</tr> +<tr class="odd"> +<td align="right">21.92209</td> +<td align="right">51.1</td> +</tr> +<tr class="even"> +<td align="right">32.88313</td> +<td align="right">42.0</td> +</tr> +<tr class="odd"> +<td align="right">43.84417</td> +<td align="right">40.8</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 728</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">91.8</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">43.6</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">22.0</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">15.9</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">8.8</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 729</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">91.6</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">60.5</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">43.5</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">28.4</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">20.5</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 730</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">92.7</td> +</tr> +<tr class="even"> +<td align="right">11.07446</td> +<td align="right">58.9</td> +</tr> +<tr class="odd"> +<td align="right">22.14893</td> +<td align="right">44.0</td> +</tr> +<tr class="even"> +<td align="right">33.22339</td> +<td align="right">46.0</td> +</tr> +<tr class="odd"> +<td align="right">44.29785</td> +<td align="right">29.3</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 731</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">92.1</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">64.4</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">45.3</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">33.6</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">23.5</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 732</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">90.3</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">58.2</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">40.1</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">33.1</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">25.8</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 741</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">90.3</td> +</tr> +<tr class="even"> +<td align="right">10.84712</td> +<td align="right">68.7</td> +</tr> +<tr class="odd"> +<td align="right">21.69424</td> +<td align="right">58.0</td> +</tr> +<tr class="even"> +<td align="right">32.54136</td> +<td align="right">52.2</td> +</tr> +<tr class="odd"> +<td align="right">43.38848</td> +<td align="right">48.0</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 742</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">92.0</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">60.9</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">36.2</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">18.3</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">8.7</td> +</tr> +</tbody> +</table> +</div> +</div> +<div class="section level2"> +<h2 id="separate-evaluations">Separate evaluations<a class="anchor" aria-label="anchor" href="#separate-evaluations"></a> +</h2> +<p>In order to obtain suitable starting parameters for the NLHM fits, +separate fits of the five models to the data for each soil are generated +using the <code>mmkin</code> function from the mkin package. In a first +step, constant variance is assumed. Convergence is checked with the +<code>status</code> function.</p> +<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">deg_mods</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>, <span class="st">"SFORB"</span>, <span class="st">"HS"</span><span class="op">)</span></span> +<span><span class="va">f_sep_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span></span> +<span> <span class="va">deg_mods</span>,</span> +<span> <span class="va">meso_ds</span>,</span> +<span> error_model <span class="op">=</span> <span class="st">"const"</span>,</span> +<span> cluster <span class="op">=</span> <span class="va">cl</span>,</span> +<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span>, <span class="fl">1</span><span class="op">:</span><span class="fl">5</span><span class="op">]</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">Richmond</th> +<th align="left">Richmond 2</th> +<th align="left">ERTC</th> +<th align="left">Toulouse</th> +<th align="left">Picket Piece</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span>, <span class="fl">6</span><span class="op">:</span><span class="fl">18</span><span class="op">]</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<colgroup> +<col width="10%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +</colgroup> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">721</th> +<th align="left">722</th> +<th align="left">723</th> +<th align="left">724</th> +<th align="left">725</th> +<th align="left">727</th> +<th align="left">728</th> +<th align="left">729</th> +<th align="left">730</th> +<th align="left">731</th> +<th align="left">732</th> +<th align="left">741</th> +<th align="left">742</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<p>In the tables above, OK indicates convergence and C indicates failure +to converge. Most separate fits with constant variance converged, with +the exception of two FOMC fits, one SFORB fit and one HS fit.