diff options
Diffstat (limited to 'docs/articles')
14 files changed, 7788 insertions, 16 deletions
diff --git a/docs/articles/index.html b/docs/articles/index.html index 5883e462..b70a25c4 100644 --- a/docs/articles/index.html +++ b/docs/articles/index.html @@ -28,7 +28,7 @@ <li><h6 class="dropdown-header" data-toc-skip>Example evaluations with hierarchical models (nonlinear mixed-effects models)</h6></li> <li><a class="dropdown-item" href="../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a></li> <li><a class="dropdown-item" href="../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a></li> - <li><a class="dropdown-item" href="../articles/prebuilt/2023_mesotrione_parent.html">Testing covariate modelling in hierarchical parent degradation kinetics with residue data on mesotrione</a></li> + <li><a class="dropdown-item" href="../articles/web_only/mesotrione_parent_2023.html">Testing covariate modelling in hierarchical parent degradation kinetics with residue data on mesotrione</a></li> <li><a class="dropdown-item" href="../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a></li> <li><a class="dropdown-item" href="../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a></li> <li><a class="dropdown-item" href="../articles/web_only/multistart.html">Short demo of the multistart method</a></li> @@ -68,8 +68,6 @@ <dd> </dd><dt><a href="prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a></dt> <dd> - </dd><dt><a href="prebuilt/2023_mesotrione_parent.html">Testing covariate modelling in hierarchical parent degradation kinetics with residue data on mesotrione</a></dt> - <dd> </dd><dt><a href="web_only/benchmarks.html">Benchmark timings for mkin</a></dt> <dd> </dd><dt><a href="web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a></dt> @@ -82,6 +80,8 @@ <dd> </dd><dt><a href="web_only/FOCUS_Z.html">Example evaluation of FOCUS dataset Z</a></dt> <dd> + </dd><dt><a href="web_only/mesotrione_parent_2023.html">Testing covariate modelling in hierarchical parent degradation kinetics with residue data on mesotrione</a></dt> + <dd> </dd><dt><a href="mkin.html">Short introduction to mkin</a></dt> <dd> </dd><dt><a href="web_only/multistart.html">Short demo of the multistart method</a></dt> diff --git a/docs/articles/web_only/benchmarks.html b/docs/articles/web_only/benchmarks.html index 52e657cb..8b16b8e1 100644 --- a/docs/articles/web_only/benchmarks.html +++ b/docs/articles/web_only/benchmarks.html @@ -43,7 +43,7 @@ <li><h6 class="dropdown-header" data-toc-skip>Example evaluations with hierarchical models (nonlinear mixed-effects models)</h6></li> <li><a class="dropdown-item" href="../../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a></li> <li><a class="dropdown-item" href="../../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a></li> - <li><a class="dropdown-item" href="../../articles/prebuilt/2023_mesotrione_parent.html">Testing covariate modelling in hierarchical parent degradation kinetics with residue data on mesotrione</a></li> + <li><a class="dropdown-item" href="../../articles/web_only/2023_mesotrione_parent.html">Testing covariate modelling in hierarchical parent degradation kinetics with residue data on mesotrione</a></li> <li><a class="dropdown-item" href="../../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a></li> <li><a class="dropdown-item" href="../../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a></li> <li><a class="dropdown-item" href="../../articles/web_only/multistart.html">Short demo of the multistart method</a></li> @@ -84,7 +84,7 @@ Ranke</h4> <h4 data-toc-skip class="date">Last change 17 February 2023 -(rebuilt 2025-05-12)</h4> +(rebuilt 2025-05-13)</h4> <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/benchmarks.rmd" class="external-link"><code>vignettes/web_only/benchmarks.rmd</code></a></small> <div class="d-none name"><code>benchmarks.rmd</code></div> @@ -435,8 +435,8 @@ models fitted to two datasets, i.e. eight fits for each test.</p> <td align="left">Ryzen 9 7950X</td> <td align="left">4.5.0</td> <td align="left">1.2.10</td> -<td align="right">1.370</td> -<td align="right">1.996</td> +<td align="right">1.355</td> +<td align="right">1.976</td> </tr> </tbody> </table> @@ -733,9 +733,9 @@ for each test.</p> <td align="left">Ryzen 9 7950X</td> <td align="left">4.5.0</td> <td align="left">1.2.10</td> -<td align="right">0.770</td> -<td align="right">2.184</td> -<td align="right">1.148</td> +<td align="right">0.774</td> +<td align="right">2.128</td> +<td align="right">1.095</td> </tr> </tbody> </table> @@ -1125,12 +1125,12 @@ dataset, i.e. one fit for each test.</p> <td align="left">Ryzen 9 7950X</td> <td align="left">4.5.0</td> <td align="left">1.2.10</td> -<td align="right">0.421</td> -<td align="right">0.536</td> -<td align="right">0.574</td> -<td align="right">1.315</td> -<td align="right">0.739</td> -<td align="right">0.997</td> +<td align="right">0.407</td> +<td align="right">0.519</td> +<td align="right">0.544</td> +<td align="right">1.266</td> +<td align="right">0.738</td> +<td align="right">0.977</td> </tr> </tbody> </table> diff --git a/docs/articles/web_only/mesotrione_parent_2023.html b/docs/articles/web_only/mesotrione_parent_2023.html new file mode 100644 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class="d-none name"><code>mesotrione_parent_2023.rmd</code></div> + </div> + + + +<div class="section level2"> +<h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#introduction"></a> +</h2> +<p>The purpose of this document is to test demonstrate how nonlinear +hierarchical models (NLHM) based on the parent degradation models SFO, +FOMC, DFOP and HS can be fitted with the mkin package, also considering +the influence of covariates like soil pH on different degradation +parameters. Because in some other case studies, the SFORB +parameterisation of biexponential decline has shown some advantages over +the DFOP parameterisation, SFORB was included in the list of tested +models as well.</p> +<p>The mkin package is used in version 1.2.10, which is contains the +functions that were used for the evaluations. The <code>saemix</code> +package is used as a backend for fitting the NLHM, but is also loaded to +make the convergence plot function available.</p> +<p>This document is processed with the <code>knitr</code> package, which +also provides the <code>kable</code> function that is used to improve +the display of tabular data in R markdown documents. For parallel +processing, the <code>parallel</code> package is used.</p> +<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://pkgdown.jrwb.de/mkin/">mkin</a></span><span class="op">)</span></span> +<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://yihui.org/knitr/" class="external-link">knitr</a></span><span class="op">)</span></span> +<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">saemix</span><span class="op">)</span></span> +<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">parallel</span><span class="op">)</span></span> +<span><span class="va">n_cores</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/detectCores.html" class="external-link">detectCores</a></span><span class="op">(</span><span class="op">)</span></span> +<span><span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/Sys.info.html" class="external-link">Sys.info</a></span><span class="op">(</span><span class="op">)</span><span class="op">[</span><span class="st">"sysname"</span><span class="op">]</span> <span class="op">==</span> <span class="st">"Windows"</span><span class="op">)</span> <span class="op">{</span></span> +<span> <span class="va">cl</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makePSOCKcluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> +<span><span class="op">}</span> <span class="kw">else</span> <span class="op">{</span></span> +<span> <span class="va">cl</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makeForkCluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> +<span><span class="op">}</span></span></code></pre></div> +<div class="section level3"> +<h3 id="test-data">Test data<a class="anchor" aria-label="anchor" href="#test-data"></a> +</h3> +<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">data_file</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.file.html" class="external-link">system.file</a></span><span class="op">(</span></span> +<span> <span class="st">"testdata"</span>, <span class="st">"mesotrione_soil_efsa_2016.xlsx"</span>, package <span class="op">=</span> <span class="st">"mkin"</span><span class="op">)</span></span> +<span><span class="va">meso_ds</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/read_spreadsheet.html">read_spreadsheet</a></span><span class="op">(</span><span class="va">data_file</span>, parent_only <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<p>The following tables show the covariate data and the 18 datasets that +were read in from the spreadsheet file.</p> +<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">pH</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/attr.html" class="external-link">attr</a></span><span class="op">(</span><span class="va">meso_ds</span>, <span class="st">"covariates"</span><span class="op">)</span></span> +<span><span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="va">pH</span>, caption <span class="op">=</span> <span class="st">"Covariate data"</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<caption>Covariate data</caption> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">pH</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">Richmond</td> +<td align="right">6.2</td> +</tr> +<tr class="even"> +<td align="left">Richmond 2</td> +<td align="right">6.2</td> +</tr> +<tr class="odd"> +<td align="left">ERTC</td> +<td align="right">6.4</td> +</tr> +<tr class="even"> +<td align="left">Toulouse</td> +<td align="right">7.7</td> +</tr> +<tr class="odd"> +<td align="left">Picket Piece</td> +<td align="right">7.1</td> +</tr> +<tr class="even"> +<td align="left">721</td> +<td align="right">5.6</td> +</tr> +<tr class="odd"> +<td align="left">722</td> +<td align="right">5.7</td> +</tr> +<tr class="even"> +<td align="left">723</td> +<td align="right">5.4</td> +</tr> +<tr class="odd"> +<td align="left">724</td> +<td align="right">4.8</td> +</tr> +<tr class="even"> +<td align="left">725</td> +<td align="right">5.8</td> +</tr> +<tr class="odd"> +<td align="left">727</td> +<td align="right">5.1</td> +</tr> +<tr class="even"> +<td align="left">728</td> +<td align="right">5.9</td> +</tr> +<tr class="odd"> +<td align="left">729</td> +<td align="right">5.6</td> +</tr> +<tr class="even"> +<td align="left">730</td> +<td align="right">5.3</td> +</tr> +<tr class="odd"> +<td align="left">731</td> +<td align="right">6.1</td> +</tr> +<tr class="even"> +<td align="left">732</td> +<td align="right">5.0</td> +</tr> +<tr class="odd"> +<td align="left">741</td> +<td align="right">5.7</td> +</tr> +<tr class="even"> +<td align="left">742</td> +<td align="right">7.2</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="kw">for</span> <span class="op">(</span><span class="va">ds_name</span> <span class="kw">in</span> <span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">meso_ds</span><span class="op">)</span><span class="op">)</span> <span class="op">{</span></span> +<span> <span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span></span> +<span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="fu"><a href="../../reference/mkin_long_to_wide.html">mkin_long_to_wide</a></span><span class="op">(</span><span class="va">meso_ds</span><span class="op">[[</span><span class="va">ds_name</span><span class="op">]</span><span class="op">]</span><span class="op">)</span>,</span> +<span> caption <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste</a></span><span class="op">(</span><span class="st">"Dataset"</span>, <span class="va">ds_name</span><span class="op">)</span>,</span> +<span> booktabs <span class="op">=</span> <span class="cn">TRUE</span>, row.names <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="op">}</span></span></code></pre></div> +<table class="table"> +<caption>Dataset Richmond</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">91.00</td> +</tr> +<tr class="even"> +<td align="right">1.179050</td> +<td align="right">86.70</td> +</tr> +<tr class="odd"> +<td align="right">3.537149</td> +<td align="right">73.60</td> +</tr> +<tr class="even"> +<td align="right">7.074299</td> +<td align="right">61.50</td> +</tr> +<tr class="odd"> +<td align="right">10.611448</td> +<td align="right">55.70</td> +</tr> +<tr class="even"> +<td align="right">15.327647</td> +<td align="right">47.70</td> +</tr> +<tr class="odd"> +<td align="right">17.685747</td> +<td align="right">39.50</td> +</tr> +<tr class="even"> +<td align="right">24.760046</td> +<td align="right">29.80</td> +</tr> +<tr class="odd"> +<td align="right">35.371494</td> +<td align="right">19.60</td> +</tr> +<tr class="even"> +<td align="right">68.384889</td> +<td align="right">5.67</td> +</tr> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">97.90</td> +</tr> +<tr class="even"> +<td align="right">1.179050</td> +<td align="right">96.40</td> +</tr> +<tr class="odd"> +<td align="right">3.537149</td> +<td align="right">89.10</td> +</tr> +<tr class="even"> +<td align="right">7.074299</td> +<td align="right">74.40</td> +</tr> +<tr class="odd"> +<td align="right">10.611448</td> +<td align="right">57.40</td> +</tr> +<tr class="even"> +<td align="right">15.327647</td> +<td align="right">46.30</td> +</tr> +<tr class="odd"> +<td align="right">18.864797</td> +<td align="right">35.50</td> +</tr> +<tr class="even"> +<td align="right">27.118146</td> +<td align="right">27.20</td> +</tr> +<tr class="odd"> +<td align="right">35.371494</td> +<td align="right">19.10</td> +</tr> +<tr class="even"> +<td align="right">74.280138</td> +<td align="right">6.50</td> +</tr> +<tr class="odd"> +<td align="right">108.472582</td> +<td align="right">3.40</td> +</tr> +<tr class="even"> +<td align="right">142.665027</td> +<td align="right">2.20</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset Richmond 2</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">96.0</td> +</tr> +<tr class="even"> +<td