diff options
Diffstat (limited to 'docs/dev/articles/prebuilt')
37 files changed, 12061 insertions, 0 deletions
diff --git a/docs/dev/articles/prebuilt/2022_cyan_pathway.html b/docs/dev/articles/prebuilt/2022_cyan_pathway.html new file mode 100644 index 00000000..0a37915d --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_cyan_pathway.html @@ -0,0 +1,5394 @@ +<!DOCTYPE html> +<!-- Generated by pkgdown: do not edit by hand --><html lang="en"> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> +<meta charset="utf-8"> +<meta http-equiv="X-UA-Compatible" content="IE=edge"> +<meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"> +<title>Testing hierarchical pathway kinetics with residue data on cyantraniliprole • mkin</title> +<script src="../../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"> +<link href="../../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"> +<script src="../../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"> +<link href="../../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"> +<script src="../../deps/headroom-0.11.0/headroom.min.js"></script><script src="../../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../../deps/search-1.0.0/fuse.min.js"></script><script src="../../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../../pkgdown.js"></script><meta property="og:title" content="Testing hierarchical pathway kinetics with residue data on cyantraniliprole"> +<meta name="robots" content="noindex"> +</head> +<body> + <a href="#main" class="visually-hidden-focusable">Skip to contents</a> + + + <nav class="navbar navbar-expand-lg fixed-top bg-light" data-bs-theme="default" aria-label="Site navigation"><div class="container"> + + <a class="navbar-brand me-2" href="../../index.html">mkin</a> + + <small class="nav-text text-info me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="In-development version">1.2.10</small> + + + <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation"> + <span class="navbar-toggler-icon"></span> + </button> + + <div id="navbar" class="collapse navbar-collapse ms-3"> + <ul class="navbar-nav me-auto"> +<li class="nav-item"><a class="nav-link" href="../../reference/index.html">Reference</a></li> +<li class="active nav-item dropdown"> + <button class="nav-link dropdown-toggle" type="button" id="dropdown-articles" data-bs-toggle="dropdown" aria-expanded="false" aria-haspopup="true">Articles</button> + <ul class="dropdown-menu" aria-labelledby="dropdown-articles"> +<li><a class="dropdown-item" href="../../articles/mkin.html">Introduction to mkin</a></li> + <li><hr class="dropdown-divider"></li> + <li><h6 class="dropdown-header" data-toc-skip>Example evaluations with (generalised) nonlinear least squares</h6></li> + <li><a class="dropdown-item" href="../../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a></li> + <li><a class="dropdown-item" href="../../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a></li> + <li><a class="dropdown-item" href="../../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a></li> + <li><hr class="dropdown-divider"></li> + <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/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> + <li><hr class="dropdown-divider"></li> + <li><h6 class="dropdown-header" data-toc-skip>Performance</h6></li> + <li><a class="dropdown-item" href="../../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a></li> + <li><a class="dropdown-item" href="../../articles/web_only/benchmarks.html">Benchmark timings for mkin</a></li> + <li><a class="dropdown-item" href="../../articles/web_only/saem_benchmarks.html">Benchmark timings for saem.mmkin</a></li> + <li><hr class="dropdown-divider"></li> + <li><h6 class="dropdown-header" data-toc-skip>Miscellaneous</h6></li> + <li><a class="dropdown-item" href="../../articles/twa.html">Calculation of time weighted average concentrations with mkin</a></li> + <li><a class="dropdown-item" href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a></li> + </ul> +</li> +<li class="nav-item"><a class="nav-link" href="../../coverage/coverage.html">Test coverage</a></li> +<li class="nav-item"><a class="nav-link" href="../../news/index.html">News</a></li> + </ul> +<ul class="navbar-nav"> +<li class="nav-item"><form class="form-inline" role="search"> + <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../../search.json"> +</form></li> +<li class="nav-item"><a class="external-link nav-link" href="https://github.com/jranke/mkin/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li> + </ul> +</div> + + + </div> +</nav><div class="container template-article"> + + + + +<div class="row"> + <main id="main" class="col-md-9"><div class="page-header"> + + <h1>Testing hierarchical pathway kinetics with residue data on cyantraniliprole</h1> + <h4 data-toc-skip class="author">Johannes +Ranke</h4> + + <h4 data-toc-skip class="date">Last change on 13 February +2023, last compiled on 16 Februar 2025</h4> + + <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/prebuilt/2022_cyan_pathway.rmd" class="external-link"><code>vignettes/prebuilt/2022_cyan_pathway.rmd</code></a></small> + <div class="d-none name"><code>2022_cyan_pathway.rmd</code></div> + </div> + + + +<div class="section level2"> +<h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#introduction"></a> +</h2> +<p>The purpose of this document is to test demonstrate how nonlinear +hierarchical models (NLHM) based on the parent degradation models SFO, +FOMC, DFOP and HS, with serial formation of two or more metabolites can +be fitted with the mkin package.</p> +<p>It was assembled in the course of work package 1.2 of Project Number +173340 (Application of nonlinear hierarchical models to the kinetic +evaluation of chemical degradation data) of the German Environment +Agency carried out in 2022 and 2023.</p> +<p>The mkin package is used in version 1.2.10 which is currently under +development. The newly introduced functionality that is used here is a +simplification of excluding random effects for a set of fits based on a +related set of fits with a reduced model, and the documentation of the +starting parameters of the fit, so that all starting parameters of +<code>saem</code> fits are now listed in the summary. The +<code>saemix</code> package is used as a backend for fitting the NLHM, +but is also loaded to make the convergence plot function available.</p> +<p>This document is processed with the <code>knitr</code> package, which +also provides the <code>kable</code> function that is used to improve +the display of tabular data in R markdown documents. For parallel +processing, the <code>parallel</code> package is used.</p> +<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://pkgdown.jrwb.de/mkin/">mkin</a></span><span class="op">)</span></span> +<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://yihui.org/knitr/" class="external-link">knitr</a></span><span class="op">)</span></span> +<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">saemix</span><span class="op">)</span></span> +<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">parallel</span><span class="op">)</span></span> +<span><span class="va">n_cores</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/detectCores.html" class="external-link">detectCores</a></span><span class="op">(</span><span class="op">)</span></span> +<span></span> +<span><span class="co"># We need to start a new cluster after defining a compiled model that is</span></span> +<span><span class="co"># saved as a DLL to the user directory, therefore we define a function</span></span> +<span><span class="co"># This is used again after defining the pathway model</span></span> +<span><span class="va">start_cluster</span> <span class="op"><-</span> <span class="kw">function</span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span> <span class="op">{</span></span> +<span> <span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/Sys.info.html" class="external-link">Sys.info</a></span><span class="op">(</span><span class="op">)</span><span class="op">[</span><span class="st">"sysname"</span><span class="op">]</span> <span class="op">==</span> <span class="st">"Windows"</span><span class="op">)</span> <span class="op">{</span></span> +<span> <span class="va">ret</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makePSOCKcluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> +<span> <span class="op">}</span> <span class="kw">else</span> <span class="op">{</span></span> +<span> <span class="va">ret</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makeForkCluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> +<span> <span class="op">}</span></span> +<span> <span class="kw"><a href="https://rdrr.io/r/base/function.html" class="external-link">return</a></span><span class="op">(</span><span class="va">ret</span><span class="op">)</span></span> +<span><span class="op">}</span></span> +<span><span class="va">cl</span> <span class="op"><-</span> <span class="fu">start_cluster</span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span></code></pre></div> +<div class="section level3"> +<h3 id="test-data">Test data<a class="anchor" aria-label="anchor" href="#test-data"></a> +</h3> +<p>The example data are taken from the final addendum to the DAR from +2014 and are distributed with the mkin package. Residue data and time +step normalisation factors are read in using the function +<code>read_spreadsheet</code> from the mkin package. This function also +performs the time step normalisation.</p> +<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">data_file</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.file.html" class="external-link">system.file</a></span><span class="op">(</span></span> +<span> <span class="st">"testdata"</span>, <span class="st">"cyantraniliprole_soil_efsa_2014.xlsx"</span>,</span> +<span> package <span class="op">=</span> <span class="st">"mkin"</span><span class="op">)</span></span> +<span><span class="va">cyan_ds</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/read_spreadsheet.html">read_spreadsheet</a></span><span class="op">(</span><span class="va">data_file</span>, parent_only <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div> +<p>The following tables show the covariate data and the 5 datasets that +were read in from the spreadsheet file.</p> +<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">pH</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/attr.html" class="external-link">attr</a></span><span class="op">(</span><span class="va">cyan_ds</span>, <span class="st">"covariates"</span><span class="op">)</span></span> +<span><span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="va">pH</span>, caption <span class="op">=</span> <span class="st">"Covariate data"</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<caption>Covariate data</caption> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">pH</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">Nambsheim</td> +<td align="right">7.90</td> +</tr> +<tr class="even"> +<td align="left">Tama</td> +<td align="right">6.20</td> +</tr> +<tr class="odd"> +<td align="left">Gross-Umstadt</td> +<td align="right">7.04</td> +</tr> +<tr class="even"> +<td align="left">Sassafras</td> +<td align="right">4.62</td> +</tr> +<tr class="odd"> +<td align="left">Lleida</td> +<td align="right">8.05</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="kw">for</span> <span class="op">(</span><span class="va">ds_name</span> <span class="kw">in</span> <span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">cyan_ds</span><span class="op">)</span><span class="op">)</span> <span class="op">{</span></span> +<span> <span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span></span> +<span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="fu"><a href="../../reference/mkin_long_to_wide.html">mkin_long_to_wide</a></span><span class="op">(</span><span class="va">cyan_ds</span><span class="op">[[</span><span class="va">ds_name</span><span class="op">]</span><span class="op">]</span><span class="op">)</span>,</span> +<span> caption <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste</a></span><span class="op">(</span><span class="st">"Dataset"</span>, <span class="va">ds_name</span><span class="op">)</span>,</span> +<span> booktabs <span class="op">=</span> <span class="cn">TRUE</span>, row.names <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">)</span></span> +<span> <span class="fu"><a href="https://rdrr.io/r/base/cat.html" class="external-link">cat</a></span><span class="op">(</span><span class="st">"\n\\clearpage\n"</span><span class="op">)</span></span> +<span><span class="op">}</span></span></code></pre></div> +<table class="table"> +<caption>Dataset Nambsheim</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">cyan</th> +<th align="right">JCZ38</th> +<th align="right">J9C38</th> +<th align="right">JSE76</th> +<th align="right">J9Z38</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">105.79</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +</tr> +<tr class="even"> +<td align="right">3.210424</td> +<td align="right">77.26</td> +<td align="right">7.92</td> +<td align="right">11.94</td> +<td align="right">5.58</td> +<td align="right">9.12</td> +</tr> +<tr class="odd"> +<td align="right">7.490988</td> +<td align="right">57.13</td> +<td align="right">15.46</td> +<td align="right">16.58</td> +<td align="right">12.59</td> +<td align="right">11.74</td> +</tr> +<tr class="even"> +<td align="right">17.122259</td> +<td align="right">37.74</td> +<td align="right">15.98</td> +<td align="right">13.36</td> +<td align="right">26.05</td> +<td align="right">10.77</td> +</tr> +<tr class="odd"> +<td align="right">23.543105</td> +<td align="right">31.47</td> +<td align="right">6.05</td> +<td align="right">14.49</td> +<td align="right">34.71</td> +<td align="right">4.96</td> +</tr> +<tr class="even"> +<td align="right">43.875788</td> +<td align="right">16.74</td> +<td align="right">6.07</td> +<td align="right">7.57</td> +<td align="right">40.38</td> +<td align="right">6.52</td> +</tr> +<tr class="odd"> +<td align="right">67.418893</td> +<td align="right">8.85</td> +<td align="right">10.34</td> +<td align="right">6.39</td> +<td align="right">30.71</td> +<td align="right">8.90</td> +</tr> +<tr class="even"> +<td align="right">107.014116</td> +<td align="right">5.19</td> +<td align="right">9.61</td> +<td align="right">1.95</td> +<td align="right">20.41</td> +<td align="right">12.93</td> +</tr> +<tr class="odd"> +<td align="right">129.487080</td> +<td align="right">3.45</td> +<td align="right">6.18</td> +<td align="right">1.36</td> +<td align="right">21.78</td> +<td align="right">6.99</td> +</tr> +<tr class="even"> +<td align="right">195.835832</td> +<td align="right">2.15</td> +<td align="right">9.13</td> +<td align="right">0.95</td> +<td align="right">16.29</td> +<td align="right">7.69</td> +</tr> +<tr class="odd"> +<td align="right">254.693596</td> +<td align="right">1.92</td> +<td align="right">6.92</td> +<td align="right">0.20</td> +<td align="right">13.57</td> +<td align="right">7.16</td> +</tr> +<tr class="even"> +<td align="right">321.042348</td> +<td align="right">2.26</td> +<td align="right">7.02</td> +<td align="right">NA</td> +<td align="right">11.12</td> +<td align="right">8.66</td> +</tr> +<tr class="odd"> +<td align="right">383.110535</td> +<td align="right">NA</td> +<td align="right">5.05</td> +<td align="right">NA</td> +<td align="right">10.64</td> +<td align="right">5.56</td> +</tr> +<tr class="even"> +<td align="right">0.000000</td> +<td align="right">105.57</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +</tr> +<tr class="odd"> +<td align="right">3.210424</td> +<td align="right">78.88</td> +<td align="right">12.77</td> +<td align="right">11.94</td> +<td align="right">5.47</td> +<td align="right">9.12</td> +</tr> +<tr class="even"> +<td align="right">7.490988</td> +<td align="right">59.94</td> +<td align="right">15.27</td> +<td align="right">16.58</td> +<td align="right">13.60</td> +<td align="right">11.74</td> +</tr> +<tr class="odd"> +<td align="right">17.122259</td> +<td align="right">39.67</td> +<td align="right">14.26</td> +<td align="right">13.36</td> +<td align="right">29.44</td> +<td align="right">10.77</td> +</tr> +<tr class="even"> +<td align="right">23.543105</td> +<td align="right">30.21</td> +<td align="right">16.07</td> +<td align="right">14.49</td> +<td align="right">35.90</td> +<td align="right">4.96</td> +</tr> +<tr class="odd"> +<td align="right">43.875788</td> +<td align="right">18.06</td> +<td align="right">9.44</td> +<td align="right">7.57</td> +<td align="right">42.30</td> +<td align="right">6.52</td> +</tr> +<tr class="even"> +<td align="right">67.418893</td> +<td align="right">8.54</td> +<td align="right">5.78</td> +<td align="right">6.39</td> +<td align="right">34.70</td> +<td align="right">8.90</td> +</tr> +<tr class="odd"> +<td align="right">107.014116</td> +<td align="right">7.26</td> +<td align="right">4.54</td> +<td align="right">1.95</td> +<td align="right">23.33</td> +<td align="right">12.93</td> +</tr> +<tr class="even"> +<td align="right">129.487080</td> +<td align="right">3.60</td> +<td align="right">4.22</td> +<td align="right">1.36</td> +<td align="right">23.56</td> +<td align="right">6.99</td> +</tr> +<tr class="odd"> +<td align="right">195.835832</td> +<td align="right">2.84</td> +<td align="right">3.05</td> +<td align="right">0.95</td> +<td align="right">16.21</td> +<td align="right">7.69</td> +</tr> +<tr class="even"> +<td align="right">254.693596</td> +<td align="right">2.00</td> +<td align="right">2.90</td> +<td align="right">0.20</td> +<td align="right">15.53</td> +<td align="right">7.16</td> +</tr> +<tr class="odd"> +<td align="right">321.042348</td> +<td align="right">1.79</td> +<td align="right">0.94</td> +<td align="right">NA</td> +<td align="right">9.80</td> +<td align="right">8.66</td> +</tr> +<tr class="even"> +<td align="right">383.110535</td> +<td align="right">NA</td> +<td align="right">1.82</td> +<td align="right">NA</td> +<td align="right">9.49</td> +<td align="right">5.56</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset Tama</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">cyan</th> +<th align="right">JCZ38</th> +<th align="right">J9Z38</th> +<th align="right">JSE76</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">106.14</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +</tr> +<tr class="even"> +<td align="right">2.400833</td> +<td align="right">93.47</td> +<td align="right">6.46</td> +<td align="right">2.85</td> +<td align="right">NA</td> +</tr> +<tr class="odd"> +<td align="right">5.601943</td> +<td align="right">88.39</td> +<td align="right">10.86</td> +<td align="right">4.65</td> +<td align="right">3.85</td> +</tr> +<tr class="even"> +<td align="right">12.804442</td> +<td align="right">72.29</td> +<td align="right">11.97</td> +<td align="right">4.91</td> +<td align="right">11.24</td> +</tr> +<tr class="odd"> +<td align="right">17.606108</td> +<td align="right">65.79</td> +<td align="right">13.11</td> +<td align="right">6.63</td> +<td align="right">13.79</td> +</tr> +<tr class="even"> +<td align="right">32.811382</td> +<td align="right">53.16</td> +<td align="right">11.24</td> +<td align="right">8.90</td> +<td align="right">23.40</td> +</tr> +<tr class="odd"> +<td align="right">50.417490</td> +<td align="right">44.01</td> +<td align="right">11.34</td> +<td align="right">9.98</td> +<td align="right">29.56</td> +</tr> +<tr class="even"> +<td align="right">80.027761</td> +<td align="right">33.23</td> +<td align="right">8.82</td> +<td align="right">11.31</td> +<td align="right">35.63</td> +</tr> +<tr class="odd"> +<td align="right">96.833591</td> +<td align="right">40.68</td> +<td align="right">5.94</td> +<td align="right">8.32</td> +<td align="right">29.09</td> +</tr> +<tr class="even"> +<td align="right">146.450803</td> +<td align="right">20.65</td> +<td align="right">4.49</td> +<td align="right">8.72</td> +<td align="right">36.88</td> +</tr> +<tr class="odd"> +<td align="right">190.466072</td> +<td align="right">17.71</td> +<td align="right">4.66</td> +<td align="right">11.10</td> +<td align="right">40.97</td> +</tr> +<tr class="even"> +<td align="right">240.083284</td> +<td align="right">14.86</td> +<td align="right">2.27</td> +<td align="right">11.62</td> +<td align="right">40.11</td> +</tr> +<tr class="odd"> +<td align="right">286.499386</td> +<td align="right">12.02</td> +<td align="right">NA</td> +<td align="right">10.73</td> +<td align="right">42.58</td> +</tr> +<tr class="even"> +<td align="right">0.000000</td> +<td align="right">109.11</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +</tr> +<tr class="odd"> +<td align="right">2.400833</td> +<td align="right">96.84</td> +<td align="right">5.52</td> +<td align="right">2.04</td> +<td align="right">2.02</td> +</tr> +<tr class="even"> +<td align="right">5.601943</td> +<td align="right">85.29</td> +<td align="right">9.65</td> +<td align="right">2.99</td> +<td align="right">4.39</td> +</tr> +<tr class="odd"> +<td align="right">12.804442</td> +<td align="right">73.68</td> +<td align="right">12.48</td> +<td align="right">5.05</td> +<td align="right">11.47</td> +</tr> +<tr class="even"> +<td align="right">17.606108</td> +<td align="right">64.89</td> +<td align="right">12.44</td> +<td align="right">6.29</td> +<td align="right">15.00</td> +</tr> +<tr class="odd"> +<td align="right">32.811382</td> +<td align="right">52.27</td> +<td align="right">10.86</td> +<td align="right">7.65</td> +<td align="right">23.30</td> +</tr> +<tr class="even"> +<td align="right">50.417490</td> +<td align="right">42.61</td> +<td align="right">10.54</td> +<td align="right">9.37</td> +<td align="right">31.06</td> +</tr> +<tr class="odd"> +<td align="right">80.027761</td> +<td align="right">34.29</td> +<td align="right">10.02</td> +<td align="right">9.04</td> +<td align="right">37.87</td> +</tr> +<tr class="even"> +<td align="right">96.833591</td> +<td align="right">30.50</td> +<td align="right">6.34</td> +<td align="right">8.14</td> +<td align="right">33.97</td> +</tr> +<tr class="odd"> +<td align="right">146.450803</td> +<td align="right">19.21</td> +<td align="right">6.29</td> +<td align="right">8.52</td> +<td align="right">26.15</td> +</tr> +<tr class="even"> +<td align="right">190.466072</td> +<td align="right">17.55</td> +<td align="right">5.81</td> +<td align="right">9.89</td> +<td align="right">32.08</td> +</tr> +<tr class="odd"> +<td align="right">240.083284</td> +<td align="right">13.22</td> +<td align="right">5.99</td> +<td align="right">10.79</td> +<td align="right">40.66</td> +</tr> +<tr class="even"> +<td align="right">286.499386</td> +<td align="right">11.09</td> +<td align="right">6.05</td> +<td align="right">8.82</td> +<td align="right">42.90</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset Gross-Umstadt</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">cyan</th> +<th align="right">JCZ38</th> +<th align="right">J9Z38</th> +<th align="right">JSE76</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.0000000</td> +<td align="right">103.03</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +</tr> +<tr class="even"> +<td align="right">2.1014681</td> +<td align="right">87.85</td> +<td align="right">4.79</td> +<td align="right">3.26</td> +<td align="right">0.62</td> +</tr> +<tr class="odd"> +<td align="right">4.9034255</td> +<td align="right">77.35</td> +<td align="right">8.05</td> +<td align="right">9.89</td> +<td align="right">1.32</td> +</tr> +<tr class="even"> +<td align="right">10.5073404</td> +<td align="right">69.33</td> +<td align="right">9.74</td> +<td align="right">12.32</td> +<td align="right">4.74</td> +</tr> +<tr class="odd"> +<td align="right">21.0146807</td> +<td align="right">55.65</td> +<td align="right">14.57</td> +<td align="right">13.59</td> +<td align="right">9.84</td> +</tr> +<tr class="even"> +<td align="right">31.5220211</td> +<td align="right">49.03</td> +<td align="right">14.66</td> +<td align="right">16.71</td> +<td align="right">12.32</td> +</tr> +<tr class="odd"> +<td align="right">42.0293615</td> +<td align="right">41.86</td> +<td align="right">15.97</td> +<td align="right">13.64</td> +<td align="right">15.53</td> +</tr> +<tr class="even"> +<td align="right">63.0440422</td> +<td align="right">34.88</td> +<td align="right">18.20</td> +<td align="right">14.12</td> +<td align="right">22.02</td> +</tr> +<tr class="odd"> +<td align="right">84.0587230</td> +<td align="right">28.26</td> +<td align="right">15.64</td> +<td align="right">14.06</td> +<td align="right">25.60</td> +</tr> +<tr class="even"> +<td align="right">0.0000000</td> +<td align="right">104.05</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +</tr> +<tr class="odd"> +<td align="right">2.1014681</td> +<td align="right">85.25</td> +<td align="right">2.68</td> +<td align="right">7.32</td> +<td align="right">0.69</td> +</tr> +<tr class="even"> +<td align="right">4.9034255</td> +<td align="right">77.22</td> +<td align="right">7.28</td> +<td align="right">8.37</td> +<td align="right">1.45</td> +</tr> +<tr class="odd"> +<td align="right">10.5073404</td> +<td align="right">65.23</td> +<td align="right">10.73</td> +<td align="right">10.93</td> +<td align="right">4.74</td> +</tr> +<tr class="even"> +<td align="right">21.0146807</td> +<td align="right">57.78</td> +<td align="right">12.29</td> +<td