</p> +<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">f_sep_tc</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_sep_const</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_tc</span><span class="op">[</span>, <span class="fl">1</span><span class="op">:</span><span class="fl">5</span><span class="op">]</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">Richmond</th> +<th align="left">Richmond 2</th> +<th align="left">ERTC</th> +<th align="left">Toulouse</th> +<th align="left">Picket Piece</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_tc</span><span class="op">[</span>, <span class="fl">6</span><span class="op">:</span><span class="fl">18</span><span class="op">]</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<colgroup> +<col width="10%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +</colgroup> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">721</th> +<th align="left">722</th> +<th align="left">723</th> +<th align="left">724</th> +<th align="left">725</th> +<th align="left">727</th> +<th align="left">728</th> +<th align="left">729</th> +<th align="left">730</th> +<th align="left">731</th> +<th align="left">732</th> +<th align="left">741</th> +<th align="left">742</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<p>With the two-component error model, the set of fits that did not +converge is larger, with convergence problems appearing for a number of +non-SFO fits.</p> +</div> +<div class="section level2"> +<h2 id="hierarchical-model-fits-without-covariate-effect">Hierarchical model fits without covariate effect<a class="anchor" aria-label="anchor" href="#hierarchical-model-fits-without-covariate-effect"></a> +</h2> +<p>The following code fits hierarchical kinetic models for the ten +combinations of the five different degradation models with the two +different error models in parallel.</p> +<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">f_saem_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mhmkin.html">mhmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">f_sep_const</span>, <span class="va">f_sep_tc</span><span class="op">)</span>, cluster <span class="op">=</span> <span class="va">cl</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<p>All fits terminate without errors (status OK).</p> +<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">npar</th> +<th align="right">AIC</th> +<th align="right">BIC</th> +<th align="right">Lik</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO const</td> +<td align="right">5</td> +<td align="right">800.0</td> +<td align="right">804.5</td> +<td align="right">-395.0</td> +</tr> +<tr class="even"> +<td align="left">SFO tc</td> +<td align="right">6</td> +<td align="right">801.9</td> +<td align="right">807.2</td> +<td align="right">-394.9</td> +</tr> +<tr class="odd"> +<td align="left">FOMC const</td> +<td align="right">7</td> +<td align="right">787.4</td> +<td align="right">793.6</td> +<td align="right">-386.7</td> +</tr> +<tr class="even"> +<td align="left">FOMC tc</td> +<td align="right">8</td> +<td align="right">788.9</td> +<td align="right">796.1</td> +<td align="right">-386.5</td> +</tr> +<tr class="odd"> +<td align="left">DFOP const</td> +<td align="right">9</td> +<td align="right">787.6</td> +<td align="right">795.6</td> +<td align="right">-384.8</td> +</tr> +<tr class="even"> +<td align="left">SFORB const</td> +<td align="right">9</td> +<td align="right">787.4</td> +<td align="right">795.4</td> +<td align="right">-384.7</td> +</tr> +<tr class="odd"> +<td align="left">HS const</td> +<td align="right">9</td> +<td align="right">781.9</td> +<td align="right">789.9</td> +<td align="right">-382.0</td> +</tr> +<tr class="even"> +<td align="left">DFOP tc</td> +<td align="right">10</td> +<td align="right">787.4</td> +<td align="right">796.3</td> +<td align="right">-383.7</td> +</tr> +<tr class="odd"> +<td align="left">SFORB tc</td> +<td align="right">10</td> +<td align="right">795.8</td> +<td align="right">804.7</td> +<td align="right">-387.9</td> +</tr> +<tr class="even"> +<td align="left">HS tc</td> +<td align="right">10</td> +<td align="right">783.7</td> +<td align="right">792.7</td> +<td align="right">-381.9</td> +</tr> +</tbody> +</table> +<p>The model comparisons show that the fits with constant variance are +consistently preferable to the corresponding fits with two-component +error for these data. This is confirmed by the fact that the parameter +<code>b.1</code> (the relative standard deviation in the fits obtained +with the saemix package), is ill-defined in all fits.</p> +<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<colgroup> +<col width="6%"> +<col width="44%"> +<col width="49%"> +</colgroup> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">sd(meso_0)</td> +<td align="left">sd(meso_0), b.1</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">sd(meso_0), sd(log_beta)</td> +<td align="left">sd(meso_0), sd(log_beta), b.1</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">sd(meso_0), sd(log_k1)</td> +<td align="left">sd(meso_0), sd(g_qlogis), b.1</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">sd(meso_free_0), sd(log_k_meso_free_bound)</td> +<td align="left">sd(meso_free_0), sd(log_k_meso_free_bound), b.1</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">sd(meso_0)</td> +<td align="left">sd(meso_0), b.1</td> +</tr> +</tbody> +</table> +<p>For obtaining fits with only well-defined random effects, we update +the set of fits, excluding random effects that were ill-defined +according to the <code>illparms</code> function.</p> +<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">f_saem_2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_saem_1</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<p>The updated fits terminate without errors.</p> +<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left"></td> +<td align="left">b.1</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left"></td> +<td align="left">b.1</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left"></td> +<td align="left">b.1</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left"></td> +<td align="left">b.1</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left"></td> +<td align="left"></td> +</tr> +</tbody> +</table> +<p>No ill-defined errors remain in the fits with constant variance.