align="right">2.422004</td> +<td align="right">82.4</td> +</tr> +<tr class="odd"> +<td align="right">5.651343</td> +<td align="right">71.2</td> +</tr> +<tr class="even"> +<td align="right">8.073348</td> +<td align="right">53.1</td> +</tr> +<tr class="odd"> +<td align="right">11.302687</td> +<td align="right">48.5</td> +</tr> +<tr class="even"> +<td align="right">16.954030</td> +<td align="right">33.4</td> +</tr> +<tr class="odd"> +<td align="right">22.605373</td> +<td align="right">24.2</td> +</tr> +<tr class="even"> +<td align="right">45.210746</td> +<td align="right">11.9</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset ERTC</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">99.9</td> +</tr> +<tr class="even"> +<td align="right">2.755193</td> +<td align="right">80.0</td> +</tr> +<tr class="odd"> +<td align="right">6.428782</td> +<td align="right">42.1</td> +</tr> +<tr class="even"> +<td align="right">9.183975</td> +<td align="right">50.1</td> +</tr> +<tr class="odd"> +<td align="right">12.857565</td> +<td align="right">28.4</td> +</tr> +<tr class="even"> +<td align="right">19.286347</td> +<td align="right">39.8</td> +</tr> +<tr class="odd"> +<td align="right">25.715130</td> +<td align="right">29.9</td> +</tr> +<tr class="even"> +<td align="right">51.430259</td> +<td align="right">2.5</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset Toulouse</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">96.8</td> +</tr> +<tr class="even"> +<td align="right">2.897983</td> +<td align="right">63.3</td> +</tr> +<tr class="odd"> +<td align="right">6.761960</td> +<td align="right">22.3</td> +</tr> +<tr class="even"> +<td align="right">9.659942</td> +<td align="right">16.6</td> +</tr> +<tr class="odd"> +<td align="right">13.523919</td> +<td align="right">16.1</td> +</tr> +<tr class="even"> +<td align="right">20.285879</td> +<td align="right">17.2</td> +</tr> +<tr class="odd"> +<td align="right">27.047838</td> +<td align="right">1.8</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset Picket Piece</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">102.0</td> +</tr> +<tr class="even"> +<td align="right">2.841195</td> +<td align="right">73.7</td> +</tr> +<tr class="odd"> +<td align="right">6.629454</td> +<td align="right">35.5</td> +</tr> +<tr class="even"> +<td align="right">9.470649</td> +<td align="right">31.8</td> +</tr> +<tr class="odd"> +<td align="right">13.258909</td> +<td align="right">18.0</td> +</tr> +<tr class="even"> +<td align="right">19.888364</td> +<td align="right">3.7</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 721</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">86.4</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">61.4</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">49.8</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">41.0</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">35.1</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 722</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">90.3</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">52.1</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">37.4</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">21.2</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">14.3</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 723</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">89.3</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">70.8</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">51.1</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">42.7</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">26.7</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 724</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">89.4</td> +</tr> +<tr class="even"> +<td align="right">9.008208</td> +<td align="right">65.2</td> +</tr> +<tr class="odd"> +<td align="right">18.016415</td> +<td align="right">55.8</td> +</tr> +<tr class="even"> +<td align="right">27.024623</td> +<td align="right">46.0</td> +</tr> +<tr class="odd"> +<td align="right">36.032831</td> +<td align="right">41.7</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 725</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">89.0</td> +</tr> +<tr class="even"> +<td align="right">10.99058</td> +<td align="right">35.4</td> +</tr> +<tr class="odd"> +<td align="right">21.98116</td> +<td align="right">18.6</td> +</tr> +<tr class="even"> +<td align="right">32.97174</td> +<td align="right">11.6</td> +</tr> +<tr class="odd"> +<td align="right">43.96232</td> +<td align="right">7.6</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 727</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">91.3</td> +</tr> +<tr class="even"> +<td align="right">10.96104</td> +<td align="right">63.2</td> +</tr> +<tr class="odd"> +<td align="right">21.92209</td> +<td align="right">51.1</td> +</tr> +<tr class="even"> +<td align="right">32.88313</td> +<td align="right">42.0</td> +</tr> +<tr class="odd"> +<td align="right">43.84417</td> +<td align="right">40.8</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 728</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">91.8</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">43.6</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">22.0</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">15.9</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">8.8</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 729</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">91.6</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">60.5</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">43.5</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">28.4</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">20.5</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 730</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">92.7</td> +</tr> +<tr class="even"> +<td align="right">11.07446</td> +<td align="right">58.9</td> +</tr> +<tr class="odd"> +<td align="right">22.14893</td> +<td align="right">44.0</td> +</tr> +<tr class="even"> +<td align="right">33.22339</td> +<td align="right">46.0</td> +</tr> +<tr class="odd"> +<td align="right">44.29785</td> +<td align="right">29.3</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 731</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">92.1</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">64.4</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">45.3</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">33.6</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">23.5</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 732</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">90.3</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">58.2</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">40.1</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">33.1</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">25.8</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 741</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">90.3</td> +</tr> +<tr class="even"> +<td align="right">10.84712</td> +<td align="right">68.7</td> +</tr> +<tr class="odd"> +<td align="right">21.69424</td> +<td align="right">58.0</td> +</tr> +<tr class="even"> +<td align="right">32.54136</td> +<td align="right">52.2</td> +</tr> +<tr class="odd"> +<td align="right">43.38848</td> +<td align="right">48.0</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 742</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">92.0</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">60.9</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">36.2</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">18.3</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">8.7</td> +</tr> +</tbody> +</table> +</div> +</div> +<div class="section level2"> +<h2 id="separate-evaluations">Separate evaluations<a class="anchor" aria-label="anchor" href="#separate-evaluations"></a> +</h2> +<p>In order to obtain suitable starting parameters for the NLHM fits, +separate fits of the five models to the data for each soil are generated +using the <code>mmkin</code> function from the mkin package. In a first +step, constant variance is assumed. Convergence is checked with the +<code>status</code> function.</p> +<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">deg_mods</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>, <span class="st">"SFORB"</span>, <span class="st">"HS"</span><span class="op">)</span></span> +<span><span class="va">f_sep_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span></span> +<span> <span class="va">deg_mods</span>,</span> +<span> <span class="va">meso_ds</span>,</span> +<span> error_model <span class="op">=</span> <span class="st">"const"</span>,</span> +<span> cluster <span class="op">=</span> <span class="va">cl</span>,</span> +<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span>, <span class="fl">1</span><span class="op">:</span><span class="fl">5</span><span class="op">]</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">Richmond</th> +<th align="left">Richmond 2</th> +<th align="left">ERTC</th> +<th align="left">Toulouse</th> +<th align="left">Picket Piece</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span>, <span class="fl">6</span><span class="op">:</span><span class="fl">18</span><span class="op">]</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<colgroup> +<col width="10%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +</colgroup> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">721</th> +<th align="left">722</th> +<th align="left">723</th> +<th align="left">724</th> +<th align="left">725</th> +<th align="left">727</th> +<th align="left">728</th> +<th align="left">729</th> +<th align="left">730</th> +<th align="left">731</th> +<th align="left">732</th> +<th align="left">741</th> +<th align="left">742</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<p>In the tables above, OK indicates convergence and C indicates failure +to converge. Most separate fits with constant variance converged, with +the exception of two FOMC fits, one SFORB fit and one HS fit.</p> +<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">f_sep_tc</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_sep_const</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_tc</span><span class="op">[</span>, <span class="fl">1</span><span class="op">:</span><span class="fl">5</span><span class="op">]</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">Richmond</th> +<th align="left">Richmond 2</th> +<th align="left">ERTC</th> +<th align="left">Toulouse</th> +<th align="left">Picket Piece</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_tc</span><span class="op">[</span>, <span class="fl">6</span><span class="op">:</span><span class="fl">18</span><span class="op">]</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<colgroup> +<col width="10%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +</colgroup> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">721</th> +<th align="left">722</th> +<th align="left">723</th> +<th align="left">724</th> +<th align="left">725</th> +<th align="left">727</th> +<th align="left">728</th> +<th align="left">729</th> +<th align="left">730</th> +<th align="left">731</th> +<th align="left">732</th> +<th align="left">741</th> +<th align="left">742</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<p>With the two-component error model, the set of fits that did not +converge is larger, with convergence problems appearing for a number of +non-SFO fits.</p> +</div> +<div class="section level2"> +<h2 id="hierarchical-models-without-covariate">Hierarchical models without covariate<a class="anchor" aria-label="anchor" href="#hierarchical-models-without-covariate"></a> +</h2> +<p>The following code fits hierarchical kinetic models for the ten +combinations of the five different degradation models with the two +different error models in parallel.</p> +<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">f_saem_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mhmkin.html">mhmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">f_sep_const</span>, <span class="va">f_sep_tc</span><span class="op">)</span>, cluster <span class="op">=</span> <span class="va">cl</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<p>All fits terminate without errors (status OK).</p> +<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">npar</th> +<th align="right">AIC</th> +<th align="right">BIC</th> +<th align="right">Lik</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO const</td> +<td align="right">5</td> +<td align="right">800.0</td> +<td align="right">804.5</td> +<td align="right">-395.0</td> +</tr> +<tr class="even"> +<td align="left">SFO tc</td> +<td align="right">6</td> +<td align="right">801.9</td> +<td align="right">807.2</td> +<td align="right">-394.9</td> +</tr> +<tr class="odd"> +<td align="left">FOMC const</td> +<td align="right">7</td> +<td align="right">787.4</td> +<td align="right">793.6</td> +<td align="right">-386.7</td> +</tr> +<tr class="even"> +<td align="left">FOMC tc</td> +<td align="right">8</td> +<td align="right">788.9</td> +<td align="right">796.1</td> +<td align="right">-386.5</td> +</tr> +<tr class="odd"> +<td align="left">DFOP const</td> +<td align="right">9</td> +<td align="right">787.6</td> +<td align="right">795.6</td> +<td align="right">-384.8</td> +</tr> +<tr class="even"> +<td align="left">SFORB const</td> +<td align="right">9</td> +<td align="right">787.4</td> +<td align="right">795.4</td> +<td align="right">-384.7</td> +</tr> +<tr class="odd"> +<td align="left">HS const</td> +<td align="right">9</td> +<td align="right">781.9</td> +<td align="right">789.9</td> +<td align="right">-382.0</td> +</tr> +<tr class="even"> +<td align="left">DFOP tc</td> +<td align="right">10</td> +<td align="right">787.4</td> +<td align="right">796.3</td> +<td align="right">-383.7</td> +</tr> +<tr class="odd"> +<td align="left">SFORB tc</td> +<td align="right">10</td> +<td align="right">795.8</td> +<td align="right">804.7</td> +<td align="right">-387.9</td> +</tr> +<tr class="even"> +<td align="left">HS tc</td> +<td align="right">10</td> +<td align="right">783.7</td> +<td align="right">792.7</td> +<td align="right">-381.9</td> +</tr> +</tbody> +</table> +<p>The model comparisons show that the fits with constant variance are +consistently preferable to the corresponding fits with two-component +error for these data. This is confirmed by the fact that the parameter +<code>b.1</code> (the relative standard deviation in the fits obtained +with the saemix package), is ill-defined in all fits.