align="right">14.80</td> +<td align="right">9.05</td> +</tr> +<tr class="odd"> +<td align="right">31.5220211</td> +<td align="right">54.83</td> +<td align="right">14.05</td> +<td align="right">12.01</td> +<td align="right">11.05</td> +</tr> +<tr class="even"> +<td align="right">42.0293615</td> +<td align="right">45.17</td> +<td align="right">12.12</td> +<td align="right">17.89</td> +<td align="right">15.71</td> +</tr> +<tr class="odd"> +<td align="right">63.0440422</td> +<td align="right">34.83</td> +<td align="right">12.90</td> +<td align="right">15.86</td> +<td align="right">22.52</td> +</tr> +<tr class="even"> +<td align="right">84.0587230</td> +<td align="right">26.59</td> +<td align="right">14.28</td> +<td align="right">14.91</td> +<td align="right">28.48</td> +</tr> +<tr class="odd"> +<td align="right">0.0000000</td> +<td align="right">104.62</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +</tr> +<tr class="even"> +<td align="right">0.8145225</td> +<td align="right">97.21</td> +<td align="right">NA</td> +<td align="right">4.00</td> +<td align="right">NA</td> +</tr> +<tr class="odd"> +<td align="right">1.9005525</td> +<td align="right">89.64</td> +<td align="right">3.59</td> +<td align="right">5.24</td> +<td align="right">NA</td> +</tr> +<tr class="even"> +<td align="right">4.0726125</td> +<td align="right">87.90</td> +<td align="right">4.10</td> +<td align="right">9.58</td> +<td align="right">NA</td> +</tr> +<tr class="odd"> +<td align="right">8.1452251</td> +<td align="right">86.90</td> +<td align="right">5.96</td> +<td align="right">9.45</td> +<td align="right">NA</td> +</tr> +<tr class="even"> +<td align="right">12.2178376</td> +<td align="right">74.74</td> +<td align="right">7.83</td> +<td align="right">15.03</td> +<td align="right">5.33</td> +</tr> +<tr class="odd"> +<td align="right">16.2904502</td> +<td align="right">74.13</td> +<td align="right">8.84</td> +<td align="right">14.41</td> +<td align="right">5.10</td> +</tr> +<tr class="even"> +<td align="right">24.4356753</td> +<td align="right">65.26</td> +<td align="right">11.84</td> +<td align="right">18.33</td> +<td align="right">6.71</td> +</tr> +<tr class="odd"> +<td align="right">32.5809004</td> +<td align="right">57.70</td> +<td align="right">12.74</td> +<td align="right">19.93</td> +<td align="right">9.74</td> +</tr> +<tr class="even"> +<td align="right">0.0000000</td> +<td align="right">101.94</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +</tr> +<tr class="odd"> +<td align="right">0.8145225</td> +<td align="right">99.94</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +</tr> +<tr class="even"> +<td align="right">1.9005525</td> +<td align="right">94.87</td> +<td align="right">NA</td> +<td align="right">4.56</td> +<td align="right">NA</td> +</tr> +<tr class="odd"> +<td align="right">4.0726125</td> +<td align="right">86.96</td> +<td align="right">6.75</td> +<td align="right">6.90</td> +<td align="right">NA</td> +</tr> +<tr class="even"> +<td align="right">8.1452251</td> +<td align="right">80.51</td> +<td align="right">10.68</td> +<td align="right">7.43</td> +<td align="right">2.58</td> +</tr> +<tr class="odd"> +<td align="right">12.2178376</td> +<td align="right">78.38</td> +<td align="right">10.35</td> +<td align="right">9.46</td> +<td align="right">3.69</td> +</tr> +<tr class="even"> +<td align="right">16.2904502</td> +<td align="right">70.05</td> +<td align="right">13.73</td> +<td align="right">9.27</td> +<td align="right">7.18</td> +</tr> +<tr class="odd"> +<td align="right">24.4356753</td> +<td align="right">61.28</td> +<td align="right">12.57</td> +<td align="right">13.28</td> +<td align="right">13.19</td> +</tr> +<tr class="even"> +<td align="right">32.5809004</td> +<td align="right">52.85</td> +<td align="right">12.67</td> +<td align="right">12.95</td> +<td align="right">13.69</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset Sassafras</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">cyan</th> +<th align="right">JCZ38</th> +<th align="right">J9Z38</th> +<th align="right">JSE76</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">102.17</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +</tr> +<tr class="even"> +<td align="right">2.216719</td> +<td align="right">95.49</td> +<td align="right">1.11</td> +<td align="right">0.10</td> +<td align="right">0.83</td> +</tr> +<tr class="odd"> +<td align="right">5.172343</td> +<td align="right">83.35</td> +<td align="right">6.43</td> +<td align="right">2.89</td> +<td align="right">3.30</td> +</tr> +<tr class="even"> +<td align="right">11.083593</td> +<td align="right">78.18</td> +<td align="right">10.00</td> +<td align="right">5.59</td> +<td align="right">0.81</td> +</tr> +<tr class="odd"> +<td align="right">22.167186</td> +<td align="right">70.44</td> +<td align="right">17.21</td> +<td align="right">4.23</td> +<td align="right">1.09</td> +</tr> +<tr class="even"> +<td align="right">33.250779</td> +<td align="right">68.00</td> +<td align="right">20.45</td> +<td align="right">5.86</td> +<td align="right">1.17</td> +</tr> +<tr class="odd"> +<td align="right">44.334371</td> +<td align="right">59.64</td> +<td align="right">24.64</td> +<td align="right">3.17</td> +<td align="right">2.72</td> +</tr> +<tr class="even"> +<td align="right">66.501557</td> +<td align="right">50.73</td> +<td align="right">27.50</td> +<td align="right">6.19</td> +<td align="right">1.27</td> +</tr> +<tr class="odd"> +<td align="right">88.668742</td> +<td align="right">45.65</td> +<td align="right">32.77</td> +<td align="right">5.69</td> +<td align="right">4.54</td> +</tr> +<tr class="even"> +<td align="right">0.000000</td> +<td align="right">100.43</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +</tr> +<tr class="odd"> +<td align="right">2.216719</td> +<td align="right">95.34</td> +<td align="right">3.21</td> +<td align="right">0.14</td> +<td align="right">0.46</td> +</tr> +<tr class="even"> +<td align="right">5.172343</td> +<td align="right">84.38</td> +<td align="right">5.73</td> +<td align="right">4.75</td> +<td align="right">0.62</td> +</tr> +<tr class="odd"> +<td align="right">11.083593</td> +<td align="right">78.50</td> +<td align="right">11.89</td> +<td align="right">3.99</td> +<td align="right">0.73</td> +</tr> +<tr class="even"> +<td align="right">22.167186</td> +<td align="right">71.17</td> +<td align="right">17.28</td> +<td align="right">4.39</td> +<td align="right">0.66</td> +</tr> +<tr class="odd"> +<td align="right">33.250779</td> +<td align="right">59.41</td> +<td align="right">18.73</td> +<td align="right">11.85</td> +<td align="right">2.65</td> +</tr> +<tr class="even"> +<td align="right">44.334371</td> +<td align="right">64.57</td> +<td align="right">22.93</td> +<td align="right">5.13</td> +<td align="right">2.01</td> +</tr> +<tr class="odd"> +<td align="right">66.501557</td> +<td align="right">49.08</td> +<td align="right">33.39</td> +<td align="right">5.67</td> +<td align="right">3.63</td> +</tr> +<tr class="even"> +<td align="right">88.668742</td> +<td align="right">40.41</td> +<td align="right">39.60</td> +<td align="right">5.93</td> +<td align="right">6.17</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset Lleida</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">cyan</th> +<th align="right">JCZ38</th> +<th align="right">J9Z38</th> +<th align="right">JSE76</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">102.71</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +</tr> +<tr class="even"> +<td align="right">2.821051</td> +<td align="right">79.11</td> +<td align="right">5.70</td> +<td align="right">8.07</td> +<td align="right">0.97</td> +</tr> +<tr class="odd"> +<td align="right">6.582451</td> +<td align="right">70.03</td> +<td align="right">7.17</td> +<td align="right">11.31</td> +<td align="right">4.72</td> +</tr> +<tr class="even"> +<td align="right">14.105253</td> +<td align="right">50.93</td> +<td align="right">10.25</td> +<td align="right">14.84</td> +<td align="right">9.95</td> +</tr> +<tr class="odd"> +<td align="right">28.210505</td> +<td align="right">33.43</td> +<td align="right">10.40</td> +<td align="right">14.82</td> +<td align="right">24.06</td> +</tr> +<tr class="even"> +<td align="right">42.315758</td> +<td align="right">24.69</td> +<td align="right">9.75</td> +<td align="right">16.38</td> +<td align="right">29.38</td> +</tr> +<tr class="odd"> +<td align="right">56.421010</td> +<td align="right">22.99</td> +<td align="right">10.06</td> +<td align="right">15.51</td> +<td align="right">29.25</td> +</tr> +<tr class="even"> +<td align="right">84.631516</td> +<td align="right">14.63</td> +<td align="right">5.63</td> +<td align="right">14.74</td> +<td align="right">31.04</td> +</tr> +<tr class="odd"> +<td align="right">112.842021</td> +<td align="right">12.43</td> +<td align="right">4.17</td> +<td align="right">13.53</td> +<td align="right">33.28</td> +</tr> +<tr class="even"> +<td align="right">0.000000</td> +<td align="right">99.31</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +</tr> +<tr class="odd"> +<td align="right">2.821051</td> +<td align="right">82.07</td> +<td align="right">6.55</td> +<td align="right">5.60</td> +<td align="right">1.12</td> +</tr> +<tr class="even"> +<td align="right">6.582451</td> +<td align="right">70.65</td> +<td align="right">7.61</td> +<td align="right">8.01</td> +<td align="right">3.21</td> +</tr> +<tr class="odd"> +<td align="right">14.105253</td> +<td align="right">53.52</td> +<td align="right">11.48</td> +<td align="right">10.82</td> +<td align="right">12.24</td> +</tr> +<tr class="even"> +<td align="right">28.210505</td> +<td align="right">35.60</td> +<td align="right">11.19</td> +<td align="right">15.43</td> +<td align="right">23.53</td> +</tr> +<tr class="odd"> +<td align="right">42.315758</td> +<td align="right">34.26</td> +<td align="right">11.09</td> +<td align="right">13.26</td> +<td align="right">27.42</td> +</tr> +<tr class="even"> +<td align="right">56.421010</td> +<td align="right">21.79</td> +<td align="right">4.80</td> +<td align="right">18.30</td> +<td align="right">30.20</td> +</tr> +<tr class="odd"> +<td align="right">84.631516</td> +<td align="right">14.06</td> +<td align="right">6.30</td> +<td align="right">16.35</td> +<td align="right">32.32</td> +</tr> +<tr class="even"> +<td align="right">112.842021</td> +<td align="right">11.51</td> +<td align="right">5.57</td> +<td align="right">12.64</td> +<td align="right">32.51</td> +</tr> +</tbody> +</table> +</div> +</div> +<div class="section level2"> +<h2 id="parent-only-evaluations">Parent only evaluations<a class="anchor" aria-label="anchor" href="#parent-only-evaluations"></a> +</h2> +<p>As the pathway fits have very long run times, evaluations of the +parent data are performed first, in order to determine for each +hierarchical parent degradation model which random effects on the +degradation model parameters are ill-defined.</p> +<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">cyan_sep_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>, <span class="st">"SFORB"</span>, <span class="st">"HS"</span><span class="op">)</span>,</span> +<span> <span class="va">cyan_ds</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>, cores <span class="op">=</span> <span class="va">n_cores</span><span class="op">)</span></span> +<span><span class="va">cyan_sep_tc</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">cyan_sep_const</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span> +<span><span class="va">cyan_saem_full</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mhmkin.html">mhmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">cyan_sep_const</span>, <span class="va">cyan_sep_tc</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">cyan_saem_full</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<p>All fits converged successfully.</p> +<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">cyan_saem_full</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">sd(cyan_0)</td> +<td align="left">sd(cyan_0)</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">sd(log_beta)</td> +<td align="left">sd(cyan_0)</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">sd(cyan_0)</td> +<td align="left">sd(cyan_0), sd(log_k1)</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">sd(cyan_free_0)</td> +<td align="left">sd(cyan_free_0), sd(log_k_cyan_free_bound)</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">sd(cyan_0)</td> +<td align="left">sd(cyan_0)</td> +</tr> +</tbody> +</table> +<p>In almost all models, the random effect for the initial concentration +of the parent compound is ill-defined. For the biexponential models DFOP +and SFORB, the random effect of one additional parameter is ill-defined +when the two-component error model is used.</p> +<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">cyan_saem_full</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">npar</th> +<th align="right">AIC</th> +<th align="right">BIC</th> +<th align="right">Lik</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO const</td> +<td align="right">5</td> +<td align="right">833.9</td> +<td align="right">832.0</td> +<td align="right">-412.0</td> +</tr> +<tr class="even"> +<td align="left">SFO tc</td> +<td align="right">6</td> +<td align="right">831.6</td> +<td align="right">829.3</td> +<td align="right">-409.8</td> +</tr> +<tr class="odd"> +<td align="left">FOMC const</td> +<td align="right">7</td> +<td align="right">709.1</td> +<td align="right">706.4</td> +<td align="right">-347.6</td> +</tr> +<tr class="even"> +<td align="left">FOMC tc</td> +<td align="right">8</td> +<td align="right">689.2</td> +<td align="right">686.1</td> +<td align="right">-336.6</td> +</tr> +<tr class="odd"> +<td align="left">DFOP const</td> +<td align="right">9</td> +<td align="right">703.0</td> +<td align="right">699.5</td> +<td align="right">-342.5</td> +</tr> +<tr class="even"> +<td align="left">SFORB const</td> +<td align="right">9</td> +<td align="right">701.3</td> +<td align="right">697.8</td> +<td align="right">-341.7</td> +</tr> +<tr class="odd"> +<td align="left">HS const</td> +<td align="right">9</td> +<td align="right">718.6</td> +<td align="right">715.1</td> +<td align="right">-350.3</td> +</tr> +<tr class="even"> +<td align="left">DFOP tc</td> +<td align="right">10</td> +<td align="right">703.1</td> +<td align="right">699.2</td> +<td align="right">-341.6</td> +</tr> +<tr class="odd"> +<td align="left">SFORB tc</td> +<td align="right">10</td> +<td align="right">700.0</td> +<td align="right">696.1</td> +<td align="right">-340.0</td> +</tr> +<tr class="even"> +<td align="left">HS tc</td> +<td align="right">10</td> +<td align="right">716.7</td> +<td align="right">712.8</td> +<td align="right">-348.3</td> +</tr> +</tbody> +</table> +<p>Model comparison based on AIC and BIC indicates that the +two-component error model is preferable for all parent models with the +exception of DFOP. The lowest AIC and BIC values are are obtained with +the FOMC model, followed by SFORB and DFOP.</p> +<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">stopCluster</a></span><span class="op">(</span><span class="va">cl</span><span class="op">)</span></span></code></pre></div> +</div> +<div class="section level2"> +<h2 id="pathway-fits">Pathway fits<a class="anchor" aria-label="anchor" href="#pathway-fits"></a> +</h2> +<div class="section level3"> +<h3 id="evaluations-with-pathway-established-previously">Evaluations with pathway established previously<a class="anchor" aria-label="anchor" href="#evaluations-with-pathway-established-previously"></a> +</h3> +<p>To test the technical feasibility of coupling the relevant parent +degradation models with different transformation pathway models, a list +of <code>mkinmod</code> models is set up below. As in the EU evaluation, +parallel formation of metabolites JCZ38 and J9Z38 and secondary +formation of metabolite JSE76 from JCZ38 is used.</p> +<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="kw">if</span> <span class="op">(</span><span class="op">!</span><span class="fu"><a href="https://rdrr.io/r/base/files2.html" class="external-link">dir.exists</a></span><span class="op">(</span><span class="st">"cyan_dlls"</span><span class="op">)</span><span class="op">)</span> <span class="fu"><a href="https://rdrr.io/r/base/files2.html" class="external-link">dir.create</a></span><span class="op">(</span><span class="st">"cyan_dlls"</span><span class="op">)</span></span> +<span><span class="va">cyan_path_1</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span></span> +<span> sfo_path_1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> +<span> cyan <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"JCZ38"</span>, <span class="st">"J9Z38"</span><span class="op">)</span><span class="op">)</span>,</span> +<span> JCZ38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JSE76"</span><span class="op">)</span>,</span> +<span> J9Z38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> +<span> JSE76 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span> +<span> name <span class="op">=</span> <span class="st">"sfo_path_1"</span>, dll_dir <span class="op">=</span> <span class="st">"cyan_dlls"</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,</span> +<span> fomc_path_1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> +<span> cyan <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"FOMC"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"JCZ38"</span>, <span class="st">"J9Z38"</span><span class="op">)</span><span class="op">)</span>,</span> +<span> JCZ38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JSE76"</span><span class="op">)</span>,</span> +<span> J9Z38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> +<span> JSE76 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span> +<span> name <span class="op">=</span> <span class="st">"fomc_path_1"</span>, dll_dir <span class="op">=</span> <span class="st">"cyan_dlls"</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,</span> +<span> dfop_path_1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> +<span> cyan <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"DFOP"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"JCZ38"</span>, <span class="st">"J9Z38"</span><span class="op">)</span><span class="op">)</span>,</span> +<span> JCZ38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JSE76"</span><span class="op">)</span>,</span> +<span> J9Z38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> +<span> JSE76 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span> +<span> name <span class="op">=</span> <span class="st">"dfop_path_1"</span>, dll_dir <span class="op">=</span> <span class="st">"cyan_dlls"</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,</span> +<span> sforb_path_1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> +<span> cyan <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"JCZ38"</span>, <span class="st">"J9Z38"</span><span class="op">)</span><span class="op">)</span>,</span> +<span> JCZ38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JSE76"</span><span class="op">)</span>,</span> +<span> J9Z38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> +<span> JSE76 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span> +<span> name <span class="op">=</span> <span class="st">"sforb_path_1"</span>, dll_dir <span class="op">=</span> <span class="st">"cyan_dlls"</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,</span> +<span> hs_path_1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> +<span> cyan <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"HS"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"JCZ38"</span>, <span class="st">"J9Z38"</span><span class="op">)</span><span class="op">)</span>,</span> +<span> JCZ38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JSE76"</span><span class="op">)</span>,</span> +<span> J9Z38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> +<span> JSE76 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span> +<span> name <span class="op">=</span> <span class="st">"hs_path_1"</span>, dll_dir <span class="op">=</span> <span class="st">"cyan_dlls"</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> +<span><span class="op">)</span></span> +<span><span class="va">cl_path_1</span> <span class="op"><-</span> <span class="fu">start_cluster</span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span></code></pre></div> +<p>To obtain suitable starting values for the NLHM fits, separate +pathway fits are performed for all datasets.</p> +<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">f_sep_1_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span></span> +<span> <span class="va">cyan_path_1</span>,</span> +<span> <span class="va">cyan_ds</span>,</span> +<span> error_model <span class="op">=</span> <span class="st">"const"</span>,</span> +<span> cluster <span class="op">=</span> <span class="va">cl_path_1</span>,</span> +<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_1_const</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">Nambsheim</th> +<th align="left">Tama</th> +<th align="left">Gross-Umstadt</th> +<th align="left">Sassafras</th> +<th align="left">Lleida</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">sfo_path_1</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">fomc_path_1</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">dfop_path_1</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">sforb_path_1</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">hs_path_1</td> +<td align="left">C</td> +<td align="left">C</td> +<td align="left">C</td> +<td align="left">C</td> +<td align="left">C</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">f_sep_1_tc</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_sep_1_const</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_1_tc</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">Nambsheim</th> +<th align="left">Tama</th> +<th align="left">Gross-Umstadt</th> +<th align="left">Sassafras</th> +<th align="left">Lleida</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">sfo_path_1</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">fomc_path_1</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">dfop_path_1</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">sforb_path_1</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">hs_path_1</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +</tr> +</tbody> +</table> +<p>Most separate fits converged successfully. The biggest convergence +problems are seen when using the HS model with constant variance.</p> +<p>For the hierarchical pathway fits, those random effects that could +not be quantified in the corresponding parent data analyses are +excluded.</p> +<p>In the code below, the output of the <code>illparms</code> function +for the parent only fits is used as an argument +<code>no_random_effect</code> to the <code>mhmkin</code> function. The +possibility to do so was introduced in mkin version <code>1.2.2</code> +which is currently under development.</p> +<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">f_saem_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mhmkin.html">mhmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">f_sep_1_const</span>, <span class="va">f_sep_1_tc</span><span class="op">)</span>,</span> +<span> no_random_effect <span class="op">=</span> <span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">cyan_saem_full</span><span class="op">)</span>,</span> +<span> cluster <span class="op">=</span> <span class="va">cl_path_1</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">sfo_path_1</td> +<td align="left">FO</td> +<td align="left">Fth, FO</td> +</tr> +<tr class="even"> +<td align="left">fomc_path_1</td> +<td align="left">OK</td> +<td align="left">Fth, FO</td> +</tr> +<tr class="odd"> +<td align="left">dfop_path_1</td> +<td align="left">Fth, FO</td> +<td align="left">Fth, FO</td> +</tr> +<tr class="even"> +<td align="left">sforb_path_1</td> +<td align="left">Fth, FO</td> +<td align="left">Fth, FO</td> +</tr> +<tr class="odd"> +<td align="left">hs_path_1</td> +<td align="left">FO</td> +<td align="left">E</td> +</tr> +</tbody> +</table> +<p>The status information from the individual fits shows that all fits +completed successfully. The matrix entries Fth and FO indicate that the +Fisher Information Matrix could not be inverted for the fixed effects +(theta) and the random effects (Omega), respectively. For the affected +fits, ill-defined parameters cannot be determined using the +<code>illparms</code> function, because it relies on the Fisher +Information Matrix.</p> +<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<colgroup> +<col width="18%"> +<col width="77%"> +<col width="4%"> +</colgroup> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">sfo_path_1</td> +<td align="left">NA</td> +<td align="left">NA</td> +</tr> +<tr class="even"> +<td align="left">fomc_path_1</td> +<td align="left">sd(log_k_J9Z38), sd(f_cyan_ilr_2), +sd(f_JCZ38_qlogis)</td> +<td align="left">NA</td> +</tr> +<tr class="odd"> +<td align="left">dfop_path_1</td> +<td align="left">NA</td> +<td align="left">NA</td> +</tr> +<tr class="even"> +<td align="left">sforb_path_1</td> +<td align="left">NA</td> +<td align="left">NA</td> +</tr> +<tr class="odd"> +<td align="left">hs_path_1</td> +<td align="left">NA</td> +<td align="left">E</td> +</tr> +</tbody> +</table> +<p>The model comparisons below suggest that the pathway fits using DFOP +or SFORB for the parent compound provide the best fit.