</p> +</div> +<div class="section level2"> +<h2 id="hierarchical-model-fits-with-covariate-effect">Hierarchical model fits with covariate effect<a class="anchor" aria-label="anchor" href="#hierarchical-model-fits-with-covariate-effect"></a> +</h2> +<p>In the following sections, hierarchical fits including a model for +the influence of pH on selected degradation parameters are shown for all +parent models. Constant variance is selected as the error model based on +the fits without covariate effects. Random effects that were ill-defined +in the fits without pH influence are excluded. A potential influence of +the soil pH is only included for parameters with a well-defined random +effect, because experience has shown that only for such parameters a +significant pH effect could be found.</p> +<div class="section level3"> +<h3 id="sfo">SFO<a class="anchor" aria-label="anchor" href="#sfo"></a> +</h3> +<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">sfo_pH</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="st">"meso_0"</span>, covariates <span class="op">=</span> <span class="va">pH</span>,</span> +<span> covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_k_meso</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">sfo_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_0</td> +<td align="right">91.35</td> +<td align="right">89.27</td> +<td align="right">93.43</td> +</tr> +<tr class="even"> +<td align="left">log_k_meso</td> +<td align="right">-6.66</td> +<td align="right">-7.97</td> +<td align="right">-5.35</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_k_meso)</td> +<td align="right">0.59</td> +<td align="right">0.37</td> +<td align="right">0.81</td> +</tr> +<tr class="even"> +<td align="left">a.1</td> +<td align="right">5.48</td> +<td align="right">4.71</td> +<td align="right">6.24</td> +</tr> +<tr class="odd"> +<td align="left">SD.log_k_meso</td> +<td align="right">0.35</td> +<td align="right">0.23</td> +<td align="right">0.47</td> +</tr> +</tbody> +</table> +<p>The parameter showing the pH influence in the above table is +<code>beta_pH(log_k_meso)</code>. Its confidence interval does not +include zero, indicating that the influence of soil pH on the log of the +degradation rate constant is significantly greater than zero.</p> +<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"SFO"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span>, <span class="va">sfo_pH</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets + + npar AIC BIC Lik Chisq Df Pr(>Chisq) +f_saem_2[["SFO", "const"]] 4 797.56 801.12 -394.78 +sfo_pH 5 783.09 787.54 -386.54 16.473 1 4.934e-05 *** +--- +Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre> +<p>The comparison with the SFO fit without covariate effect confirms +that considering the soil pH improves the model, both by comparison of +AIC and BIC and by the likelihood ratio test.</p> +<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">sfo_pH</span><span class="op">)</span></span></code></pre></div> +<p><img src="2023_mesotrione_parent_files/figure-html/unnamed-chunk-8-1.png" width="700" style="display: block; margin: auto;"></p> +<p>Endpoints for a model with covariates are by default calculated for +the median of the covariate values. This quantile can be adapted, or a +specific covariate value can be given as shown below.</p> +<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">sfo_pH</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +50% 5.75 + +$distimes + DT50 DT90 +meso 18.52069 61.52441</code></pre> +<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">sfo_pH</span>, covariate_quantile <span class="op">=</span> <span class="fl">0.9</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +90% 7.13 + +$distimes + DT50 DT90 +meso 8.237019 27.36278</code></pre> +<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">sfo_pH</span>, covariates <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>pH <span class="op">=</span> <span class="fl">7.0</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +User 7 + +$distimes + DT50 DT90 +meso 8.89035 29.5331</code></pre> +</div> +<div class="section level3"> +<h3 id="fomc">FOMC<a class="anchor" aria-label="anchor" href="#fomc"></a> +</h3> +<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">fomc_pH</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"FOMC"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="st">"meso_0"</span>, covariates <span class="op">=</span> <span class="va">pH</span>,</span> +<span> covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_alpha</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb28"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">fomc_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_0</td> +<td align="right">92.84</td> +<td align="right">90.75</td> +<td align="right">94.93</td> +</tr> +<tr class="even"> +<td align="left">log_alpha</td> +<td align="right">-2.21</td> +<td align="right">-3.49</td> +<td align="right">-0.92</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_alpha)</td> +<td align="right">0.58</td> +<td align="right">0.37</td> +<td align="right">0.79</td> +</tr> +<tr class="even"> +<td align="left">log_beta</td> +<td align="right">4.21</td> +<td align="right">3.44</td> +<td align="right">4.99</td> +</tr> +<tr class="odd"> +<td align="left">a.1</td> +<td align="right">5.03</td> +<td align="right">4.32</td> +<td align="right">5.73</td> +</tr> +<tr class="even"> +<td align="left">SD.log_alpha</td> +<td align="right">0.00</td> +<td align="right">-23.77</td> +<td align="right">23.78</td> +</tr> +<tr class="odd"> +<td align="left">SD.log_beta</td> +<td align="right">0.37</td> +<td align="right">0.01</td> +<td align="right">0.74</td> +</tr> +</tbody> +</table> +<p>As in the case of SFO, the confidence interval of the slope parameter +(here <code>beta_pH(log_alpha)</code>) quantifying the influence of soil +pH does not include zero, and the model comparison clearly indicates +that the model with covariate influence is preferable. However, the +random effect for <code>alpha</code> is not well-defined any more after +inclusion of the covariate effect (the confidence interval of +<code>SD.log_alpha</code> includes zero).