</p> +<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<colgroup> +<col width="6%"> +<col width="44%"> +<col width="49%"> +</colgroup> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">sd(meso_0)</td> +<td align="left">sd(meso_0), b.1</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">sd(meso_0), sd(log_beta)</td> +<td align="left">sd(meso_0), sd(log_beta), b.1</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">sd(meso_0), sd(log_k1)</td> +<td align="left">sd(meso_0), sd(g_qlogis), b.1</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">sd(meso_free_0), sd(log_k_meso_free_bound)</td> +<td align="left">sd(meso_free_0), sd(log_k_meso_free_bound), b.1</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">sd(meso_0)</td> +<td align="left">sd(meso_0), b.1</td> +</tr> +</tbody> +</table> +<p>For obtaining fits with only well-defined random effects, we update +the set of fits, excluding random effects that were ill-defined +according to the <code>illparms</code> function.</p> +<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">f_saem_2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_saem_1</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<p>The updated fits terminate without errors.</p> +<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left"></td> +<td align="left">b.1</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left"></td> +<td align="left">b.1</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left"></td> +<td align="left">b.1</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left"></td> +<td align="left">b.1</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left"></td> +<td align="left">b.1</td> +</tr> +</tbody> +</table> +<p>No ill-defined errors remain in the fits with constant variance.</p> +</div> +<div class="section level2"> +<h2 id="hierarchical-models-with-covariate">Hierarchical models with covariate<a class="anchor" aria-label="anchor" href="#hierarchical-models-with-covariate"></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="mesotrione_parent_2023_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="mesotrione_parent_2023_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="mesotrione_parent_2023_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="mesotrione_parent_2023_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="mesotrione_parent_2023_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> +<caption> +Hierarchical SFO fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Wed May 14 05:12:46 2025 +Date of summary: Wed May 14 05:13:35 2025 + +Equations: +d_meso/dt = - k_meso * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 0.71 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_k_meso + 90.832 -3.192 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k_meso +meso_0 6.752 0.0000 +log_k_meso 0.000 0.9155 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 800 804.5 -395 + +Optimised parameters: + est. lower upper +meso_0 92.0705 89.9917 94.1493 +log_k_meso -3.1641 -3.4286 -2.8996 +a.1 5.4628 4.6421 6.2835 +SD.meso_0 0.0611 -98.3545 98.4767 +SD.log_k_meso 0.5616 0.3734 0.7499 + +Correlation: + meso_0 +log_k_meso 0.1132 + +Random effects: + est. lower upper +SD.meso_0 0.0611 -98.3545 98.4767 +SD.log_k_meso 0.5616 0.3734 0.7499 + +Variance model: + est. lower upper +a.1 5.463 4.642 6.284 + +Backtransformed parameters: + est. lower upper +meso_0 92.07053 89.99172 94.14933 +k_meso 0.04225 0.03243 0.05505 + +Estimated disappearance times: + DT50 DT90 +meso 16.41 54.5 + +</code></pre> +<p></p> +<caption> +Hierarchical FOMC fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Wed May 14 05:12:46 2025 +Date of summary: Wed May 14 05:13:35 2025 + +Equations: +d_meso/dt = - (alpha/beta) * 1/((time/beta) + 1) * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 0.842 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_alpha log_beta + 93.0520 0.6008 3.4176 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_alpha log_beta +meso_0 6.287 0.00 0.000 +log_alpha 0.000 1.53 0.000 +log_beta 0.000 0.00 1.724 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 787.4 793.6 -386.7 + +Optimised parameters: + est. lower upper +meso_0 93.5648 91.42864 95.7009 +log_alpha 0.7645 0.28068 1.2484 +log_beta 3.6597 3.05999 4.2594 +a.1 5.0708 4.29823 5.8435 +SD.meso_0 0.1691 -34.01517 34.3535 +SD.log_alpha 0.3764 0.05834 0.6945 +SD.log_beta 0.3903 -0.06074 0.8414 + +Correlation: + meso_0 log_lph +log_alpha -0.2839 +log_beta -0.3443 0.8855 + +Random effects: + est. lower upper +SD.meso_0 0.1691 -34.01517 34.3535 +SD.log_alpha 0.3764 0.05834 0.6945 +SD.log_beta 0.3903 -0.06074 0.8414 + +Variance model: + est. lower upper +a.1 5.071 4.298 5.843 + +Backtransformed parameters: + est. lower upper +meso_0 93.565 91.429 95.701 +alpha 2.148 1.324 3.485 +beta 38.850 21.327 70.770 + +Estimated disappearance times: + DT50 DT90 DT50back +meso 14.8 74.64 22.47 + +</code></pre> +<p></p> +<caption> +Hierarchical DFOP fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Wed May 14 05:12:47 2025 +Date of summary: Wed May 14 05:13:35 2025 + +Equations: +d_meso/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * + time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) + * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 1.168 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_k1 log_k2 g_qlogis +93.14689 -2.05241 -3.53079 -0.09522 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k1 log_k2 g_qlogis +meso_0 6.418 0.000 0.000 0.00 +log_k1 0.000 1.018 0.000 0.00 +log_k2 0.000 0.000 1.694 0.00 +g_qlogis 0.000 0.000 0.000 2.37 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 787.6 795.6 -384.8 + +Optimised parameters: + est. lower upper +meso_0 93.6684 91.63599 95.7008 +log_k1 -1.7354 -2.61433 -0.8565 +log_k2 -3.4015 -3.73323 -3.0697 +g_qlogis -1.6341 -2.66133 -0.6069 +a.1 4.7803 4.01269 5.5479 +SD.meso_0 0.1661 -30.97086 31.3031 +SD.log_k1 0.1127 -2.59680 2.8223 +SD.log_k2 0.6394 0.41499 0.8638 +SD.g_qlogis 0.8166 0.09785 1.5353 + +Correlation: + meso_0 log_k1 log_k2 +log_k1 0.1757 +log_k2 0.0199 0.2990 +g_qlogis 0.0813 -0.7431 -0.3826 + +Random effects: + est. lower upper +SD.meso_0 0.1661 -30.97086 31.3031 +SD.log_k1 0.1127 -2.59680 2.8223 +SD.log_k2 0.6394 0.41499 0.8638 +SD.g_qlogis 0.8166 0.09785 1.5353 + +Variance model: + est. lower upper +a.1 4.78 4.013 5.548 + +Backtransformed parameters: + est. lower upper +meso_0 93.66841 91.63599 95.70082 +k1 0.17633 0.07322 0.42466 +k2 0.03332 0.02392 0.04643 +g 0.16327 0.06529 0.35277 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 16.04 63.75 19.19 3.931 20.8 + +</code></pre> +<p></p> +<caption> +Hierarchical SFORB fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Wed May 14 05:12:47 2025 +Date of summary: Wed May 14 05:13:35 2025 + +Equations: +d_meso_free/dt = - k_meso_free * meso_free - k_meso_free_bound * + meso_free + k_meso_bound_free * meso_bound +d_meso_bound/dt = + k_meso_free_bound * meso_free - k_meso_bound_free * + meso_bound + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 1.256 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_free_0 log_k_meso_free log_k_meso_free_bound + 93.147 -2.305 -4.230 +log_k_meso_bound_free + -3.761 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_free_0 log_k_meso_free log_k_meso_free_bound +meso_free_0 6.418 0.0000 0.000 +log_k_meso_free 0.000 0.9276 0.000 +log_k_meso_free_bound 0.000 0.0000 2.272 +log_k_meso_bound_free 0.000 0.0000 0.000 + log_k_meso_bound_free +meso_free_0 0.000 +log_k_meso_free 0.000 +log_k_meso_free_bound 0.000 +log_k_meso_bound_free 1.447 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 787.4 795.4 -384.7 + +Optimised parameters: + est. lower upper +meso_free_0 93.6285 91.6262 95.631 +log_k_meso_free -2.8314 -3.1375 -2.525 +log_k_meso_free_bound -3.2213 -4.4695 -1.973 +log_k_meso_bound_free -2.4246 -3.5668 -1.282 +a.1 4.7372 3.9542 5.520 +SD.meso_free_0 0.1634 -32.7769 33.104 +SD.log_k_meso_free 0.4885 0.3080 0.669 +SD.log_k_meso_free_bound 0.2876 -1.7955 2.371 +SD.log_k_meso_bound_free 0.9942 0.2181 1.770 + +Correlation: + ms_fr_0 lg_k_m_ lg_k_ms_f_ +log_k_meso_free 0.2332 +log_k_meso_free_bound 0.1100 0.5964 +log_k_meso_bound_free -0.0413 0.3697 0.8025 + +Random effects: + est. lower upper +SD.meso_free_0 0.1634 -32.7769 33.104 +SD.log_k_meso_free 0.4885 0.3080 0.669 +SD.log_k_meso_free_bound 0.2876 -1.7955 2.371 +SD.log_k_meso_bound_free 0.9942 0.2181 1.770 + +Variance model: + est. lower upper +a.1 4.737 3.954 5.52 + +Backtransformed parameters: + est. lower upper +meso_free_0 93.62849 91.62622 95.63075 +k_meso_free 0.05893 0.04339 0.08004 +k_meso_free_bound 0.03990 0.01145 0.13903 +k_meso_bound_free 0.08851 0.02825 0.27736 + +Estimated Eigenvalues of SFORB model(s): +meso_b1 meso_b2 meso_g +0.15333 0.03402 0.20881 + +Resulting formation fractions: + ff +meso_free 1 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_meso_b1 DT50_meso_b2 +meso 14.79 60.81 18.3 4.521 20.37 + +</code></pre> +<p></p> +<caption> +Hierarchical HS fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Wed May 14 05:12:48 2025 +Date of summary: Wed May 14 05:13:35 2025 + +Equations: +d_meso/dt = - ifelse(time <= tb, k1, k2) * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 1.653 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: +meso_0 log_k1 log_k2 log_tb +92.920 -2.409 -3.295 2.471 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k1 log_k2 log_tb +meso_0 6.477 0.0000 0.0000 0.00 +log_k1 0.000 0.8675 0.0000 0.00 +log_k2 0.000 0.0000 0.4035 0.00 +log_tb 0.000 0.0000 0.0000 1.16 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 781.9 789.9 -382 + +Optimised parameters: + est. lower upper +meso_0 93.34242 91.4730 95.2118 +log_k1 -2.77312 -3.0826 -2.4637 +log_k2 -3.61854 -3.8430 -3.3941 +log_tb 2.00266 1.3357 2.6696 +a.1 4.47693 3.7059 5.2479 +SD.meso_0 0.07963 -63.1661 63.3253 +SD.log_k1 0.47817 0.2467 0.7097 +SD.log_k2 0.39216 0.2137 0.5706 +SD.log_tb 0.94683 0.4208 1.4728 + +Correlation: + meso_0 log_k1 log_k2 +log_k1 0.1627 +log_k2 0.0063 -0.0301 +log_tb 0.0083 -0.3931 -0.1225 + +Random effects: + est. lower upper +SD.meso_0 0.07963 -63.1661 63.3253 +SD.log_k1 0.47817 0.2467 0.7097 +SD.log_k2 0.39216 0.2137 0.5706 +SD.log_tb 0.94683 0.4208 1.4728 + +Variance model: + est. lower upper +a.1 4.477 3.706 5.248 + +Backtransformed parameters: + est. lower upper +meso_0 93.34242 91.47303 95.21181 +k1 0.06247 0.04584 0.08512 +k2 0.02682 0.02143 0.03357 +tb 7.40872 3.80282 14.43376 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 16 76 22.88 11.1 25.84 + +</code></pre> +<p></p> +</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> +<caption> +Hierarchichal SFO fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Wed May 14 05:13:00 2025 +Date of summary: Wed May 14 05:13:35 2025 + +Equations: +d_meso/dt = - k_meso * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 1.343 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_k_meso + 90.832 -3.192 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k_meso +meso_0 6.752 0.0000 +log_k_meso 0.000 0.9155 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 783.1 787.5 -386.5 + +Optimised parameters: + est. lower upper +meso_0 91.3481 89.2688 93.4275 +log_k_meso -6.6614 -7.9715 -5.3514 +beta_pH(log_k_meso) 0.5871 0.3684 0.8059 +a.1 5.4750 4.7085 6.2415 +SD.log_k_meso 0.3471 0.2258 0.4684 + +Correlation: + meso_0 lg_k_ms +log_k_meso 0.0414 +beta_pH(log_k_meso) -0.0183 -0.9917 + +Random effects: + est. lower upper +SD.log_k_meso 0.3471 0.2258 0.4684 + +Variance model: + est. lower upper +a.1 5.475 4.709 6.242 + +Backtransformed parameters: + est. lower upper +meso_0 91.348139 8.927e+01 93.427476 +k_meso 0.001279 3.452e-04 0.004741 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated disappearance times: + DT50 DT90 +meso 18.52 61.52 + +</code></pre> +<p></p> +<caption> +Hierarchichal FOMC fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Wed May 14 05:13:03 2025 +Date of summary: Wed May 14 05:13:35 2025 + +Equations: +d_meso/dt = - (alpha/beta) * 1/((time/beta) + 1) * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 1.897 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_alpha log_beta + 93.0520 0.6008 3.4176 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_alpha log_beta +meso_0 6.287 0.00 0.000 +log_alpha 0.000 1.53 0.000 +log_beta 0.000 0.00 1.724 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 770.1 776.3 -378 + +Optimised parameters: + est. lower upper +meso_0 92.840646 90.750461 94.9308 +log_alpha -2.206602 -3.494546 -0.9187 +beta_pH(log_alpha) 0.577505 0.369805 0.7852 +log_beta 4.214099 3.438851 4.9893 +a.1 5.027768 4.322028 5.7335 +SD.log_alpha 0.004034 -23.766993 23.7751 +SD.log_beta 0.374640 0.009252 0.7400 + +Correlation: + meso_0 log_lph bt_H(_) +log_alpha -0.0865 +beta_pH(log_alpha) -0.0789 -0.8704 +log_beta -0.3544 0.3302 0.1628 + +Random effects: + est. lower upper +SD.log_alpha 0.004034 -23.766993 23.78 +SD.log_beta 0.374640 0.009252 0.74 + +Variance model: + est. lower upper +a.1 5.028 4.322 5.734 + +Backtransformed parameters: + est. lower upper +meso_0 92.8406 90.75046 94.9308 +alpha 0.1101 0.03036 0.3991 +beta 67.6332 31.15113 146.8404 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated disappearance times: + DT50 DT90 DT50back +meso 17.28 76.37 22.99 + +</code></pre> +<p></p> +<caption> +Refined hierarchichal FOMC fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Wed May 14 05:13:08 2025 +Date of summary: Wed May 14 05:13:35 2025 + +Equations: +d_meso/dt = - (alpha/beta) * 1/((time/beta) + 1) * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 4.184 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_alpha log_beta + 93.0520 0.6008 3.4176 