</p> +<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">[</span>, <span class="st">"const"</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>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">npar</th> +<th align="right">AIC</th> +<th align="right">BIC</th> +<th align="right">Lik</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">sfo_path_1 const</td> +<td align="right">16</td> +<td align="right">2693.0</td> +<td align="right">2686.8</td> +<td align="right">-1330.5</td> +</tr> +<tr class="even"> +<td align="left">fomc_path_1 const</td> +<td align="right">18</td> +<td align="right">2427.9</td> +<td align="right">2420.9</td> +<td align="right">-1196.0</td> +</tr> +<tr class="odd"> +<td align="left">dfop_path_1 const</td> +<td align="right">20</td> +<td align="right">2403.2</td> +<td align="right">2395.4</td> +<td align="right">-1181.6</td> +</tr> +<tr class="even"> +<td align="left">sforb_path_1 const</td> +<td align="right">20</td> +<td align="right">2401.4</td> +<td align="right">2393.6</td> +<td align="right">-1180.7</td> +</tr> +<tr class="odd"> +<td align="left">hs_path_1 const</td> +<td align="right">20</td> +<td align="right">2427.2</td> +<td align="right">2419.4</td> +<td align="right">-1193.6</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb16"><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="fl">1</span><span class="op">:</span><span class="fl">4</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>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">npar</th> +<th align="right">AIC</th> +<th align="right">BIC</th> +<th align="right">Lik</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">sfo_path_1 const</td> +<td align="right">16</td> +<td align="right">2693.0</td> +<td align="right">2686.8</td> +<td align="right">-1330.5</td> +</tr> +<tr class="even"> +<td align="left">sfo_path_1 tc</td> +<td align="right">17</td> +<td align="right">2657.6</td> +<td align="right">2651.0</td> +<td align="right">-1311.8</td> +</tr> +<tr class="odd"> +<td align="left">fomc_path_1 const</td> +<td align="right">18</td> +<td align="right">2427.9</td> +<td align="right">2420.9</td> +<td align="right">-1196.0</td> +</tr> +<tr class="even"> +<td align="left">fomc_path_1 tc</td> +<td align="right">19</td> +<td align="right">2423.6</td> +<td align="right">2416.2</td> +<td align="right">-1192.8</td> +</tr> +<tr class="odd"> +<td align="left">dfop_path_1 const</td> +<td align="right">20</td> +<td align="right">2403.2</td> +<td align="right">2395.4</td> +<td align="right">-1181.6</td> +</tr> +<tr class="even"> +<td align="left">sforb_path_1 const</td> +<td align="right">20</td> +<td align="right">2401.4</td> +<td align="right">2393.6</td> +<td align="right">-1180.7</td> +</tr> +<tr class="odd"> +<td align="left">dfop_path_1 tc</td> +<td align="right">20</td> +<td align="right">2398.0</td> +<td align="right">2390.1</td> +<td align="right">-1179.0</td> +</tr> +<tr class="even"> +<td align="left">sforb_path_1 tc</td> +<td align="right">20</td> +<td align="right">2399.9</td> +<td align="right">2392.1</td> +<td align="right">-1180.0</td> +</tr> +</tbody> +</table> +<p>For these two parent model, successful fits are shown below. Plots of +the fits with the other parent models are shown in the Appendix.</p> +<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">[[</span><span class="st">"dfop_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> +<div class="figure" style="text-align: center"> +<img src="2022_cyan_pathway_files/figure-html/unnamed-chunk-7-1.png" alt="DFOP pathway fit with two-component error" width="700"><p class="caption"> +DFOP pathway fit with two-component error +</p> +</div> +<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">[[</span><span class="st">"sforb_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> +<div class="figure" style="text-align: center"> +<img src="2022_cyan_pathway_files/figure-html/unnamed-chunk-8-1.png" alt="SFORB pathway fit with two-component error" width="700"><p class="caption"> +SFORB pathway fit with two-component error +</p> +</div> +<p>A closer graphical analysis of these Figures shows that the residues +of transformation product JCZ38 in the soils Tama and Nambsheim observed +at later time points are strongly and systematically underestimated.</p> +<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">stopCluster</a></span><span class="op">(</span><span class="va">cl_path_1</span><span class="op">)</span></span></code></pre></div> +</div> +<div class="section level3"> +<h3 id="alternative-pathway-fits">Alternative pathway fits<a class="anchor" aria-label="anchor" href="#alternative-pathway-fits"></a> +</h3> +<p>To improve the fit for JCZ38, a back-reaction from JSE76 to JCZ38 was +introduced in an alternative version of the transformation pathway, in +analogy to the back-reaction from K5A78 to K5A77. Both pairs of +transformation products are pairs of an organic acid with its +corresponding amide (Addendum 2014, p. 109). As FOMC provided the best +fit for the parent, and the biexponential models DFOP and SFORB provided +the best initial pathway fits, these three parent models are used in the +alternative pathway fits.</p> +<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">cyan_path_2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span></span> +<span> fomc_path_2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> +<span> cyan <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"FOMC"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"JCZ38"</span>, <span class="st">"J9Z38"</span><span class="op">)</span><span class="op">)</span>,</span> +<span> JCZ38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JSE76"</span><span class="op">)</span>,</span> +<span> J9Z38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> +<span> JSE76 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JCZ38"</span><span class="op">)</span>,</span> +<span> name <span class="op">=</span> <span class="st">"fomc_path_2"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span> +<span> dll_dir <span class="op">=</span> <span class="st">"cyan_dlls"</span>,</span> +<span> overwrite <span class="op">=</span> <span class="cn">TRUE</span></span> +<span> <span class="op">)</span>,</span> +<span> dfop_path_2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> +<span> cyan <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"DFOP"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"JCZ38"</span>, <span class="st">"J9Z38"</span><span class="op">)</span><span class="op">)</span>,</span> +<span> JCZ38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JSE76"</span><span class="op">)</span>,</span> +<span> J9Z38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> +<span> JSE76 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JCZ38"</span><span class="op">)</span>,</span> +<span> name <span class="op">=</span> <span class="st">"dfop_path_2"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span> +<span> dll_dir <span class="op">=</span> <span class="st">"cyan_dlls"</span>,</span> +<span> overwrite <span class="op">=</span> <span class="cn">TRUE</span></span> +<span> <span class="op">)</span>,</span> +<span> sforb_path_2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> +<span> cyan <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"JCZ38"</span>, <span class="st">"J9Z38"</span><span class="op">)</span><span class="op">)</span>,</span> +<span> JCZ38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JSE76"</span><span class="op">)</span>,</span> +<span> J9Z38 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> +<span> JSE76 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"JCZ38"</span><span class="op">)</span>,</span> +<span> name <span class="op">=</span> <span class="st">"sforb_path_2"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span> +<span> dll_dir <span class="op">=</span> <span class="st">"cyan_dlls"</span>,</span> +<span> overwrite <span class="op">=</span> <span class="cn">TRUE</span></span> +<span> <span class="op">)</span></span> +<span><span class="op">)</span></span> +<span></span> +<span><span class="va">cl_path_2</span> <span class="op"><-</span> <span class="fu">start_cluster</span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> +<span><span class="va">f_sep_2_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span></span> +<span> <span class="va">cyan_path_2</span>,</span> +<span> <span class="va">cyan_ds</span>,</span> +<span> error_model <span class="op">=</span> <span class="st">"const"</span>,</span> +<span> cluster <span class="op">=</span> <span class="va">cl_path_2</span>,</span> +<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> +<span></span> +<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_2_const</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">Nambsheim</th> +<th align="left">Tama</th> +<th align="left">Gross-Umstadt</th> +<th align="left">Sassafras</th> +<th align="left">Lleida</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">fomc_path_2</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">dfop_path_2</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">sforb_path_2</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<p>Using constant variance, separate fits converge with the exception of +the fits to the Sassafras soil data.</p> +<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">f_sep_2_tc</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_sep_2_const</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_2_tc</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">Nambsheim</th> +<th align="left">Tama</th> +<th align="left">Gross-Umstadt</th> +<th align="left">Sassafras</th> +<th align="left">Lleida</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">fomc_path_2</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">dfop_path_2</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">sforb_path_2</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<p>Using the two-component error model, all separate fits converge with +the exception of the alternative pathway fit with DFOP used for the +parent and the Sassafras dataset.</p> +<div class="sourceCode" id="cb22"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">f_saem_2</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mhmkin.html">mhmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">f_sep_2_const</span>, <span class="va">f_sep_2_tc</span><span class="op">)</span>,</span> +<span> no_random_effect <span class="op">=</span> <span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">cyan_saem_full</span><span class="op">[</span><span class="fl">2</span><span class="op">:</span><span class="fl">4</span>, <span class="op">]</span><span class="op">)</span>,</span> +<span> cluster <span class="op">=</span> <span class="va">cl_path_2</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">fomc_path_2</td> +<td align="left">E</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">dfop_path_2</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">sforb_path_2</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<p>The hierarchical fits for the alternative pathway completed +successfully, with the exception of the model using FOMC for the parent +compound and constant variance as the error model.</p> +<div class="sourceCode" id="cb24"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<colgroup> +<col width="14%"> +<col width="42%"> +<col width="42%"> +</colgroup> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">fomc_path_2</td> +<td align="left">E</td> +<td align="left">sd(f_JSE76_qlogis)</td> +</tr> +<tr class="even"> +<td align="left">dfop_path_2</td> +<td align="left">sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)</td> +<td align="left">sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)</td> +</tr> +<tr class="odd"> +<td align="left">sforb_path_2</td> +<td align="left">sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)</td> +<td align="left">sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)</td> +</tr> +</tbody> +</table> +<p>In all biphasic fits (DFOP or SFORB for the parent compound), the +random effects for the formation fractions for the pathways from JCZ38 +to JSE76, and for the reverse pathway from JSE76 to JCZ38 are +ill-defined.</p> +<div class="sourceCode" id="cb25"><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">"tc"</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>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">npar</th> +<th align="right">AIC</th> +<th align="right">BIC</th> +<th align="right">Lik</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">fomc_path_2 tc</td> +<td align="right">21</td> +<td align="right">2249.0</td> +<td align="right">2240.8</td> +<td align="right">-1103.5</td> +</tr> +<tr class="even"> +<td align="left">dfop_path_2 tc</td> +<td align="right">22</td> +<td align="right">2234.4</td> +<td align="right">2225.8</td> +<td align="right">-1095.2</td> +</tr> +<tr class="odd"> +<td align="left">sforb_path_2 tc</td> +<td align="right">22</td> +<td align="right">2239.7</td> +<td align="right">2231.1</td> +<td align="right">-1097.9</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb26"><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="fl">2</span><span class="op">:</span><span class="fl">3</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>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">dfop_path_2 const</td> +<td align="right">22</td> +<td align="right">2288.4</td> +<td align="right">2279.8</td> +<td align="right">-1122.2</td> +</tr> +<tr class="even"> +<td align="left">sforb_path_2 const</td> +<td align="right">22</td> +<td align="right">2283.3</td> +<td align="right">2274.7</td> +<td align="right">-1119.7</td> +</tr> +<tr class="odd"> +<td align="left">dfop_path_2 tc</td> +<td align="right">22</td> +<td align="right">2234.4</td> +<td align="right">2225.8</td> +<td align="right">-1095.2</td> +</tr> +<tr class="even"> +<td align="left">sforb_path_2 tc</td> +<td align="right">22</td> +<td align="right">2239.7</td> +<td align="right">2231.1</td> +<td align="right">-1097.9</td> +</tr> +</tbody> +</table> +<p>The variants using the biexponential models DFOP and SFORB for the +parent compound and the two-component error model give the lowest AIC +and BIC values and are plotted below. Compared with the original +pathway, the AIC and BIC values indicate a large improvement. This is +confirmed by the plots, which show that the metabolite JCZ38 is fitted +much better with this model.</p> +<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"fomc_path_2"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> +<div class="figure" style="text-align: center"> +<img src="2022_cyan_pathway_files/figure-html/unnamed-chunk-13-1.png" alt="FOMC pathway fit with two-component error, alternative pathway" width="700"><p class="caption"> +FOMC pathway fit with two-component error, alternative pathway +</p> +</div> +<div class="sourceCode" id="cb28"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"dfop_path_2"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> +<div class="figure" style="text-align: center"> +<img src="2022_cyan_pathway_files/figure-html/unnamed-chunk-14-1.png" alt="DFOP pathway fit with two-component error, alternative pathway" width="700"><p class="caption"> +DFOP pathway fit with two-component error, alternative pathway +</p> +</div> +<div class="sourceCode" id="cb29"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"sforb_path_2"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> +<div class="figure" style="text-align: center"> +<img src="2022_cyan_pathway_files/figure-html/unnamed-chunk-15-1.png" alt="SFORB pathway fit with two-component error, alternative pathway" width="700"><p class="caption"> +SFORB pathway fit with two-component error, alternative pathway +</p> +</div> +</div> +<div class="section level3"> +<h3 id="refinement-of-alternative-pathway-fits">Refinement of alternative pathway fits<a class="anchor" aria-label="anchor" href="#refinement-of-alternative-pathway-fits"></a> +</h3> +<p>All ill-defined random effects that were identified in the parent +only fits and in the above pathway fits, are excluded for the final +evaluations below. For this purpose, a list of character vectors is +created below that can be indexed by row and column indices, and which +contains the degradation parameter names for which random effects should +be excluded for each of the hierarchical fits contained in +<code>f_saem_2</code>.</p> +<div class="sourceCode" id="cb30"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">no_ranef</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/matrix.html" class="external-link">matrix</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="op">)</span>, nrow <span class="op">=</span> <span class="fl">3</span>, ncol <span class="op">=</span> <span class="fl">2</span>, dimnames <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/dimnames.html" class="external-link">dimnames</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="va">no_ranef</span><span class="op">[[</span><span class="st">"fomc_path_2"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"log_beta"</span>, <span class="st">"f_JCZ38_qlogis"</span>, <span class="st">"f_JSE76_qlogis"</span><span class="op">)</span></span> +<span><span class="va">no_ranef</span><span class="op">[[</span><span class="st">"fomc_path_2"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"cyan_0"</span>, <span class="st">"f_JCZ38_qlogis"</span>, <span class="st">"f_JSE76_qlogis"</span><span class="op">)</span></span> +<span><span class="va">no_ranef</span><span class="op">[[</span><span class="st">"dfop_path_2"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"cyan_0"</span>, <span class="st">"f_JCZ38_qlogis"</span>, <span class="st">"f_JSE76_qlogis"</span><span class="op">)</span></span> +<span><span class="va">no_ranef</span><span class="op">[[</span><span class="st">"dfop_path_2"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"cyan_0"</span>, <span class="st">"log_k1"</span>, <span class="st">"f_JCZ38_qlogis"</span>, <span class="st">"f_JSE76_qlogis"</span><span class="op">)</span></span> +<span><span class="va">no_ranef</span><span class="op">[[</span><span class="st">"sforb_path_2"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"cyan_free_0"</span>,</span> +<span> <span class="st">"f_JCZ38_qlogis"</span>, <span class="st">"f_JSE76_qlogis"</span><span class="op">)</span></span> +<span><span class="va">no_ranef</span><span class="op">[[</span><span class="st">"sforb_path_2"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"cyan_free_0"</span>, <span class="st">"log_k_cyan_free_bound"</span>,</span> +<span> <span class="st">"f_JCZ38_qlogis"</span>, <span class="st">"f_JSE76_qlogis"</span><span class="op">)</span></span> +<span><span class="fu"><a href="https://rdrr.io/r/parallel/clusterApply.html" class="external-link">clusterExport</a></span><span class="op">(</span><span class="va">cl_path_2</span>, <span class="st">"no_ranef"</span><span class="op">)</span></span> +<span></span> +<span><span class="va">f_saem_3</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_saem_2</span>,</span> +<span> no_random_effect <span class="op">=</span> <span class="va">no_ranef</span>,</span> +<span> cluster <span class="op">=</span> <span class="va">cl_path_2</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb31"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_saem_3</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">fomc_path_2</td> +<td align="left">E</td> +<td align="left">Fth</td> +</tr> +<tr class="even"> +<td align="left">dfop_path_2</td> +<td align="left">Fth</td> +<td align="left">Fth</td> +</tr> +<tr class="odd"> +<td align="left">sforb_path_2</td> +<td align="left">Fth</td> +<td align="left">Fth</td> +</tr> +</tbody> +</table> +<p>With the exception of the FOMC pathway fit with constant variance, +all updated fits completed successfully. However, the Fisher Information +Matrix for the fixed effects (Fth) could not be inverted, so no +confidence intervals for the optimised parameters are available.</p> +<div class="sourceCode" id="cb32"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_3</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">fomc_path_2</td> +<td align="left">E</td> +<td align="left"></td> +</tr> +<tr class="even"> +<td align="left">dfop_path_2</td> +<td align="left"></td> +<td align="left"></td> +</tr> +<tr class="odd"> +<td align="left">sforb_path_2</td> +<td align="left"></td> +<td align="left"></td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb33"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_3</span><span class="op">[</span>, <span class="st">"tc"</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>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">npar</th> +<th align="right">AIC</th> +<th align="right">BIC</th> +<th align="right">Lik</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">fomc_path_2 tc</td> +<td align="right">19</td> +<td align="right">2249.1</td> +<td align="right">2241.6</td> +<td align="right">-1105.5</td> +</tr> +<tr class="even"> +<td align="left">dfop_path_2 tc</td> +<td align="right">20</td> +<td align="right">2237.3</td> +<td align="right">2229.5</td> +<td align="right">-1098.6</td> +</tr> +<tr class="odd"> +<td align="left">sforb_path_2 tc</td> +<td align="right">20</td> +<td align="right">2241.3</td> +<td align="right">2233.5</td> +<td align="right">-1100.7</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb34"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_3</span><span class="op">[</span><span class="fl">2</span><span class="op">:</span><span class="fl">3</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>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">dfop_path_2 const</td> +<td align="right">20</td> +<td align="right">2282.2</td> +<td align="right">2274.4</td> +<td align="right">-1121.1</td> +</tr> +<tr class="even"> +<td align="left">sforb_path_2 const</td> +<td align="right">20</td> +<td align="right">2279.7</td> +<td align="right">2271.9</td> +<td align="right">-1119.9</td> +</tr> +<tr class="odd"> +<td align="left">dfop_path_2 tc</td> +<td align="right">20</td> +<td align="right">2237.3</td> +<td align="right">2229.5</td> +<td align="right">-1098.6</td> +</tr> +<tr class="even"> +<td align="left">sforb_path_2 tc</td> +<td align="right">20</td> +<td align="right">2241.3</td> +<td align="right">2233.5</td> +<td align="right">-1100.7</td> +</tr> +</tbody> +</table> +<p>While the AIC and BIC values of the best fit (DFOP pathway fit with +two-component error) are lower than in the previous fits with the +alternative pathway, the practical value of these refined evaluations is +limited as no confidence intervals are obtained.</p> +<div class="sourceCode" id="cb35"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">stopCluster</a></span><span class="op">(</span><span class="va">cl_path_2</span><span class="op">)</span></span></code></pre></div> +</div> +</div> +<div class="section level2"> +<h2 id="conclusion">Conclusion<a class="anchor" aria-label="anchor" href="#conclusion"></a> +</h2> +<p>It was demonstrated that a relatively complex transformation pathway +with parallel formation of two primary metabolites and one secondary +metabolite can be fitted even if the data in the individual datasets are +quite different and partly only cover the formation phase.</p> +<p>The run times of the pathway fits were several hours, limiting the +practical feasibility of iterative refinements based on ill-defined +parameters and of alternative checks of parameter identifiability based +on multistart runs.</p> +</div> +<div class="section level2"> +<h2 id="acknowledgements">Acknowledgements<a class="anchor" aria-label="anchor" href="#acknowledgements"></a> +</h2> +<p>The helpful comments by Janina Wöltjen of the German Environment +Agency are gratefully acknowledged.