</p> +<div class="sourceCode" id="cb29"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">fomc_pH</span><span class="op">)</span></span></code></pre></div> +<pre><code>[1] "sd(log_alpha)"</code></pre> +<p>Therefore, the model is updated without this random effect, and no +ill-defined parameters remain.</p> +<div class="sourceCode" id="cb31"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">fomc_pH_2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">fomc_pH</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_0"</span>, <span class="st">"log_alpha"</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">fomc_pH_2</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb32"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"FOMC"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span>, <span class="va">fomc_pH</span>, <span class="va">fomc_pH_2</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets + + npar AIC BIC Lik Chisq Df Pr(>Chisq) +f_saem_2[["FOMC", "const"]] 5 783.25 787.71 -386.63 +fomc_pH_2 6 767.49 772.83 -377.75 17.762 1 2.503e-05 *** +fomc_pH 7 770.07 776.30 -378.04 0.000 1 1 +--- +Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre> +<p>Model comparison indicates that including pH dependence significantly +improves the fit, and that the reduced model with covariate influence +results in the most preferable FOMC fit.</p> +<div class="sourceCode" id="cb34"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">fomc_pH_2</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_0</td> +<td align="right">93.05</td> +<td align="right">90.98</td> +<td align="right">95.13</td> +</tr> +<tr class="even"> +<td align="left">log_alpha</td> +<td align="right">-2.91</td> +<td align="right">-4.18</td> +<td align="right">-1.63</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_alpha)</td> +<td align="right">0.66</td> +<td align="right">0.44</td> +<td align="right">0.87</td> +</tr> +<tr class="even"> +<td align="left">log_beta</td> +<td align="right">3.95</td> +<td align="right">3.29</td> +<td align="right">4.62</td> +</tr> +<tr class="odd"> +<td align="left">a.1</td> +<td align="right">4.98</td> +<td align="right">4.28</td> +<td align="right">5.68</td> +</tr> +<tr class="even"> +<td align="left">SD.log_beta</td> +<td align="right">0.40</td> +<td align="right">0.26</td> +<td align="right">0.54</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb35"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">fomc_pH_2</span><span class="op">)</span></span></code></pre></div> +<p><img src="2023_mesotrione_parent_files/figure-html/unnamed-chunk-14-1.png" width="700" style="display: block; margin: auto;"></p> +<div class="sourceCode" id="cb36"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">fomc_pH_2</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +50% 5.75 + +$distimes + DT50 DT90 DT50back +meso 17.30248 82.91343 24.95943</code></pre> +<div class="sourceCode" id="cb38"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">fomc_pH_2</span>, covariates <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>pH <span class="op">=</span> <span class="fl">7</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +User 7 + +$distimes + DT50 DT90 DT50back +meso 6.986239 27.02927 8.136621</code></pre> +</div> +<div class="section level3"> +<h3 id="dfop">DFOP<a class="anchor" aria-label="anchor" href="#dfop"></a> +</h3> +<p>In the DFOP fits without covariate effects, random effects for two +degradation parameters (<code>k2</code> and <code>g</code>) were +identifiable.</p> +<div class="sourceCode" id="cb40"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_0</td> +<td align="right">93.61</td> +<td align="right">91.58</td> +<td align="right">95.63</td> +</tr> +<tr class="even"> +<td align="left">log_k1</td> +<td align="right">-1.53</td> +<td align="right">-2.27</td> +<td align="right">-0.79</td> +</tr> +<tr class="odd"> +<td align="left">log_k2</td> +<td align="right">-3.42</td> +<td align="right">-3.73</td> +<td align="right">-3.11</td> +</tr> +<tr class="even"> +<td align="left">g_qlogis</td> +<td align="right">-1.67</td> +<td align="right">-2.57</td> +<td align="right">-0.77</td> +</tr> +<tr class="odd"> +<td align="left">a.1</td> +<td align="right">4.74</td> +<td align="right">4.02</td> +<td align="right">5.45</td> +</tr> +<tr class="even"> +<td align="left">SD.log_k2</td> +<td align="right">0.60</td> +<td align="right">0.38</td> +<td align="right">0.81</td> +</tr> +<tr class="odd"> +<td align="left">SD.g_qlogis</td> +<td align="right">0.94</td> +<td align="right">0.33</td> +<td align="right">1.54</td> +</tr> +</tbody> +</table> +<p>A fit with pH dependent degradation parameters was obtained by +excluding the same random effects as in the refined DFOP fit without +covariate influence, and including covariate models for the two +identifiable parameters <code>k2</code> and <code>g</code>.</p> +<div class="sourceCode" id="cb41"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">dfop_pH</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_0"</span>, <span class="st">"log_k1"</span><span class="op">)</span>,</span> +<span> covariates <span class="op">=</span> <span class="va">pH</span>,</span> +<span> covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_k2</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">g_qlogis</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<p>The corresponding parameters for the influence of soil pH are +<code>beta_pH(log_k2)</code> for the influence of soil pH on +<code>k2</code>, and <code>beta_pH(g_qlogis)</code> for its influence on +<code>g</code>.