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_alpha log_beta +meso_0 6.287 0.00 0.000 +log_alpha 0.000 1.53 0.000 +log_beta 0.000 0.00 1.724 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 767.5 772.8 -377.7 + +Optimised parameters: + est. lower upper +meso_0 93.0536 90.9771 95.1300 +log_alpha -2.9054 -4.1803 -1.6304 +beta_pH(log_alpha) 0.6590 0.4437 0.8744 +log_beta 3.9549 3.2860 4.6239 +a.1 4.9784 4.2815 5.6754 +SD.log_beta 0.4019 0.2632 0.5406 + +Correlation: + meso_0 log_lph bt_H(_) +log_alpha -0.0397 +beta_pH(log_alpha) -0.0899 -0.9146 +log_beta -0.3473 0.2038 0.1919 + +Random effects: + est. lower upper +SD.log_beta 0.4019 0.2632 0.5406 + +Variance model: + est. lower upper +a.1 4.978 4.281 5.675 + +Backtransformed parameters: + est. lower upper +meso_0 93.05359 90.97713 95.1300 +alpha 0.05473 0.01529 0.1958 +beta 52.19251 26.73597 101.8874 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated disappearance times: + DT50 DT90 DT50back +meso 17.3 82.91 24.96 + +</code></pre> +<p></p> +<caption> +Hierarchichal DFOP fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Wed May 14 05:13:11 2025 +Date of summary: Wed May 14 05:13:35 2025 + +Equations: +d_meso/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * + time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) + * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 2.18 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_k1 log_k2 g_qlogis +93.14689 -2.05241 -3.53079 -0.09522 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k1 log_k2 g_qlogis +meso_0 6.418 0.000 0.000 0.00 +log_k1 0.000 1.018 0.000 0.00 +log_k2 0.000 0.000 1.694 0.00 +g_qlogis 0.000 0.000 0.000 2.37 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 769.1 777.1 -375.5 + +Optimised parameters: + est. lower upper +meso_0 92.843344 90.8464 94.84028 +log_k1 -2.815685 -3.0888 -2.54261 +log_k2 -11.479779 -15.3203 -7.63923 +beta_pH(log_k2) 1.308417 0.6948 1.92203 +g_qlogis 3.133036 0.4657 5.80035 +beta_pH(g_qlogis) -0.565988 -1.0394 -0.09262 +a.1 4.955518 4.2597 5.65135 +SD.log_k2 0.758963 0.4685 1.04943 +SD.g_qlogis 0.005215 -9.9561 9.96656 + +Correlation: + meso_0 log_k1 log_k2 b_H(_2) g_qlogs +log_k1 0.2706 +log_k2 -0.0571 0.1096 +beta_pH(log_k2) 0.0554 -0.1291 -0.9937 +g_qlogis -0.1125 -0.5062 -0.1305 0.1294 +beta_pH(g_qlogis) 0.1267 0.4226 0.0419 -0.0438 -0.9864 + +Random effects: + est. lower upper +SD.log_k2 0.758963 0.4685 1.049 +SD.g_qlogis 0.005215 -9.9561 9.967 + +Variance model: + est. lower upper +a.1 4.956 4.26 5.651 + +Backtransformed parameters: + est. lower upper +meso_0 9.284e+01 9.085e+01 9.484e+01 +k1 5.986e-02 4.556e-02 7.866e-02 +k2 1.034e-05 2.221e-07 4.812e-04 +g 9.582e-01 6.144e-01 9.970e-01 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 20.23 88.45 26.62 11.58 36.23 + +</code></pre> +<p></p> +<caption> +Refined hierarchical DFOP fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Wed May 14 05:13:14 2025 +Date of summary: Wed May 14 05:13:35 2025 + +Equations: +d_meso/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * + time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) + * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 2.424 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_k1 log_k2 g_qlogis +93.14689 -2.05241 -3.53079 -0.09522 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k1 log_k2 g_qlogis +meso_0 6.418 0.000 0.000 0.00 +log_k1 0.000 1.018 0.000 0.00 +log_k2 0.000 0.000 1.694 0.00 +g_qlogis 0.000 0.000 0.000 2.37 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 765.1 772.3 -374.6 + +Optimised parameters: + est. lower upper +meso_0 93.3333 91.2427 95.42394 +log_k1 -1.7997 -2.9124 -0.68698 +log_k2 -8.1810 -10.1819 -6.18008 +beta_pH(log_k2) 0.8064 0.4903 1.12257 +g_qlogis 3.3513 -1.1792 7.88182 +beta_pH(g_qlogis) -0.8672 -1.7661 0.03177 +a.1 4.9158 4.2277 5.60390 +SD.log_k2 0.3946 0.2565 0.53281 + +Correlation: + meso_0 log_k1 log_k2 b_H(_2) g_qlogs +log_k1 0.1730 +log_k2 0.0442 0.5370 +beta_pH(log_k2) -0.0392 -0.4880 -0.9923 +g_qlogis -0.1536 0.1431 -0.1129 0.1432 +beta_pH(g_qlogis) 0.1504 -0.3151 -0.0196 -0.0212 -0.9798 + +Random effects: + est. lower upper +SD.log_k2 0.3946 0.2565 0.5328 + +Variance model: + est. lower upper +a.1 4.916 4.228 5.604 + +Backtransformed parameters: + est. lower upper +meso_0 9.333e+01 9.124e+01 95.42394 +k1 1.654e-01 5.435e-02 0.50309 +k2 2.799e-04 3.785e-05 0.00207 +g 9.661e-01 2.352e-01 0.99962 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 18.37 73.52 22.13 4.192 23.99 + +</code></pre> +<p></p> +<caption> +Further refined hierarchical DFOP fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Wed May 14 05:13:23 2025 +Date of summary: Wed May 14 05:13:35 2025 + +Equations: +d_meso/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * + time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) + * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 3.211 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_k1 log_k2 g_qlogis +93.14689 -2.05241 -3.53079 -0.09522 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k1 log_k2 g_qlogis +meso_0 6.418 0.000 0.000 0.00 +log_k1 0.000 1.018 0.000 0.00 +log_k2 0.000 0.000 1.694 0.00 +g_qlogis 0.000 0.000 0.000 2.37 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 767.4 773.6 -376.7 + +Optimised parameters: + est. lower upper +meso_0 93.3011 91.1905 95.4118 +log_k1 -2.1487 -2.7607 -1.5367 +log_k2 -8.1039 -10.4225 -5.7853 +beta_pH(log_k2) 0.7821 0.4126 1.1517 +g_qlogis -1.0373 -1.9337 -0.1409 +a.1 5.0095 4.3082 5.7108 +SD.log_k2 0.4622 0.3009 0.6235 + +Correlation: + meso_0 log_k1 log_k2 b_H(_2) +log_k1 0.2179 +log_k2 0.0337 0.5791 +beta_pH(log_k2) -0.0326 -0.5546 -0.9932 +g_qlogis 0.0237 -0.8479 -0.6571 0.6123 + +Random effects: + est. lower upper +SD.log_k2 0.4622 0.3009 0.6235 + +Variance model: + est. lower upper +a.1 5.009 4.308 5.711 + +Backtransformed parameters: + est. lower upper +meso_0 9.330e+01 9.119e+01 95.411751 +k1 1.166e-01 6.325e-02 0.215084 +k2 3.024e-04 2.975e-05 0.003072 +g 2.617e-01 1.263e-01 0.464832 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 17.09 73.67 22.18 5.943 25.54 + +</code></pre> +<p></p> +<caption> +Hierarchichal SFORB fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Wed May 14 05:13:26 2025 +Date of summary: Wed May 14 05:13:35 2025 + +Equations: +d_meso_free/dt = - k_meso_free * meso_free - k_meso_free_bound * + meso_free + k_meso_bound_free * meso_bound +d_meso_bound/dt = + k_meso_free_bound * meso_free - k_meso_bound_free * + meso_bound + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 2.649 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_free_0 log_k_meso_free log_k_meso_free_bound + 93.147 -2.305 -4.230 +log_k_meso_bound_free + -3.761 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_free_0 log_k_meso_free log_k_meso_free_bound +meso_free_0 6.418 0.0000 0.000 +log_k_meso_free 0.000 0.9276 0.000 +log_k_meso_free_bound 0.000 0.0000 2.272 +log_k_meso_bound_free 0.000 0.0000 0.000 + log_k_meso_bound_free +meso_free_0 0.000 +log_k_meso_free 0.000 +log_k_meso_free_bound 0.000 +log_k_meso_bound_free 1.447 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 768.8 776.8 -375.4 + +Optimised parameters: + est. lower upper +meso_free_0 93.4204 91.3213 95.5195 +log_k_meso_free -5.3742 -6.9366 -3.8117 +beta_pH(log_k_meso_free) 0.4232 0.1769 0.6695 +log_k_meso_free_bound -3.4889 -4.9243 -2.0535 +log_k_meso_bound_free -9.9797 -19.2232 -0.7362 +beta_pH(log_k_meso_bound_free) 1.2290 -0.2107 2.6687 +a.1 4.9031 4.1795 5.6268 +SD.log_k_meso_free 0.3454 0.2252 0.4656 +SD.log_k_meso_bound_free 0.1277 -1.9459 2.2012 + +Correlation: + ms_fr_0 lg_k_m_ b_H(___) lg_k_ms_f_ lg_k_ms_b_ +log_k_meso_free 0.1493 +beta_pH(log_k_meso_free) -0.0930 -0.9854 +log_k_meso_free_bound 0.2439 0.4621 -0.3492 +log_k_meso_bound_free 0.2188 0.1292 -0.0339 0.7287 +beta_pH(log_k_meso_bound_free) -0.2216 -0.0797 -0.0111 -0.6566 -0.9934 + +Random effects: + est. lower upper +SD.log_k_meso_free 0.3454 0.2252 0.4656 +SD.log_k_meso_bound_free 0.1277 -1.9459 2.2012 + +Variance model: + est. lower upper +a.1 4.903 4.18 5.627 + +Backtransformed parameters: + est. lower upper +meso_free_0 9.342e+01 9.132e+01 95.51946 +k_meso_free 4.635e-03 9.716e-04 0.02211 +k_meso_free_bound 3.054e-02 7.268e-03 0.12829 +k_meso_bound_free 4.633e-05 4.482e-09 0.47894 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated Eigenvalues of SFORB model(s): +meso_b1 meso_b2 meso_g + 0.1121 0.0256 0.3148 + +Resulting formation fractions: + ff +meso_free 1 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_meso_b1 DT50_meso_b2 +meso 16.42 75.2 22.64 6.185 27.08 + +</code></pre> +<p> </p> +<caption> +Refined hierarchichal SFORB fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Wed May 14 05:13:30 2025 +Date of summary: Wed May 14 05:13:35 2025 + +Equations: +d_meso_free/dt = - k_meso_free * meso_free - k_meso_free_bound * + meso_free + k_meso_bound_free * meso_bound +d_meso_bound/dt = + k_meso_free_bound * meso_free - k_meso_bound_free * + meso_bound + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 3.186 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_free_0 log_k_meso_free log_k_meso_free_bound + 93.147 -2.305 -4.230 +log_k_meso_bound_free + -3.761 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_free_0 log_k_meso_free log_k_meso_free_bound +meso_free_0 6.418 0.0000 0.000 +log_k_meso_free 0.000 0.9276 0.000 +log_k_meso_free_bound 0.000 0.0000 2.272 +log_k_meso_bound_free 0.000 0.0000 0.000 + log_k_meso_bound_free +meso_free_0 0.000 +log_k_meso_free 0.000 +log_k_meso_free_bound 0.000 +log_k_meso_bound_free 1.447 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 770.9 777.2 -378.5 + +Optimised parameters: + est. lower upper +meso_free_0 93.3196 91.1633 95.4760 +log_k_meso_free -6.1460 -7.4306 -4.8614 +beta_pH(log_k_meso_free) 0.5435 0.3329 0.7542 +log_k_meso_free_bound -3.8001 -5.2027 -2.3975 +log_k_meso_bound_free -2.9462 -4.2565 -1.6359 +a.1 5.0825 4.3793 5.7856 +SD.log_k_meso_free 0.3338 0.2175 0.4502 + +Correlation: + ms_fr_0 lg_k_m_ b_H(___ lg_k_ms_f_ +log_k_meso_free 0.1086 +beta_pH(log_k_meso_free) -0.0426 -0.9821 +log_k_meso_free_bound 0.2513 0.1717 -0.0409 +log_k_meso_bound_free 0.1297 0.1171 -0.0139 0.9224 + +Random effects: + est. lower upper +SD.log_k_meso_free 0.3338 0.2175 0.4502 + +Variance model: + est. lower upper +a.1 5.082 4.379 5.786 + +Backtransformed parameters: + est. lower upper +meso_free_0 93.319649 9.116e+01 95.47601 +k_meso_free 0.002142 5.928e-04 0.00774 +k_meso_free_bound 0.022369 5.502e-03 0.09095 +k_meso_bound_free 0.052539 1.417e-02 0.19478 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated Eigenvalues of SFORB model(s): +meso_b1 meso_b2 meso_g +0.09736 0.02632 0.31602 + +Resulting formation fractions: + ff +meso_free 1 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_meso_b1 DT50_meso_b2 +meso 16.87 73.16 22.02 7.12 26.34 + +</code></pre> +<p> </p> +<caption> +Hierarchichal HS fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Wed May 14 05:13:32 2025 +Date of summary: Wed May 14 05:13:35 2025 + +Equations: +d_meso/dt = - ifelse(time <= tb, k1, k2) * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 1.833 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: +meso_0 log_k1 log_k2 log_tb +92.920 -2.409 -3.295 2.471 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k1 log_k2 log_tb +meso_0 6.477 0.0000 0.0000 0.00 +log_k1 0.000 0.8675 0.0000 0.00 +log_k2 0.000 0.0000 0.4035 0.00 +log_tb 0.000 0.0000 0.0000 1.16 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 769.8 779.6 -373.9 + +Optimised parameters: + est. lower upper +meso_0 93.32599 91.4658 95.1862 +log_k1 -5.81463 -7.2710 -4.3583 +beta_pH(log_k1) 0.47472 0.2334 0.7160 +log_k2 -6.79633 -8.7605 -4.8322 +beta_pH(log_k2) 0.54151 0.2124 0.8706 +log_tb 3.24674 1.2470 5.2465 +beta_pH(log_tb) -0.09889 -0.4258 0.2280 +a.1 4.49487 3.7766 5.2132 +SD.log_k1 0.37191 0.2370 0.5068 +SD.log_k2 0.29210 0.0994 0.4848 +SD.log_tb 0.25353 -0.0664 0.5735 + +Correlation: + meso_0 log_k1 b_H(_1) log_k2 b_H(_2) log_tb +log_k1 0.0744 +beta_pH(log_k1) -0.0452 -0.9915 +log_k2 0.0066 -0.0363 0.0376 +beta_pH(log_k2) -0.0071 0.0372 -0.0391 -0.9939 +log_tb -0.0238 -0.1483 0.1362 -0.3836 0.3696 +beta_pH(log_tb) 0.0097 0.1359 -0.1265 0.3736 -0.3653 -0.9905 + +Random effects: + est. lower upper +SD.log_k1 0.3719 0.2370 0.5068 +SD.log_k2 0.2921 0.0994 0.4848 +SD.log_tb 0.2535 -0.0664 0.5735 + +Variance model: + est. lower upper +a.1 4.495 3.777 5.213 + +Backtransformed parameters: + est. lower upper +meso_0 93.325994 9.147e+01 9.519e+01 +k1 0.002984 6.954e-04 1.280e-02 +k2 0.001118 1.568e-04 7.969e-03 +tb 25.706437 3.480e+00 1.899e+02 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 15.65 79.63 23.97 15.16 27.55 + +</code></pre> +<p> </p> +<caption> +Refined hierarchichal HS fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Wed May 14 05:13:35 2025 +Date of summary: Wed May 14 05:13:35 2025 + +Equations: +d_meso/dt = - ifelse(time <= tb, k1, k2) * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 1.852 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: +meso_0 log_k1 log_k2 log_tb +92.920 -2.409 -3.295 2.471 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k1 log_k2 log_tb +meso_0 6.477 0.0000 0.0000 0.00 +log_k1 0.000 0.8675 0.0000 0.00 +log_k2 0.000 0.0000 0.4035 0.00 +log_tb 0.000 0.0000 0.0000 1.16 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 766.5 775.4 -373.2 + +Optimised parameters: + est. lower upper +meso_0 93.3251 91.49823 95.1520 +log_k1 -5.6796 -7.08789 -4.2714 +beta_pH(log_k1) 0.4567 0.22400 0.6894 +log_k2 -6.6083 -8.33839 -4.8781 +beta_pH(log_k2) 0.4982 0.20644 0.7899 +log_tb 2.7040 2.33033 3.0777 +a.1 4.4452 3.73537 5.1551 +SD.log_k1 0.3570 0.22104 0.4930 +SD.log_k2 0.2252 0.01864 0.4318 +SD.log_tb 0.5488 0.24560 0.8521 + +Correlation: + meso_0 log_k1 b_H(_1) log_k2 b_H(_2) +log_k1 0.0740 +beta_pH(log_k1) -0.0453 -0.9912 +log_k2 0.0115 -0.0650 0.0661 +beta_pH(log_k2) -0.0116 0.0649 -0.0667 -0.9936 +log_tb -0.0658 -0.1135 0.0913 -0.1500 0.1210 + +Random effects: + est. lower upper +SD.log_k1 0.3570 0.22104 0.4930 +SD.log_k2 0.2252 0.01864 0.4318 +SD.log_tb 0.5488 0.24560 0.8521 + +Variance model: + est. lower upper +a.1 4.445 3.735 5.155 + +Backtransformed parameters: + est. lower upper +meso_0 93.325134 9.150e+01 95.152036 +k1 0.003415 8.352e-04 0.013962 +k2 0.001349 2.392e-04 0.007611 +tb 14.939247 1.028e+01 21.707445 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 14.69 82.45 24.82 14.69 29.29 + +</code></pre> +<p></p> +</div> +</div> +<div class="section level3"> +<h3 id="session-info">Session info<a class="anchor" aria-label="anchor" href="#session-info"></a> +</h3> +<pre><code>R version 4.5.0 (2025-04-11) +Platform: x86_64-pc-linux-gnu +Running under: Debian GNU/Linux 12 (bookworm) + +Matrix products: default +BLAS: /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.11.0 +LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.11.0 LAPACK version 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] rmarkdown_2.29 nvimcom_0.9-167 saemix_3.3 npde_3.5 +[5] knitr_1.49 mkin_1.2.10 + +loaded via a namespace (and not attached): + [1] gtable_0.3.6 jsonlite_1.9.0 dplyr_1.1.4 compiler_4.5.0 + [5] tidyselect_1.2.1 gridExtra_2.3 jquerylib_0.1.4 systemfonts_1.2.1 + [9] scales_1.3.0 textshaping_1.0.0 readxl_1.4.4 yaml_2.3.10 +[13] fastmap_1.2.0 lattice_0.22-6 ggplot2_3.5.1 R6_2.6.1 +[17] generics_0.1.3 lmtest_0.9-40 MASS_7.3-65 htmlwidgets_1.6.4 +[21] tibble_3.2.1 desc_1.4.3 munsell_0.5.1 bslib_0.9.0 +[25] pillar_1.10.1 rlang_1.1.5 cachem_1.1.0 xfun_0.51 +[29] fs_1.6.5 sass_0.4.9 cli_3.6.4 pkgdown_2.1.1 +[33] magrittr_2.0.3 digest_0.6.37 grid_4.5.0 mclust_6.1.1 +[37] lifecycle_1.0.4 nlme_3.1-168 vctrs_0.6.5 evaluate_1.0.3 +[41] glue_1.8.0 cellranger_1.1.0 codetools_0.2-20 ragg_1.3.3 +[45] zoo_1.8-13 colorspace_2.1-1 tools_4.5.0 pkgconfig_2.0.3 +[49] htmltools_0.5.8.1</code></pre> +</div> +<div class="section level3"> +<h3 id="hardware-info">Hardware info<a class="anchor" aria-label="anchor" href="#hardware-info"></a> +</h3> +<pre><code>CPU model: AMD Ryzen 9 7950X 16-Core Processor</code></pre> +<pre><code>MemTotal: 64927780 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<h1>Testing covariate modelling in hierarchical parent degradation kinetics with residue data on mesotrione</h1> + <h4 data-toc-skip class="author">Johannes +Ranke</h4> + + <h4 data-toc-skip class="date">Last change 13 May 2025 +(rebuilt 2025-05-13)</h4> + + <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/mesotrione_parent_2023_prebuilt.rmd" class="external-link"><code>vignettes/web_only/mesotrione_parent_2023_prebuilt.rmd</code></a></small> + <div class="d-none name"><code>mesotrione_parent_2023_prebuilt.rmd</code></div> + </div> + + + +<div class="section level2"> +<h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#introduction"></a> +</h2> +<p>The purpose of this document is to test demonstrate how nonlinear +hierarchical models (NLHM) based on the parent degradation models SFO, +FOMC, DFOP and HS can be fitted with the mkin package, also considering +the influence of covariates like soil pH on different degradation +parameters. Because in some other case studies, the SFORB +parameterisation of biexponential decline has shown some advantages over +the DFOP parameterisation, SFORB was included in the list of tested +models as well.</p> +<p>The mkin package is used in version 1.2.10, which is contains the +functions that were used for the evaluations. The <code>saemix</code> +package is used as a backend for fitting the NLHM, but is also loaded to +make the convergence plot function available.</p> +<p>This document is processed with the <code>knitr</code> package, which +also provides the <code>kable</code> function that is used to improve +the display of tabular data in R markdown documents. For parallel +processing, the <code>parallel</code> package is used.</p> +<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://pkgdown.jrwb.de/mkin/">mkin</a></span><span class="op">)</span></span> +<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://yihui.org/knitr/" class="external-link">knitr</a></span><span class="op">)</span></span> +<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">saemix</span><span class="op">)</span></span> +<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">parallel</span><span class="op">)</span></span> +<span><span class="va">n_cores</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/detectCores.html" class="external-link">detectCores</a></span><span class="op">(</span><span class="op">)</span></span> +<span><span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/Sys.info.html" class="external-link">Sys.info</a></span><span class="op">(</span><span class="op">)</span><span class="op">[</span><span class="st">"sysname"</span><span class="op">]</span> <span class="op">==</span> <span class="st">"Windows"</span><span class="op">)</span> <span class="op">{</span></span> +<span> <span class="va">cl</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makePSOCKcluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> +<span><span class="op">}</span> <span class="kw">else</span> <span class="op">{</span></span> +<span> <span class="va">cl</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makeForkCluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> +<span><span class="op">}</span></span></code></pre></div> +<div class="section level3"> +<h3 id="test-data">Test data<a class="anchor" aria-label="anchor" href="#test-data"></a> +</h3> +<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">data_file</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.file.html" class="external-link">system.file</a></span><span class="op">(</span></span> +<span> <span class="st">"testdata"</span>, <span class="st">"mesotrione_soil_efsa_2016.xlsx"</span>, package <span class="op">=</span> <span class="st">"mkin"</span><span class="op">)</span></span> +<span><span class="va">meso_ds</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/read_spreadsheet.html">read_spreadsheet</a></span><span class="op">(</span><span class="va">data_file</span>, parent_only <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<p>The following tables show the covariate data and the 18 datasets that +were read in from the spreadsheet file.</p> +<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">pH</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/attr.html" class="external-link">attr</a></span><span class="op">(</span><span class="va">meso_ds</span>, <span class="st">"covariates"</span><span class="op">)</span></span> +<span><span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="va">pH</span>, caption <span class="op">=</span> <span class="st">"Covariate data"</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<caption>Covariate data</caption> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">pH</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">Richmond</td> +<td align="right">6.2</td> +</tr> +<tr class="even"> +<td align="left">Richmond 2</td> +<td align="right">6.2</td> +</tr> +<tr class="odd"> +<td align="left">ERTC</td> +<td align="right">6.4</td> +</tr> +<tr class="even"> +<td align="left">Toulouse</td> +<td align="right">7.7</td> +</tr> +<tr class="odd"> +<td align="left">Picket Piece</td> +<td align="right">7.1</td> +</tr> +<tr class="even"> +<td align="left">721</td> +<td align="right">5.6</td> +</tr> +<tr class="odd"> +<td align="left">722</td> +<td align="right">5.7</td> +</tr> +<tr class="even"> +<td align="left">723</td> +<td align="right">5.4</td> +</tr> +<tr class="odd"> +<td align="left">724</td> +<td align="right">4.8</td> +</tr> +<tr class="even"> +<td align="left">725</td> +<td align="right">5.8</td> +</tr> +<tr class="odd"> +<td align="left">727</td> +<td align="right">5.1</td> +</tr> +<tr class="even"> +<td align="left">728</td> +<td align="right">5.9</td> +</tr> +<tr class="odd"> +<td align="left">729</td> +<td align="right">5.6</td> +</tr> +<tr class="even"> +<td align="left">730</td> +<td align="right">5.3</td> +</tr> +<tr class="odd"> +<td align="left">731</td> +<td align="right">6.1</td> +</tr> +<tr class="even"> +<td align="left">732</td> +<td align="right">5.0</td> +</tr> +<tr class="odd"> +<td align="left">741</td> +<td align="right">5.7</td> +</tr> +<tr class="even"> +<td align="left">742</td> +<td align="right">7.2</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="kw">for</span> <span class="op">(</span><span class="va">ds_name</span> <span class="kw">in</span> <span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">meso_ds</span><span class="op">)</span><span class="op">)</span> <span class="op">{</span></span> +<span> <span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span></span> +<span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="fu"><a href="../../reference/mkin_long_to_wide.html">mkin_long_to_wide</a></span><span class="op">(</span><span class="va">meso_ds</span><span class="op">[[</span><span class="va">ds_name</span><span class="op">]</span><span class="op">]</span><span class="op">)</span>,</span> +<span> caption <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste</a></span><span class="op">(</span><span class="st">"Dataset"</span>, <span class="va">ds_name</span><span class="op">)</span>,</span> +<span> booktabs <span class="op">=</span> <span class="cn">TRUE</span>, row.names <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="op">}</span></span></code></pre></div> +<table class="table"> +<caption>Dataset Richmond</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">91.00</td> +</tr> +<tr class="even"> +<td align="right">1.179050</td> +<td align="right">86.70</td> +</tr> +<tr class="odd"> +<td align="right">3.537149</td> +<td align="right">73.60</td> +</tr> +<tr class="even"> +<td align="right">7.074299</td> +<td align="right">61.50</td> +</tr> +<tr class="odd"> +<td align="right">10.611448</td> +<td align="right">55.70</td> +</tr> +<tr class="even"> +<td align="right">15.327647</td> +<td align="right">47.70</td> +</tr> +<tr class="odd"> +<td align="right">17.685747</td> +<td align="right">39.50</td> +</tr> +<tr class="even"> +<td align="right">24.760046</td> +<td align="right">29.80</td> +</tr> +<tr class="odd"> +<td align="right">35.371494</td> +<td align="right">19.60</td> +</tr> +<tr class="even"> +<td align="right">68.384889</td> +<td align="right">5.67</td> +</tr> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">97.90</td> +</tr> +<tr class="even"> +<td align="right">1.179050</td> +<td align="right">96.40</td> +</tr> +<tr class="odd"> +<td align="right">3.537149</td> +<td align="right">89.10</td> +</tr> +<tr class="even"> +<td align="right">7.074299</td> +<td align="right">74.40</td> +</tr> +<tr class="odd"> +<td align="right">10.611448</td> +<td align="right">57.40</td> +</tr> +<tr class="even"> +<td align="right">15.327647</td> +<td align="right">46.30</td> +</tr> +<tr class="odd"> +<td align="right">18.864797</td> +<td align="right">35.50</td> +</tr> +<tr class="even"> +<td align="right">27.118146</td> +<td align="right">27.20</td> +</tr> +<tr class="odd"> +<td align="right">35.371494</td> +<td align="right">19.10</td> +</tr> +<tr class="even"> +<td align="right">74.280138</td> +<td align="right">6.50</td> +</tr> +<tr class="odd"> +<td align="right">108.472582</td> +<td align="right">3.40</td> +</tr> +<tr class="even"> +<td align="right">142.665027</td> +<td align="right">2.20</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset Richmond 2</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">96.0</td> +</tr> +<tr class="even"> +<td align="right">2.422004</td> +<td align="right">82.4</td> +</tr> +<tr class="odd"> +<td align="right">5.651343</td> +<td align="right">71.2</td> +</tr> +<tr class="even"> +<td align="right">8.073348</td> +<td align="right">53.1</td> +</tr> +<tr class="odd"> +<td align="right">11.302687</td> +<td align="right">48.5</td> +</tr> +<tr class="even"> +<td align="right">16.954030</td> +<td align="right">33.4</td> +</tr> +<tr class="odd"> +<td align="right">22.605373</td> +<td align="right">24.2</td> +</tr> +<tr class="even"> +<td align="right">45.210746</td> +<td align="right">11.9</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset ERTC</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">99.9</td> +</tr> +<tr class="even"> +<td align="right">2.755193</td> +<td align="right">80.0</td> +</tr> +<tr class="odd"> +<td align="right">6.428782</td> +<td align="right">42.1</td> +</tr> +<tr class="even"> +<td align="right">9.183975</td> +<td align="right">50.1</td> +</tr> +<tr class="odd"> +<td align="right">12.857565</td> +<td align="right">28.4</td> +</tr> +<tr class="even"> +<td align="right">19.286347</td> +<td align="right">39.8</td> +</tr> +<tr class="odd"> +<td align="right">25.715130</td> +<td align="right">29.9</td> +</tr> +<tr class="even"> +<td align="right">51.430259</td> +<td align="right">2.5</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset Toulouse</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">96.8</td> +</tr> +<tr class="even"> +<td align="right">2.897983</td> +<td align="right">63.3</td> +</tr> +<tr class="odd"> +<td align="right">6.761960</td> +<td align="right">22.3</td> +</tr> +<tr class="even"> +<td align="right">9.659942</td> +<td align="right">16.6</td> +</tr> +<tr class="odd"> +<td align="right">13.523919</td> +<td align="right">16.1</td> +</tr> +<tr class="even"> +<td align="right">20.285879</td> +<td align="right">17.2</td> +</tr> +<tr class="odd"> +<td align="right">27.047838</td> +<td align="right">1.8</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset Picket Piece</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">102.0</td> +</tr> +<tr class="even"> +<td align="right">2.841195</td> +<td align="right">73.7</td> +</tr> +<tr class="odd"> +<td align="right">6.629454</td> +<td align="right">35.5</td> +</tr> +<tr class="even"> +<td align="right">9.470649</td> +<td align="right">31.8</td> +</tr> +<tr class="odd"> +<td align="right">13.258909</td> +<td align="right">18.0</td> +</tr> +<tr class="even"> +<td align="right">19.888364</td> +<td align="right">3.7</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 721</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">86.4</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">61.4</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">49.8</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">41.0</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">35.1</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 