</p> +</div> +<div class="section level2"> +<h2 id="appendix">Appendix<a class="anchor" aria-label="anchor" href="#appendix"></a> +</h2> +<div class="section level3"> +<h3 id="plots-of-fits-that-were-not-refined-further">Plots of fits that were not refined further<a class="anchor" aria-label="anchor" href="#plots-of-fits-that-were-not-refined-further"></a> +</h3> +<div class="sourceCode" id="cb36"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">[[</span><span class="st">"sfo_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> +<div class="figure" style="text-align: center"> +<img src="2022_cyan_pathway_files/figure-html/unnamed-chunk-20-1.png" alt="SFO pathway fit with two-component error" width="700"><p class="caption"> +SFO pathway fit with two-component error +</p> +</div> +<div class="sourceCode" id="cb37"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">[[</span><span class="st">"fomc_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> +<div class="figure" style="text-align: center"> +<img src="2022_cyan_pathway_files/figure-html/unnamed-chunk-21-1.png" alt="FOMC pathway fit with two-component error" width="700"><p class="caption"> +FOMC pathway fit with two-component error +</p> +</div> +<div class="sourceCode" id="cb38"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">[[</span><span class="st">"sforb_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> +<div class="figure" style="text-align: center"> +<img src="2022_cyan_pathway_files/figure-html/unnamed-chunk-22-1.png" alt="HS pathway fit with two-component error" width="700"><p class="caption"> +HS pathway fit with two-component error +</p> +</div> +</div> +<div class="section level3"> +<h3 id="hierarchical-fit-listings">Hierarchical fit listings<a class="anchor" aria-label="anchor" href="#hierarchical-fit-listings"></a> +</h3> +<div class="section level4"> +<h4 id="pathway-1">Pathway 1<a class="anchor" aria-label="anchor" href="#pathway-1"></a> +</h4> +<caption> +Hierarchical SFO path 1 fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.4.2 +Date of fit: Fri Feb 14 07:42:26 2025 +Date of summary: Sun Feb 16 17:03:40 2025 + +Equations: +d_cyan/dt = - k_cyan * cyan +d_JCZ38/dt = + f_cyan_to_JCZ38 * k_cyan * cyan - k_JCZ38 * JCZ38 +d_J9Z38/dt = + f_cyan_to_J9Z38 * k_cyan * cyan - k_J9Z38 * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 437.151 s +Using 300, 100 iterations and 10 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + cyan_0 log_k_cyan log_k_JCZ38 log_k_J9Z38 log_k_JSE76 + 95.3304 -3.8459 -3.1305 -5.0678 -5.3196 + f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis + 0.8158 23.5335 11.8774 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_0 log_k_cyan log_k_JCZ38 log_k_J9Z38 log_k_JSE76 +cyan_0 4.797 0.0000 0.000 0.000 0.0000 +log_k_cyan 0.000 0.9619 0.000 0.000 0.0000 +log_k_JCZ38 0.000 0.0000 2.139 0.000 0.0000 +log_k_J9Z38 0.000 0.0000 0.000 1.639 0.0000 +log_k_JSE76 0.000 0.0000 0.000 0.000 0.7894 +f_cyan_ilr_1 0.000 0.0000 0.000 0.000 0.0000 +f_cyan_ilr_2 0.000 0.0000 0.000 0.000 0.0000 +f_JCZ38_qlogis 0.000 0.0000 0.000 0.000 0.0000 + f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis +cyan_0 0.0000 0.000 0.00 +log_k_cyan 0.0000 0.000 0.00 +log_k_JCZ38 0.0000 0.000 0.00 +log_k_J9Z38 0.0000 0.000 0.00 +log_k_JSE76 0.0000 0.000 0.00 +f_cyan_ilr_1 0.7714 0.000 0.00 +f_cyan_ilr_2 0.0000 9.247 0.00 +f_JCZ38_qlogis 0.0000 0.000 16.61 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2693 2687 -1331 + +Optimised parameters: + est. lower upper +cyan_0 95.1279 9.354e+01 9.671e+01 +log_k_cyan -3.8527 -4.367e+00 -3.338e+00 +log_k_JCZ38 -3.0381 -4.187e+00 -1.889e+00 +log_k_J9Z38 -5.0095 -5.623e+00 -4.396e+00 +log_k_JSE76 -5.3357 -6.025e+00 -4.646e+00 +f_cyan_ilr_1 0.8050 5.174e-01 1.093e+00 +f_cyan_ilr_2 12.4820 -1.050e+06 1.051e+06 +f_JCZ38_qlogis 1.2912 3.561e-01 2.226e+00 +a.1 4.8393 NA NA +SD.log_k_cyan 0.5840 NA NA +SD.log_k_JCZ38 1.2740 NA NA +SD.log_k_J9Z38 0.3172 NA NA +SD.log_k_JSE76 0.5677 NA NA +SD.f_cyan_ilr_1 0.2623 NA NA +SD.f_cyan_ilr_2 1.3724 NA NA +SD.f_JCZ38_qlogis 0.1464 NA NA + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_cyan 0.5840 NA NA +SD.log_k_JCZ38 1.2740 NA NA +SD.log_k_J9Z38 0.3172 NA NA +SD.log_k_JSE76 0.5677 NA NA +SD.f_cyan_ilr_1 0.2623 NA NA +SD.f_cyan_ilr_2 1.3724 NA NA +SD.f_JCZ38_qlogis 0.1464 NA NA + +Variance model: + est. lower upper +a.1 4.839 NA NA + +Backtransformed parameters: + est. lower upper +cyan_0 95.127935 93.542456 96.713413 +k_cyan 0.021221 0.012687 0.035497 +k_JCZ38 0.047924 0.015189 0.151213 +k_J9Z38 0.006674 0.003612 0.012332 +k_JSE76 0.004817 0.002417 0.009601 +f_cyan_to_JCZ38 0.757402 NA NA +f_cyan_to_J9Z38 0.242597 NA NA +f_JCZ38_to_JSE76 0.784347 0.588098 0.902582 + +Resulting formation fractions: + ff +cyan_JCZ38 7.574e-01 +cyan_J9Z38 2.426e-01 +cyan_sink 9.839e-08 +JCZ38_JSE76 7.843e-01 +JCZ38_sink 2.157e-01 + +Estimated disappearance times: + DT50 DT90 +cyan 32.66 108.50 +JCZ38 14.46 48.05 +J9Z38 103.86 345.00 +JSE76 143.91 478.04 + +</code></pre> +<p></p> +<caption> +Hierarchical SFO path 1 fit with two-component error +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.4.2 +Date of fit: Fri Feb 14 07:42:06 2025 +Date of summary: Sun Feb 16 17:03:40 2025 + +Equations: +d_cyan/dt = - k_cyan * cyan +d_JCZ38/dt = + f_cyan_to_JCZ38 * k_cyan * cyan - k_JCZ38 * JCZ38 +d_J9Z38/dt = + f_cyan_to_J9Z38 * k_cyan * cyan - k_J9Z38 * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 417.143 s +Using 300, 100 iterations and 10 chains + +Variance model: Two-component variance function + +Starting values for degradation parameters: + cyan_0 log_k_cyan log_k_JCZ38 log_k_J9Z38 log_k_JSE76 + 96.0039 -3.8907 -3.1276 -5.0069 -4.9367 + f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis + 0.7937 22.3422 17.8932 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_0 log_k_cyan log_k_JCZ38 log_k_J9Z38 log_k_JSE76 +cyan_0 4.859 0.000 0.00 0.00 0.0000 +log_k_cyan 0.000 0.962 0.00 0.00 0.0000 +log_k_JCZ38 0.000 0.000 2.04 0.00 0.0000 +log_k_J9Z38 0.000 0.000 0.00 1.72 0.0000 +log_k_JSE76 0.000 0.000 0.00 0.00 0.9076 +f_cyan_ilr_1 0.000 0.000 0.00 0.00 0.0000 +f_cyan_ilr_2 0.000 0.000 0.00 0.00 0.0000 +f_JCZ38_qlogis 0.000 0.000 0.00 0.00 0.0000 + f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis +cyan_0 0.0000 0.000 0.00 +log_k_cyan 0.0000 0.000 0.00 +log_k_JCZ38 0.0000 0.000 0.00 +log_k_J9Z38 0.0000 0.000 0.00 +log_k_JSE76 0.0000 0.000 0.00 +f_cyan_ilr_1 0.7598 0.000 0.00 +f_cyan_ilr_2 0.0000 8.939 0.00 +f_JCZ38_qlogis 0.0000 0.000 14.49 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2658 2651 -1312 + +Optimised parameters: + est. lower upper +cyan_0 94.81681 NA NA +log_k_cyan -3.91558 NA NA +log_k_JCZ38 -3.12715 NA NA +log_k_J9Z38 -5.04840 NA NA +log_k_JSE76 -5.10443 NA NA +f_cyan_ilr_1 0.80760 NA NA +f_cyan_ilr_2 48.66960 NA NA +f_JCZ38_qlogis 3.03397 NA NA +a.1 3.93879 NA NA +b.1 0.08057 NA NA +SD.log_k_cyan 0.58921 NA NA +SD.log_k_JCZ38 1.29813 NA NA +SD.log_k_J9Z38 0.68372 NA NA +SD.log_k_JSE76 0.35128 NA NA +SD.f_cyan_ilr_1 0.38352 NA NA +SD.f_cyan_ilr_2 4.98884 NA NA +SD.f_JCZ38_qlogis 1.75636 NA NA + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_cyan 0.5892 NA NA +SD.log_k_JCZ38 1.2981 NA NA +SD.log_k_J9Z38 0.6837 NA NA +SD.log_k_JSE76 0.3513 NA NA +SD.f_cyan_ilr_1 0.3835 NA NA +SD.f_cyan_ilr_2 4.9888 NA NA +SD.f_JCZ38_qlogis 1.7564 NA NA + +Variance model: + est. lower upper +a.1 3.93879 NA NA +b.1 0.08057 NA NA + +Backtransformed parameters: + est. lower upper +cyan_0 94.81681 NA NA +k_cyan 0.01993 NA NA +k_JCZ38 0.04384 NA NA +k_J9Z38 0.00642 NA NA +k_JSE76 0.00607 NA NA +f_cyan_to_JCZ38 0.75807 NA NA +f_cyan_to_J9Z38 0.24193 NA NA +f_JCZ38_to_JSE76 0.95409 NA NA + +Resulting formation fractions: + ff +cyan_JCZ38 0.75807 +cyan_J9Z38 0.24193 +cyan_sink 0.00000 +JCZ38_JSE76 0.95409 +JCZ38_sink 0.04591 + +Estimated disappearance times: + DT50 DT90 +cyan 34.78 115.54 +JCZ38 15.81 52.52 +J9Z38 107.97 358.68 +JSE76 114.20 379.35 + +</code></pre> +<p></p> +<caption> +Hierarchical FOMC path 1 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: 4.4.2 +Date of fit: Fri Feb 14 07:42:57 2025 +Date of summary: Sun Feb 16 17:03:40 2025 + +Equations: +d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan +d_JCZ38/dt = + f_cyan_to_JCZ38 * (alpha/beta) * 1/((time/beta) + 1) * + cyan - k_JCZ38 * JCZ38 +d_J9Z38/dt = + f_cyan_to_J9Z38 * (alpha/beta) * 1/((time/beta) + 1) * + cyan - k_J9Z38 * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 468.609 s +Using 300, 100 iterations and 10 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 + 101.2314 -3.3680 -5.1108 -5.9416 0.7144 + f_cyan_ilr_2 f_JCZ38_qlogis log_alpha log_beta + 7.0229 14.9234 -0.1791 2.9811 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 +cyan_0 5.416 0.000 0.0 0.000 0.0000 +log_k_JCZ38 0.000 2.439 0.0 0.000 0.0000 +log_k_J9Z38 0.000 0.000 1.7 0.000 0.0000 +log_k_JSE76 0.000 0.000 0.0 1.856 0.0000 +f_cyan_ilr_1 0.000 0.000 0.0 0.000 0.7164 +f_cyan_ilr_2 0.000 0.000 0.0 0.000 0.0000 +f_JCZ38_qlogis 0.000 0.000 0.0 0.000 0.0000 +log_alpha 0.000 0.000 0.0 0.000 0.0000 +log_beta 0.000 0.000 0.0 0.000 0.0000 + f_cyan_ilr_2 f_JCZ38_qlogis log_alpha log_beta +cyan_0 0.00 0.00 0.0000 0.0000 +log_k_JCZ38 0.00 0.00 0.0000 0.0000 +log_k_J9Z38 0.00 0.00 0.0000 0.0000 +log_k_JSE76 0.00 0.00 0.0000 0.0000 +f_cyan_ilr_1 0.00 0.00 0.0000 0.0000 +f_cyan_ilr_2 11.57 0.00 0.0000 0.0000 +f_JCZ38_qlogis 0.00 18.81 0.0000 0.0000 +log_alpha 0.00 0.00 0.4144 0.0000 +log_beta 0.00 0.00 0.0000 0.5077 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2428 2421 -1196 + +Optimised parameters: + est. lower upper +cyan_0 101.1664 98.51265 103.8202 +log_k_JCZ38 -3.3883 -4.78250 -1.9941 +log_k_J9Z38 -5.3087 -5.91564 -4.7017 +log_k_JSE76 -6.1313 -7.30061 -4.9619 +f_cyan_ilr_1 0.7456 0.43782 1.0534 +f_cyan_ilr_2 0.8181 0.24956 1.3866 +f_JCZ38_qlogis 2.0467 0.61165 3.4817 +log_alpha -0.2391 -0.62806 0.1499 +log_beta 2.8739 2.67664 3.0711 +a.1 3.4160 3.17960 3.6525 +SD.cyan_0 2.4355 0.40399 4.4671 +SD.log_k_JCZ38 1.5654 0.57311 2.5576 +SD.log_k_J9Z38 0.4645 -0.06533 0.9943 +SD.log_k_JSE76 0.9841 0.10738 1.8609 +SD.f_cyan_ilr_1 0.3285 0.10546 0.5515 +SD.f_cyan_ilr_2 0.2276 -0.38711 0.8424 +SD.f_JCZ38_qlogis 0.8340 -0.20970 1.8777 +SD.log_alpha 0.4250 0.16017 0.6898 + +Correlation: + cyan_0 l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 log_lph +log_k_JCZ38 -0.0159 +log_k_J9Z38 -0.0546 0.0080 +log_k_JSE76 -0.0337 0.0016 0.0074 +f_cyan_ilr_1 -0.0095 0.0194 -0.1573 0.0003 +f_cyan_ilr_2 -0.2733 0.0799 0.3059 0.0263 0.0125 +f_JCZ38_qlogis 0.0755 -0.0783 -0.0516 0.1222 -0.1155 -0.5231 +log_alpha -0.0567 0.0120 0.0351 0.0189 0.0040 0.0829 -0.0502 +log_beta -0.2980 0.0461 0.1382 0.0758 0.0209 0.4079 -0.2053 0.2759 + +Random effects: + est. lower upper +SD.cyan_0 2.4355 0.40399 4.4671 +SD.log_k_JCZ38 1.5654 0.57311 2.5576 +SD.log_k_J9Z38 0.4645 -0.06533 0.9943 +SD.log_k_JSE76 0.9841 0.10738 1.8609 +SD.f_cyan_ilr_1 0.3285 0.10546 0.5515 +SD.f_cyan_ilr_2 0.2276 -0.38711 0.8424 +SD.f_JCZ38_qlogis 0.8340 -0.20970 1.8777 +SD.log_alpha 0.4250 0.16017 0.6898 + +Variance model: + est. lower upper +a.1 3.416 3.18 3.652 + +Backtransformed parameters: + est. lower upper +cyan_0 1.012e+02 9.851e+01 103.82023 +k_JCZ38 3.377e-02 8.375e-03 0.13614 +k_J9Z38 4.948e-03 2.697e-03 0.00908 +k_JSE76 2.174e-03 6.751e-04 0.00700 +f_cyan_to_JCZ38 6.389e-01 NA NA +f_cyan_to_J9Z38 2.226e-01 NA NA +f_JCZ38_to_JSE76 8.856e-01 6.483e-01 0.97016 +alpha 7.873e-01 5.336e-01 1.16166 +beta 1.771e+01 1.454e+01 21.56509 + +Resulting formation fractions: + ff +cyan_JCZ38 0.6389 +cyan_J9Z38 0.2226 +cyan_sink 0.1385 +JCZ38_JSE76 0.8856 +JCZ38_sink 0.1144 + +Estimated disappearance times: + DT50 DT90 DT50back +cyan 25.00 312.06 93.94 +JCZ38 20.53 68.19 NA +J9Z38 140.07 465.32 NA +JSE76 318.86 1059.22 NA + +</code></pre> +<p></p> +<caption> +Hierarchical FOMC path 1 fit with two-component error +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.4.2 +Date of fit: Fri Feb 14 07:42:50 2025 +Date of summary: Sun Feb 16 17:03:40 2025 + +Equations: +d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan +d_JCZ38/dt = + f_cyan_to_JCZ38 * (alpha/beta) * 1/((time/beta) + 1) * + cyan - k_JCZ38 * JCZ38 +d_J9Z38/dt = + f_cyan_to_J9Z38 * (alpha/beta) * 1/((time/beta) + 1) * + cyan - k_J9Z38 * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 460.309 s +Using 300, 100 iterations and 10 chains + +Variance model: Two-component variance function + +Starting values for degradation parameters: + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 + 101.13294 -3.32499 -5.09097 -5.93566 0.71359 + f_cyan_ilr_2 f_JCZ38_qlogis log_alpha log_beta + 10.30315 14.62272 -0.09633 3.10634 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 +cyan_0 5.649 0.000 0.00 0.00 0.0000 +log_k_JCZ38 0.000 2.319 0.00 0.00 0.0000 +log_k_J9Z38 0.000 0.000 1.73 0.00 0.0000 +log_k_JSE76 0.000 0.000 0.00 1.86 0.0000 +f_cyan_ilr_1 0.000 0.000 0.00 0.00 0.7183 +f_cyan_ilr_2 0.000 0.000 0.00 0.00 0.0000 +f_JCZ38_qlogis 0.000 0.000 0.00 0.00 0.0000 +log_alpha 0.000 0.000 0.00 0.00 0.0000 +log_beta 0.000 0.000 0.00 0.00 0.0000 + f_cyan_ilr_2 f_JCZ38_qlogis log_alpha log_beta +cyan_0 0.00 0.00 0.0000 0.0000 +log_k_JCZ38 0.00 0.00 0.0000 0.0000 +log_k_J9Z38 0.00 0.00 0.0000 0.0000 +log_k_JSE76 0.00 0.00 0.0000 0.0000 +f_cyan_ilr_1 0.00 0.00 0.0000 0.0000 +f_cyan_ilr_2 12.85 0.00 0.0000 0.0000 +f_JCZ38_qlogis 0.00 18.54 0.0000 0.0000 +log_alpha 0.00 0.00 0.3142 0.0000 +log_beta 0.00 0.00 0.0000 0.7333 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2424 2416 -1193 + +Optimised parameters: + est. lower upper +cyan_0 100.65667 NA NA +log_k_JCZ38 -3.45782 NA NA +log_k_J9Z38 -5.23476 NA NA +log_k_JSE76 -5.71827 NA NA +f_cyan_ilr_1 0.68389 NA NA +f_cyan_ilr_2 0.61027 NA NA +f_JCZ38_qlogis 116.27482 NA NA +log_alpha -0.14484 NA NA +log_beta 3.03220 NA NA +a.1 3.11051 NA NA +b.1 0.04508 NA NA +SD.log_k_JCZ38 1.39961 NA NA +SD.log_k_J9Z38 0.57920 NA NA +SD.log_k_JSE76 0.68364 NA NA +SD.f_cyan_ilr_1 0.31477 NA NA +SD.f_cyan_ilr_2 0.37716 NA NA +SD.f_JCZ38_qlogis 5.52695 NA NA +SD.log_alpha 0.22823 NA NA +SD.log_beta 0.39161 NA NA + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_JCZ38 1.3996 NA NA +SD.log_k_J9Z38 0.5792 NA NA +SD.log_k_JSE76 0.6836 NA NA +SD.f_cyan_ilr_1 0.3148 NA NA +SD.f_cyan_ilr_2 0.3772 NA NA +SD.f_JCZ38_qlogis 5.5270 NA NA +SD.log_alpha 0.2282 NA NA +SD.log_beta 0.3916 NA NA + +Variance model: + est. lower upper +a.1 3.11051 NA NA +b.1 0.04508 NA NA + +Backtransformed parameters: + est. lower upper +cyan_0 1.007e+02 NA NA +k_JCZ38 3.150e-02 NA NA +k_J9Z38 5.328e-03 NA NA +k_JSE76 3.285e-03 NA NA +f_cyan_to_JCZ38 5.980e-01 NA NA +f_cyan_to_J9Z38 2.273e-01 NA NA +f_JCZ38_to_JSE76 1.000e+00 NA NA +alpha 8.652e-01 NA NA +beta 2.074e+01 NA NA + +Resulting formation fractions: + ff +cyan_JCZ38 0.5980 +cyan_J9Z38 0.2273 +cyan_sink 0.1746 +JCZ38_JSE76 1.0000 +JCZ38_sink 0.0000 + +Estimated disappearance times: + DT50 DT90 DT50back +cyan 25.48 276.2 83.15 +JCZ38 22.01 73.1 NA +J9Z38 130.09 432.2 NA +JSE76 210.98 700.9 NA + +</code></pre> +<p></p> +<caption> +Hierarchical DFOP path 1 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: 4.4.2 +Date of fit: Fri Feb 14 07:43:33 2025 +Date of summary: Sun Feb 16 17:03:40 2025 + +Equations: +d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * + time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) + * cyan +d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - + g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * + exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38 +d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - + g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * + exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 504.014 s +Using 300, 100 iterations and 10 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 + 102.0643 -3.4008 -5.0024 -5.8612 0.6855 + f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 g_qlogis + 1.2366 13.6901 -1.8641 -4.5063 -0.6468 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 +cyan_0 4.466 0.000 0.000 0.000 0.0000 +log_k_JCZ38 0.000 2.382 0.000 0.000 0.0000 +log_k_J9Z38 0.000 0.000 1.595 0.000 0.0000 +log_k_JSE76 0.000 0.000 0.000 1.245 0.0000 +f_cyan_ilr_1 0.000 0.000 0.000 0.000 0.6852 +f_cyan_ilr_2 0.000 0.000 0.000 0.000 0.0000 +f_JCZ38_qlogis 0.000 0.000 0.000 0.000 0.0000 +log_k1 0.000 0.000 0.000 0.000 0.0000 +log_k2 0.000 0.000 0.000 0.000 0.0000 +g_qlogis 0.000 0.000 0.000 0.000 0.0000 + f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 g_qlogis +cyan_0 0.00 0.00 0.0000 0.0000 0.000 +log_k_JCZ38 0.00 0.00 0.0000 0.0000 0.000 +log_k_J9Z38 0.00 0.00 0.0000 0.0000 0.000 +log_k_JSE76 0.00 0.00 0.0000 0.0000 0.000 +f_cyan_ilr_1 0.00 0.00 0.0000 0.0000 0.000 +f_cyan_ilr_2 1.28 0.00 0.0000 0.0000 0.000 +f_JCZ38_qlogis 0.00 16.08 0.0000 0.0000 0.000 +log_k1 0.00 0.00 0.9866 0.0000 0.000 +log_k2 0.00 0.00 0.0000 0.5953 0.000 +g_qlogis 0.00 0.00 0.0000 0.0000 1.583 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2403 2395 -1182 + +Optimised parameters: + est. lower upper +cyan_0 102.5565 NA NA +log_k_JCZ38 -3.4729 NA NA +log_k_J9Z38 -5.1533 NA NA +log_k_JSE76 -5.6669 NA NA +f_cyan_ilr_1 0.6665 NA NA +f_cyan_ilr_2 0.5191 NA NA +f_JCZ38_qlogis 37.0113 NA NA +log_k1 -1.8497 NA NA +log_k2 -4.4931 NA NA +g_qlogis -0.6383 NA NA +a.1 3.2397 NA NA +SD.log_k_JCZ38 1.4286 NA NA +SD.log_k_J9Z38 0.5312 NA NA +SD.log_k_JSE76 0.6627 NA NA +SD.f_cyan_ilr_1 0.3013 NA NA +SD.f_cyan_ilr_2 0.2980 NA NA +SD.f_JCZ38_qlogis 0.1637 NA NA +SD.log_k1 0.5069 NA NA +SD.log_k2 0.3828 NA NA +SD.g_qlogis 0.8641 NA NA + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_JCZ38 1.4286 NA NA +SD.log_k_J9Z38 0.5312 NA NA +SD.log_k_JSE76 0.6627 NA NA +SD.f_cyan_ilr_1 0.3013 NA NA +SD.f_cyan_ilr_2 0.2980 NA NA +SD.f_JCZ38_qlogis 0.1637 NA NA +SD.log_k1 0.5069 NA NA +SD.log_k2 0.3828 NA NA +SD.g_qlogis 0.8641 NA NA + +Variance model: + est. lower upper +a.1 3.24 NA NA + +Backtransformed parameters: + est. lower upper +cyan_0 1.026e+02 NA NA +k_JCZ38 3.103e-02 NA NA +k_J9Z38 5.780e-03 NA NA +k_JSE76 3.459e-03 NA NA +f_cyan_to_JCZ38 5.813e-01 NA NA +f_cyan_to_J9Z38 2.265e-01 NA NA +f_JCZ38_to_JSE76 1.000e+00 NA NA +k1 1.573e-01 NA NA +k2 1.119e-02 NA NA +g 3.456e-01 NA NA + +Resulting formation fractions: + ff +cyan_JCZ38 0.5813 +cyan_J9Z38 0.2265 +cyan_sink 0.1922 +JCZ38_JSE76 1.0000 +JCZ38_sink 0.0000 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +cyan 25.23 167.94 50.55 4.407 61.97 +JCZ38 22.34 74.22 NA NA NA +J9Z38 119.92 398.36 NA NA NA +JSE76 200.41 665.76 NA NA NA + +</code></pre> +<p></p> +<caption> +Hierarchical DFOP path 1 fit with two-component error +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.4.2 +Date of fit: Fri Feb 14 07:46:07 2025 +Date of summary: Sun Feb 16 17:03:40 2025 + +Equations: +d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * + time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) + * cyan +d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - + g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * + exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38 +d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - + g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * + exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 658.043 s +Using 300, 100 iterations and 10 chains + +Variance model: Two-component variance function + +Starting values for degradation parameters: + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 + 101.3964 -3.3626 -4.9792 -5.8727 0.6814 + f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 g_qlogis + 6.8713 13.6901 -1.9222 -4.5035 -0.7172 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 +cyan_0 5.317 0.000 0.000 0.000 0.0000 +log_k_JCZ38 0.000 2.272 0.000 0.000 0.0000 +log_k_J9Z38 0.000 0.000 1.633 0.000 0.0000 +log_k_JSE76 0.000 0.000 0.000 1.271 0.0000 +f_cyan_ilr_1 0.000 0.000 0.000 0.000 0.6839 +f_cyan_ilr_2 0.000 0.000 0.000 0.000 0.0000 +f_JCZ38_qlogis 0.000 0.000 0.000 0.000 0.0000 +log_k1 0.000 0.000 0.000 0.000 0.0000 +log_k2 0.000 0.000 0.000 0.000 0.0000 +g_qlogis 0.000 0.000 0.000 0.000 0.0000 + f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 g_qlogis +cyan_0 0.00 0.00 0.0000 0.0000 0.000 +log_k_JCZ38 0.00 0.00 0.0000 0.0000 0.000 +log_k_J9Z38 0.00 0.00 0.0000 0.0000 0.000 +log_k_JSE76 0.00 0.00 0.0000 0.0000 0.000 +f_cyan_ilr_1 0.00 0.00 0.0000 0.0000 0.000 +f_cyan_ilr_2 11.95 0.00 0.0000 0.0000 0.000 +f_JCZ38_qlogis 0.00 16.08 0.0000 0.0000 0.000 +log_k1 0.00 0.00 0.9496 0.0000 0.000 +log_k2 0.00 0.00 0.0000 0.5846 0.000 +g_qlogis 0.00 0.00 0.0000 0.0000 1.719 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2398 2390 -1179 + +Optimised parameters: + est. lower upper +cyan_0 100.69709 NA NA +log_k_JCZ38 -3.46669 NA NA +log_k_J9Z38 -5.05076 NA NA +log_k_JSE76 -5.55558 NA NA +f_cyan_ilr_1 0.66045 NA NA +f_cyan_ilr_2 0.84275 NA NA +f_JCZ38_qlogis 64.22404 NA NA +log_k1 -2.17715 NA NA +log_k2 -4.55002 NA NA +g_qlogis -0.55920 NA NA +a.1 2.95785 NA NA +b.1 0.04456 NA NA +SD.log_k_JCZ38 1.39881 NA NA +SD.log_k_J9Z38 0.67788 NA NA +SD.log_k_JSE76 0.52603 NA NA +SD.f_cyan_ilr_1 0.32490 NA NA +SD.f_cyan_ilr_2 0.53923 NA NA +SD.f_JCZ38_qlogis 2.75576 NA NA +SD.log_k2 0.30694 NA NA +SD.g_qlogis 0.83619 NA NA + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_JCZ38 1.3988 NA NA +SD.log_k_J9Z38 0.6779 NA NA +SD.log_k_JSE76 0.5260 NA NA +SD.f_cyan_ilr_1 0.3249 NA NA +SD.f_cyan_ilr_2 0.5392 NA NA +SD.f_JCZ38_qlogis 2.7558 NA NA +SD.log_k2 0.3069 NA NA +SD.g_qlogis 0.8362 NA NA + +Variance model: + est. lower upper +a.1 2.95785 NA NA +b.1 0.04456 NA NA + +Backtransformed parameters: + est. lower upper +cyan_0 1.007e+02 NA NA +k_JCZ38 3.122e-02 NA NA +k_J9Z38 6.404e-03 NA NA +k_JSE76 3.866e-03 NA NA +f_cyan_to_JCZ38 6.187e-01 NA NA +f_cyan_to_J9Z38 2.431e-01 NA NA +f_JCZ38_to_JSE76 1.000e+00 NA NA +k1 1.134e-01 NA NA +k2 1.057e-02 NA NA +g 3.637e-01 NA NA + +Resulting formation fractions: + ff +cyan_JCZ38 0.6187 +cyan_J9Z38 0.2431 +cyan_sink 0.1382 +JCZ38_JSE76 1.0000 +JCZ38_sink 0.0000 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +cyan 26.35 175.12 52.72 6.114 65.6 +JCZ38 22.20 73.75 NA NA NA +J9Z38 108.23 359.53 NA NA NA +JSE76 179.30 595.62 NA NA NA + +</code></pre> +<p></p> +<caption> +Hierarchical SFORB path 1 fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.4.2 +Date of fit: Fri Feb 14 07:43:36 2025 +Date of summary: Sun Feb 16 17:03:40 2025 + +Equations: +d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound * + cyan_free + k_cyan_bound_free * cyan_bound +d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free * + cyan_bound +d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38 + * JCZ38 +d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38 + * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 507.042 s +Using 300, 100 iterations and 10 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + cyan_free_0 log_k_cyan_free log_k_cyan_free_bound + 102.0643 -2.8987 -2.7077 +log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 + -3.4717 -3.4008 -5.0024 + log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 + -5.8613 0.6855 1.2366 + f_JCZ38_qlogis + 13.7395 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_free_0 log_k_cyan_free log_k_cyan_free_bound +cyan_free_0 4.466 0.0000 0.000 +log_k_cyan_free 0.000 0.6158 0.000 +log_k_cyan_free_bound 0.000 0.0000 1.463 +log_k_cyan_bound_free 0.000 0.0000 0.000 +log_k_JCZ38 0.000 0.0000 0.000 +log_k_J9Z38 0.000 0.0000 0.000 +log_k_JSE76 0.000 0.0000 0.000 +f_cyan_ilr_1 0.000 0.0000 0.000 +f_cyan_ilr_2 0.000 0.0000 0.000 +f_JCZ38_qlogis 0.000 0.0000 0.000 + log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 +cyan_free_0 0.000 0.000 0.000 0.000 +log_k_cyan_free 0.000 0.000 0.000 0.000 +log_k_cyan_free_bound 0.000 0.000 0.000 0.000 +log_k_cyan_bound_free 1.058 0.000 0.000 0.000 +log_k_JCZ38 0.000 2.382 0.000 0.000 +log_k_J9Z38 0.000 0.000 1.595 0.000 +log_k_JSE76 0.000 0.000 0.000 1.245 +f_cyan_ilr_1 0.000 0.000 0.000 0.000 +f_cyan_ilr_2 0.000 0.000 0.000 0.000 +f_JCZ38_qlogis 0.000 0.000 0.000 0.000 + f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis +cyan_free_0 0.0000 0.00 0.00 +log_k_cyan_free 0.0000 0.00 0.00 +log_k_cyan_free_bound 0.0000 0.00 0.00 +log_k_cyan_bound_free 0.0000 0.00 0.00 +log_k_JCZ38 0.0000 0.00 0.00 +log_k_J9Z38 0.0000 0.00 0.00 +log_k_JSE76 0.0000 0.00 0.00 +f_cyan_ilr_1 0.6852 0.00 0.00 +f_cyan_ilr_2 0.0000 1.28 0.00 +f_JCZ38_qlogis 0.0000 0.00 16.13 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2401 2394 -1181 + +Optimised parameters: + est. lower upper +cyan_free_0 102.8136 NA NA +log_k_cyan_free -2.7935 NA NA +log_k_cyan_free_bound -2.5440 NA NA +log_k_cyan_bound_free -3.4303 NA NA +log_k_JCZ38 -3.5010 NA NA +log_k_J9Z38 -5.1226 NA NA +log_k_JSE76 -5.6314 NA NA +f_cyan_ilr_1 0.6609 NA NA +f_cyan_ilr_2 0.5085 NA NA +f_JCZ38_qlogis 44.0153 NA NA +a.1 3.2318 NA NA +SD.log_k_cyan_free 0.3211 NA NA +SD.log_k_cyan_free_bound 0.8408 NA NA +SD.log_k_cyan_bound_free 0.5724 NA NA +SD.log_k_JCZ38 1.4925 NA NA +SD.log_k_J9Z38 0.5816 NA NA +SD.log_k_JSE76 0.6037 NA NA +SD.f_cyan_ilr_1 0.3115 NA NA +SD.f_cyan_ilr_2 0.3436 NA NA +SD.f_JCZ38_qlogis 4.8937 NA NA + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_cyan_free 0.3211 NA NA +SD.log_k_cyan_free_bound 0.8408 NA NA +SD.log_k_cyan_bound_free 0.5724 NA NA +SD.log_k_JCZ38 1.4925 NA NA +SD.log_k_J9Z38 0.5816 NA NA +SD.log_k_JSE76 0.6037 NA NA +SD.f_cyan_ilr_1 0.3115 NA NA +SD.f_cyan_ilr_2 0.3436 NA NA +SD.f_JCZ38_qlogis 4.8937 NA NA + +Variance model: + est. lower upper +a.1 3.232 NA NA + +Backtransformed parameters: + est. lower upper +cyan_free_0 1.028e+02 NA NA +k_cyan_free 6.120e-02 NA NA +k_cyan_free_bound 7.855e-02 NA NA +k_cyan_bound_free 3.238e-02 NA NA +k_JCZ38 3.017e-02 NA NA +k_J9Z38 5.961e-03 NA NA +k_JSE76 3.584e-03 NA NA +f_cyan_free_to_JCZ38 5.784e-01 NA NA +f_cyan_free_to_J9Z38 2.271e-01 NA NA +f_JCZ38_to_JSE76 1.000e+00 NA NA + +Estimated Eigenvalues of SFORB model(s): +cyan_b1 cyan_b2 cyan_g +0.15973 0.01241 0.33124 + +Resulting formation fractions: + ff +cyan_free_JCZ38 0.5784 +cyan_free_J9Z38 0.2271 +cyan_free_sink 0.1945 +cyan_free 1.0000 +JCZ38_JSE76 1.0000 +JCZ38_sink 0.0000 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 +cyan 24.51 153.18 46.11 4.34 55.87 +JCZ38 22.98 76.33 NA NA NA +J9Z38 116.28 386.29 NA NA NA +JSE76 193.42 642.53 NA NA NA + +</code></pre> +<p></p> +<caption> +Hierarchical SFORB path 1 fit with two-component error +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.4.2 +Date of fit: Fri Feb 14 07:46:14 2025 +Date of summary: Sun Feb 16 17:03:40 2025 + +Equations: +d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound * + cyan_free + k_cyan_bound_free * cyan_bound +d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free * + cyan_bound +d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38 + * JCZ38 +d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38 + * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 664.11 s +Using 300, 100 iterations and 10 chains + +Variance model: Two-component variance function + +Starting values for degradation parameters: + cyan_free_0 log_k_cyan_free log_k_cyan_free_bound + 101.3964 -2.9881 -2.7949 +log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 + -3.4376 -3.3626 -4.9792 + log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 + -5.8727 0.6814 6.7399 + f_JCZ38_qlogis + 13.7395 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_free_0 log_k_cyan_free log_k_cyan_free_bound +cyan_free_0 5.317 0.0000 0.000 +log_k_cyan_free 0.000 0.7301 0.000 +log_k_cyan_free_bound 0.000 0.0000 1.384 +log_k_cyan_bound_free 0.000 0.0000 0.000 +log_k_JCZ38 0.000 0.0000 0.000 +log_k_J9Z38 0.000 0.0000 0.000 +log_k_JSE76 0.000 0.0000 0.000 +f_cyan_ilr_1 0.000 0.0000 0.000 +f_cyan_ilr_2 0.000 0.0000 0.000 +f_JCZ38_qlogis 0.000 0.0000 0.000 + log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 +cyan_free_0 0.000 0.000 0.000 0.000 +log_k_cyan_free 0.000 0.000 0.000 0.000 +log_k_cyan_free_bound 0.000 0.000 0.000 0.000 +log_k_cyan_bound_free 1.109 0.000 0.000 0.000 +log_k_JCZ38 0.000 2.272 0.000 0.000 +log_k_J9Z38 0.000 0.000 1.633 0.000 +log_k_JSE76 0.000 0.000 0.000 1.271 +f_cyan_ilr_1 0.000 0.000 0.000 0.000 +f_cyan_ilr_2 0.000 0.000 0.000 0.000 +f_JCZ38_qlogis 0.000 0.000 0.000 0.000 + f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis +cyan_free_0 0.0000 0.00 0.00 +log_k_cyan_free 0.0000 0.00 0.00 +log_k_cyan_free_bound 0.0000 0.00 0.00 +log_k_cyan_bound_free 0.0000 0.00 0.00 +log_k_JCZ38 0.0000 0.00 0.00 +log_k_J9Z38 0.0000 0.00 0.00 +log_k_JSE76 0.0000 0.00 0.00 +f_cyan_ilr_1 0.6838 0.00 0.00 +f_cyan_ilr_2 0.0000 11.69 0.00 +f_JCZ38_qlogis 0.0000 0.00 16.13 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2400 2392 -1180 + +Optimised parameters: + est. lower upper +cyan_free_0 100.56004 NA NA +log_k_cyan_free -3.12657 NA NA +log_k_cyan_free_bound -3.16825 NA NA +log_k_cyan_bound_free -3.66003 NA NA +log_k_JCZ38 -3.47278 NA NA +log_k_J9Z38 -5.06823 NA NA +log_k_JSE76 -5.54327 NA NA +f_cyan_ilr_1 0.66631 NA NA +f_cyan_ilr_2 0.82898 NA NA +f_JCZ38_qlogis 38.31115 NA NA +a.1 2.98352 NA NA +b.1 0.04388 NA NA +SD.log_k_cyan_free 0.49145 NA NA +SD.log_k_cyan_bound_free 0.27347 NA NA +SD.log_k_JCZ38 1.41193 NA NA +SD.log_k_J9Z38 0.66073 NA NA +SD.log_k_JSE76 0.55885 NA NA +SD.f_cyan_ilr_1 0.33020 NA NA +SD.f_cyan_ilr_2 0.51367 NA NA +SD.f_JCZ38_qlogis 5.52122 NA NA + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_cyan_free 0.4914 NA NA +SD.log_k_cyan_bound_free 0.2735 NA NA +SD.log_k_JCZ38 1.4119 NA NA +SD.log_k_J9Z38 0.6607 NA NA +SD.log_k_JSE76 0.5589 NA NA +SD.f_cyan_ilr_1 0.3302 NA NA +SD.f_cyan_ilr_2 0.5137 NA NA +SD.f_JCZ38_qlogis 5.5212 NA NA + +Variance model: + est. lower upper +a.1 2.98352 NA NA +b.1 0.04388 NA NA + +Backtransformed parameters: + est. lower upper +cyan_free_0 1.006e+02 NA NA +k_cyan_free 4.387e-02 NA NA +k_cyan_free_bound 4.208e-02 NA NA +k_cyan_bound_free 2.573e-02 NA NA +k_JCZ38 3.103e-02 NA NA +k_J9Z38 6.294e-03 NA NA +k_JSE76 3.914e-03 NA NA +f_cyan_free_to_JCZ38 6.188e-01 NA NA +f_cyan_free_to_J9Z38 2.412e-01 NA NA +f_JCZ38_to_JSE76 1.000e+00 NA NA + +Estimated Eigenvalues of SFORB model(s): +cyan_b1 cyan_b2 cyan_g +0.10044 0.01124 0.36580 + +Resulting formation fractions: + ff +cyan_free_JCZ38 0.6188 +cyan_free_J9Z38 0.2412 +cyan_free_sink 0.1400 +cyan_free 1.0000 +JCZ38_JSE76 1.0000 +JCZ38_sink 0.0000 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 +cyan 26.05 164.4 49.48 6.901 61.67 +JCZ38 22.34 74.2 NA NA NA +J9Z38 110.14 365.9 NA NA NA +JSE76 177.11 588.3 NA NA NA + +</code></pre> +<p></p> +<caption> +Hierarchical HS path 1 fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.4.2 +Date of fit: Fri Feb 14 07:43:42 2025 +Date of summary: Sun Feb 16 17:03:40 2025 + +Equations: +d_cyan/dt = - ifelse(time <= tb, k1, k2) * cyan +d_JCZ38/dt = + f_cyan_to_JCZ38 * ifelse(time <= tb, k1, k2) * cyan - + k_JCZ38 * JCZ38 +d_J9Z38/dt = + f_cyan_to_J9Z38 * ifelse(time <= tb, k1, k2) * cyan - + k_J9Z38 * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 512.818 s +Using 300, 100 iterations and 10 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 + 102.8845 -3.4495 -4.9355 -5.6040 0.6468 + f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 log_tb + 1.2396 9.7220 -2.9079 -4.1810 1.7813 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 +cyan_0 5.406 0.00 0.00 0.000 0.0000 +log_k_JCZ38 0.000 2.33 0.00 0.000 0.0000 +log_k_J9Z38 0.000 0.00 1.59 0.000 0.0000 +log_k_JSE76 0.000 0.00 0.00 1.013 0.0000 +f_cyan_ilr_1 0.000 0.00 0.00 0.000 0.6367 +f_cyan_ilr_2 0.000 0.00 0.00 0.000 0.0000 +f_JCZ38_qlogis 0.000 0.00 0.00 0.000 0.0000 +log_k1 0.000 0.00 0.00 0.000 0.0000 +log_k2 0.000 0.00 0.00 0.000 0.0000 +log_tb 0.000 0.00 0.00 0.000 0.0000 + f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 log_tb +cyan_0 0.000 0.00 0.0000 0.0000 0.0000 +log_k_JCZ38 0.000 0.00 0.0000 0.0000 0.0000 +log_k_J9Z38 0.000 0.00 0.0000 0.0000 0.0000 +log_k_JSE76 0.000 0.00 0.0000 0.0000 0.0000 +f_cyan_ilr_1 0.000 0.00 0.0000 0.0000 0.0000 +f_cyan_ilr_2 2.038 0.00 0.0000 0.0000 0.0000 +f_JCZ38_qlogis 0.000 10.33 0.0000 0.0000 0.0000 +log_k1 0.000 0.00 0.7006 0.0000 0.0000 +log_k2 0.000 0.00 0.0000 0.8928 0.0000 +log_tb 0.000 0.00 0.0000 0.0000 0.6773 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2427 2419 -1194 + +Optimised parameters: + est. lower upper +cyan_0 101.9660 1.005e+02 1.035e+02 +log_k_JCZ38 -3.4698 -4.716e+00 -2.224e+00 +log_k_J9Z38 -5.0947 -5.740e+00 -4.450e+00 +log_k_JSE76 -5.5977 -6.321e+00 -4.875e+00 +f_cyan_ilr_1 0.6595 3.734e-01 9.456e-01 +f_cyan_ilr_2 0.5905 1.664e-01 1.015e+00 +f_JCZ38_qlogis 25.8627 -4.224e+05 4.225e+05 +log_k1 -3.0884 -3.453e+00 -2.723e+00 +log_k2 -4.3877 -4.778e+00 -3.998e+00 +log_tb 2.3057 1.715e+00 2.896e+00 +a.1 3.3228 NA NA +SD.log_k_JCZ38 1.4071 NA NA +SD.log_k_J9Z38 0.5774 NA NA +SD.log_k_JSE76 0.6214 NA NA +SD.f_cyan_ilr_1 0.3058 NA NA +SD.f_cyan_ilr_2 0.3470 NA NA +SD.f_JCZ38_qlogis 0.0644 NA NA +SD.log_k1 0.3994 NA NA +SD.log_k2 0.4373 NA NA +SD.log_tb 0.6419 NA NA + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_JCZ38 1.4071 NA NA +SD.log_k_J9Z38 0.5774 NA NA +SD.log_k_JSE76 0.6214 NA NA +SD.f_cyan_ilr_1 0.3058 NA NA +SD.f_cyan_ilr_2 0.3470 NA NA +SD.f_JCZ38_qlogis 0.0644 NA NA +SD.log_k1 0.3994 NA NA +SD.log_k2 0.4373 NA NA +SD.log_tb 0.6419 NA NA + +Variance model: + est. lower upper +a.1 3.323 NA NA + +Backtransformed parameters: + est. lower upper +cyan_0 1.020e+02 1.005e+02 1.035e+02 +k_JCZ38 3.112e-02 8.951e-03 1.082e-01 +k_J9Z38 6.129e-03 3.216e-03 1.168e-02 +k_JSE76 3.706e-03 1.798e-03 7.639e-03 +f_cyan_to_JCZ38 5.890e-01 NA NA +f_cyan_to_J9Z38 2.318e-01 NA NA +f_JCZ38_to_JSE76 1.000e+00 0.000e+00 1.000e+00 +k1 4.558e-02 3.164e-02 6.565e-02 +k2 1.243e-02 8.417e-03 1.835e-02 +tb 1.003e+01 5.557e+00 1.811e+01 + +Resulting formation fractions: + ff +cyan_JCZ38 5.890e-01 +cyan_J9Z38 2.318e-01 +cyan_sink 1.793e-01 +JCZ38_JSE76 1.000e+00 +JCZ38_sink 5.861e-12 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +cyan 29.02 158.51 47.72 15.21 55.77 +JCZ38 22.27 73.98 NA NA NA +J9Z38 113.09 375.69 NA NA NA +JSE76 187.01 621.23 NA NA NA + +</code></pre> +<p></p> +</div> +<div class="section level4"> +<h4 id="pathway-2">Pathway 2<a class="anchor" aria-label="anchor" href="#pathway-2"></a> +</h4> +<caption> +Hierarchical FOMC path 2 fit with two-component error +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.4.2 +Date of fit: Fri Feb 14 07:54:36 2025 +Date of summary: Sun Feb 16 17:03:40 2025 + +Equations: +d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan +d_JCZ38/dt = + f_cyan_to_JCZ38 * (alpha/beta) * 1/((time/beta) + 1) * + cyan - k_JCZ38 * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76 +d_J9Z38/dt = + f_cyan_to_J9Z38 * (alpha/beta) * 1/((time/beta) + 1) * + cyan - k_J9Z38 * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 491.928 s +Using 300, 100 iterations and 10 chains + +Variance model: Two-component variance function + +Starting values for degradation parameters: + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 + 102.4477 -1.8631 -5.1087 -2.5114 0.6826 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta + 4.7944 15.9616 13.1566 -0.1564 2.9781 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 +cyan_0 7.701 0.000 0.000 0.000 0.0000 +log_k_JCZ38 0.000 1.448 0.000 0.000 0.0000 +log_k_J9Z38 0.000 0.000 1.724 0.000 0.0000 +log_k_JSE76 0.000 0.000 0.000 3.659 0.0000 +f_cyan_ilr_1 0.000 0.000 0.000 0.000 0.6356 +f_cyan_ilr_2 0.000 0.000 0.000 0.000 0.0000 +f_JCZ38_qlogis 0.000 0.000 0.000 0.000 0.0000 +f_JSE76_qlogis 0.000 0.000 0.000 0.000 0.0000 +log_alpha 0.000 0.000 0.000 0.000 0.0000 +log_beta 0.000 0.000 0.000 0.000 0.0000 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta +cyan_0 0.00 0.00 0.00 0.0000 0.0000 +log_k_JCZ38 0.00 0.00 0.00 0.0000 0.0000 +log_k_J9Z38 0.00 0.00 0.00 0.0000 0.0000 +log_k_JSE76 0.00 0.00 0.00 0.0000 0.0000 +f_cyan_ilr_1 0.00 0.00 0.00 0.0000 0.0000 +f_cyan_ilr_2 10.32 0.00 0.00 0.0000 0.0000 +f_JCZ38_qlogis 0.00 12.23 0.00 0.0000 0.0000 +f_JSE76_qlogis 0.00 0.00 14.99 0.0000 0.0000 +log_alpha 0.00 0.00 0.00 0.3924 0.0000 +log_beta 0.00 0.00 0.00 0.0000 0.5639 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2249 2241 -1104 + +Optimised parameters: + est. lower upper +cyan_0 101.55265 9.920e+01 103.9059 +log_k_JCZ38 -2.32302 -2.832e+00 -1.8142 +log_k_J9Z38 -5.13082 -5.942e+00 -4.3199 +log_k_JSE76 -3.01756 -4.262e+00 -1.7736 +f_cyan_ilr_1 0.70850 3.657e-01 1.0513 +f_cyan_ilr_2 0.95775 2.612e-01 1.6543 +f_JCZ38_qlogis 3.86105 9.248e-01 6.7973 +f_JSE76_qlogis 7.51583 -1.120e+02 127.0392 +log_alpha -0.15308 -4.508e-01 0.1446 +log_beta 2.99165 2.711e+00 3.2720 +a.1 2.04034 1.843e+00 2.2382 +b.1 0.06924 5.749e-02 0.0810 +SD.log_k_JCZ38 0.50818 1.390e-01 0.8774 +SD.log_k_J9Z38 0.86597 2.652e-01 1.4667 +SD.log_k_JSE76 1.38092 4.864e-01 2.2754 +SD.f_cyan_ilr_1 0.38204 1.354e-01 0.6286 +SD.f_cyan_ilr_2 0.55129 7.198e-02 1.0306 +SD.f_JCZ38_qlogis 1.88457 1.711e-02 3.7520 +SD.f_JSE76_qlogis 2.64018 -2.450e+03 2454.9447 +SD.log_alpha 0.31860 1.047e-01 0.5325 +SD.log_beta 0.24195 1.273e-02 0.4712 + +Correlation: + cyan_0 l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76 +log_k_JCZ38 -0.0235 +log_k_J9Z38 -0.0442 0.0047 +log_k_JSE76 -0.0023 0.0966 0.0006 +f_cyan_ilr_1 -0.0032 0.0070 -0.0536 -0.0001 +f_cyan_ilr_2 -0.5189 0.0452 0.1152 0.0013 -0.0304 +f_JCZ38_qlogis 0.1088 -0.0848 -0.0240 0.0040 -0.0384 -0.2303 +f_JSE76_qlogis -0.0545 0.1315 0.0195 0.0020 0.0252 0.1737 -0.5939 +log_alpha -0.0445 0.0056 0.0261 0.0019 -0.0055 0.0586 -0.0239 -0.0284 +log_beta -0.2388 0.0163 0.0566 0.0040 -0.0078 0.2183 -0.0714 -0.0332 + log_lph +log_k_JCZ38 +log_k_J9Z38 +log_k_JSE76 +f_cyan_ilr_1 +f_cyan_ilr_2 +f_JCZ38_qlogis +f_JSE76_qlogis +log_alpha +log_beta 0.2135 + +Random effects: + est. lower upper +SD.log_k_JCZ38 0.5082 1.390e-01 0.8774 +SD.log_k_J9Z38 0.8660 2.652e-01 1.4667 +SD.log_k_JSE76 1.3809 4.864e-01 2.2754 +SD.f_cyan_ilr_1 0.3820 1.354e-01 0.6286 +SD.f_cyan_ilr_2 0.5513 7.198e-02 1.0306 +SD.f_JCZ38_qlogis 1.8846 1.711e-02 3.7520 +SD.f_JSE76_qlogis 2.6402 -2.450e+03 2454.9447 +SD.log_alpha 0.3186 1.047e-01 0.5325 +SD.log_beta 0.2420 1.273e-02 0.4712 + +Variance model: + est. lower upper +a.1 2.04034 1.84252 2.238 +b.1 0.06924 0.05749 0.081 + +Backtransformed parameters: + est. lower upper +cyan_0 1.016e+02 9.920e+01 103.9059 +k_JCZ38 9.798e-02 5.890e-02 0.1630 +k_J9Z38 5.912e-03 2.627e-03 0.0133 +k_JSE76 4.892e-02 1.410e-02 0.1697 +f_cyan_to_JCZ38 6.432e-01 NA NA +f_cyan_to_J9Z38 2.362e-01 NA NA +f_JCZ38_to_JSE76 9.794e-01 7.160e-01 0.9989 +f_JSE76_to_JCZ38 9.995e-01 2.268e-49 1.0000 +alpha 8.581e-01 6.371e-01 1.1556 +beta 1.992e+01 1.505e+01 26.3646 + +Resulting formation fractions: + ff +cyan_JCZ38 0.6432301 +cyan_J9Z38 0.2361657 +cyan_sink 0.1206042 +JCZ38_JSE76 0.9793879 +JCZ38_sink 0.0206121 +JSE76_JCZ38 0.9994559 +JSE76_sink 0.0005441 + +Estimated disappearance times: + DT50 DT90 DT50back +cyan 24.759 271.61 81.76 +JCZ38 7.075 23.50 NA +J9Z38 117.249 389.49 NA +JSE76 14.169 47.07 NA + +</code></pre> +<p></p> +<caption> +Hierarchical DFOP path 2 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: 4.4.2 +Date of fit: Fri Feb 14 07:55:32 2025 +Date of summary: Sun Feb 16 17:03:40 2025 + +Equations: +d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * + time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) + * cyan +d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - + g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * + exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38 + + f_JSE76_to_JCZ38 * k_JSE76 * JSE76 +d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - + g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * + exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 548.554 s +Using 300, 100 iterations and 10 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 + 102.4380 -2.3107 -5.3123 -3.7120 0.6757 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 + 1.1439 13.1194 12.3492 -1.9317 -4.4557 + g_qlogis + -0.5644 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 +cyan_0 4.591 0.0000 0.000 0.0 0.0000 +log_k_JCZ38 0.000 0.7966 0.000 0.0 0.0000 +log_k_J9Z38 0.000 0.0000 1.561 0.0 0.0000 +log_k_JSE76 0.000 0.0000 0.000 0.8 0.0000 +f_cyan_ilr_1 0.000 0.0000 0.000 0.0 0.6349 +f_cyan_ilr_2 0.000 0.0000 0.000 0.0 0.0000 +f_JCZ38_qlogis 0.000 0.0000 0.000 0.0 0.0000 +f_JSE76_qlogis 0.000 0.0000 0.000 0.0 0.0000 +log_k1 0.000 0.0000 0.000 0.0 0.0000 +log_k2 0.000 0.0000 0.000 0.0 0.0000 +g_qlogis 0.000 0.0000 0.000 0.0 0.0000 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 +cyan_0 0.000 0.00 0.00 0.000 0.0000 +log_k_JCZ38 0.000 0.00 0.00 0.000 0.0000 +log_k_J9Z38 0.000 0.00 0.00 0.000 0.0000 +log_k_JSE76 0.000 0.00 0.00 0.000 0.0000 +f_cyan_ilr_1 0.000 0.00 0.00 0.000 0.0000 +f_cyan_ilr_2 1.797 0.00 0.00 0.000 0.0000 +f_JCZ38_qlogis 0.000 13.86 0.00 0.000 0.0000 +f_JSE76_qlogis 0.000 0.00 13.91 0.000 0.0000 +log_k1 0.000 0.00 0.00 1.106 0.0000 +log_k2 0.000 0.00 0.00 0.000 0.6141 +g_qlogis 0.000 0.00 0.00 0.000 0.0000 + g_qlogis +cyan_0 0.000 +log_k_JCZ38 0.000 +log_k_J9Z38 0.000 +log_k_JSE76 0.000 +f_cyan_ilr_1 0.000 +f_cyan_ilr_2 0.000 +f_JCZ38_qlogis 0.000 +f_JSE76_qlogis 0.000 +log_k1 0.000 +log_k2 0.000 +g_qlogis 1.595 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2288 2280 -1122 + +Optimised parameters: + est. lower upper +cyan_0 102.7204 1.014e+02 1.040e+02 +log_k_JCZ38 -2.8925 -4.044e+00 -1.741e+00 +log_k_J9Z38 -5.1430 -5.828e+00 -4.457e+00 +log_k_JSE76 -3.5577 -4.174e+00 -2.941e+00 +f_cyan_ilr_1 0.6929 3.788e-01 1.007e+00 +f_cyan_ilr_2 0.6066 5.342e-02 1.160e+00 +f_JCZ38_qlogis 9.8071 -2.819e+03 2.838e+03 +f_JSE76_qlogis 2.2229 5.684e-01 3.877e+00 +log_k1 -1.9339 -2.609e+00 -1.258e+00 +log_k2 -4.4709 -4.935e+00 -4.007e+00 +g_qlogis -0.4987 -1.373e+00 3.757e-01 +a.1 2.7368 2.545e+00 2.928e+00 +SD.log_k_JCZ38 1.2747 4.577e-01 2.092e+00 +SD.log_k_J9Z38 0.6758 1.418e-01 1.210e+00 +SD.log_k_JSE76 0.5869 1.169e-01 1.057e+00 +SD.f_cyan_ilr_1 0.3392 1.161e-01 5.622e-01 +SD.f_cyan_ilr_2 0.4200 8.501e-02 7.550e-01 +SD.f_JCZ38_qlogis 0.8511 -1.137e+06 1.137e+06 +SD.f_JSE76_qlogis 0.3767 -5.238e-01 1.277e+00 +SD.log_k1 0.7475 2.601e-01 1.235e+00 +SD.log_k2 0.5179 1.837e-01 8.521e-01 +SD.g_qlogis 0.9817 3.553e-01 1.608e+00 + +Correlation: + cyan_0 l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76 +log_k_JCZ38 -0.0351 +log_k_J9Z38 -0.0541 0.0043 +log_k_JSE76 -0.0078 0.0900 -0.0014 +f_cyan_ilr_1 -0.0249 0.0268 -0.0962 0.0000 +f_cyan_ilr_2 -0.3560 0.0848 0.1545 -0.0022 0.0463 +f_JCZ38_qlogis 0.2005 -0.1226 -0.0347 0.0514 -0.1840 -0.5906 +f_JSE76_qlogis -0.1638 0.1307 0.0266 0.0001 0.1645 0.5181 -0.9297 +log_k1 0.0881 -0.0071 0.0005 -0.0070 -0.0064 -0.0346 0.0316 -0.0341 +log_k2 0.0238 -0.0003 0.0082 -0.0022 -0.0017 -0.0017 -0.0002 -0.0076 +g_qlogis 0.0198 -0.0002 -0.0109 0.0034 0.0017 -0.0176 0.0044 0.0051 + log_k1 log_k2 +log_k_JCZ38 +log_k_J9Z38 +log_k_JSE76 +f_cyan_ilr_1 +f_cyan_ilr_2 +f_JCZ38_qlogis +f_JSE76_qlogis +log_k1 +log_k2 0.0276 +g_qlogis -0.0283 -0.0309 + +Random effects: + est. lower upper +SD.log_k_JCZ38 1.2747 4.577e-01 2.092e+00 +SD.log_k_J9Z38 0.6758 1.418e-01 1.210e+00 +SD.log_k_JSE76 0.5869 1.169e-01 1.057e+00 +SD.f_cyan_ilr_1 0.3392 1.161e-01 5.622e-01 +SD.f_cyan_ilr_2 0.4200 8.501e-02 7.550e-01 +SD.f_JCZ38_qlogis 0.8511 -1.137e+06 1.137e+06 +SD.f_JSE76_qlogis 0.3767 -5.238e-01 1.277e+00 +SD.log_k1 0.7475 2.601e-01 1.235e+00 +SD.log_k2 0.5179 1.837e-01 8.521e-01 +SD.g_qlogis 0.9817 3.553e-01 1.608e+00 + +Variance model: + est. lower upper +a.1 2.737 2.545 2.928 + +Backtransformed parameters: + est. lower upper +cyan_0 102.72037 1.014e+02 104.00464 +k_JCZ38 0.05544 1.752e-02 0.17539 +k_J9Z38 0.00584 2.942e-03 0.01159 +k_JSE76 0.02850 1.539e-02 0.05279 +f_cyan_to_JCZ38 0.59995 NA NA +f_cyan_to_J9Z38 0.22519 NA NA +f_JCZ38_to_JSE76 0.99994 0.000e+00 1.00000 +f_JSE76_to_JCZ38 0.90229 6.384e-01 0.97971 +k1 0.14459 7.357e-02 0.28414 +k2 0.01144 7.192e-03 0.01819 +g 0.37784 2.021e-01 0.59284 + +Resulting formation fractions: + ff +cyan_JCZ38 5.999e-01 +cyan_J9Z38 2.252e-01 +cyan_sink 1.749e-01 +JCZ38_JSE76 9.999e-01 +JCZ38_sink 5.506e-05 +JSE76_JCZ38 9.023e-01 +JSE76_sink 9.771e-02 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +cyan 21.93 159.83 48.11 4.794 60.6 +JCZ38 12.50 41.53 NA NA NA +J9Z38 118.69 394.27 NA NA NA +JSE76 24.32 80.78 NA NA NA + +</code></pre> +<p></p> +<caption> +Hierarchical DFOP path 2 fit with two-component error +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.4.2 +Date of fit: Fri Feb 14 07:57:56 2025 +Date of summary: Sun Feb 16 17:03:40 2025 + +Equations: +d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * + time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) + * cyan +d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - + g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * + exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38 + + f_JSE76_to_JCZ38 * k_JSE76 * JSE76 +d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - + g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * + exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 691.67 s +Using 300, 100 iterations and 10 chains + +Variance model: Two-component variance function + +Starting values for degradation parameters: + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 + 101.7393 -1.4493 -5.0118 -2.1269 0.6720 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 + 7.3362 13.4423 13.2659 -2.0061 -4.5527 + g_qlogis + -0.5806 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 +cyan_0 5.604 0.00 0.000 0.000 0.0000 +log_k_JCZ38 0.000 2.77 0.000 0.000 0.0000 +log_k_J9Z38 0.000 0.00 1.662 0.000 0.0000 +log_k_JSE76 0.000 0.00 0.000 5.021 0.0000 +f_cyan_ilr_1 0.000 0.00 0.000 0.000 0.6519 +f_cyan_ilr_2 0.000 0.00 0.000 0.000 0.0000 +f_JCZ38_qlogis 0.000 0.00 0.000 0.000 0.0000 +f_JSE76_qlogis 0.000 0.00 0.000 0.000 0.0000 +log_k1 0.000 0.00 0.000 0.000 0.0000 +log_k2 0.000 0.00 0.000 0.000 0.0000 +g_qlogis 0.000 0.00 0.000 0.000 0.0000 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 +cyan_0 0.00 0.00 0.00 0.0000 0.0000 +log_k_JCZ38 0.00 0.00 0.00 0.0000 0.0000 +log_k_J9Z38 0.00 0.00 0.00 0.0000 0.0000 +log_k_JSE76 0.00 0.00 0.00 0.0000 0.0000 +f_cyan_ilr_1 0.00 0.00 0.00 0.0000 0.0000 +f_cyan_ilr_2 13.37 0.00 0.00 0.0000 0.0000 +f_JCZ38_qlogis 0.00 14.21 0.00 0.0000 0.0000 +f_JSE76_qlogis 0.00 0.00 14.58 0.0000 0.0000 +log_k1 0.00 0.00 0.00 0.8453 0.0000 +log_k2 0.00 0.00 0.00 0.0000 0.5969 +g_qlogis 0.00 0.00 0.00 0.0000 0.0000 + g_qlogis +cyan_0 0.00 +log_k_JCZ38 0.00 +log_k_J9Z38 0.00 +log_k_JSE76 0.00 +f_cyan_ilr_1 0.00 +f_cyan_ilr_2 0.00 +f_JCZ38_qlogis 0.00 +f_JSE76_qlogis 0.00 +log_k1 0.00 +log_k2 0.00 +g_qlogis 1.69 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2234 2226 -1095 + +Optimised parameters: + est. lower upper +cyan_0 101.25496 99.14662 103.36331 +log_k_JCZ38 -2.55593 -3.32972 -1.78215 +log_k_J9Z38 -5.07103 -5.85423 -4.28783 +log_k_JSE76 -3.25468 -4.17577 -2.33360 +f_cyan_ilr_1 0.70139 0.35924 1.04355 +f_cyan_ilr_2 1.07712 0.17789 1.97636 +f_JCZ38_qlogis 3.57483 0.05990 7.08976 +f_JSE76_qlogis 4.54884 -7.25628 16.35395 +log_k1 -2.38201 -2.51639 -2.24763 +log_k2 -4.66741 -4.91865 -4.41617 +g_qlogis -0.28446 -1.14192 0.57300 +a.1 2.05925 1.86481 2.25369 +b.1 0.06172 0.05062 0.07282 +SD.log_k_JCZ38 0.81137 0.25296 1.36977 +SD.log_k_J9Z38 0.83542 0.25395 1.41689 +SD.log_k_JSE76 0.97903 0.30100 1.65707 +SD.f_cyan_ilr_1 0.37878 0.13374 0.62382 +SD.f_cyan_ilr_2 0.67274 0.10102 1.24446 +SD.f_JCZ38_qlogis 1.35327 -0.42359 3.13012 +SD.f_JSE76_qlogis 1.43956 -19.14972 22.02884 +SD.log_k2 0.25329 0.07521 0.43138 +SD.g_qlogis 0.95167 0.35149 1.55184 + +Correlation: + cyan_0 l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76 +log_k_JCZ38 -0.0265 +log_k_J9Z38 -0.0392 0.0024 +log_k_JSE76 0.0011 0.1220 -0.0016 +f_cyan_ilr_1 -0.0161 0.0217 -0.0552 0.0034 +f_cyan_ilr_2 -0.4718 0.0829 0.1102 0.0042 0.0095 +f_JCZ38_qlogis 0.1609 -0.1318 -0.0277 0.0081 -0.1040 -0.4559 +f_JSE76_qlogis -0.1289 0.1494 0.0219 0.0012 0.1004 0.4309 -0.8543 +log_k1 0.2618 -0.0739 -0.0167 -0.0148 -0.0444 -0.2768 0.3518 -0.3818 +log_k2 0.0603 -0.0217 0.0174 -0.0058 -0.0197 -0.0533 0.0923 -0.1281 +g_qlogis 0.0362 0.0115 -0.0111 0.0040 0.0095 -0.0116 -0.0439 0.0651 + log_k1 log_k2 +log_k_JCZ38 +log_k_J9Z38 +log_k_JSE76 +f_cyan_ilr_1 +f_cyan_ilr_2 +f_JCZ38_qlogis +f_JSE76_qlogis +log_k1 +log_k2 0.3269 +g_qlogis -0.1656 -0.0928 + +Random effects: + est. lower upper +SD.log_k_JCZ38 0.8114 0.25296 1.3698 +SD.log_k_J9Z38 0.8354 0.25395 1.4169 +SD.log_k_JSE76 0.9790 0.30100 1.6571 +SD.f_cyan_ilr_1 0.3788 0.13374 0.6238 +SD.f_cyan_ilr_2 0.6727 0.10102 1.2445 +SD.f_JCZ38_qlogis 1.3533 -0.42359 3.1301 +SD.f_JSE76_qlogis 1.4396 -19.14972 22.0288 +SD.log_k2 0.2533 0.07521 0.4314 +SD.g_qlogis 0.9517 0.35149 1.5518 + +Variance model: + est. lower upper +a.1 2.05925 1.86481 2.25369 +b.1 0.06172 0.05062 0.07282 + +Backtransformed parameters: + est. lower upper +cyan_0 1.013e+02 9.915e+01 103.36331 +k_JCZ38 7.762e-02 3.580e-02 0.16828 +k_J9Z38 6.276e-03 2.868e-03 0.01373 +k_JSE76 3.859e-02 1.536e-02 0.09695 +f_cyan_to_JCZ38 6.520e-01 NA NA +f_cyan_to_J9Z38 2.418e-01 NA NA +f_JCZ38_to_JSE76 9.727e-01 5.150e-01 0.99917 +f_JSE76_to_JCZ38 9.895e-01 7.052e-04 1.00000 +k1 9.236e-02 8.075e-02 0.10565 +k2 9.397e-03 7.309e-03 0.01208 +g 4.294e-01 2.420e-01 0.63945 + +Resulting formation fractions: + ff +cyan_JCZ38 0.65203 +cyan_J9Z38 0.24181 +cyan_sink 0.10616 +JCZ38_JSE76 0.97274 +JCZ38_sink 0.02726 +JSE76_JCZ38 0.98953 +JSE76_sink 0.01047 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +cyan 24.26 185.34 55.79 7.504 73.77 +JCZ38 8.93 29.66 NA NA NA +J9Z38 110.45 366.89 NA NA NA +JSE76 17.96 59.66 NA NA NA + +</code></pre> +<p></p> +<caption> +Hierarchical SFORB path 2 fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.4.2 +Date of fit: Fri Feb 14 07:55:26 2025 +Date of summary: Sun Feb 16 17:03:40 2025 + +Equations: +d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound * + cyan_free + k_cyan_bound_free * cyan_bound +d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free * + cyan_bound +d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38 + * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76 +d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38 + * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 542.162 s +Using 300, 100 iterations and 10 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + cyan_free_0 log_k_cyan_free log_k_cyan_free_bound + 102.4395 -2.7673 -2.8942 +log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 + -3.6201 -2.3107 -5.3123 + log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 + -3.7120 0.6754 1.1448 + f_JCZ38_qlogis f_JSE76_qlogis + 14.8408 15.4734 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_free_0 log_k_cyan_free log_k_cyan_free_bound +cyan_free_0 4.589 0.0000 0.00 +log_k_cyan_free 0.000 0.4849 0.00 +log_k_cyan_free_bound 0.000 0.0000 1.62 +log_k_cyan_bound_free 0.000 0.0000 0.00 +log_k_JCZ38 0.000 0.0000 0.00 +log_k_J9Z38 0.000 0.0000 0.00 +log_k_JSE76 0.000 0.0000 0.00 +f_cyan_ilr_1 0.000 0.0000 0.00 +f_cyan_ilr_2 0.000 0.0000 0.00 +f_JCZ38_qlogis 0.000 0.0000 0.00 +f_JSE76_qlogis 0.000 0.0000 0.00 + log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 +cyan_free_0 0.000 0.0000 0.000 0.0 +log_k_cyan_free 0.000 0.0000 0.000 0.0 +log_k_cyan_free_bound 0.000 0.0000 0.000 0.0 +log_k_cyan_bound_free 1.197 0.0000 0.000 0.0 +log_k_JCZ38 0.000 0.7966 0.000 0.0 +log_k_J9Z38 0.000 0.0000 1.561 0.0 +log_k_JSE76 0.000 0.0000 0.000 0.8 +f_cyan_ilr_1 0.000 0.0000 0.000 0.0 +f_cyan_ilr_2 0.000 0.0000 0.000 0.0 +f_JCZ38_qlogis 0.000 0.0000 0.000 0.0 +f_JSE76_qlogis 0.000 0.0000 0.000 0.0 + f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis +cyan_free_0 0.0000 0.000 0.0 0.00 +log_k_cyan_free 0.0000 0.000 0.0 0.00 +log_k_cyan_free_bound 0.0000 0.000 0.0 0.00 +log_k_cyan_bound_free 0.0000 0.000 0.0 0.00 +log_k_JCZ38 0.0000 0.000 0.0 0.00 +log_k_J9Z38 0.0000 0.000 0.0 0.00 +log_k_JSE76 0.0000 0.000 0.0 0.00 +f_cyan_ilr_1 0.6349 0.000 0.0 0.00 +f_cyan_ilr_2 0.0000 1.797 0.0 0.00 +f_JCZ38_qlogis 0.0000 0.000 15.6 0.00 +f_JSE76_qlogis 0.0000 0.000 0.0 17.52 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2283 2275 -1120 + +Optimised parameters: + est. lower upper +cyan_free_0 102.6517 101.40815 103.8952 +log_k_cyan_free -2.8729 -3.18649 -2.5593 +log_k_cyan_free_bound -2.7803 -3.60525 -1.9552 +log_k_cyan_bound_free -3.5845 -4.16644 -3.0026 +log_k_JCZ38 -2.3411 -2.89698 -1.7852 +log_k_J9Z38 -5.2487 -6.01271 -4.4847 +log_k_JSE76 -3.0259 -4.28274 -1.7690 +f_cyan_ilr_1 0.7289 0.38214 1.0756 +f_cyan_ilr_2 0.6891 0.18277 1.1954 +f_JCZ38_qlogis 4.2162 0.47015 7.9622 +f_JSE76_qlogis 5.8911 -20.19088 31.9730 +a.1 2.7159 2.52587 2.9060 +SD.log_k_cyan_free 0.3354 0.10979 0.5610 +SD.log_k_cyan_free_bound 0.9061 0.30969 1.5025 +SD.log_k_cyan_bound_free 0.6376 0.21229 1.0628 +SD.log_k_JCZ38 0.5499 0.14533 0.9545 +SD.log_k_J9Z38 0.7457 0.15106 1.3404 +SD.log_k_JSE76 1.3822 0.47329 2.2912 +SD.f_cyan_ilr_1 0.3820 0.13280 0.6313 +SD.f_cyan_ilr_2 0.4317 0.06803 0.7953 +SD.f_JCZ38_qlogis 1.8258 -0.25423 3.9059 +SD.f_JSE76_qlogis 2.2348 -83.33679 87.8065 + +Correlation: + cyn_f_0 lg_k_c_ lg_k_cyn_f_ lg_k_cyn_b_ l__JCZ3 l__J9Z3 +log_k_cyan_free 0.1944 +log_k_cyan_free_bound 0.0815 0.0814 +log_k_cyan_bound_free 0.0106 0.0426 0.0585 +log_k_JCZ38 -0.0231 -0.0106 -0.0089 -0.0051 +log_k_J9Z38 -0.0457 -0.0108 0.0019 0.0129 0.0032 +log_k_JSE76 -0.0054 -0.0024 -0.0017 -0.0005 0.1108 0.0009 +f_cyan_ilr_1 0.0051 -0.0005 -0.0035 -0.0056 0.0131 -0.0967 +f_cyan_ilr_2 -0.3182 -0.0771 -0.0309 -0.0038 0.0680 0.1643 +f_JCZ38_qlogis 0.0834 0.0369 0.0302 0.0172 -0.1145 -0.0204 +f_JSE76_qlogis -0.0553 -0.0365 -0.0441 -0.0414 0.1579 0.0175 + l__JSE7 f_cy__1 f_cy__2 f_JCZ38 +log_k_cyan_free +log_k_cyan_free_bound +log_k_cyan_bound_free +log_k_JCZ38 +log_k_J9Z38 +log_k_JSE76 +f_cyan_ilr_1 -0.0002 +f_cyan_ilr_2 0.0020 -0.0415 +f_JCZ38_qlogis 0.0052 -0.0665 -0.3437 +f_JSE76_qlogis 0.0066 0.0635 0.3491 -0.7487 + +Random effects: + est. lower upper +SD.log_k_cyan_free 0.3354 0.10979 0.5610 +SD.log_k_cyan_free_bound 0.9061 0.30969 1.5025 +SD.log_k_cyan_bound_free 0.6376 0.21229 1.0628 +SD.log_k_JCZ38 0.5499 0.14533 0.9545 +SD.log_k_J9Z38 0.7457 0.15106 1.3404 +SD.log_k_JSE76 1.3822 0.47329 2.2912 +SD.f_cyan_ilr_1 0.3820 0.13280 0.6313 +SD.f_cyan_ilr_2 0.4317 0.06803 0.7953 +SD.f_JCZ38_qlogis 1.8258 -0.25423 3.9059 +SD.f_JSE76_qlogis 2.2348 -83.33679 87.8065 + +Variance model: + est. lower upper +a.1 2.716 2.526 2.906 + +Backtransformed parameters: + est. lower upper +cyan_free_0 1.027e+02 1.014e+02 103.89517 +k_cyan_free 5.654e-02 4.132e-02 0.07736 +k_cyan_free_bound 6.202e-02 2.718e-02 0.14153 +k_cyan_bound_free 2.775e-02 1.551e-02 0.04966 +k_JCZ38 9.622e-02 5.519e-02 0.16777 +k_J9Z38 5.254e-03 2.447e-03 0.01128 +k_JSE76 4.852e-02 1.380e-02 0.17051 +f_cyan_free_to_JCZ38 6.197e-01 5.643e-01 0.84429 +f_cyan_free_to_J9Z38 2.211e-01 5.643e-01 0.84429 +f_JCZ38_to_JSE76 9.855e-01 6.154e-01 0.99965 +f_JSE76_to_JCZ38 9.972e-01 1.703e-09 1.00000 + +Estimated Eigenvalues of SFORB model(s): +cyan_b1 cyan_b2 cyan_g +0.13466 0.01165 0.36490 + +Resulting formation fractions: + ff +cyan_free_JCZ38 0.619745 +cyan_free_J9Z38 0.221083 +cyan_free_sink 0.159172 +cyan_free 1.000000 +JCZ38_JSE76 0.985460 +JCZ38_sink 0.014540 +JSE76_JCZ38 0.997244 +JSE76_sink 0.002756 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 +cyan 23.293 158.67 47.77 5.147 59.5 +JCZ38 7.203 23.93 NA NA NA +J9Z38 131.918 438.22 NA NA NA +JSE76 14.287 47.46 NA NA NA + +</code></pre> +<p></p> +<caption> +Hierarchical SFORB path 2 fit with two-component error +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.4.2 +Date of fit: Fri Feb 14 07:58:06 2025 +Date of summary: Sun Feb 16 17:03:40 2025 + +Equations: +d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound * + cyan_free + k_cyan_bound_free * cyan_bound +d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free * + cyan_bound +d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38 + * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76 +d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38 + * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 701.582 s +Using 300, 100 iterations and 10 chains + +Variance model: Two-component variance function + +Starting values for degradation parameters: + cyan_free_0 log_k_cyan_free log_k_cyan_free_bound + 101.7511 -2.8370 -3.0162 +log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 + -3.6600 -2.2988 -5.3129 + log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 + -3.6991 0.6722 4.8596 + f_JCZ38_qlogis f_JSE76_qlogis + 13.4678 14.2149 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_free_0 log_k_cyan_free log_k_cyan_free_bound +cyan_free_0 5.629 0.000 0.000 +log_k_cyan_free 0.000 0.446 0.000 +log_k_cyan_free_bound 0.000 0.000 1.449 +log_k_cyan_bound_free 0.000 0.000 0.000 +log_k_JCZ38 0.000 0.000 0.000 +log_k_J9Z38 0.000 0.000 0.000 +log_k_JSE76 0.000 0.000 0.000 +f_cyan_ilr_1 0.000 0.000 0.000 +f_cyan_ilr_2 0.000 0.000 0.000 +f_JCZ38_qlogis 0.000 0.000 0.000 +f_JSE76_qlogis 0.000 0.000 0.000 + log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 +cyan_free_0 0.000 0.0000 0.000 0.0000 +log_k_cyan_free 0.000 0.0000 0.000 0.0000 +log_k_cyan_free_bound 0.000 0.0000 0.000 0.0000 +log_k_cyan_bound_free 1.213 0.0000 0.000 0.0000 +log_k_JCZ38 0.000 0.7801 0.000 0.0000 +log_k_J9Z38 0.000 0.0000 1.575 0.0000 +log_k_JSE76 0.000 0.0000 0.000 0.8078 +f_cyan_ilr_1 0.000 0.0000 0.000 0.0000 +f_cyan_ilr_2 0.000 0.0000 0.000 0.0000 +f_JCZ38_qlogis 0.000 0.0000 0.000 0.0000 +f_JSE76_qlogis 0.000 0.0000 0.000 0.0000 + f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis +cyan_free_0 0.0000 0.000 0.00 0.00 +log_k_cyan_free 0.0000 0.000 0.00 0.00 +log_k_cyan_free_bound 0.0000 0.000 0.00 0.00 +log_k_cyan_bound_free 0.0000 0.000 0.00 0.00 +log_k_JCZ38 0.0000 0.000 0.00 0.00 +log_k_J9Z38 0.0000 0.000 0.00 0.00 +log_k_JSE76 0.0000 0.000 0.00 0.00 +f_cyan_ilr_1 0.6518 0.000 0.00 0.00 +f_cyan_ilr_2 0.0000 9.981 0.00 0.00 +f_JCZ38_qlogis 0.0000 0.000 14.26 0.00 +f_JSE76_qlogis 0.0000 0.000 0.00 16.17 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2240 2231 -1098 + +Optimised parameters: + est. lower upper +cyan_free_0 100.73014 9.873e+01 1.027e+02 +log_k_cyan_free -3.19634 -3.641e+00 -2.752e+00 +log_k_cyan_free_bound -3.43533 -3.674e+00 -3.197e+00 +log_k_cyan_bound_free -3.83282 -4.163e+00 -3.503e+00 +log_k_JCZ38 -2.51065 -3.225e+00 -1.796e+00 +log_k_J9Z38 -5.02539 -5.825e+00 -4.226e+00 +log_k_JSE76 -3.24777 -4.163e+00 -2.333e+00 +f_cyan_ilr_1 0.70640 3.562e-01 1.057e+00 +f_cyan_ilr_2 1.42704 3.170e-01 2.537e+00 +f_JCZ38_qlogis 2.84779 1.042e+00 4.654e+00 +f_JSE76_qlogis 8.63674 -6.407e+02 6.580e+02 +a.1 2.07082 1.877e+00 2.265e+00 +b.1 0.06227 5.098e-02 7.355e-02 +SD.log_k_cyan_free 0.49674 1.865e-01 8.069e-01 +SD.log_k_cyan_bound_free 0.28537 6.809e-02 5.027e-01 +SD.log_k_JCZ38 0.74846 2.305e-01 1.266e+00 +SD.log_k_J9Z38 0.86077 2.713e-01 1.450e+00 +SD.log_k_JSE76 0.97613 3.030e-01 1.649e+00 +SD.f_cyan_ilr_1 0.38994 1.382e-01 6.417e-01 +SD.f_cyan_ilr_2 0.82869 3.917e-02 1.618e+00 +SD.f_JCZ38_qlogis 1.05000 -2.808e-02 2.128e+00 +SD.f_JSE76_qlogis 0.44681 -3.985e+05 3.985e+05 + +Correlation: + cyn_f_0 lg_k_c_ lg_k_cyn_f_ lg_k_cyn_b_ l__JCZ3 l__J9Z3 +log_k_cyan_free 0.0936 +log_k_cyan_free_bound 0.1302 0.1627 +log_k_cyan_bound_free 0.0029 0.0525 0.5181 +log_k_JCZ38 -0.0116 -0.0077 -0.0430 -0.0236 +log_k_J9Z38 -0.0192 -0.0077 -0.0048 0.0229 -0.0005 +log_k_JSE76 0.0007 -0.0020 -0.0134 -0.0072 0.1225 -0.0016 +f_cyan_ilr_1 -0.0118 -0.0027 -0.0132 -0.0118 0.0127 -0.0505 +f_cyan_ilr_2 -0.4643 -0.0762 -0.1245 0.0137 0.0497 0.1003 +f_JCZ38_qlogis 0.0710 0.0371 0.1826 0.0925 -0.0869 -0.0130 +f_JSE76_qlogis -0.0367 -0.0270 -0.2274 -0.1865 0.1244 0.0098 + l__JSE7 f_cy__1 f_cy__2 f_JCZ38 +log_k_cyan_free +log_k_cyan_free_bound +log_k_cyan_bound_free +log_k_JCZ38 +log_k_J9Z38 +log_k_JSE76 +f_cyan_ilr_1 0.0036 +f_cyan_ilr_2 0.0050 -0.0201 +f_JCZ38_qlogis 0.0142 -0.0529 -0.2698 +f_JSE76_qlogis 0.0064 0.0345 0.2015 -0.7058 + +Random effects: + est. lower upper +SD.log_k_cyan_free 0.4967 1.865e-01 8.069e-01 +SD.log_k_cyan_bound_free 0.2854 6.809e-02 5.027e-01 +SD.log_k_JCZ38 0.7485 2.305e-01 1.266e+00 +SD.log_k_J9Z38 0.8608 2.713e-01 1.450e+00 +SD.log_k_JSE76 0.9761 3.030e-01 1.649e+00 +SD.f_cyan_ilr_1 0.3899 1.382e-01 6.417e-01 +SD.f_cyan_ilr_2 0.8287 3.917e-02 1.618e+00 +SD.f_JCZ38_qlogis 1.0500 -2.808e-02 2.128e+00 +SD.f_JSE76_qlogis 0.4468 -3.985e+05 3.985e+05 + +Variance model: + est. lower upper +a.1 2.07082 1.87680 2.26483 +b.1 0.06227 0.05098 0.07355 + +Backtransformed parameters: + est. lower upper +cyan_free_0 1.007e+02 9.873e+01 102.72898 +k_cyan_free 4.091e-02 2.623e-02 0.06382 +k_cyan_free_bound 3.221e-02 2.537e-02 0.04090 +k_cyan_bound_free 2.165e-02 1.557e-02 0.03011 +k_JCZ38 8.122e-02 3.975e-02 0.16594 +k_J9Z38 6.569e-03 2.954e-03 0.01461 +k_JSE76 3.886e-02 1.556e-02 0.09703 +f_cyan_free_to_JCZ38 6.785e-01 6.102e-01 0.97309 +f_cyan_free_to_J9Z38 2.498e-01 6.102e-01 0.97309 +f_JCZ38_to_JSE76 9.452e-01 7.392e-01 0.99056 +f_JSE76_to_JCZ38 9.998e-01 5.580e-279 1.00000 + +Estimated Eigenvalues of SFORB model(s): +cyan_b1 cyan_b2 cyan_g +0.08426 0.01051 0.41220 + +Resulting formation fractions: + ff +cyan_free_JCZ38 0.6784541 +cyan_free_J9Z38 0.2498405 +cyan_free_sink 0.0717054 +cyan_free 1.0000000 +JCZ38_JSE76 0.9452043 +JCZ38_sink 0.0547957 +JSE76_JCZ38 0.9998226 +JSE76_sink 0.0001774 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 +cyan 25.237 168.51 50.73 8.226 65.95 +JCZ38 8.535 28.35 NA NA NA +J9Z38 105.517 350.52 NA NA NA +JSE76 17.837 59.25 NA NA NA + +</code></pre> +<p></p> +</div> +<div class="section level4"> +<h4 id="pathway-2-refined-fits">Pathway 2, refined fits<a class="anchor" aria-label="anchor" href="#pathway-2-refined-fits"></a> +</h4> +<caption> +Hierarchical FOMC path 2 fit with reduced random effects, two-component +error +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.4.2 +Date of fit: Fri Feb 14 08:11:01 2025 +Date of summary: Sun Feb 16 17:03:41 2025 + +Equations: +d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan +d_JCZ38/dt = + f_cyan_to_JCZ38 * (alpha/beta) * 1/((time/beta) + 1) * + cyan - k_JCZ38 * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76 +d_J9Z38/dt = + f_cyan_to_J9Z38 * (alpha/beta) * 1/((time/beta) + 1) * + cyan - k_J9Z38 * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 773.693 s +Using 300, 100 iterations and 10 chains + +Variance model: Two-component variance function + +Starting values for degradation parameters: + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 + 102.4477 -1.8631 -5.1087 -2.5114 0.6826 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta + 4.7944 15.9616 13.1566 -0.1564 2.9781 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 +cyan_0 7.701 0.000 0.000 0.000 0.0000 +log_k_JCZ38 0.000 1.448 0.000 0.000 0.0000 +log_k_J9Z38 0.000 0.000 1.724 0.000 0.0000 +log_k_JSE76 0.000 0.000 0.000 3.659 0.0000 +f_cyan_ilr_1 0.000 0.000 0.000 0.000 0.6356 +f_cyan_ilr_2 0.000 0.000 0.000 0.000 0.0000 +f_JCZ38_qlogis 0.000 0.000 0.000 0.000 0.0000 +f_JSE76_qlogis 0.000 0.000 0.000 0.000 0.0000 +log_alpha 0.000 0.000 0.000 0.000 0.0000 +log_beta 0.000 0.000 0.000 0.000 0.0000 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta +cyan_0 0.00 0.00 0.00 0.0000 0.0000 +log_k_JCZ38 0.00 0.00 0.00 0.0000 0.0000 +log_k_J9Z38 0.00 0.00 0.00 0.0000 0.0000 +log_k_JSE76 0.00 0.00 0.00 0.0000 0.0000 +f_cyan_ilr_1 0.00 0.00 0.00 0.0000 0.0000 +f_cyan_ilr_2 10.32 0.00 0.00 0.0000 0.0000 +f_JCZ38_qlogis 0.00 12.23 0.00 0.0000 0.0000 +f_JSE76_qlogis 0.00 0.00 14.99 0.0000 0.0000 +log_alpha 0.00 0.00 0.00 0.3924 0.0000 +log_beta 0.00 0.00 0.00 0.0000 0.5639 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2249 2242 -1106 + +Optimised parameters: + est. lower upper +cyan_0 101.24524 NA NA +log_k_JCZ38 -2.85375 NA NA +log_k_J9Z38 -5.07729 NA NA +log_k_JSE76 -3.53511 NA NA +f_cyan_ilr_1 0.67478 NA NA +f_cyan_ilr_2 0.97152 NA NA +f_JCZ38_qlogis 213.48001 NA NA +f_JSE76_qlogis 2.02040 NA NA +log_alpha -0.11041 NA NA +log_beta 3.06575 NA NA +a.1 2.05279 1.85495 2.2506 +b.1 0.07116 0.05912 0.0832 +SD.log_k_JCZ38 1.21713 0.44160 1.9927 +SD.log_k_J9Z38 0.88268 0.27541 1.4900 +SD.log_k_JSE76 0.59452 0.15005 1.0390 +SD.f_cyan_ilr_1 0.35370 0.12409 0.5833 +SD.f_cyan_ilr_2 0.78186 0.18547 1.3782 +SD.log_alpha 0.27781 0.08168 0.4739 +SD.log_beta 0.32608 0.06490 0.5873 + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_JCZ38 1.2171 0.44160 1.9927 +SD.log_k_J9Z38 0.8827 0.27541 1.4900 +SD.log_k_JSE76 0.5945 0.15005 1.0390 +SD.f_cyan_ilr_1 0.3537 0.12409 0.5833 +SD.f_cyan_ilr_2 0.7819 0.18547 1.3782 +SD.log_alpha 0.2778 0.08168 0.4739 +SD.log_beta 0.3261 0.06490 0.5873 + +Variance model: + est. lower upper +a.1 2.05279 1.85495 2.2506 +b.1 0.07116 0.05912 0.0832 + +Backtransformed parameters: + est. lower upper +cyan_0 1.012e+02 NA NA +k_JCZ38 5.763e-02 NA NA +k_J9Z38 6.237e-03 NA NA +k_JSE76 2.916e-02 NA NA +f_cyan_to_JCZ38 6.354e-01 NA NA +f_cyan_to_J9Z38 2.447e-01 NA NA +f_JCZ38_to_JSE76 1.000e+00 NA NA +f_JSE76_to_JCZ38 8.829e-01 NA NA +alpha 8.955e-01 NA NA +beta 2.145e+01 NA NA + +Resulting formation fractions: + ff +cyan_JCZ38 0.6354 +cyan_J9Z38 0.2447 +cyan_sink 0.1200 +JCZ38_JSE76 1.0000 +JCZ38_sink 0.0000 +JSE76_JCZ38 0.8829 +JSE76_sink 0.1171 + +Estimated disappearance times: + DT50 DT90 DT50back +cyan 25.07 259.21 78.03 +JCZ38 12.03 39.96 NA +J9Z38 111.14 369.19 NA +JSE76 23.77 78.98 NA + +</code></pre> +<p></p> +<caption> +Hierarchical DFOP path 2 fit with reduced random effects, constant +variance +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.4.2 +Date of fit: Fri Feb 14 08:12:27 2025 +Date of summary: Sun Feb 16 17:03:41 2025 + +Equations: +d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * + time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) + * cyan +d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - + g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * + exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38 + + f_JSE76_to_JCZ38 * k_JSE76 * JSE76 +d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - + g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * + exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 859.906 s +Using 300, 100 iterations and 10 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 + 102.4380 -2.3107 -5.3123 -3.7120 0.6757 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 + 1.1439 13.1194 12.3492 -1.9317 -4.4557 + g_qlogis + -0.5644 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 +cyan_0 4.591 0.0000 0.000 0.0 0.0000 +log_k_JCZ38 0.000 0.7966 0.000 0.0 0.0000 +log_k_J9Z38 0.000 0.0000 1.561 0.0 0.0000 +log_k_JSE76 0.000 0.0000 0.000 0.8 0.0000 +f_cyan_ilr_1 0.000 0.0000 0.000 0.0 0.6349 +f_cyan_ilr_2 0.000 0.0000 0.000 0.0 0.0000 +f_JCZ38_qlogis 0.000 0.0000 0.000 0.0 0.0000 +f_JSE76_qlogis 0.000 0.0000 0.000 0.0 0.0000 +log_k1 0.000 0.0000 0.000 0.0 0.0000 +log_k2 0.000 0.0000 0.000 0.0 0.0000 +g_qlogis 0.000 0.0000 0.000 0.0 0.0000 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 +cyan_0 0.000 0.00 0.00 0.000 0.0000 +log_k_JCZ38 0.000 0.00 0.00 0.000 0.0000 +log_k_J9Z38 0.000 0.00 0.00 0.000 0.0000 +log_k_JSE76 0.000 0.00 0.00 0.000 0.0000 +f_cyan_ilr_1 0.000 0.00 0.00 0.000 0.0000 +f_cyan_ilr_2 1.797 0.00 0.00 0.000 0.0000 +f_JCZ38_qlogis 0.000 13.86 0.00 0.000 0.0000 +f_JSE76_qlogis 0.000 0.00 13.91 0.000 0.0000 +log_k1 0.000 0.00 0.00 1.106 0.0000 +log_k2 0.000 0.00 0.00 0.000 0.6141 +g_qlogis 0.000 0.00 0.00 0.000 0.0000 + g_qlogis +cyan_0 0.000 +log_k_JCZ38 0.000 +log_k_J9Z38 0.000 +log_k_JSE76 0.000 +f_cyan_ilr_1 0.000 +f_cyan_ilr_2 0.000 +f_JCZ38_qlogis 0.000 +f_JSE76_qlogis 0.000 +log_k1 0.000 +log_k2 0.000 +g_qlogis 1.595 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2282 2274 -1121 + +Optimised parameters: + est. lower upper +cyan_0 102.6036 NA NA +log_k_JCZ38 -2.9348 NA NA +log_k_J9Z38 -5.1617 NA NA +log_k_JSE76 -3.6396 NA NA +f_cyan_ilr_1 0.6991 NA NA +f_cyan_ilr_2 0.6341 NA NA +f_JCZ38_qlogis 4232.3011 NA NA +f_JSE76_qlogis 1.9658 NA NA +log_k1 -1.9503 NA NA +log_k2 -4.4745 NA NA +g_qlogis -0.4967 NA NA +a.1 2.7461 2.59274 2.8994 +SD.log_k_JCZ38 1.3178 0.47602 2.1596 +SD.log_k_J9Z38 0.7022 0.15061 1.2538 +SD.log_k_JSE76 0.6566 0.15613 1.1570 +SD.f_cyan_ilr_1 0.3409 0.11666 0.5652 +SD.f_cyan_ilr_2 0.4385 0.09482 0.7821 +SD.log_k1 0.7381 0.25599 1.2202 +SD.log_k2 0.5133 0.18152 0.8450 +SD.g_qlogis 0.9866 0.35681 1.6164 + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_JCZ38 1.3178 0.47602 2.1596 +SD.log_k_J9Z38 0.7022 0.15061 1.2538 +SD.log_k_JSE76 0.6566 0.15613 1.1570 +SD.f_cyan_ilr_1 0.3409 0.11666 0.5652 +SD.f_cyan_ilr_2 0.4385 0.09482 0.7821 +SD.log_k1 0.7381 0.25599 1.2202 +SD.log_k2 0.5133 0.18152 0.8450 +SD.g_qlogis 0.9866 0.35681 1.6164 + +Variance model: + est. lower upper +a.1 2.746 2.593 2.899 + +Backtransformed parameters: + est. lower upper +cyan_0 1.026e+02 NA NA +k_JCZ38 5.314e-02 NA NA +k_J9Z38 5.732e-03 NA NA +k_JSE76 2.626e-02 NA NA +f_cyan_to_JCZ38 6.051e-01 NA NA +f_cyan_to_J9Z38 2.251e-01 NA NA +f_JCZ38_to_JSE76 1.000e+00 NA NA +f_JSE76_to_JCZ38 8.772e-01 NA NA +k1 1.422e-01 NA NA +k2 1.140e-02 NA NA +g 3.783e-01 NA NA + +Resulting formation fractions: + ff +cyan_JCZ38 0.6051 +cyan_J9Z38 0.2251 +cyan_sink 0.1698 +JCZ38_JSE76 1.0000 +JCZ38_sink 0.0000 +JSE76_JCZ38 0.8772 +JSE76_sink 0.1228 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +cyan 22.05 160.35 48.27 4.873 60.83 +JCZ38 13.04 43.33 NA NA NA +J9Z38 120.93 401.73 NA NA NA +JSE76 26.39 87.68 NA NA NA + +</code></pre> +<p></p> +<caption> +Hierarchical DFOP path 2 fit with reduced random effects, two-component +error +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.4.2 +Date of fit: Fri Feb 14 08:12:54 2025 +Date of summary: Sun Feb 16 17:03:41 2025 + +Equations: +d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * + time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) + * cyan +d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - + g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * + exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38 + + f_JSE76_to_JCZ38 * k_JSE76 * JSE76 +d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 - + g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * + exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 886.298 s +Using 300, 100 iterations and 10 chains + +Variance model: Two-component variance function + +Starting values for degradation parameters: + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 + 101.7393 -1.4493 -5.0118 -2.1269 0.6720 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 + 7.3362 13.4423 13.2659 -2.0061 -4.5527 + g_qlogis + -0.5806 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1 +cyan_0 5.604 0.00 0.000 0.000 0.0000 +log_k_JCZ38 0.000 2.77 0.000 0.000 0.0000 +log_k_J9Z38 0.000 0.00 1.662 0.000 0.0000 +log_k_JSE76 0.000 0.00 0.000 5.021 0.0000 +f_cyan_ilr_1 0.000 0.00 0.000 0.000 0.6519 +f_cyan_ilr_2 0.000 0.00 0.000 0.000 0.0000 +f_JCZ38_qlogis 0.000 0.00 0.000 0.000 0.0000 +f_JSE76_qlogis 0.000 0.00 0.000 0.000 0.0000 +log_k1 0.000 0.00 0.000 0.000 0.0000 +log_k2 0.000 0.00 0.000 0.000 0.0000 +g_qlogis 0.000 0.00 0.000 0.000 0.0000 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 +cyan_0 0.00 0.00 0.00 0.0000 0.0000 +log_k_JCZ38 0.00 0.00 0.00 0.0000 0.0000 +log_k_J9Z38 0.00 0.00 0.00 0.0000 0.0000 +log_k_JSE76 0.00 0.00 0.00 0.0000 0.0000 +f_cyan_ilr_1 0.00 0.00 0.00 0.0000 0.0000 +f_cyan_ilr_2 13.37 0.00 0.00 0.0000 0.0000 +f_JCZ38_qlogis 0.00 14.21 0.00 0.0000 0.0000 +f_JSE76_qlogis 0.00 0.00 14.58 0.0000 0.0000 +log_k1 0.00 0.00 0.00 0.8453 0.0000 +log_k2 0.00 0.00 0.00 0.0000 0.5969 +g_qlogis 0.00 0.00 0.00 0.0000 0.0000 + g_qlogis +cyan_0 0.00 +log_k_JCZ38 0.00 +log_k_J9Z38 0.00 +log_k_JSE76 0.00 +f_cyan_ilr_1 0.00 +f_cyan_ilr_2 0.00 +f_JCZ38_qlogis 0.00 +f_JSE76_qlogis 0.00 +log_k1 0.00 +log_k2 0.00 +g_qlogis 1.69 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2237 2229 -1099 + +Optimised parameters: + est. lower upper +cyan_0 101.00243 NA NA +log_k_JCZ38 -2.80828 NA NA +log_k_J9Z38 -5.04449 NA NA +log_k_JSE76 -3.66981 NA NA +f_cyan_ilr_1 0.72564 NA NA +f_cyan_ilr_2 1.37978 NA NA +f_JCZ38_qlogis 1.98726 NA NA +f_JSE76_qlogis 414.80884 NA NA +log_k1 -2.38601 NA NA +log_k2 -4.63632 NA NA +g_qlogis -0.33920 NA NA +a.1 2.10837 1.91261 2.30413 +b.1 0.06223 0.05085 0.07361 +SD.log_k_JCZ38 1.30902 0.48128 2.13675 +SD.log_k_J9Z38 0.83882 0.25790 1.41974 +SD.log_k_JSE76 0.58104 0.14201 1.02008 +SD.f_cyan_ilr_1 0.35421 0.12398 0.58443 +SD.f_cyan_ilr_2 0.79373 0.12007 1.46739 +SD.log_k2 0.27476 0.08557 0.46394 +SD.g_qlogis 0.96170 0.35463 1.56878 + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_JCZ38 1.3090 0.48128 2.1367 +SD.log_k_J9Z38 0.8388 0.25790 1.4197 +SD.log_k_JSE76 0.5810 0.14201 1.0201 +SD.f_cyan_ilr_1 0.3542 0.12398 0.5844 +SD.f_cyan_ilr_2 0.7937 0.12007 1.4674 +SD.log_k2 0.2748 0.08557 0.4639 +SD.g_qlogis 0.9617 0.35463 1.5688 + +Variance model: + est. lower upper +a.1 2.10837 1.91261 2.30413 +b.1 0.06223 0.05085 0.07361 + +Backtransformed parameters: + est. lower upper +cyan_0 1.010e+02 NA NA +k_JCZ38 6.031e-02 NA NA +k_J9Z38 6.445e-03 NA NA +k_JSE76 2.548e-02 NA NA +f_cyan_to_JCZ38 6.808e-01 NA NA +f_cyan_to_J9Z38 2.440e-01 NA NA +f_JCZ38_to_JSE76 8.795e-01 NA NA +f_JSE76_to_JCZ38 1.000e+00 NA NA +k1 9.200e-02 NA NA +k2 9.693e-03 NA NA +g 4.160e-01 NA NA + +Resulting formation fractions: + ff +cyan_JCZ38 0.68081 +cyan_J9Z38 0.24398 +cyan_sink 0.07521 +JCZ38_JSE76 0.87945 +JCZ38_sink 0.12055 +JSE76_JCZ38 1.00000 +JSE76_sink 0.00000 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +cyan 25.00 182.05 54.8 7.535 71.51 +JCZ38 11.49 38.18 NA NA NA +J9Z38 107.55 357.28 NA NA NA +JSE76 27.20 90.36 NA NA NA + +</code></pre> +<p></p> +<caption> +Hierarchical SFORB path 2 fit with reduced random effects, constant +variance +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.4.2 +Date of fit: Fri Feb 14 08:12:32 2025 +Date of summary: Sun Feb 16 17:03:41 2025 + +Equations: +d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound * + cyan_free + k_cyan_bound_free * cyan_bound +d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free * + cyan_bound +d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38 + * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76 +d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38 + * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 865.121 s +Using 300, 100 iterations and 10 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + cyan_free_0 log_k_cyan_free log_k_cyan_free_bound + 102.4395 -2.7673 -2.8942 +log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 + -3.6201 -2.3107 -5.3123 + log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 + -3.7120 0.6754 1.1448 + f_JCZ38_qlogis f_JSE76_qlogis + 14.8408 15.4734 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_free_0 log_k_cyan_free log_k_cyan_free_bound +cyan_free_0 4.589 0.0000 0.00 +log_k_cyan_free 0.000 0.4849 0.00 +log_k_cyan_free_bound 0.000 0.0000 1.62 +log_k_cyan_bound_free 0.000 0.0000 0.00 +log_k_JCZ38 0.000 0.0000 0.00 +log_k_J9Z38 0.000 0.0000 0.00 +log_k_JSE76 0.000 0.0000 0.00 +f_cyan_ilr_1 0.000 0.0000 0.00 +f_cyan_ilr_2 0.000 0.0000 0.00 +f_JCZ38_qlogis 0.000 0.0000 0.00 +f_JSE76_qlogis 0.000 0.0000 0.00 + log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 +cyan_free_0 0.000 0.0000 0.000 0.0 +log_k_cyan_free 0.000 0.0000 0.000 0.0 +log_k_cyan_free_bound 0.000 0.0000 0.000 0.0 +log_k_cyan_bound_free 1.197 0.0000 0.000 0.0 +log_k_JCZ38 0.000 0.7966 0.000 0.0 +log_k_J9Z38 0.000 0.0000 1.561 0.0 +log_k_JSE76 0.000 0.0000 0.000 0.8 +f_cyan_ilr_1 0.000 0.0000 0.000 0.0 +f_cyan_ilr_2 0.000 0.0000 0.000 0.0 +f_JCZ38_qlogis 0.000 0.0000 0.000 0.0 +f_JSE76_qlogis 0.000 0.0000 0.000 0.0 + f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis +cyan_free_0 0.0000 0.000 0.0 0.00 +log_k_cyan_free 0.0000 0.000 0.0 0.00 +log_k_cyan_free_bound 0.0000 0.000 0.0 0.00 +log_k_cyan_bound_free 0.0000 0.000 0.0 0.00 +log_k_JCZ38 0.0000 0.000 0.0 0.00 +log_k_J9Z38 0.0000 0.000 0.0 0.00 +log_k_JSE76 0.0000 0.000 0.0 0.00 +f_cyan_ilr_1 0.6349 0.000 0.0 0.00 +f_cyan_ilr_2 0.0000 1.797 0.0 0.00 +f_JCZ38_qlogis 0.0000 0.000 15.6 0.00 +f_JSE76_qlogis 0.0000 0.000 0.0 17.52 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2280 2272 -1120 + +Optimised parameters: + est. lower upper +cyan_free_0 102.6532 NA NA +log_k_cyan_free -2.8547 NA NA +log_k_cyan_free_bound -2.7004 NA NA +log_k_cyan_bound_free -3.5078 NA NA +log_k_JCZ38 -2.9255 NA NA +log_k_J9Z38 -5.1089 NA NA +log_k_JSE76 -3.6263 NA NA +f_cyan_ilr_1 0.6873 NA NA +f_cyan_ilr_2 0.6498 NA NA +f_JCZ38_qlogis 3624.2149 NA NA +f_JSE76_qlogis 1.9991 NA NA +a.1 2.7472 2.55559 2.9388 +SD.log_k_cyan_free 0.3227 0.10296 0.5423 +SD.log_k_cyan_free_bound 0.8757 0.29525 1.4562 +SD.log_k_cyan_bound_free 0.6128 0.20220 1.0233 +SD.log_k_JCZ38 1.3431 0.48474 2.2014 +SD.log_k_J9Z38 0.6881 0.14714 1.2291 +SD.log_k_JSE76 0.6461 0.15321 1.1390 +SD.f_cyan_ilr_1 0.3361 0.11376 0.5585 +SD.f_cyan_ilr_2 0.4286 0.08419 0.7730 + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_cyan_free 0.3227 0.10296 0.5423 +SD.log_k_cyan_free_bound 0.8757 0.29525 1.4562 +SD.log_k_cyan_bound_free 0.6128 0.20220 1.0233 +SD.log_k_JCZ38 1.3431 0.48474 2.2014 +SD.log_k_J9Z38 0.6881 0.14714 1.2291 +SD.log_k_JSE76 0.6461 0.15321 1.1390 +SD.f_cyan_ilr_1 0.3361 0.11376 0.5585 +SD.f_cyan_ilr_2 0.4286 0.08419 0.7730 + +Variance model: + est. lower upper +a.1 2.747 2.556 2.939 + +Backtransformed parameters: + est. lower upper +cyan_free_0 1.027e+02 NA NA +k_cyan_free 5.758e-02 NA NA +k_cyan_free_bound 6.718e-02 NA NA +k_cyan_bound_free 2.996e-02 NA NA +k_JCZ38 5.364e-02 NA