</p> +<div class="sourceCode" id="cb42"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">dfop_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_0</td> +<td align="right">92.84</td> +<td align="right">90.85</td> +<td align="right">94.84</td> +</tr> +<tr class="even"> +<td align="left">log_k1</td> +<td align="right">-2.82</td> +<td align="right">-3.09</td> +<td align="right">-2.54</td> +</tr> +<tr class="odd"> +<td align="left">log_k2</td> +<td align="right">-11.48</td> +<td align="right">-15.32</td> +<td align="right">-7.64</td> +</tr> +<tr class="even"> +<td align="left">beta_pH(log_k2)</td> +<td align="right">1.31</td> +<td align="right">0.69</td> +<td align="right">1.92</td> +</tr> +<tr class="odd"> +<td align="left">g_qlogis</td> +<td align="right">3.13</td> +<td align="right">0.47</td> +<td align="right">5.80</td> +</tr> +<tr class="even"> +<td align="left">beta_pH(g_qlogis)</td> +<td align="right">-0.57</td> +<td align="right">-1.04</td> +<td align="right">-0.09</td> +</tr> +<tr class="odd"> +<td align="left">a.1</td> +<td align="right">4.96</td> +<td align="right">4.26</td> +<td align="right">5.65</td> +</tr> +<tr class="even"> +<td align="left">SD.log_k2</td> +<td align="right">0.76</td> +<td align="right">0.47</td> +<td align="right">1.05</td> +</tr> +<tr class="odd"> +<td align="left">SD.g_qlogis</td> +<td align="right">0.01</td> +<td align="right">-9.96</td> +<td align="right">9.97</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb43"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">dfop_pH</span><span class="op">)</span></span></code></pre></div> +<pre><code>[1] "sd(g_qlogis)"</code></pre> +<p>Confidence intervals for neither of them include zero, indicating a +significant difference from zero. However, the random effect for +<code>g</code> is now ill-defined. The fit is updated without this +ill-defined random effect.</p> +<div class="sourceCode" id="cb45"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">dfop_pH_2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">dfop_pH</span>,</span> +<span> no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_0"</span>, <span class="st">"log_k1"</span>, <span class="st">"g_qlogis"</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">dfop_pH_2</span><span class="op">)</span></span></code></pre></div> +<pre><code>[1] "beta_pH(g_qlogis)"</code></pre> +<p>Now, the slope parameter for the pH effect on <code>g</code> is +ill-defined. Therefore, another attempt is made without the +corresponding covariate model.</p> +<div class="sourceCode" id="cb47"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">dfop_pH_3</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_0"</span>, <span class="st">"log_k1"</span><span class="op">)</span>,</span> +<span> covariates <span class="op">=</span> <span class="va">pH</span>,</span> +<span> covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_k2</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">dfop_pH_3</span><span class="op">)</span></span></code></pre></div> +<pre><code>[1] "sd(g_qlogis)"</code></pre> +<p>As the random effect for <code>g</code> is again ill-defined, the fit +is repeated without it.</p> +<div class="sourceCode" id="cb49"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">dfop_pH_4</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">dfop_pH_3</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_0"</span>, <span class="st">"log_k1"</span>, <span class="st">"g_qlogis"</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">dfop_pH_4</span><span class="op">)</span></span></code></pre></div> +<p>While no ill-defined parameters remain, model comparison suggests +that the previous model <code>dfop_pH_2</code> with two pH dependent +parameters is preferable, based on information criteria as well as based +on the likelihood ratio test.</p> +<div class="sourceCode" id="cb50"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span>, <span class="va">dfop_pH</span>, <span class="va">dfop_pH_2</span>, <span class="va">dfop_pH_3</span>, <span class="va">dfop_pH_4</span><span class="op">)</span></span></code></pre></div> +<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets + + npar AIC BIC Lik +f_saem_2[["DFOP", "const"]] 7 782.94 789.18 -384.47 +dfop_pH_4 7 767.35 773.58 -376.68 +dfop_pH_2 8 765.14 772.26 -374.57 +dfop_pH_3 8 769.00 776.12 -376.50 +dfop_pH 9 769.10 777.11 -375.55</code></pre> +<div class="sourceCode" id="cb52"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">dfop_pH_2</span>, <span class="va">dfop_pH_4</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets + + npar AIC BIC Lik Chisq Df Pr(>Chisq) +dfop_pH_4 7 767.35 773.58 -376.68 +dfop_pH_2 8 765.14 772.26 -374.57 4.2153 1 0.04006 * +--- +Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre> +<p>When focussing on parameter identifiability using the test if the +confidence interval includes zero, <code>dfop_pH_4</code> would still be +the preferred model. However, it should be kept in mind that parameter +confidence intervals are constructed using a simple linearisation of the +likelihood. As the confidence interval of the random effect for +<code>g</code> only marginally includes zero, it is suggested that this +is acceptable, and that <code>dfop_pH_2</code> can be considered the +most preferable model.