722</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">90.3</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">52.1</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">37.4</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">21.2</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">14.3</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 723</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">89.3</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">70.8</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">51.1</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">42.7</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">26.7</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 724</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">89.4</td> +</tr> +<tr class="even"> +<td align="right">9.008208</td> +<td align="right">65.2</td> +</tr> +<tr class="odd"> +<td align="right">18.016415</td> +<td align="right">55.8</td> +</tr> +<tr class="even"> +<td align="right">27.024623</td> +<td align="right">46.0</td> +</tr> +<tr class="odd"> +<td align="right">36.032831</td> +<td align="right">41.7</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 725</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">89.0</td> +</tr> +<tr class="even"> +<td align="right">10.99058</td> +<td align="right">35.4</td> +</tr> +<tr class="odd"> +<td align="right">21.98116</td> +<td align="right">18.6</td> +</tr> +<tr class="even"> +<td align="right">32.97174</td> +<td align="right">11.6</td> +</tr> +<tr class="odd"> +<td align="right">43.96232</td> +<td align="right">7.6</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 727</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">91.3</td> +</tr> +<tr class="even"> +<td align="right">10.96104</td> +<td align="right">63.2</td> +</tr> +<tr class="odd"> +<td align="right">21.92209</td> +<td align="right">51.1</td> +</tr> +<tr class="even"> +<td align="right">32.88313</td> +<td align="right">42.0</td> +</tr> +<tr class="odd"> +<td align="right">43.84417</td> +<td align="right">40.8</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 728</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">91.8</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">43.6</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">22.0</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">15.9</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">8.8</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 729</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">91.6</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">60.5</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">43.5</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">28.4</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">20.5</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 730</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">92.7</td> +</tr> +<tr class="even"> +<td align="right">11.07446</td> +<td align="right">58.9</td> +</tr> +<tr class="odd"> +<td align="right">22.14893</td> +<td align="right">44.0</td> +</tr> +<tr class="even"> +<td align="right">33.22339</td> +<td align="right">46.0</td> +</tr> +<tr class="odd"> +<td align="right">44.29785</td> +<td align="right">29.3</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 731</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">92.1</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">64.4</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">45.3</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">33.6</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">23.5</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 732</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">90.3</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">58.2</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">40.1</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">33.1</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">25.8</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 741</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">90.3</td> +</tr> +<tr class="even"> +<td align="right">10.84712</td> +<td align="right">68.7</td> +</tr> +<tr class="odd"> +<td align="right">21.69424</td> +<td align="right">58.0</td> +</tr> +<tr class="even"> +<td align="right">32.54136</td> +<td align="right">52.2</td> +</tr> +<tr class="odd"> +<td align="right">43.38848</td> +<td align="right">48.0</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 742</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">92.0</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">60.9</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">36.2</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">18.3</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">8.7</td> +</tr> +</tbody> +</table> +</div> +</div> +<div class="section level2"> +<h2 id="separate-evaluations">Separate evaluations<a class="anchor" aria-label="anchor" href="#separate-evaluations"></a> +</h2> +<p>In order to obtain suitable starting parameters for the NLHM fits, +separate fits of the five models to the data for each soil are generated +using the <code>mmkin</code> function from the mkin package. In a first +step, constant variance is assumed. Convergence is checked with the +<code>status</code> function.</p> +<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">deg_mods</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>, <span class="st">"SFORB"</span>, <span class="st">"HS"</span><span class="op">)</span></span> +<span><span class="va">f_sep_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span></span> +<span> <span class="va">deg_mods</span>,</span> +<span> <span class="va">meso_ds</span>,</span> +<span> error_model <span class="op">=</span> <span class="st">"const"</span>,</span> +<span> cluster <span class="op">=</span> <span class="va">cl</span>,</span> +<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span>, <span class="fl">1</span><span class="op">:</span><span class="fl">5</span><span class="op">]</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">Richmond</th> +<th align="left">Richmond 2</th> +<th align="left">ERTC</th> +<th align="left">Toulouse</th> +<th align="left">Picket Piece</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span>, <span class="fl">6</span><span class="op">:</span><span class="fl">18</span><span class="op">]</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<colgroup> +<col width="10%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +</colgroup> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">721</th> +<th align="left">722</th> +<th align="left">723</th> +<th align="left">724</th> +<th align="left">725</th> +<th align="left">727</th> +<th align="left">728</th> +<th align="left">729</th> +<th align="left">730</th> +<th align="left">731</th> +<th align="left">732</th> +<th align="left">741</th> +<th align="left">742</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<p>In the tables above, OK indicates convergence and C indicates failure +to converge. Most separate fits with constant variance converged, with +the exception of two FOMC fits, one SFORB fit and one HS fit.</p> +<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">f_sep_tc</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_sep_const</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_tc</span><span class="op">[</span>, <span class="fl">1</span><span class="op">:</span><span class="fl">5</span><span class="op">]</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">Richmond</th> +<th align="left">Richmond 2</th> +<th align="left">ERTC</th> +<th align="left">Toulouse</th> +<th align="left">Picket Piece</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_tc</span><span class="op">[</span>, <span class="fl">6</span><span class="op">:</span><span class="fl">18</span><span class="op">]</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<colgroup> +<col width="10%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +</colgroup> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">721</th> +<th align="left">722</th> +<th align="left">723</th> +<th align="left">724</th> +<th align="left">725</th> +<th align="left">727</th> +<th align="left">728</th> +<th align="left">729</th> +<th align="left">730</th> +<th align="left">731</th> +<th align="left">732</th> +<th align="left">741</th> +<th align="left">742</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<p>With the two-component error model, the set of fits that did not +converge is larger, with convergence problems appearing for a number of +non-SFO fits.</p> +</div> +<div class="section level2"> +<h2 id="hierarchical-models-without-covariate">Hierarchical models without covariate<a class="anchor" aria-label="anchor" href="#hierarchical-models-without-covariate"></a> +</h2> +<p>The following code fits hierarchical kinetic models for the ten +combinations of the five different degradation models with the two +different error models in parallel.</p> +<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">f_saem_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mhmkin.html">mhmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">f_sep_const</span>, <span class="va">f_sep_tc</span><span class="op">)</span>, cluster <span class="op">=</span> <span class="va">cl</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<p>All fits terminate without errors (status OK).</p> +<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">npar</th> +<th align="right">AIC</th> +<th align="right">BIC</th> +<th align="right">Lik</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO const</td> +<td align="right">5</td> +<td align="right">800.0</td> +<td align="right">804.5</td> +<td align="right">-395.0</td> +</tr> +<tr class="even"> +<td align="left">SFO tc</td> +<td align="right">6</td> +<td align="right">801.9</td> +<td align="right">807.2</td> +<td align="right">-394.9</td> +</tr> +<tr class="odd"> +<td align="left">FOMC const</td> +<td align="right">7</td> +<td align="right">787.4</td> +<td align="right">793.6</td> +<td align="right">-386.7</td> +</tr> +<tr class="even"> +<td align="left">FOMC tc</td> +<td align="right">8</td> +<td align="right">788.9</td> +<td align="right">796.1</td> +<td align="right">-386.5</td> +</tr> +<tr class="odd"> +<td align="left">DFOP const</td> +<td align="right">9</td> +<td align="right">787.6</td> +<td align="right">795.6</td> +<td align="right">-384.8</td> +</tr> +<tr class="even"> +<td align="left">SFORB const</td> +<td align="right">9</td> +<td align="right">787.4</td> +<td align="right">795.4</td> +<td align="right">-384.7</td> +</tr> +<tr class="odd"> +<td align="left">HS const</td> +<td align="right">9</td> +<td align="right">781.9</td> +<td align="right">789.9</td> +<td align="right">-382.0</td> +</tr> +<tr class="even"> +<td align="left">DFOP tc</td> +<td align="right">10</td> +<td align="right">787.4</td> +<td align="right">796.3</td> +<td align="right">-383.7</td> +</tr> +<tr class="odd"> +<td align="left">SFORB tc</td> +<td align="right">10</td> +<td align="right">795.8</td> +<td align="right">804.7</td> +<td align="right">-387.9</td> +</tr> +<tr class="even"> +<td align="left">HS tc</td> +<td align="right">10</td> +<td align="right">783.7</td> +<td align="right">792.7</td> +<td align="right">-381.9</td> +</tr> +</tbody> +</table> +<p>The model comparisons show that the fits with constant variance are +consistently preferable to the corresponding fits with two-component +error for these data. This is confirmed by the fact that the parameter +<code>b.1</code> (the relative standard deviation in the fits obtained +with the saemix package), is ill-defined in all fits.</p> +<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<colgroup> +<col width="6%"> +<col width="44%"> +<col width="49%"> +</colgroup> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">sd(meso_0)</td> +<td align="left">sd(meso_0), b.1</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">sd(meso_0), sd(log_beta)</td> +<td align="left">sd(meso_0), sd(log_beta), b.1</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">sd(meso_0), sd(log_k1)</td> +<td align="left">sd(meso_0), sd(g_qlogis), b.1</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">sd(meso_free_0), sd(log_k_meso_free_bound)</td> +<td align="left">sd(meso_free_0), sd(log_k_meso_free_bound), b.1</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">sd(meso_0)</td> +<td align="left">sd(meso_0), b.1</td> +</tr> +</tbody> +</table> +<p>For obtaining fits with only well-defined random effects, we update +the set of fits, excluding random effects that were ill-defined +according to the <code>illparms</code> function.</p> +<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">f_saem_2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_saem_1</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<p>The updated fits terminate without errors.</p> +<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left"></td> +<td align="left">b.1</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left"></td> +<td align="left">b.1</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left"></td> +<td align="left">b.1</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left"></td> +<td align="left">b.1</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left"></td> +<td align="left">b.1</td> +</tr> +</tbody> +</table> +<p>No ill-defined errors remain in the fits with constant variance.