NA +k_J9Z38 6.042e-03 NA NA +k_JSE76 2.662e-02 NA NA +f_cyan_free_to_JCZ38 6.039e-01 NA NA +f_cyan_free_to_J9Z38 2.285e-01 NA NA +f_JCZ38_to_JSE76 1.000e+00 NA NA +f_JSE76_to_JCZ38 8.807e-01 NA NA + +Estimated Eigenvalues of SFORB model(s): +cyan_b1 cyan_b2 cyan_g + 0.1426 0.0121 0.3484 + +Resulting formation fractions: + ff +cyan_free_JCZ38 0.6039 +cyan_free_J9Z38 0.2285 +cyan_free_sink 0.1676 +cyan_free 1.0000 +JCZ38_JSE76 1.0000 +JCZ38_sink 0.0000 +JSE76_JCZ38 0.8807 +JSE76_sink 0.1193 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 +cyan 23.84 154.95 46.65 4.86 57.31 +JCZ38 12.92 42.93 NA NA NA +J9Z38 114.71 381.07 NA NA NA +JSE76 26.04 86.51 NA NA NA + +</code></pre> +<p></p> +<caption> +Hierarchical SFORB path 2 fit with reduced random effects, two-component +error +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.4.2 +Date of fit: Fri Feb 14 08:12:36 2025 +Date of summary: Sun Feb 16 17:03:41 2025 + +Equations: +d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound * + cyan_free + k_cyan_bound_free * cyan_bound +d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free * + cyan_bound +d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38 + * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76 +d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38 + * J9Z38 +d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76 + +Data: +433 observations of 4 variable(s) grouped in 5 datasets + +Model predictions using solution type deSolve + +Fitted in 868.952 s +Using 300, 100 iterations and 10 chains + +Variance model: Two-component variance function + +Starting values for degradation parameters: + cyan_free_0 log_k_cyan_free log_k_cyan_free_bound + 101.7511 -2.8370 -3.0162 +log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 + -3.6600 -2.2988 -5.3129 + log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 + -3.6991 0.6722 4.8596 + f_JCZ38_qlogis f_JSE76_qlogis + 13.4678 14.2149 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + cyan_free_0 log_k_cyan_free log_k_cyan_free_bound +cyan_free_0 5.629 0.000 0.000 +log_k_cyan_free 0.000 0.446 0.000 +log_k_cyan_free_bound 0.000 0.000 1.449 +log_k_cyan_bound_free 0.000 0.000 0.000 +log_k_JCZ38 0.000 0.000 0.000 +log_k_J9Z38 0.000 0.000 0.000 +log_k_JSE76 0.000 0.000 0.000 +f_cyan_ilr_1 0.000 0.000 0.000 +f_cyan_ilr_2 0.000 0.000 0.000 +f_JCZ38_qlogis 0.000 0.000 0.000 +f_JSE76_qlogis 0.000 0.000 0.000 + log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76 +cyan_free_0 0.000 0.0000 0.000 0.0000 +log_k_cyan_free 0.000 0.0000 0.000 0.0000 +log_k_cyan_free_bound 0.000 0.0000 0.000 0.0000 +log_k_cyan_bound_free 1.213 0.0000 0.000 0.0000 +log_k_JCZ38 0.000 0.7801 0.000 0.0000 +log_k_J9Z38 0.000 0.0000 1.575 0.0000 +log_k_JSE76 0.000 0.0000 0.000 0.8078 +f_cyan_ilr_1 0.000 0.0000 0.000 0.0000 +f_cyan_ilr_2 0.000 0.0000 0.000 0.0000 +f_JCZ38_qlogis 0.000 0.0000 0.000 0.0000 +f_JSE76_qlogis 0.000 0.0000 0.000 0.0000 + f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis +cyan_free_0 0.0000 0.000 0.00 0.00 +log_k_cyan_free 0.0000 0.000 0.00 0.00 +log_k_cyan_free_bound 0.0000 0.000 0.00 0.00 +log_k_cyan_bound_free 0.0000 0.000 0.00 0.00 +log_k_JCZ38 0.0000 0.000 0.00 0.00 +log_k_J9Z38 0.0000 0.000 0.00 0.00 +log_k_JSE76 0.0000 0.000 0.00 0.00 +f_cyan_ilr_1 0.6518 0.000 0.00 0.00 +f_cyan_ilr_2 0.0000 9.981 0.00 0.00 +f_JCZ38_qlogis 0.0000 0.000 14.26 0.00 +f_JSE76_qlogis 0.0000 0.000 0.00 16.17 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2241 2233 -1101 + +Optimised parameters: + est. lower upper +cyan_free_0 100.95469 NA NA +log_k_cyan_free -3.18706 NA NA +log_k_cyan_free_bound -3.38455 NA NA +log_k_cyan_bound_free -3.75788 NA NA +log_k_JCZ38 -2.77024 NA NA +log_k_J9Z38 -5.03665 NA NA +log_k_JSE76 -3.60289 NA NA +f_cyan_ilr_1 0.72263 NA NA +f_cyan_ilr_2 1.45352 NA NA +f_JCZ38_qlogis 2.00778 NA NA +f_JSE76_qlogis 941.58570 NA NA +a.1 2.11130 1.91479 2.30780 +b.1 0.06299 0.05152 0.07445 +SD.log_k_cyan_free 0.50098 0.18805 0.81390 +SD.log_k_cyan_bound_free 0.31671 0.08467 0.54875 +SD.log_k_JCZ38 1.25865 0.45932 2.05798 +SD.log_k_J9Z38 0.86833 0.27222 1.46444 +SD.log_k_JSE76 0.59325 0.14711 1.03940 +SD.f_cyan_ilr_1 0.35705 0.12521 0.58890 +SD.f_cyan_ilr_2 0.88541 0.13797 1.63286 + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_cyan_free 0.5010 0.18805 0.8139 +SD.log_k_cyan_bound_free 0.3167 0.08467 0.5487 +SD.log_k_JCZ38 1.2587 0.45932 2.0580 +SD.log_k_J9Z38 0.8683 0.27222 1.4644 +SD.log_k_JSE76 0.5933 0.14711 1.0394 +SD.f_cyan_ilr_1 0.3571 0.12521 0.5889 +SD.f_cyan_ilr_2 0.8854 0.13797 1.6329 + +Variance model: + est. lower upper +a.1 2.11130 1.91479 2.30780 +b.1 0.06299 0.05152 0.07445 + +Backtransformed parameters: + est. lower upper +cyan_free_0 1.010e+02 NA NA +k_cyan_free 4.129e-02 NA NA +k_cyan_free_bound 3.389e-02 NA NA +k_cyan_bound_free 2.333e-02 NA NA +k_JCZ38 6.265e-02 NA NA +k_J9Z38 6.495e-03 NA NA +k_JSE76 2.724e-02 NA NA +f_cyan_free_to_JCZ38 6.844e-01 NA NA +f_cyan_free_to_J9Z38 2.463e-01 NA NA +f_JCZ38_to_JSE76 8.816e-01 NA NA +f_JSE76_to_JCZ38 1.000e+00 NA NA + +Estimated Eigenvalues of SFORB model(s): +cyan_b1 cyan_b2 cyan_g +0.08751 0.01101 0.39586 + +Resulting formation fractions: + ff +cyan_free_JCZ38 0.68444 +cyan_free_J9Z38 0.24633 +cyan_free_sink 0.06923 +cyan_free 1.00000 +JCZ38_JSE76 0.88161 +JCZ38_sink 0.11839 +JSE76_JCZ38 1.00000 +JSE76_sink 0.00000 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 +cyan 25.36 163.36 49.18 7.921 62.95 +JCZ38 11.06 36.75 NA NA NA +J9Z38 106.71 354.49 NA NA NA +JSE76 25.44 84.51 NA NA NA + +</code></pre> +<p></p> +</div> +</div> +<div class="section level3"> +<h3 id="session-info">Session info<a class="anchor" aria-label="anchor" href="#session-info"></a> +</h3> +<pre><code>R version 4.4.2 (2024-10-31) +Platform: x86_64-pc-linux-gnu +Running under: Debian GNU/Linux 12 (bookworm) + +Matrix products: default +BLAS: /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.11.0 +LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.11.0 + +locale: + [1] LC_CTYPE=de_DE.UTF-8 LC_NUMERIC=C + [3] LC_TIME=de_DE.UTF-8 LC_COLLATE=de_DE.UTF-8 + [5] LC_MONETARY=de_DE.UTF-8 LC_MESSAGES=de_DE.UTF-8 + [7] LC_PAPER=de_DE.UTF-8 LC_NAME=C + [9] LC_ADDRESS=C LC_TELEPHONE=C +[11] LC_MEASUREMENT=de_DE.UTF-8 LC_IDENTIFICATION=C + +time zone: Europe/Berlin +tzcode source: system (glibc) + +attached base packages: +[1] parallel stats graphics grDevices utils datasets methods +[8] base + +other attached packages: +[1] saemix_3.3 npde_3.5 knitr_1.49 mkin_1.2.10 + +loaded via a namespace (and not attached): + [1] gtable_0.3.6 jsonlite_1.8.9 dplyr_1.1.4 compiler_4.4.2 + [5] tidyselect_1.2.1 gridExtra_2.3 jquerylib_0.1.4 systemfonts_1.1.0 + [9] scales_1.3.0 textshaping_0.4.1 yaml_2.3.10 fastmap_1.2.0 +[13] lattice_0.22-6 ggplot2_3.5.1 R6_2.5.1 generics_0.1.3 +[17] lmtest_0.9-40 MASS_7.3-61 htmlwidgets_1.6.4 tibble_3.2.1 +[21] desc_1.4.3 munsell_0.5.1 bslib_0.8.0 pillar_1.9.0 +[25] rlang_1.1.4 utf8_1.2.4 inline_0.3.20 cachem_1.1.0 +[29] xfun_0.49 fs_1.6.5 sass_0.4.9 cli_3.6.3 +[33] pkgdown_2.1.1 magrittr_2.0.3 digest_0.6.37 grid_4.4.2 +[37] mclust_6.1.1 lifecycle_1.0.4 nlme_3.1-166 vctrs_0.6.5 +[41] evaluate_1.0.1 glue_1.8.0 ragg_1.3.3 zoo_1.8-12 +[45] fansi_1.0.6 colorspace_2.1-1 rmarkdown_2.29 pkgconfig_2.0.3 +[49] tools_4.4.2 htmltools_0.5.8.1</code></pre> +</div> +<div class="section level3"> +<h3 id="hardware-info">Hardware info<a class="anchor" aria-label="anchor" href="#hardware-info"></a> +</h3> +<pre><code>CPU model: AMD Ryzen 9 7950X 16-Core Processor</code></pre> +<pre><code>MemTotal: 64927788 kB</code></pre> +</div> +</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/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-13-1.png b/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-13-1.png Binary files differnew file mode 100644 index 00000000..d2201974 --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-13-1.png diff --git a/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-14-1.png b/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-14-1.png Binary files differnew file mode 100644 index 00000000..7380ba4c --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-14-1.png diff --git a/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-15-1.png b/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-15-1.png Binary files differnew file mode 100644 index 00000000..4de15105 --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-15-1.png diff --git a/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-20-1.png b/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-20-1.png Binary files differnew file mode 100644 index 00000000..d57badf1 --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-20-1.png diff --git a/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-21-1.png b/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-21-1.png Binary files differnew file mode 100644 index 00000000..eb629c4d --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-21-1.png diff --git a/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-22-1.png b/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-22-1.png Binary files differnew file mode 100644 index 00000000..a2abb2f7 --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-22-1.png diff --git a/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-7-1.png b/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-7-1.png Binary files differnew file mode 100644 index 00000000..28ec82ba --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-7-1.png diff --git a/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-8-1.png b/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-8-1.png Binary files differnew file mode 100644 index 00000000..a2abb2f7 --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-8-1.png diff --git a/docs/dev/articles/prebuilt/2022_dmta_parent.html b/docs/dev/articles/prebuilt/2022_dmta_parent.html new file mode 100644 index 00000000..e4943574 --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_dmta_parent.html @@ -0,0 +1,2166 @@ +<!DOCTYPE html> +<!-- Generated by pkgdown: do not edit by hand --><html lang="en"> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> +<meta charset="utf-8"> +<meta http-equiv="X-UA-Compatible" content="IE=edge"> +<meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"> +<title>Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P • mkin</title> +<script src="../../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"> +<link href="../../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"> +<script src="../../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"> +<link href="../../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"> +<script src="../../deps/headroom-0.11.0/headroom.min.js"></script><script src="../../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../../deps/search-1.0.0/fuse.min.js"></script><script src="../../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../../pkgdown.js"></script><meta property="og:title" content="Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P"> +<meta name="robots" content="noindex"> +</head> +<body> + <a href="#main" class="visually-hidden-focusable">Skip to contents</a> + + + <nav class="navbar navbar-expand-lg fixed-top bg-light" data-bs-theme="default" aria-label="Site navigation"><div class="container"> + + <a class="navbar-brand me-2" href="../../index.html">mkin</a> + + <small class="nav-text text-info me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="In-development version">1.2.10</small> + + + <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation"> + <span class="navbar-toggler-icon"></span> + </button> + + <div id="navbar" class="collapse navbar-collapse ms-3"> + <ul class="navbar-nav me-auto"> +<li class="nav-item"><a class="nav-link" href="../../reference/index.html">Reference</a></li> +<li class="active nav-item dropdown"> + <button class="nav-link dropdown-toggle" type="button" id="dropdown-articles" data-bs-toggle="dropdown" aria-expanded="false" aria-haspopup="true">Articles</button> + <ul class="dropdown-menu" aria-labelledby="dropdown-articles"> +<li><a class="dropdown-item" href="../../articles/mkin.html">Introduction to mkin</a></li> + <li><hr class="dropdown-divider"></li> + <li><h6 class="dropdown-header" data-toc-skip>Example evaluations with (generalised) nonlinear least squares</h6></li> + <li><a class="dropdown-item" href="../../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a></li> + <li><a class="dropdown-item" href="../../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a></li> + <li><a class="dropdown-item" href="../../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a></li> + <li><hr class="dropdown-divider"></li> + <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/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> + <li><hr class="dropdown-divider"></li> + <li><h6 class="dropdown-header" data-toc-skip>Performance</h6></li> + <li><a class="dropdown-item" href="../../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a></li> + <li><a class="dropdown-item" href="../../articles/web_only/benchmarks.html">Benchmark timings for mkin</a></li> + <li><a class="dropdown-item" href="../../articles/web_only/saem_benchmarks.html">Benchmark timings for saem.mmkin</a></li> + <li><hr class="dropdown-divider"></li> + <li><h6 class="dropdown-header" data-toc-skip>Miscellaneous</h6></li> + <li><a class="dropdown-item" href="../../articles/twa.html">Calculation of time weighted average concentrations with mkin</a></li> + <li><a class="dropdown-item" href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a></li> + </ul> +</li> +<li class="nav-item"><a class="nav-link" href="../../coverage/coverage.html">Test coverage</a></li> +<li class="nav-item"><a class="nav-link" href="../../news/index.html">News</a></li> + </ul> +<ul class="navbar-nav"> +<li class="nav-item"><form class="form-inline" role="search"> + <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../../search.json"> +</form></li> +<li class="nav-item"><a class="external-link nav-link" href="https://github.com/jranke/mkin/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li> + </ul> +</div> + + + </div> +</nav><div class="container template-article"> + + + + +<div class="row"> + <main id="main" class="col-md-9"><div class="page-header"> + + <h1>Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</h1> + <h4 data-toc-skip class="author">Johannes +Ranke</h4> + + <h4 data-toc-skip class="date">Last change on 5 January +2023, last compiled on 16 Februar 2025</h4> + + <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/prebuilt/2022_dmta_parent.rmd" class="external-link"><code>vignettes/prebuilt/2022_dmta_parent.rmd</code></a></small> + <div class="d-none name"><code>2022_dmta_parent.rmd</code></div> + </div> + + + +<div class="section level2"> +<h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#introduction"></a> +</h2> +<p>The purpose of this document is to demonstrate how nonlinear +hierarchical models (NLHM) based on the parent degradation models SFO, +FOMC, DFOP and HS can be fitted with the mkin package.</p> +<p>It was assembled in the course of work package 1.1 of Project Number +173340 (Application of nonlinear hierarchical models to the kinetic +evaluation of chemical degradation data) of the German Environment +Agency carried out in 2022 and 2023.</p> +<p>The mkin package is used in version 1.2.10. It contains the test data +and the functions used in the evaluations. The <code>saemix</code> +package is used as a backend for fitting the NLHM, but is also loaded to +make the convergence plot function available.</p> +<p>This document is processed with the <code>knitr</code> package, which +also provides the <code>kable</code> function that is used to improve +the display of tabular data in R markdown documents. For parallel +processing, the <code>parallel</code> package is used.</p> +<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://pkgdown.jrwb.de/mkin/">mkin</a></span><span class="op">)</span></span> +<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://yihui.org/knitr/" class="external-link">knitr</a></span><span class="op">)</span></span> +<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">saemix</span><span class="op">)</span></span> +<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">parallel</span><span class="op">)</span></span> +<span><span class="va">n_cores</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/detectCores.html" class="external-link">detectCores</a></span><span class="op">(</span><span class="op">)</span></span> +<span><span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/Sys.info.html" class="external-link">Sys.info</a></span><span class="op">(</span><span class="op">)</span><span class="op">[</span><span class="st">"sysname"</span><span class="op">]</span> <span class="op">==</span> <span class="st">"Windows"</span><span class="op">)</span> <span class="op">{</span></span> +<span> <span class="va">cl</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makePSOCKcluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> +<span><span class="op">}</span> <span class="kw">else</span> <span class="op">{</span></span> +<span> <span class="va">cl</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makeForkCluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> +<span><span class="op">}</span></span></code></pre></div> +</div> +<div class="section level2"> +<h2 id="data">Data<a class="anchor" aria-label="anchor" href="#data"></a> +</h2> +<p>The test data are available in the mkin package as an object of class +<code>mkindsg</code> (mkin dataset group) under the identifier +<code>dimethenamid_2018</code>. The following preprocessing steps are +still necessary:</p> +<ul> +<li>The data available for the enantiomer dimethenamid-P (DMTAP) are +renamed to have the same substance name as the data for the racemic +mixture dimethenamid (DMTA). The reason for this is that no difference +between their degradation behaviour was identified in the EU risk +assessment.</li> +<li>The data for transformation products and unnecessary columns are +discarded</li> +<li>The observation times of each dataset are multiplied with the +corresponding normalisation factor also available in the dataset, in +order to make it possible to describe all datasets with a single set of +parameters that are independent of temperature</li> +<li>Finally, datasets observed in the same soil (<code>Elliot 1</code> +and <code>Elliot 2</code>) are combined, resulting in dimethenamid +(DMTA) data from six soils.</li> +</ul> +<p>The following commented R code performs this preprocessing.</p> +<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="co"># Apply a function to each of the seven datasets in the mkindsg object to create a list</span></span> +<span><span class="va">dmta_ds</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">lapply</a></span><span class="op">(</span><span class="fl">1</span><span class="op">:</span><span class="fl">7</span>, <span class="kw">function</span><span class="op">(</span><span class="va">i</span><span class="op">)</span> <span class="op">{</span></span> +<span> <span class="va">ds_i</span> <span class="op"><-</span> <span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">ds</span><span class="op">[[</span><span class="va">i</span><span class="op">]</span><span class="op">]</span><span class="op">$</span><span class="va">data</span> <span class="co"># Get a dataset</span></span> +<span> <span class="va">ds_i</span><span class="op">[</span><span class="va">ds_i</span><span class="op">$</span><span class="va">name</span> <span class="op">==</span> <span class="st">"DMTAP"</span>, <span class="st">"name"</span><span class="op">]</span> <span class="op"><-</span> <span class="st">"DMTA"</span> <span class="co"># Rename DMTAP to DMTA</span></span> +<span> <span class="va">ds_i</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/subset.html" class="external-link">subset</a></span><span class="op">(</span><span class="va">ds_i</span>, <span class="va">name</span> <span class="op">==</span> <span class="st">"DMTA"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"name"</span>, <span class="st">"time"</span>, <span class="st">"value"</span><span class="op">)</span><span class="op">)</span> <span class="co"># Select data</span></span> +<span> <span class="va">ds_i</span><span class="op">$</span><span class="va">time</span> <span class="op"><-</span> <span class="va">ds_i</span><span class="op">$</span><span class="va">time</span> <span class="op">*</span> <span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">f_time_norm</span><span class="op">[</span><span class="va">i</span><span class="op">]</span> <span class="co"># Normalise time</span></span> +<span> <span class="va">ds_i</span> <span class="co"># Return the dataset</span></span> +<span><span class="op">}</span><span class="op">)</span></span> +<span></span> +<span><span class="co"># Use dataset titles as names for the list elements</span></span> +<span><span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">)</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</span><span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">ds</span>, <span class="kw">function</span><span class="op">(</span><span class="va">ds</span><span class="op">)</span> <span class="va">ds</span><span class="op">$</span><span class="va">title</span><span class="op">)</span></span> +<span></span> +<span><span class="co"># Combine data for Elliot soil to obtain a named list with six elements</span></span> +<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/cbind.html" class="external-link">rbind</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 1"</span><span class="op">]</span><span class="op">]</span>, <span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 2"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span> <span class="co">#</span></span> +<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 1"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="cn">NULL</span></span> +<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 2"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="cn">NULL</span></span></code></pre></div> +<p>The following tables show the 6 datasets.