</p> +<div class="sourceCode" id="cb54"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">dfop_pH_2</span><span class="op">)</span></span></code></pre></div> +<p><img src="2023_mesotrione_parent_files/figure-html/unnamed-chunk-19-1.png" width="700" style="display: block; margin: auto;"></p> +<div class="sourceCode" id="cb55"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">dfop_pH_2</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +50% 5.75 + +$distimes + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 18.36876 73.51841 22.13125 4.191901 23.98672</code></pre> +<div class="sourceCode" id="cb57"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">dfop_pH_2</span>, covariates <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>pH <span class="op">=</span> <span class="fl">7</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +User 7 + +$distimes + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 8.346428 28.34437 8.532507 4.191901 8.753618</code></pre> +</div> +<div class="section level3"> +<h3 id="sforb">SFORB<a class="anchor" aria-label="anchor" href="#sforb"></a> +</h3> +<div class="sourceCode" id="cb59"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">sforb_pH</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"SFORB"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_free_0"</span>, <span class="st">"log_k_meso_free_bound"</span><span class="op">)</span>,</span> +<span> covariates <span class="op">=</span> <span class="va">pH</span>,</span> +<span> covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_k_meso_free</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">log_k_meso_bound_free</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb60"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">sforb_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_free_0</td> +<td align="right">93.42</td> +<td align="right">91.32</td> +<td align="right">95.52</td> +</tr> +<tr class="even"> +<td align="left">log_k_meso_free</td> +<td align="right">-5.37</td> +<td align="right">-6.94</td> +<td align="right">-3.81</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_k_meso_free)</td> +<td align="right">0.42</td> +<td align="right">0.18</td> +<td align="right">0.67</td> +</tr> +<tr class="even"> +<td align="left">log_k_meso_free_bound</td> +<td align="right">-3.49</td> +<td align="right">-4.92</td> +<td align="right">-2.05</td> +</tr> +<tr class="odd"> +<td align="left">log_k_meso_bound_free</td> +<td align="right">-9.98</td> +<td align="right">-19.22</td> +<td align="right">-0.74</td> +</tr> +<tr class="even"> +<td align="left">beta_pH(log_k_meso_bound_free)</td> +<td align="right">1.23</td> +<td align="right">-0.21</td> +<td align="right">2.67</td> +</tr> +<tr class="odd"> +<td align="left">a.1</td> +<td align="right">4.90</td> +<td align="right">4.18</td> +<td align="right">5.63</td> +</tr> +<tr class="even"> +<td align="left">SD.log_k_meso_free</td> +<td align="right">0.35</td> +<td align="right">0.23</td> +<td align="right">0.47</td> +</tr> +<tr class="odd"> +<td align="left">SD.log_k_meso_bound_free</td> +<td align="right">0.13</td> +<td align="right">-1.95</td> +<td align="right">2.20</td> +</tr> +</tbody> +</table> +<p>The confidence interval of +<code>beta_pH(log_k_meso_bound_free)</code> includes zero, indicating +that the influence of soil pH on <code>k_meso_bound_free</code> cannot +reliably be quantified. Also, the confidence interval for the random +effect on this parameter (<code>SD.log_k_meso_bound_free</code>) +includes zero.</p> +<p>Using the <code>illparms</code> function, these ill-defined +parameters can be found more conveniently.</p> +<div class="sourceCode" id="cb61"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">sforb_pH</span><span class="op">)</span></span></code></pre></div> +<pre><code>[1] "sd(log_k_meso_bound_free)" "beta_pH(log_k_meso_bound_free)"</code></pre> +<p>To remove the ill-defined parameters, a second variant of the SFORB +model with pH influence is fitted. No ill-defined parameters remain.</p> +<div class="sourceCode" id="cb63"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">sforb_pH_2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">sforb_pH</span>,</span> +<span> no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_free_0"</span>, <span class="st">"log_k_meso_free_bound"</span>, <span class="st">"log_k_meso_bound_free"</span><span class="op">)</span>,</span> +<span> covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_k_meso_free</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">sforb_pH_2</span><span class="op">)</span></span></code></pre></div> +<p>The model comparison of the SFORB fits includes the refined model +without covariate effect, and both versions of the SFORB fit with +covariate effect.</p> +<div class="sourceCode" id="cb64"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"SFORB"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span>, <span class="va">sforb_pH</span>, <span class="va">sforb_pH_2</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets + + npar AIC BIC Lik Chisq Df Pr(>Chisq) +f_saem_2[["SFORB", "const"]] 7 783.40 789.63 -384.70 +sforb_pH_2 7 770.94 777.17 -378.47 12.4616 0 +sforb_pH 9 768.81 776.83 -375.41 6.1258 2 0.04675 * +--- +Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre> +<p>The first model including pH influence is preferable based on +information criteria and the likelihood ratio test. However, as it is +not fully identifiable, the second model is selected.