</p> +</div> +<div class="section level2"> +<h2 id="hierarchical-models-with-covariate">Hierarchical models with covariate<a class="anchor" aria-label="anchor" href="#hierarchical-models-with-covariate"></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="mesotrione_parent_2023_prebuilt_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="mesotrione_parent_2023_prebuilt_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="mesotrione_parent_2023_prebuilt_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="mesotrione_parent_2023_prebuilt_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="mesotrione_parent_2023_prebuilt_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> +<caption> +Hierarchical SFO fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Tue May 13 19:59:35 2025 +Date of summary: Tue May 13 20:00:23 2025 + +Equations: +d_meso/dt = - k_meso * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 0.682 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_k_meso + 90.832 -3.192 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k_meso +meso_0 6.752 0.0000 +log_k_meso 0.000 0.9155 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 800 804.5 -395 + +Optimised parameters: + est. lower upper +meso_0 92.0705 89.9917 94.1493 +log_k_meso -3.1641 -3.4286 -2.8996 +a.1 5.4628 4.6421 6.2835 +SD.meso_0 0.0611 -98.3545 98.4767 +SD.log_k_meso 0.5616 0.3734 0.7499 + +Correlation: + meso_0 +log_k_meso 0.1132 + +Random effects: + est. lower upper +SD.meso_0 0.0611 -98.3545 98.4767 +SD.log_k_meso 0.5616 0.3734 0.7499 + +Variance model: + est. lower upper +a.1 5.463 4.642 6.284 + +Backtransformed parameters: + est. lower upper +meso_0 92.07053 89.99172 94.14933 +k_meso 0.04225 0.03243 0.05505 + +Estimated disappearance times: + DT50 DT90 +meso 16.41 54.5 + +</code></pre> +<p></p> +<caption> +Hierarchical FOMC fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Tue May 13 19:59:35 2025 +Date of summary: Tue May 13 20:00:23 2025 + +Equations: +d_meso/dt = - (alpha/beta) * 1/((time/beta) + 1) * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 0.817 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_alpha log_beta + 93.0520 0.6008 3.4176 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_alpha log_beta +meso_0 6.287 0.00 0.000 +log_alpha 0.000 1.53 0.000 +log_beta 0.000 0.00 1.724 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 787.4 793.6 -386.7 + +Optimised parameters: + est. lower upper +meso_0 93.5648 91.42864 95.7009 +log_alpha 0.7645 0.28068 1.2484 +log_beta 3.6597 3.05999 4.2594 +a.1 5.0708 4.29823 5.8435 +SD.meso_0 0.1691 -34.01517 34.3535 +SD.log_alpha 0.3764 0.05834 0.6945 +SD.log_beta 0.3903 -0.06074 0.8414 + +Correlation: + meso_0 log_lph +log_alpha -0.2839 +log_beta -0.3443 0.8855 + +Random effects: + est. lower upper +SD.meso_0 0.1691 -34.01517 34.3535 +SD.log_alpha 0.3764 0.05834 0.6945 +SD.log_beta 0.3903 -0.06074 0.8414 + +Variance model: + est. lower upper +a.1 5.071 4.298 5.843 + +Backtransformed parameters: + est. lower upper +meso_0 93.565 91.429 95.701 +alpha 2.148 1.324 3.485 +beta 38.850 21.327 70.770 + +Estimated disappearance times: + DT50 DT90 DT50back +meso 14.8 74.64 22.47 + +</code></pre> +<p></p> +<caption> +Hierarchical DFOP fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Tue May 13 19:59:35 2025 +Date of summary: Tue May 13 20:00:23 2025 + +Equations: +d_meso/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * + time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) + * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 1.188 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_k1 log_k2 g_qlogis +93.14689 -2.05241 -3.53079 -0.09522 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k1 log_k2 g_qlogis +meso_0 6.418 0.000 0.000 0.00 +log_k1 0.000 1.018 0.000 0.00 +log_k2 0.000 0.000 1.694 0.00 +g_qlogis 0.000 0.000 0.000 2.37 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 787.6 795.6 -384.8 + +Optimised parameters: + est. lower upper +meso_0 93.6684 91.63599 95.7008 +log_k1 -1.7354 -2.61433 -0.8565 +log_k2 -3.4015 -3.73323 -3.0697 +g_qlogis -1.6341 -2.66133 -0.6069 +a.1 4.7803 4.01269 5.5479 +SD.meso_0 0.1661 -30.97086 31.3031 +SD.log_k1 0.1127 -2.59680 2.8223 +SD.log_k2 0.6394 0.41499 0.8638 +SD.g_qlogis 0.8166 0.09785 1.5353 + +Correlation: + meso_0 log_k1 log_k2 +log_k1 0.1757 +log_k2 0.0199 0.2990 +g_qlogis 0.0813 -0.7431 -0.3826 + +Random effects: + est. lower upper +SD.meso_0 0.1661 -30.97086 31.3031 +SD.log_k1 0.1127 -2.59680 2.8223 +SD.log_k2 0.6394 0.41499 0.8638 +SD.g_qlogis 0.8166 0.09785 1.5353 + +Variance model: + est. lower upper +a.1 4.78 4.013 5.548 + +Backtransformed parameters: + est. lower upper +meso_0 93.66841 91.63599 95.70082 +k1 0.17633 0.07322 0.42466 +k2 0.03332 0.02392 0.04643 +g 0.16327 0.06529 0.35277 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 16.04 63.75 19.19 3.931 20.8 + +</code></pre> +<p></p> +<caption> +Hierarchical SFORB fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Tue May 13 19:59:35 2025 +Date of summary: Tue May 13 20:00:23 2025 + +Equations: +d_meso_free/dt = - k_meso_free * meso_free - k_meso_free_bound * + meso_free + k_meso_bound_free * meso_bound +d_meso_bound/dt = + k_meso_free_bound * meso_free - k_meso_bound_free * + meso_bound + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 1.223 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_free_0 log_k_meso_free log_k_meso_free_bound + 93.147 -2.305 -4.230 +log_k_meso_bound_free + -3.761 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_free_0 log_k_meso_free log_k_meso_free_bound +meso_free_0 6.418 0.0000 0.000 +log_k_meso_free 0.000 0.9276 0.000 +log_k_meso_free_bound 0.000 0.0000 2.272 +log_k_meso_bound_free 0.000 0.0000 0.000 + log_k_meso_bound_free +meso_free_0 0.000 +log_k_meso_free 0.000 +log_k_meso_free_bound 0.000 +log_k_meso_bound_free 1.447 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 787.4 795.4 -384.7 + +Optimised parameters: + est. lower upper +meso_free_0 93.6285 91.6262 95.631 +log_k_meso_free -2.8314 -3.1375 -2.525 +log_k_meso_free_bound -3.2213 -4.4695 -1.973 +log_k_meso_bound_free -2.4246 -3.5668 -1.282 +a.1 4.7372 3.9542 5.520 +SD.meso_free_0 0.1634 -32.7769 33.104 +SD.log_k_meso_free 0.4885 0.3080 0.669 +SD.log_k_meso_free_bound 0.2876 -1.7955 2.371 +SD.log_k_meso_bound_free 0.9942 0.2181 1.770 + +Correlation: + ms_fr_0 lg_k_m_ lg_k_ms_f_ +log_k_meso_free 0.2332 +log_k_meso_free_bound 0.1100 0.5964 +log_k_meso_bound_free -0.0413 0.3697 0.8025 + +Random effects: + est. lower upper +SD.meso_free_0 0.1634 -32.7769 33.104 +SD.log_k_meso_free 0.4885 0.3080 0.669 +SD.log_k_meso_free_bound 0.2876 -1.7955 2.371 +SD.log_k_meso_bound_free 0.9942 0.2181 1.770 + +Variance model: + est. lower upper +a.1 4.737 3.954 5.52 + +Backtransformed parameters: + est. lower upper +meso_free_0 93.62849 91.62622 95.63075 +k_meso_free 0.05893 0.04339 0.08004 +k_meso_free_bound 0.03990 0.01145 0.13903 +k_meso_bound_free 0.08851 0.02825 0.27736 + +Estimated Eigenvalues of SFORB model(s): +meso_b1 meso_b2 meso_g +0.15333 0.03402 0.20881 + +Resulting formation fractions: + ff +meso_free 1 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_meso_b1 DT50_meso_b2 +meso 14.79 60.81 18.3 4.521 20.37 + +</code></pre> +<p></p> +<caption> +Hierarchical HS fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Tue May 13 19:59:36 2025 +Date of summary: Tue May 13 20:00:23 2025 + +Equations: +d_meso/dt = - ifelse(time <= tb, k1, k2) * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 1.307 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: +meso_0 log_k1 log_k2 log_tb +92.920 -2.409 -3.295 2.471 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k1 log_k2 log_tb +meso_0 6.477 0.0000 0.0000 0.00 +log_k1 0.000 0.8675 0.0000 0.00 +log_k2 0.000 0.0000 0.4035 0.00 +log_tb 0.000 0.0000 0.0000 1.16 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 781.9 789.9 -382 + +Optimised parameters: + est. lower upper +meso_0 93.34242 91.4730 95.2118 +log_k1 -2.77312 -3.0826 -2.4637 +log_k2 -3.61854 -3.8430 -3.3941 +log_tb 2.00266 1.3357 2.6696 +a.1 4.47693 3.7059 5.2479 +SD.meso_0 0.07963 -63.1661 63.3253 +SD.log_k1 0.47817 0.2467 0.7097 +SD.log_k2 0.39216 0.2137 0.5706 +SD.log_tb 0.94683 0.4208 1.4728 + +Correlation: + meso_0 log_k1 log_k2 +log_k1 0.1627 +log_k2 0.0063 -0.0301 +log_tb 0.0083 -0.3931 -0.1225 + +Random effects: + est. lower upper +SD.meso_0 0.07963 -63.1661 63.3253 +SD.log_k1 0.47817 0.2467 0.7097 +SD.log_k2 0.39216 0.2137 0.5706 +SD.log_tb 0.94683 0.4208 1.4728 + +Variance model: + est. lower upper +a.1 4.477 3.706 5.248 + +Backtransformed parameters: + est. lower upper +meso_0 93.34242 91.47303 95.21181 +k1 0.06247 0.04584 0.08512 +k2 0.02682 0.02143 0.03357 +tb 7.40872 3.80282 14.43376 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 16 76 22.88 11.1 25.84 + +</code></pre> +<p></p> +</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> +<caption> +Hierarchichal SFO fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Tue May 13 19:59:49 2025 +Date of summary: Tue May 13 20:00:23 2025 + +Equations: +d_meso/dt = - k_meso * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 1.739 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_k_meso + 90.832 -3.192 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k_meso +meso_0 6.752 0.0000 +log_k_meso 0.000 0.9155 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 783.1 787.5 -386.5 + +Optimised parameters: + est. lower upper +meso_0 91.3481 89.2688 93.4275 +log_k_meso -6.6614 -7.9715 -5.3514 +beta_pH(log_k_meso) 0.5871 0.3684 0.8059 +a.1 5.4750 4.7085 6.2415 +SD.log_k_meso 0.3471 0.2258 0.4684 + +Correlation: + meso_0 lg_k_ms +log_k_meso 0.0414 +beta_pH(log_k_meso) -0.0183 -0.9917 + +Random effects: + est. lower upper +SD.log_k_meso 0.3471 0.2258 0.4684 + +Variance model: + est. lower upper +a.1 5.475 4.709 6.242 + +Backtransformed parameters: + est. lower upper +meso_0 91.348139 8.927e+01 93.427476 +k_meso 0.001279 3.452e-04 0.004741 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated disappearance times: + DT50 DT90 +meso 18.52 61.52 + +</code></pre> +<p></p> +<caption> +Hierarchichal FOMC fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Tue May 13 19:59:51 2025 +Date of summary: Tue May 13 20:00:23 2025 + +Equations: +d_meso/dt = - (alpha/beta) * 1/((time/beta) + 1) * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 1.076 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_alpha log_beta + 93.0520 0.6008 3.4176 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_alpha log_beta +meso_0 6.287 0.00 0.000 +log_alpha 0.000 1.53 0.000 +log_beta 0.000 0.00 1.724 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 770.1 776.3 -378 + +Optimised parameters: + est. lower upper +meso_0 92.840646 90.750461 94.9308 +log_alpha -2.206602 -3.494546 -0.9187 +beta_pH(log_alpha) 0.577505 0.369805 0.7852 +log_beta 4.214099 3.438851 4.9893 +a.1 5.027768 4.322028 5.7335 +SD.log_alpha 0.004034 -23.766993 23.7751 +SD.log_beta 0.374640 0.009252 0.7400 + +Correlation: + meso_0 log_lph bt_H(_) +log_alpha -0.0865 +beta_pH(log_alpha) -0.0789 -0.8704 +log_beta -0.3544 0.3302 0.1628 + +Random effects: + est. lower upper +SD.log_alpha 0.004034 -23.766993 23.78 +SD.log_beta 0.374640 0.009252 0.74 + +Variance model: + est. lower upper +a.1 5.028 4.322 5.734 + +Backtransformed parameters: + est. lower upper +meso_0 92.8406 90.75046 94.9308 +alpha 0.1101 0.03036 0.3991 +beta 67.6332 31.15113 146.8404 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated disappearance times: + DT50 DT90 DT50back +meso 17.28 76.37 22.99 + +</code></pre> +<p></p> +<caption> +Refined hierarchichal FOMC fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Tue May 13 19:59:55 2025 +Date of summary: Tue May 13 20:00:23 2025 + +Equations: +d_meso/dt = - (alpha/beta) * 1/((time/beta) + 1) * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 3.361 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_alpha log_beta + 93.0520 0.6008 3.4176 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_alpha log_beta +meso_0 6.287 0.00 0.000 +log_alpha 0.000 1.53 0.000 +log_beta 0.000 0.00 1.724 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 767.5 772.8 -377.7 + +Optimised parameters: + est. lower upper +meso_0 93.0536 90.9771 95.1300 +log_alpha -2.9054 -4.1803 -1.6304 +beta_pH(log_alpha) 0.6590 0.4437 0.8744 +log_beta 3.9549 3.2860 4.6239 +a.1 4.9784 4.2815 5.6754 +SD.log_beta 0.4019 0.2632 0.5406 + +Correlation: + meso_0 log_lph bt_H(_) +log_alpha -0.0397 +beta_pH(log_alpha) -0.0899 -0.9146 +log_beta -0.3473 0.2038 0.1919 + +Random effects: + est. lower upper +SD.log_beta 0.4019 0.2632 0.5406 + +Variance model: + est. lower upper +a.1 4.978 4.281 5.675 + +Backtransformed parameters: + est. lower upper +meso_0 93.05359 90.97713 95.1300 +alpha 0.05473 0.01529 0.1958 +beta 52.19251 26.73597 101.8874 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated disappearance times: + DT50 DT90 DT50back +meso 17.3 82.91 24.96 + +</code></pre> +<p></p> +<caption> +Hierarchichal DFOP fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Tue May 13 19:59:58 2025 +Date of summary: Tue May 13 20:00:23 2025 + +Equations: +d_meso/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * + time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) + * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 1.758 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_k1 log_k2 g_qlogis +93.14689 -2.05241 -3.53079 -0.09522 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k1 log_k2 g_qlogis +meso_0 6.418 0.000 0.000 0.00 +log_k1 0.000 1.018 0.000 0.00 +log_k2 0.000 0.000 1.694 0.00 +g_qlogis 0.000 0.000 0.000 2.37 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 769.1 777.1 -375.5 + +Optimised parameters: + est. lower upper +meso_0 92.843344 90.8464 94.84028 +log_k1 -2.815685 -3.0888 -2.54261 +log_k2 -11.479779 -15.3203 -7.63923 +beta_pH(log_k2) 1.308417 0.6948 1.92203 +g_qlogis 3.133036 0.4657 5.80035 +beta_pH(g_qlogis) -0.565988 -1.0394 -0.09262 +a.1 4.955518 4.2597 5.65135 +SD.log_k2 0.758963 0.4685 1.04943 +SD.g_qlogis 0.005215 -9.9561 9.96656 + +Correlation: + meso_0 log_k1 log_k2 b_H(_2) g_qlogs +log_k1 0.2706 +log_k2 -0.0571 0.1096 +beta_pH(log_k2) 0.0554 -0.1291 -0.9937 +g_qlogis -0.1125 -0.5062 -0.1305 0.1294 +beta_pH(g_qlogis) 0.1267 0.4226 0.0419 -0.0438 -0.9864 + +Random effects: + est. lower upper +SD.log_k2 0.758963 0.4685 1.049 +SD.g_qlogis 0.005215 -9.9561 9.967 + +Variance model: + est. lower upper +a.1 4.956 4.26 5.651 + +Backtransformed parameters: + est. lower upper +meso_0 9.284e+01 9.085e+01 9.484e+01 +k1 5.986e-02 4.556e-02 7.866e-02 +k2 1.034e-05 2.221e-07 4.812e-04 +g 9.582e-01 6.144e-01 9.970e-01 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 20.23 88.45 26.62 11.58 36.23 + +</code></pre> +<p></p> +<caption> +Refined