</p> +<div class="sourceCode" id="cb66"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">sforb_pH_2</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_free_0</td> +<td align="right">93.32</td> +<td align="right">91.16</td> +<td align="right">95.48</td> +</tr> +<tr class="even"> +<td align="left">log_k_meso_free</td> +<td align="right">-6.15</td> +<td align="right">-7.43</td> +<td align="right">-4.86</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_k_meso_free)</td> +<td align="right">0.54</td> +<td align="right">0.33</td> +<td align="right">0.75</td> +</tr> +<tr class="even"> +<td align="left">log_k_meso_free_bound</td> +<td align="right">-3.80</td> +<td align="right">-5.20</td> +<td align="right">-2.40</td> +</tr> +<tr class="odd"> +<td align="left">log_k_meso_bound_free</td> +<td align="right">-2.95</td> +<td align="right">-4.26</td> +<td align="right">-1.64</td> +</tr> +<tr class="even"> +<td align="left">a.1</td> +<td align="right">5.08</td> +<td align="right">4.38</td> +<td align="right">5.79</td> +</tr> +<tr class="odd"> +<td align="left">SD.log_k_meso_free</td> +<td align="right">0.33</td> +<td align="right">0.22</td> +<td align="right">0.45</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb67"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">sforb_pH_2</span><span class="op">)</span></span></code></pre></div> +<p><img src="2023_mesotrione_parent_files/figure-html/unnamed-chunk-25-1.png" width="700" style="display: block; margin: auto;"></p> +<div class="sourceCode" id="cb68"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">sforb_pH_2</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +50% 5.75 + +$ff +meso_free + 1 + +$SFORB + meso_b1 meso_b2 meso_g +0.09735824 0.02631699 0.31602120 + +$distimes + DT50 DT90 DT50back DT50_meso_b1 DT50_meso_b2 +meso 16.86549 73.15824 22.02282 7.119554 26.33839</code></pre> +<div class="sourceCode" id="cb70"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">sforb_pH_2</span>, covariates <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>pH <span class="op">=</span> <span class="fl">7</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +User 7 + +$ff +meso_free + 1 + +$SFORB + meso_b1 meso_b2 meso_g +0.13315233 0.03795988 0.61186191 + +$distimes + DT50 DT90 DT50back DT50_meso_b1 DT50_meso_b2 +meso 7.932495 36.93311 11.11797 5.205671 18.26</code></pre> +</div> +<div class="section level3"> +<h3 id="hs">HS<a class="anchor" aria-label="anchor" href="#hs"></a> +</h3> +<div class="sourceCode" id="cb72"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">hs_pH</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"HS"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_0"</span><span class="op">)</span>,</span> +<span> covariates <span class="op">=</span> <span class="va">pH</span>,</span> +<span> covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_k1</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">log_k2</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">log_tb</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb73"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">hs_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_0</td> +<td align="right">93.33</td> +<td align="right">91.47</td> +<td align="right">95.19</td> +</tr> +<tr class="even"> +<td align="left">log_k1</td> +<td align="right">-5.81</td> +<td align="right">-7.27</td> +<td align="right">-4.36</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_k1)</td> +<td align="right">0.47</td> +<td align="right">0.23</td> +<td align="right">0.72</td> +</tr> +<tr class="even"> +<td align="left">log_k2</td> +<td align="right">-6.80</td> +<td align="right">-8.76</td> +<td align="right">-4.83</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_k2)</td> +<td align="right">0.54</td> +<td align="right">0.21</td> +<td align="right">0.87</td> +</tr> +<tr class="even"> +<td align="left">log_tb</td> +<td align="right">3.25</td> +<td align="right">1.25</td> +<td align="right">5.25</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_tb)</td> +<td align="right">-0.10</td> +<td align="right">-0.43</td> +<td align="right">0.23</td> +</tr> +<tr class="even"> +<td align="left">a.1</td> +<td align="right">4.49</td> +<td align="right">3.78</td> +<td align="right">5.21</td> +</tr> +<tr class="odd"> +<td align="left">SD.log_k1</td> +<td align="right">0.37</td> +<td align="right">0.24</td> +<td align="right">0.51</td> +</tr> +<tr class="even"> +<td align="left">SD.log_k2</td> +<td align="right">0.29</td> +<td align="right">0.10</td> +<td align="right">0.48</td> +</tr> +<tr class="odd"> +<td align="left">SD.log_tb</td> +<td align="right">0.25</td> +<td align="right">-0.07</td> +<td align="right">0.57</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb74"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">hs_pH</span><span class="op">)</span></span></code></pre></div> +<pre><code>[1] "sd(log_tb)" "beta_pH(log_tb)"</code></pre> +<p>According to the output of the <code>illparms</code> function, the +random effect on the break time <code>tb</code> cannot reliably be +quantified, neither can the influence of soil pH on <code>tb</code>. The +fit is repeated without the corresponding covariate model, and no +ill-defined parameters remain.</p> +<div class="sourceCode" id="cb76"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">hs_pH_2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">hs_pH</span>, covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_k1</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">log_k2</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">hs_pH_2</span><span class="op">)</span></span></code></pre></div> +<p>Model comparison confirms that this model is preferable to the fit +without covariate influence, and also to the first version with +covariate influence.