hierarchical DFOP fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Tue May 13 20:00:03 2025 +Date of summary: Tue May 13 20:00:23 2025 + +Equations: +d_meso/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * + time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) + * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 4.465 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_k1 log_k2 g_qlogis +93.14689 -2.05241 -3.53079 -0.09522 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k1 log_k2 g_qlogis +meso_0 6.418 0.000 0.000 0.00 +log_k1 0.000 1.018 0.000 0.00 +log_k2 0.000 0.000 1.694 0.00 +g_qlogis 0.000 0.000 0.000 2.37 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 765.1 772.3 -374.6 + +Optimised parameters: + est. lower upper +meso_0 93.3333 91.2427 95.42394 +log_k1 -1.7997 -2.9124 -0.68698 +log_k2 -8.1810 -10.1819 -6.18008 +beta_pH(log_k2) 0.8064 0.4903 1.12257 +g_qlogis 3.3513 -1.1792 7.88182 +beta_pH(g_qlogis) -0.8672 -1.7661 0.03177 +a.1 4.9158 4.2277 5.60390 +SD.log_k2 0.3946 0.2565 0.53281 + +Correlation: + meso_0 log_k1 log_k2 b_H(_2) g_qlogs +log_k1 0.1730 +log_k2 0.0442 0.5370 +beta_pH(log_k2) -0.0392 -0.4880 -0.9923 +g_qlogis -0.1536 0.1431 -0.1129 0.1432 +beta_pH(g_qlogis) 0.1504 -0.3151 -0.0196 -0.0212 -0.9798 + +Random effects: + est. lower upper +SD.log_k2 0.3946 0.2565 0.5328 + +Variance model: + est. lower upper +a.1 4.916 4.228 5.604 + +Backtransformed parameters: + est. lower upper +meso_0 9.333e+01 9.124e+01 95.42394 +k1 1.654e-01 5.435e-02 0.50309 +k2 2.799e-04 3.785e-05 0.00207 +g 9.661e-01 2.352e-01 0.99962 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 18.37 73.52 22.13 4.192 23.99 + +</code></pre> +<p></p> +<caption> +Further refined hierarchical DFOP fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Tue May 13 20:00:10 2025 +Date of summary: Tue May 13 20:00:23 2025 + +Equations: +d_meso/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * + time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) + * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 2.781 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_k1 log_k2 g_qlogis +93.14689 -2.05241 -3.53079 -0.09522 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k1 log_k2 g_qlogis +meso_0 6.418 0.000 0.000 0.00 +log_k1 0.000 1.018 0.000 0.00 +log_k2 0.000 0.000 1.694 0.00 +g_qlogis 0.000 0.000 0.000 2.37 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 767.4 773.6 -376.7 + +Optimised parameters: + est. lower upper +meso_0 93.3011 91.1905 95.4118 +log_k1 -2.1487 -2.7607 -1.5367 +log_k2 -8.1039 -10.4225 -5.7853 +beta_pH(log_k2) 0.7821 0.4126 1.1517 +g_qlogis -1.0373 -1.9337 -0.1409 +a.1 5.0095 4.3082 5.7108 +SD.log_k2 0.4622 0.3009 0.6235 + +Correlation: + meso_0 log_k1 log_k2 b_H(_2) +log_k1 0.2179 +log_k2 0.0337 0.5791 +beta_pH(log_k2) -0.0326 -0.5546 -0.9932 +g_qlogis 0.0237 -0.8479 -0.6571 0.6123 + +Random effects: + est. lower upper +SD.log_k2 0.4622 0.3009 0.6235 + +Variance model: + est. lower upper +a.1 5.009 4.308 5.711 + +Backtransformed parameters: + est. lower upper +meso_0 9.330e+01 9.119e+01 95.411751 +k1 1.166e-01 6.325e-02 0.215084 +k2 3.024e-04 2.975e-05 0.003072 +g 2.617e-01 1.263e-01 0.464832 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 17.09 73.67 22.18 5.943 25.54 + +</code></pre> +<p></p> +<caption> +Hierarchichal SFORB fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Tue May 13 20:00:14 2025 +Date of summary: Tue May 13 20:00:23 2025 + +Equations: +d_meso_free/dt = - k_meso_free * meso_free - k_meso_free_bound * + meso_free + k_meso_bound_free * meso_bound +d_meso_bound/dt = + k_meso_free_bound * meso_free - k_meso_bound_free * + meso_bound + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 3.54 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_free_0 log_k_meso_free log_k_meso_free_bound + 93.147 -2.305 -4.230 +log_k_meso_bound_free + -3.761 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_free_0 log_k_meso_free log_k_meso_free_bound +meso_free_0 6.418 0.0000 0.000 +log_k_meso_free 0.000 0.9276 0.000 +log_k_meso_free_bound 0.000 0.0000 2.272 +log_k_meso_bound_free 0.000 0.0000 0.000 + log_k_meso_bound_free +meso_free_0 0.000 +log_k_meso_free 0.000 +log_k_meso_free_bound 0.000 +log_k_meso_bound_free 1.447 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 768.8 776.8 -375.4 + +Optimised parameters: + est. lower upper +meso_free_0 93.4204 91.3213 95.5195 +log_k_meso_free -5.3742 -6.9366 -3.8117 +beta_pH(log_k_meso_free) 0.4232 0.1769 0.6695 +log_k_meso_free_bound -3.4889 -4.9243 -2.0535 +log_k_meso_bound_free -9.9797 -19.2232 -0.7362 +beta_pH(log_k_meso_bound_free) 1.2290 -0.2107 2.6687 +a.1 4.9031 4.1795 5.6268 +SD.log_k_meso_free 0.3454 0.2252 0.4656 +SD.log_k_meso_bound_free 0.1277 -1.9459 2.2012 + +Correlation: + ms_fr_0 lg_k_m_ b_H(___) lg_k_ms_f_ lg_k_ms_b_ +log_k_meso_free 0.1493 +beta_pH(log_k_meso_free) -0.0930 -0.9854 +log_k_meso_free_bound 0.2439 0.4621 -0.3492 +log_k_meso_bound_free 0.2188 0.1292 -0.0339 0.7287 +beta_pH(log_k_meso_bound_free) -0.2216 -0.0797 -0.0111 -0.6566 -0.9934 + +Random effects: + est. lower upper +SD.log_k_meso_free 0.3454 0.2252 0.4656 +SD.log_k_meso_bound_free 0.1277 -1.9459 2.2012 + +Variance model: + est. lower upper +a.1 4.903 4.18 5.627 + +Backtransformed parameters: + est. lower upper +meso_free_0 9.342e+01 9.132e+01 95.51946 +k_meso_free 4.635e-03 9.716e-04 0.02211 +k_meso_free_bound 3.054e-02 7.268e-03 0.12829 +k_meso_bound_free 4.633e-05 4.482e-09 0.47894 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated Eigenvalues of SFORB model(s): +meso_b1 meso_b2 meso_g + 0.1121 0.0256 0.3148 + +Resulting formation fractions: + ff +meso_free 1 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_meso_b1 DT50_meso_b2 +meso 16.42 75.2 22.64 6.185 27.08 + +</code></pre> +<p> </p> +<caption> +Refined hierarchichal SFORB fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Tue May 13 20:00:18 2025 +Date of summary: Tue May 13 20:00:23 2025 + +Equations: +d_meso_free/dt = - k_meso_free * meso_free - k_meso_free_bound * + meso_free + k_meso_bound_free * meso_bound +d_meso_bound/dt = + k_meso_free_bound * meso_free - k_meso_bound_free * + meso_bound + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 2.815 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_free_0 log_k_meso_free log_k_meso_free_bound + 93.147 -2.305 -4.230 +log_k_meso_bound_free + -3.761 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_free_0 log_k_meso_free log_k_meso_free_bound +meso_free_0 6.418 0.0000 0.000 +log_k_meso_free 0.000 0.9276 0.000 +log_k_meso_free_bound 0.000 0.0000 2.272 +log_k_meso_bound_free 0.000 0.0000 0.000 + log_k_meso_bound_free +meso_free_0 0.000 +log_k_meso_free 0.000 +log_k_meso_free_bound 0.000 +log_k_meso_bound_free 1.447 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 770.9 777.2 -378.5 + +Optimised parameters: + est. lower upper +meso_free_0 93.3196 91.1633 95.4760 +log_k_meso_free -6.1460 -7.4306 -4.8614 +beta_pH(log_k_meso_free) 0.5435 0.3329 0.7542 +log_k_meso_free_bound -3.8001 -5.2027 -2.3975 +log_k_meso_bound_free -2.9462 -4.2565 -1.6359 +a.1 5.0825 4.3793 5.7856 +SD.log_k_meso_free 0.3338 0.2175 0.4502 + +Correlation: + ms_fr_0 lg_k_m_ b_H(___ lg_k_ms_f_ +log_k_meso_free 0.1086 +beta_pH(log_k_meso_free) -0.0426 -0.9821 +log_k_meso_free_bound 0.2513 0.1717 -0.0409 +log_k_meso_bound_free 0.1297 0.1171 -0.0139 0.9224 + +Random effects: + est. lower upper +SD.log_k_meso_free 0.3338 0.2175 0.4502 + +Variance model: + est. lower upper +a.1 5.082 4.379 5.786 + +Backtransformed parameters: + est. lower upper +meso_free_0 93.319649 9.116e+01 95.47601 +k_meso_free 0.002142 5.928e-04 0.00774 +k_meso_free_bound 0.022369 5.502e-03 0.09095 +k_meso_bound_free 0.052539 1.417e-02 0.19478 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated Eigenvalues of SFORB model(s): +meso_b1 meso_b2 meso_g +0.09736 0.02632 0.31602 + +Resulting formation fractions: + ff +meso_free 1 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_meso_b1 DT50_meso_b2 +meso 16.87 73.16 22.02 7.12 26.34 + +</code></pre> +<p> </p> +<caption> +Hierarchichal HS fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Tue May 13 20:00:20 2025 +Date of summary: Tue May 13 20:00:23 2025 + +Equations: +d_meso/dt = - ifelse(time <= tb, k1, k2) * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 1.849 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: +meso_0 log_k1 log_k2 log_tb +92.920 -2.409 -3.295 2.471 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k1 log_k2 log_tb +meso_0 6.477 0.0000 0.0000 0.00 +log_k1 0.000 0.8675 0.0000 0.00 +log_k2 0.000 0.0000 0.4035 0.00 +log_tb 0.000 0.0000 0.0000 1.16 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 769.8 779.6 -373.9 + +Optimised parameters: + est. lower upper +meso_0 93.32599 91.4658 95.1862 +log_k1 -5.81463 -7.2710 -4.3583 +beta_pH(log_k1) 0.47472 0.2334 0.7160 +log_k2 -6.79633 -8.7605 -4.8322 +beta_pH(log_k2) 0.54151 0.2124 0.8706 +log_tb 3.24674 1.2470 5.2465 +beta_pH(log_tb) -0.09889 -0.4258 0.2280 +a.1 4.49487 3.7766 5.2132 +SD.log_k1 0.37191 0.2370 0.5068 +SD.log_k2 0.29210 0.0994 0.4848 +SD.log_tb 0.25353 -0.0664 0.5735 + +Correlation: + meso_0 log_k1 b_H(_1) log_k2 b_H(_2) log_tb +log_k1 0.0744 +beta_pH(log_k1) -0.0452 -0.9915 +log_k2 0.0066 -0.0363 0.0376 +beta_pH(log_k2) -0.0071 0.0372 -0.0391 -0.9939 +log_tb -0.0238 -0.1483 0.1362 -0.3836 0.3696 +beta_pH(log_tb) 0.0097 0.1359 -0.1265 0.3736 -0.3653 -0.9905 + +Random effects: + est. lower upper +SD.log_k1 0.3719 0.2370 0.5068 +SD.log_k2 0.2921 0.0994 0.4848 +SD.log_tb 0.2535 -0.0664 0.5735 + +Variance model: + est. lower upper +a.1 4.495 3.777 5.213 + +Backtransformed parameters: + est. lower upper +meso_0 93.325994 9.147e+01 9.519e+01 +k1 0.002984 6.954e-04 1.280e-02 +k2 0.001118 1.568e-04 7.969e-03 +tb 25.706437 3.480e+00 1.899e+02 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 15.65 79.63 23.97 15.16 27.55 + +</code></pre> +<p> </p> +<caption> +Refined hierarchichal HS fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Tue May 13 20:00:22 2025 +Date of summary: Tue May 13 20:00:23 2025 + +Equations: +d_meso/dt = - ifelse(time <= tb, k1, k2) * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 1.439 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: +meso_0 log_k1 log_k2 log_tb +92.920 -2.409 -3.295 2.471 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k1 log_k2 log_tb +meso_0 6.477 0.0000 0.0000 0.00 +log_k1 0.000 0.8675 0.0000 0.00 +log_k2 0.000 0.0000 0.4035 0.00 +log_tb 0.000 0.0000 0.0000 1.16 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 766.5 775.4 -373.2 + +Optimised parameters: + est. lower upper +meso_0 93.3251 91.49823 95.1520 +log_k1 -5.6796 -7.08789 -4.2714 +beta_pH(log_k1) 0.4567 0.22400 0.6894 +log_k2 -6.6083 -8.33839 -4.8781 +beta_pH(log_k2) 0.4982 0.20644 0.7899 +log_tb 2.7040 2.33033 3.0777 +a.1 4.4452 3.73537 5.1551 +SD.log_k1 0.3570 0.22104 0.4930 +SD.log_k2 0.2252 0.01864 0.4318 +SD.log_tb 0.5488 0.24560 0.8521 + +Correlation: + meso_0 log_k1 b_H(_1) log_k2 b_H(_2) +log_k1 0.0740 +beta_pH(log_k1) -0.0453 -0.9912 +log_k2 0.0115 -0.0650 0.0661 +beta_pH(log_k2) -0.0116 0.0649 -0.0667 -0.9936 +log_tb -0.0658 -0.1135 0.0913 -0.1500 0.1210 + +Random effects: + est. lower upper +SD.log_k1 0.3570 0.22104 0.4930 +SD.log_k2 0.2252 0.01864 0.4318 +SD.log_tb 0.5488 0.24560 0.8521 + +Variance model: + est. lower upper +a.1 4.445 3.735 5.155 + +Backtransformed parameters: + est. lower upper +meso_0 93.325134 9.150e+01 95.152036 +k1 0.003415 8.352e-04 0.013962 +k2 0.001349 2.392e-04 0.007611 +tb 14.939247 1.028e+01 21.707445 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 14.69 82.45 24.82 14.69 29.29 + +</code></pre> +<p></p> +</div> +</div> +<div class="section level3"> +<h3 id="session-info">Session info<a class="anchor" aria-label="anchor" href="#session-info"></a> +</h3> +<pre><code>R version 4.5.0 (2025-04-11) +Platform: x86_64-pc-linux-gnu +Running under: Debian GNU/Linux 12 (bookworm) + +Matrix products: default +BLAS: /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.11.0 +LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.11.0 LAPACK version 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] rmarkdown_2.29 nvimcom_0.9-167 saemix_3.3 npde_3.5 +[5] knitr_1.49 mkin_1.2.10 + +loaded via a namespace (and not attached): + [1] gtable_0.3.6 jsonlite_1.9.0 dplyr_1.1.4 compiler_4.5.0 + [5] tidyselect_1.2.1 gridExtra_2.3 jquerylib_0.1.4 systemfonts_1.2.1 + [9] scales_1.3.0 textshaping_1.0.0 readxl_1.4.4 yaml_2.3.10 +[13] fastmap_1.2.0 lattice_0.22-6 ggplot2_3.5.1 R6_2.6.1 +[17] generics_0.1.3 lmtest_0.9-40 MASS_7.3-65 htmlwidgets_1.6.4 +[21] tibble_3.2.1 desc_1.4.3 munsell_0.5.1 bslib_0.9.0 +[25] pillar_1.10.1 rlang_1.1.5 cachem_1.1.0 xfun_0.51 +[29] fs_1.6.5 sass_0.4.9 cli_3.6.4 pkgdown_2.1.1 +[33] magrittr_2.0.3 digest_0.6.37 grid_4.5.0 mclust_6.1.1 +[37] lifecycle_1.0.4 nlme_3.1-168 vctrs_0.6.5 evaluate_1.0.3 +[41] glue_1.8.0 cellranger_1.1.0 codetools_0.2-20 ragg_1.3.3 +[45] zoo_1.8-13 colorspace_2.1-1 tools_4.5.0 pkgconfig_2.0.3 +[49] htmltools_0.5.8.1</code></pre> +</div> +<div class="section level3"> +<h3 id="hardware-info">Hardware info<a class="anchor" aria-label="anchor" href="#hardware-info"></a> +</h3> +<pre><code>CPU model: AMD Ryzen 9 7950X 16-Core Processor</code></pre> +<pre><code>MemTotal: 64927780 kB</code></pre> +</div> +</div> + </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2> + </nav></aside> +</div> + + + + <footer><div class="pkgdown-footer-left"> + <p>Developed by Johannes Ranke.</p> +</div> + +<div class="pkgdown-footer-right"> + <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p> +</div> + + </footer> +</div> + + + + + + </body> +</html> diff --git a/docs/articles/web_only/mesotrione_parent_2023_prebuilt_files/figure-html/unnamed-chunk-14-1.png b/docs/articles/web_only/mesotrione_parent_2023_prebuilt_files/figure-html/unnamed-chunk-14-1.png Binary files differnew file mode 100644 index 00000000..67fa91dc --- /dev/null +++ b/docs/articles/web_only/mesotrione_parent_2023_prebuilt_files/figure-html/unnamed-chunk-14-1.png diff --git a/docs/articles/web_only/mesotrione_parent_2023_prebuilt_files/figure-html/unnamed-chunk-19-1.png 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