</p> +<div class="sourceCode" id="cb77"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"HS"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span>, <span class="va">hs_pH</span>, <span class="va">hs_pH_2</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets + + npar AIC BIC Lik Chisq Df Pr(>Chisq) +f_saem_2[["HS", "const"]] 8 780.08 787.20 -382.04 +hs_pH_2 10 766.47 775.37 -373.23 17.606 2 0.0001503 *** +hs_pH 11 769.80 779.59 -373.90 0.000 1 1.0000000 +--- +Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre> +<div class="sourceCode" id="cb79"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">hs_pH_2</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_0</td> +<td align="right">93.33</td> +<td align="right">91.50</td> +<td align="right">95.15</td> +</tr> +<tr class="even"> +<td align="left">log_k1</td> +<td align="right">-5.68</td> +<td align="right">-7.09</td> +<td align="right">-4.27</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_k1)</td> +<td align="right">0.46</td> +<td align="right">0.22</td> +<td align="right">0.69</td> +</tr> +<tr class="even"> +<td align="left">log_k2</td> +<td align="right">-6.61</td> +<td align="right">-8.34</td> +<td align="right">-4.88</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_k2)</td> +<td align="right">0.50</td> +<td align="right">0.21</td> +<td align="right">0.79</td> +</tr> +<tr class="even"> +<td align="left">log_tb</td> +<td align="right">2.70</td> +<td align="right">2.33</td> +<td align="right">3.08</td> +</tr> +<tr class="odd"> +<td align="left">a.1</td> +<td align="right">4.45</td> +<td align="right">3.74</td> +<td align="right">5.16</td> +</tr> +<tr class="even"> +<td align="left">SD.log_k1</td> +<td align="right">0.36</td> +<td align="right">0.22</td> +<td align="right">0.49</td> +</tr> +<tr class="odd"> +<td align="left">SD.log_k2</td> +<td align="right">0.23</td> +<td align="right">0.02</td> +<td align="right">0.43</td> +</tr> +<tr class="even"> +<td align="left">SD.log_tb</td> +<td align="right">0.55</td> +<td align="right">0.25</td> +<td align="right">0.85</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb80"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">hs_pH_2</span><span class="op">)</span></span></code></pre></div> +<p><img src="2023_mesotrione_parent_files/figure-html/unnamed-chunk-30-1.png" width="700" style="display: block; margin: auto;"></p> +<div class="sourceCode" id="cb81"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">hs_pH_2</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +50% 5.75 + +$distimes + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 14.68725 82.45287 24.82079 14.68725 29.29299</code></pre> +<div class="sourceCode" id="cb83"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">hs_pH_2</span>, covariates <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>pH <span class="op">=</span> <span class="fl">7</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +User 7 + +$distimes + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 8.298536 38.85371 11.69613 8.298536 15.71561</code></pre> +</div> +<div class="section level3"> +<h3 id="comparison-across-parent-models">Comparison across parent models<a class="anchor" aria-label="anchor" href="#comparison-across-parent-models"></a> +</h3> +<p>After model reduction for all models with pH influence, they are +compared with each other.</p> +<div class="sourceCode" id="cb85"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">sfo_pH</span>, <span class="va">fomc_pH_2</span>, <span class="va">dfop_pH_2</span>, <span class="va">dfop_pH_4</span>, <span class="va">sforb_pH_2</span>, <span class="va">hs_pH_2</span><span class="op">)</span></span></code></pre></div> +<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets + + npar AIC BIC Lik +sfo_pH 5 783.09 787.54 -386.54 +fomc_pH_2 6 767.49 772.83 -377.75 +dfop_pH_4 7 767.35 773.58 -376.68 +sforb_pH_2 7 770.94 777.17 -378.47 +dfop_pH_2 8 765.14 772.26 -374.57 +hs_pH_2 10 766.47 775.37 -373.23</code></pre> +<p>The DFOP model with pH influence on <code>k2</code> and +<code>g</code> and a random effect only on <code>k2</code> is finally +selected as the best fit.</p> +<p>The endpoints resulting from this model are listed below. Please +refer to the Appendix for a detailed listing.</p> +<div class="sourceCode" id="cb87"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">dfop_pH_2</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +50% 5.75 + +$distimes + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 18.36876 73.51841 22.13125 4.191901 23.98672</code></pre> +<div class="sourceCode" id="cb89"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">dfop_pH_2</span>, covariates <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>pH <span class="op">=</span> <span class="fl">7</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +User 7 + +$distimes + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 8.346428 28.34437 8.532507 4.191901 8.753618</code></pre> +</div> +</div> +<div class="section level2"> +<h2 id="conclusions">Conclusions<a class="anchor" aria-label="anchor" href="#conclusions"></a> +</h2> +<p>These evaluations demonstrate that covariate effects can be included +for all types of parent degradation models. These models can then be +further refined to make them fully identifiable.</p> +</div> +<div class="section level2"> +<h2 id="appendix">Appendix<a class="anchor" aria-label="anchor" href="#appendix"></a> +</h2> +<div class="section level3"> +<h3 id="hierarchical-fit-listings">Hierarchical fit listings<a class="anchor" aria-label="anchor" href="#hierarchical-fit-listings"></a> +</h3> +<div class="section level4"> +<h4 id="fits-without-covariate-effects">Fits without covariate effects<a class="anchor" aria-label="anchor" href="#fits-without-covariate-effects"></a> +</h4> + +</div> +<div class="section level4"> +<h4 id="fits-with-covariate-effects">Fits with covariate effects<a class="anchor" aria-label="anchor" href="#fits-with-covariate-effects"></a> +</h4> + +</div> +</div> +<div class="section level3"> +<h3 id="session-info">Session info<a class="anchor" aria-label="anchor" href="#session-info"></a> +</h3> +<pre><code>R version 4.3.1 (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" 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