</p> +<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="kw">for</span> <span class="op">(</span><span class="va">ds_name</span> <span class="kw">in</span> <span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">)</span><span class="op">)</span> <span class="op">{</span></span> +<span> <span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="fu"><a href="../../reference/mkin_long_to_wide.html">mkin_long_to_wide</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">[[</span><span class="va">ds_name</span><span class="op">]</span><span class="op">]</span><span class="op">)</span>,</span> +<span> caption <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste</a></span><span class="op">(</span><span class="st">"Dataset"</span>, <span class="va">ds_name</span><span class="op">)</span>,</span> +<span> label <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste0</a></span><span class="op">(</span><span class="st">"tab:"</span>, <span class="va">ds_name</span><span class="op">)</span>, booktabs <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span><span class="op">)</span></span> +<span> <span class="fu"><a href="https://rdrr.io/r/base/cat.html" class="external-link">cat</a></span><span class="op">(</span><span class="st">"\n\\clearpage\n"</span><span class="op">)</span></span> +<span><span class="op">}</span></span></code></pre></div> +<table class="table"> +<caption>Dataset Calke</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">DMTA</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0</td> +<td align="right">95.8</td> +</tr> +<tr class="even"> +<td align="right">0</td> +<td align="right">98.7</td> +</tr> +<tr class="odd"> +<td align="right">14</td> +<td align="right">60.5</td> +</tr> +<tr class="even"> +<td align="right">30</td> +<td align="right">39.1</td> +</tr> +<tr class="odd"> +<td align="right">59</td> +<td align="right">15.2</td> +</tr> +<tr class="even"> +<td align="right">120</td> +<td align="right">4.8</td> +</tr> +<tr class="odd"> +<td align="right">120</td> +<td align="right">4.6</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset Borstel</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">DMTA</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">100.5</td> +</tr> +<tr class="even"> +<td align="right">0.000000</td> +<td align="right">99.6</td> +</tr> +<tr class="odd"> +<td align="right">1.941295</td> +<td align="right">91.9</td> +</tr> +<tr class="even"> +<td align="right">1.941295</td> +<td align="right">91.3</td> +</tr> +<tr class="odd"> +<td align="right">6.794534</td> +<td align="right">81.8</td> +</tr> +<tr class="even"> +<td align="right">6.794534</td> +<td align="right">82.1</td> +</tr> +<tr class="odd"> +<td align="right">13.589067</td> +<td align="right">69.1</td> +</tr> +<tr class="even"> +<td align="right">13.589067</td> +<td align="right">68.0</td> +</tr> +<tr class="odd"> +<td align="right">27.178135</td> +<td align="right">51.4</td> +</tr> +<tr class="even"> +<td align="right">27.178135</td> +<td align="right">51.4</td> +</tr> +<tr class="odd"> +<td align="right">56.297565</td> +<td align="right">27.6</td> +</tr> +<tr class="even"> +<td align="right">56.297565</td> +<td align="right">26.8</td> +</tr> +<tr class="odd"> +<td align="right">86.387643</td> +<td align="right">15.7</td> +</tr> +<tr class="even"> +<td align="right">86.387643</td> +<td align="right">15.3</td> +</tr> +<tr class="odd"> +<td align="right">115.507073</td> +<td align="right">7.9</td> +</tr> +<tr class="even"> +<td align="right">115.507073</td> +<td align="right">8.1</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset Flaach</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">DMTA</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.0000000</td> +<td align="right">96.5</td> +</tr> +<tr class="even"> +<td align="right">0.0000000</td> +<td align="right">96.8</td> +</tr> +<tr class="odd"> +<td align="right">0.0000000</td> +<td align="right">97.0</td> +</tr> +<tr class="even"> +<td align="right">0.6233856</td> +<td align="right">82.9</td> +</tr> +<tr class="odd"> +<td align="right">0.6233856</td> +<td align="right">86.7</td> +</tr> +<tr class="even"> +<td align="right">0.6233856</td> +<td align="right">87.4</td> +</tr> +<tr class="odd"> +<td align="right">1.8701567</td> +<td align="right">72.8</td> +</tr> +<tr class="even"> +<td align="right">1.8701567</td> +<td align="right">69.9</td> +</tr> +<tr class="odd"> +<td align="right">1.8701567</td> +<td align="right">71.9</td> +</tr> +<tr class="even"> +<td align="right">4.3636989</td> +<td align="right">51.4</td> +</tr> +<tr class="odd"> +<td align="right">4.3636989</td> +<td align="right">52.9</td> +</tr> +<tr class="even"> +<td align="right">4.3636989</td> +<td align="right">48.6</td> +</tr> +<tr class="odd"> +<td align="right">8.7273979</td> +<td align="right">28.5</td> +</tr> +<tr class="even"> +<td align="right">8.7273979</td> +<td align="right">27.3</td> +</tr> +<tr class="odd"> +<td align="right">8.7273979</td> +<td align="right">27.5</td> +</tr> +<tr class="even"> +<td align="right">13.0910968</td> +<td align="right">14.8</td> +</tr> +<tr class="odd"> +<td align="right">13.0910968</td> +<td align="right">13.4</td> +</tr> +<tr class="even"> +<td align="right">13.0910968</td> +<td align="right">14.4</td> +</tr> +<tr class="odd"> +<td align="right">17.4547957</td> +<td align="right">7.7</td> +</tr> +<tr class="even"> +<td align="right">17.4547957</td> +<td align="right">7.3</td> +</tr> +<tr class="odd"> +<td align="right">17.4547957</td> +<td align="right">8.1</td> +</tr> +<tr class="even"> +<td align="right">26.1821936</td> +<td align="right">2.0</td> +</tr> +<tr class="odd"> +<td align="right">26.1821936</td> +<td align="right">1.5</td> +</tr> +<tr class="even"> +<td align="right">26.1821936</td> +<td align="right">1.9</td> +</tr> +<tr class="odd"> +<td align="right">34.9095915</td> +<td align="right">1.3</td> +</tr> +<tr class="even"> +<td align="right">34.9095915</td> +<td align="right">1.0</td> +</tr> +<tr class="odd"> +<td align="right">34.9095915</td> +<td align="right">1.1</td> +</tr> +<tr class="even"> +<td align="right">43.6369893</td> +<td align="right">0.9</td> +</tr> +<tr class="odd"> +<td align="right">43.6369893</td> +<td align="right">0.7</td> +</tr> +<tr class="even"> +<td align="right">43.6369893</td> +<td align="right">0.7</td> +</tr> +<tr class="odd"> +<td align="right">52.3643872</td> +<td align="right">0.6</td> +</tr> +<tr class="even"> +<td align="right">52.3643872</td> +<td align="right">0.4</td> +</tr> +<tr class="odd"> +<td align="right">52.3643872</td> +<td align="right">0.5</td> +</tr> +<tr class="even"> +<td align="right">74.8062674</td> +<td align="right">0.4</td> +</tr> +<tr class="odd"> +<td align="right">74.8062674</td> +<td align="right">0.3</td> +</tr> +<tr class="even"> +<td align="right">74.8062674</td> +<td align="right">0.3</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset BBA 2.2</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">DMTA</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.0000000</td> +<td align="right">98.09</td> +</tr> +<tr class="even"> +<td align="right">0.0000000</td> +<td align="right">98.77</td> +</tr> +<tr class="odd"> +<td align="right">0.7678922</td> +<td align="right">93.52</td> +</tr> +<tr class="even"> +<td align="right">0.7678922</td> +<td align="right">92.03</td> +</tr> +<tr class="odd"> +<td align="right">2.3036765</td> +<td align="right">88.39</td> +</tr> +<tr class="even"> +<td align="right">2.3036765</td> +<td align="right">87.18</td> +</tr> +<tr class="odd"> +<td align="right">5.3752452</td> +<td align="right">69.38</td> +</tr> +<tr class="even"> +<td align="right">5.3752452</td> +<td align="right">71.06</td> +</tr> +<tr class="odd"> +<td align="right">10.7504904</td> +<td align="right">45.21</td> +</tr> +<tr class="even"> +<td align="right">10.7504904</td> +<td align="right">46.81</td> +</tr> +<tr class="odd"> +<td align="right">16.1257355</td> +<td align="right">30.54</td> +</tr> +<tr class="even"> +<td align="right">16.1257355</td> +<td align="right">30.07</td> +</tr> +<tr class="odd"> +<td align="right">21.5009807</td> +<td align="right">21.60</td> +</tr> +<tr class="even"> +<td align="right">21.5009807</td> +<td align="right">20.41</td> +</tr> +<tr class="odd"> +<td align="right">32.2514711</td> +<td align="right">9.10</td> +</tr> +<tr class="even"> +<td align="right">32.2514711</td> +<td align="right">9.70</td> +</tr> +<tr class="odd"> +<td align="right">43.0019614</td> +<td align="right">6.58</td> +</tr> +<tr class="even"> +<td align="right">43.0019614</td> +<td align="right">6.31</td> +</tr> +<tr class="odd"> +<td align="right">53.7524518</td> +<td align="right">3.47</td> +</tr> +<tr class="even"> +<td align="right">53.7524518</td> +<td align="right">3.52</td> +</tr> +<tr class="odd"> +<td align="right">64.5029421</td> +<td align="right">3.40</td> +</tr> +<tr class="even"> +<td align="right">64.5029421</td> +<td align="right">3.67</td> +</tr> +<tr class="odd"> +<td align="right">91.3791680</td> +<td align="right">1.62</td> +</tr> +<tr class="even"> +<td align="right">91.3791680</td> +<td align="right">1.62</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset BBA 2.3</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">DMTA</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.0000000</td> +<td align="right">99.33</td> +</tr> +<tr class="even"> +<td align="right">0.0000000</td> +<td align="right">97.44</td> +</tr> +<tr class="odd"> +<td align="right">0.6733938</td> +<td align="right">93.73</td> +</tr> +<tr class="even"> +<td align="right">0.6733938</td> +<td align="right">93.77</td> +</tr> +<tr class="odd"> +<td align="right">2.0201814</td> +<td align="right">87.84</td> +</tr> +<tr class="even"> +<td align="right">2.0201814</td> +<td align="right">89.82</td> +</tr> +<tr class="odd"> +<td align="right">4.7137565</td> +<td align="right">71.61</td> +</tr> +<tr class="even"> +<td align="right">4.7137565</td> +<td align="right">71.42</td> +</tr> +<tr class="odd"> +<td align="right">9.4275131</td> +<td align="right">45.60</td> +</tr> +<tr class="even"> +<td align="right">9.4275131</td> +<td align="right">45.42</td> +</tr> +<tr class="odd"> +<td align="right">14.1412696</td> +<td align="right">31.12</td> +</tr> +<tr class="even"> +<td align="right">14.1412696</td> +<td align="right">31.68</td> +</tr> +<tr class="odd"> +<td align="right">18.8550262</td> +<td align="right">23.20</td> +</tr> +<tr class="even"> +<td align="right">18.8550262</td> +<td align="right">24.13</td> +</tr> +<tr class="odd"> +<td align="right">28.2825393</td> +<td align="right">9.43</td> +</tr> +<tr class="even"> +<td align="right">28.2825393</td> +<td align="right">9.82</td> +</tr> +<tr class="odd"> +<td align="right">37.7100523</td> +<td align="right">7.08</td> +</tr> +<tr class="even"> +<td align="right">37.7100523</td> +<td align="right">8.64</td> +</tr> +<tr class="odd"> +<td align="right">47.1375654</td> +<td align="right">4.41</td> +</tr> +<tr class="even"> +<td align="right">47.1375654</td> +<td align="right">4.78</td> +</tr> +<tr class="odd"> +<td align="right">56.5650785</td> +<td align="right">4.92</td> +</tr> +<tr class="even"> +<td align="right">56.5650785</td> +<td align="right">5.08</td> +</tr> +<tr class="odd"> +<td align="right">80.1338612</td> +<td align="right">2.13</td> +</tr> +<tr class="even"> +<td align="right">80.1338612</td> +<td align="right">2.23</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset Elliot</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">DMTA</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">97.5</td> +</tr> +<tr class="even"> +<td align="right">0.000000</td> +<td align="right">100.7</td> +</tr> +<tr class="odd"> +<td align="right">1.228478</td> +<td align="right">86.4</td> +</tr> +<tr class="even"> +<td align="right">1.228478</td> +<td align="right">88.5</td> +</tr> +<tr class="odd"> +<td align="right">3.685435</td> +<td align="right">69.8</td> +</tr> +<tr class="even"> +<td align="right">3.685435</td> +<td align="right">77.1</td> +</tr> +<tr class="odd"> +<td align="right">8.599349</td> +<td align="right">59.0</td> +</tr> +<tr class="even"> +<td align="right">8.599349</td> +<td align="right">54.2</td> +</tr> +<tr class="odd"> +<td align="right">17.198697</td> +<td align="right">31.3</td> +</tr> +<tr class="even"> +<td align="right">17.198697</td> +<td align="right">33.5</td> +</tr> +<tr class="odd"> +<td align="right">25.798046</td> +<td align="right">19.6</td> +</tr> +<tr class="even"> +<td align="right">25.798046</td> +<td align="right">20.9</td> +</tr> +<tr class="odd"> +<td align="right">34.397395</td> +<td align="right">13.3</td> +</tr> +<tr class="even"> +<td align="right">34.397395</td> +<td align="right">15.8</td> +</tr> +<tr class="odd"> +<td align="right">51.596092</td> +<td align="right">6.7</td> +</tr> +<tr class="even"> +<td align="right">51.596092</td> +<td align="right">8.7</td> +</tr> +<tr class="odd"> +<td align="right">68.794789</td> +<td align="right">8.8</td> +</tr> +<tr class="even"> +<td align="right">68.794789</td> +<td align="right">8.7</td> +</tr> +<tr class="odd"> +<td align="right">103.192184</td> +<td align="right">6.0</td> +</tr> +<tr class="even"> +<td align="right">103.192184</td> +<td align="right">4.4</td> +</tr> +<tr class="odd"> +<td align="right">146.188928</td> +<td align="right">3.3</td> +</tr> +<tr class="even"> +<td align="right">146.188928</td> +<td align="right">2.8</td> +</tr> +<tr class="odd"> +<td align="right">223.583066</td> +<td align="right">1.4</td> +</tr> +<tr class="even"> +<td align="right">223.583066</td> +<td align="right">1.8</td> +</tr> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">93.4</td> +</tr> +<tr class="even"> +<td align="right">0.000000</td> +<td align="right">103.2</td> +</tr> +<tr class="odd"> +<td align="right">1.228478</td> +<td align="right">89.2</td> +</tr> +<tr class="even"> +<td align="right">1.228478</td> +<td align="right">86.6</td> +</tr> +<tr class="odd"> +<td align="right">3.685435</td> +<td align="right">78.2</td> +</tr> +<tr class="even"> +<td align="right">3.685435</td> +<td align="right">78.1</td> +</tr> +<tr class="odd"> +<td align="right">8.599349</td> +<td align="right">55.6</td> +</tr> +<tr class="even"> +<td align="right">8.599349</td> +<td align="right">53.0</td> +</tr> +<tr class="odd"> +<td align="right">17.198697</td> +<td align="right">33.7</td> +</tr> +<tr class="even"> +<td align="right">17.198697</td> +<td align="right">33.2</td> +</tr> +<tr class="odd"> +<td align="right">25.798046</td> +<td align="right">20.9</td> +</tr> +<tr class="even"> +<td align="right">25.798046</td> +<td align="right">19.9</td> +</tr> +<tr class="odd"> +<td align="right">34.397395</td> +<td align="right">18.2</td> +</tr> +<tr class="even"> +<td align="right">34.397395</td> +<td align="right">12.7</td> +</tr> +<tr class="odd"> +<td align="right">51.596092</td> +<td align="right">7.8</td> +</tr> +<tr class="even"> +<td align="right">51.596092</td> +<td align="right">9.0</td> +</tr> +<tr class="odd"> +<td align="right">68.794789</td> +<td align="right">11.4</td> +</tr> +<tr class="even"> +<td align="right">68.794789</td> +<td align="right">9.0</td> +</tr> +<tr class="odd"> +<td align="right">103.192184</td> +<td align="right">3.9</td> +</tr> +<tr class="even"> +<td align="right">103.192184</td> +<td align="right">4.4</td> +</tr> +<tr class="odd"> +<td align="right">146.188928</td> +<td align="right">2.6</td> +</tr> +<tr class="even"> +<td align="right">146.188928</td> +<td align="right">3.4</td> +</tr> +<tr class="odd"> +<td align="right">223.583066</td> +<td align="right">2.0</td> +</tr> +<tr class="even"> +<td align="right">223.583066</td> +<td align="right">1.7</td> +</tr> +</tbody> +</table> +</div> +<div class="section level2"> +<h2 id="separate-evaluations">Separate evaluations<a class="anchor" aria-label="anchor" href="#separate-evaluations"></a> +</h2> +<p>In order to obtain suitable starting parameters for the NLHM fits, +separate fits of the four models to the data for each soil are generated +using the <code>mmkin</code> function from the <code>mkin</code> +package. In a first step, constant variance is assumed. Convergence is +checked with the <code>status</code> function.</p> +<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">deg_mods</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>, <span class="st">"HS"</span><span class="op">)</span></span> +<span><span class="va">f_sep_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span></span> +<span> <span class="va">deg_mods</span>,</span> +<span> <span class="va">dmta_ds</span>,</span> +<span> error_model <span class="op">=</span> <span class="st">"const"</span>,</span> +<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> +<span></span> +<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">Calke</th> +<th align="left">Borstel</th> +<th align="left">Flaach</th> +<th align="left">BBA 2.2</th> +<th align="left">BBA 2.3</th> +<th align="left">Elliot</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<p>In the table above, OK indicates convergence, and C indicates failure +to converge. All separate fits with constant variance converged, with +the sole exception of the HS fit to the BBA 2.2 data. To prepare for +fitting NLHM using the two-component error model, the separate fits are +updated assuming two-component error.</p> +<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">f_sep_tc</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_sep_const</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_tc</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">Calke</th> +<th align="left">Borstel</th> +<th align="left">Flaach</th> +<th align="left">BBA 2.2</th> +<th align="left">BBA 2.3</th> +<th align="left">Elliot</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<p>Using the two-component error model, the one fit that did not +converge with constant variance did converge, but other non-SFO fits +failed to converge.</p> +</div> +<div class="section level2"> +<h2 id="hierarchichal-model-fits">Hierarchichal model fits<a class="anchor" aria-label="anchor" href="#hierarchichal-model-fits"></a> +</h2> +<p>The following code fits eight versions of hierarchical models to the +data, using SFO, FOMC, DFOP and HS for the parent compound, and using +either constant variance or two-component error for the error model. The +default parameter distribution model in mkin allows for variation of all +degradation parameters across the assumed population of soils. In other +words, each degradation parameter is associated with a random effect as +a first step. The <code>mhmkin</code> function makes it possible to fit +all eight versions in parallel (given a sufficient number of computing +cores being available) to save execution time.</p> +<p>Convergence plots and summaries for these fits are shown in the +appendix.</p> +<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">f_saem</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mhmkin.html">mhmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">f_sep_const</span>, <span class="va">f_sep_tc</span><span class="op">)</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span></span></code></pre></div> +<p>The output of the <code>status</code> function shows that all fits +terminated successfully.</p> +<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_saem</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<p>The AIC and BIC values show that the biphasic models DFOP and HS give +the best fits.</p> +<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">npar</th> +<th align="right">AIC</th> +<th align="right">BIC</th> +<th align="right">Lik</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO const</td> +<td align="right">5</td> +<td align="right">796.3</td> +<td align="right">795.3</td> +<td align="right">-393.2</td> +</tr> +<tr class="even"> +<td align="left">SFO tc</td> +<td align="right">6</td> +<td align="right">798.3</td> +<td align="right">797.1</td> +<td align="right">-393.2</td> +</tr> +<tr class="odd"> +<td align="left">FOMC const</td> +<td align="right">7</td> +<td align="right">734.2</td> +<td align="right">732.7</td> +<td align="right">-360.1</td> +</tr> +<tr class="even"> +<td align="left">FOMC tc</td> +<td align="right">8</td> +<td align="right">720.7</td> +<td align="right">719.1</td> +<td align="right">-352.4</td> +</tr> +<tr class="odd"> +<td align="left">DFOP const</td> +<td align="right">9</td> +<td align="right">711.8</td> +<td align="right">710.0</td> +<td align="right">-346.9</td> +</tr> +<tr class="even"> +<td align="left">HS const</td> +<td align="right">9</td> +<td align="right">714.0</td> +<td align="right">712.1</td> +<td align="right">-348.0</td> +</tr> +<tr class="odd"> +<td align="left">DFOP tc</td> +<td align="right">10</td> +<td align="right">665.7</td> +<td align="right">663.6</td> +<td align="right">-322.9</td> +</tr> +<tr class="even"> +<td align="left">HS tc</td> +<td align="right">10</td> +<td align="right">667.1</td> +<td align="right">665.0</td> +<td align="right">-323.6</td> +</tr> +</tbody> +</table> +<p>The DFOP model is preferred here, as it has a better mechanistic +basis for batch experiments with constant incubation conditions. Also, +it shows the lowest AIC and BIC values in the first set of fits when +combined with the two-component error model. Therefore, the DFOP model +was selected for further refinements of the fits with the aim to make +the model fully identifiable.</p> +<div class="section level3"> +<h3 id="parameter-identifiability-based-on-the-fisher-information-matrix">Parameter identifiability based on the Fisher Information +Matrix<a class="anchor" aria-label="anchor" href="#parameter-identifiability-based-on-the-fisher-information-matrix"></a> +</h3> +<p>Using the <code>illparms</code> function, ill-defined statistical +model parameters such as standard deviations of the degradation +parameters in the population and error model parameters can be +found.</p> +<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left"></td> +<td align="left">b.1</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left"></td> +<td align="left">sd(DMTA_0)</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">sd(k2)</td> +<td align="left">sd(k2)</td> +</tr> +<tr class="even"> +<td align="left">HS</td> +<td align="left"></td> +<td align="left">sd(tb)</td> +</tr> +</tbody> +</table> +<p>According to the <code>illparms</code> function, the fitted standard +deviation of the second kinetic rate constant <code>k2</code> is +ill-defined in both DFOP fits. This suggests that different values would +be obtained for this standard deviation when using different starting +values.</p> +<p>The thus identified overparameterisation is addressed by removing the +random effect for <code>k2</code> from the parameter model.</p> +<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">f_saem_dfop_tc_no_ranef_k2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_saem</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span>,</span> +<span> no_random_effect <span class="op">=</span> <span class="st">"k2"</span><span class="op">)</span></span></code></pre></div> +<p>For the resulting fit, it is checked whether there are still +ill-defined parameters,</p> +<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_dfop_tc_no_ranef_k2</span><span class="op">)</span></span></code></pre></div> +<p>which is not the case. Below, the refined model is compared with the +previous best model. The model without random effect for <code>k2</code> +is a reduced version of the previous model. Therefore, the models are +nested and can be compared using the likelihood ratio test. This is +achieved with the argument <code>test = TRUE</code> to the +<code>anova</code> function.</p> +<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span>, <span class="va">f_saem_dfop_tc_no_ranef_k2</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|></span></span> +<span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>format.args <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">4</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<colgroup> +<col width="38%"> +<col width="7%"> +<col width="8%"> +<col width="8%"> +<col width="9%"> +<col width="8%"> +<col width="4%"> +<col width="15%"> +</colgroup> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">npar</th> +<th align="right">AIC</th> +<th align="right">BIC</th> +<th align="right">Lik</th> +<th align="right">Chisq</th> +<th align="right">Df</th> +<th align="right">Pr(>Chisq)</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">f_saem_dfop_tc_no_ranef_k2</td> +<td align="right">9</td> +<td align="right">663.7</td> +<td align="right">661.8</td> +<td align="right">-322.9</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +</tr> +<tr class="even"> +<td align="left">f_saem[[“DFOP”, “tc”]]</td> +<td align="right">10</td> +<td align="right">665.7</td> +<td align="right">663.6</td> +<td align="right">-322.9</td> +<td align="right">0</td> +<td align="right">1</td> +<td align="right">1</td> +</tr> +</tbody> +</table> +<p>The AIC and BIC criteria are lower after removal of the ill-defined +random effect for <code>k2</code>. The p value of the likelihood ratio +test is much greater than 0.05, indicating that the model with the +higher likelihood (here the model with random effects for all +degradation parameters <code>f_saem[["DFOP", "tc"]]</code>) does not fit +significantly better than the model with the lower likelihood (the +reduced model <code>f_saem_dfop_tc_no_ranef_k2</code>).</p> +<p>Therefore, AIC, BIC and likelihood ratio test suggest the use of the +reduced model.</p> +<p>The convergence of the fit is checked visually.</p> +<div class="figure" style="text-align: center"> +<img src="2022_dmta_parent_files/figure-html/convergence-saem-dfop-tc-no-ranef-k2-1.png" alt="Convergence plot for the NLHM DFOP fit with two-component error and without a random effect on 'k2'" width="864"><p class="caption"> +Convergence plot for the NLHM DFOP fit with two-component error and +without a random effect on ‘k2’ +</p> +</div> +<p>All parameters appear to have converged to a satisfactory degree. The +final fit is plotted using the plot method from the mkin package.</p> +<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_dfop_tc_no_ranef_k2</span><span class="op">)</span></span></code></pre></div> +<div class="figure" style="text-align: center"> +<img src="2022_dmta_parent_files/figure-html/plot-saem-dfop-tc-no-ranef-k2-1.png" alt="Plot of the final NLHM DFOP fit" width="864"><p class="caption"> +Plot of the final NLHM DFOP fit +</p> +</div> +<p>Finally, a summary report of the fit is produced.</p> +<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">f_saem_dfop_tc_no_ranef_k2</span><span class="op">)</span></span></code></pre></div> +<pre><code>saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.4.2 +Date of fit: Fri Feb 14 08:13:19 2025 +Date of summary: Fri Feb 14 08:13:19 2025 + +Equations: +d_DMTA/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * + time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) + * DMTA + +Data: +155 observations of 1 variable(s) grouped in 6 datasets + +Model predictions using solution type analytical + +Fitted in 4.154 s +Using 300, 100 iterations and 9 chains + +Variance model: Two-component variance function + +Starting values for degradation parameters: + DMTA_0 k1 k2 g +98.71186 0.08675 0.01374 0.93491 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + DMTA_0 k1 k2 g +DMTA_0 98.71 0 0 0 +k1 0.00 1 0 0 +k2 0.00 0 1 0 +g 0.00 0 0 1 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 663.7 661.8 -322.9 + +Optimised parameters: + est. lower upper +DMTA_0 98.256267 96.286112 100.22642 +k1 0.064037 0.033281 0.09479 +k2 0.008469 0.006002 0.01094 +g 0.954167 0.914460 0.99387 +a.1 1.061795 0.878608 1.24498 +b.1 0.029550 0.022593 0.03651 +SD.DMTA_0 2.068581 0.427178 3.70998 +SD.k1 0.598285 0.258235 0.93833 +SD.g 1.016689 0.360061 1.67332 + +Correlation: + DMTA_0 k1 k2 +k1 0.0213 +k2 0.0541 0.0344 +g -0.0521 -0.0286 -0.2744 + +Random effects: + est. lower upper +SD.DMTA_0 2.0686 0.4272 3.7100 +SD.k1 0.5983 0.2582 0.9383 +SD.g 1.0167 0.3601 1.6733 + +Variance model: + est. lower upper +a.1 1.06180 0.87861 1.24498 +b.1 0.02955 0.02259 0.03651 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +DMTA 11.45 41.32 12.44 10.82 81.85</code></pre> +</div> +<div class="section level3"> +<h3 id="alternative-check-of-parameter-identifiability">Alternative check of parameter identifiability<a class="anchor" aria-label="anchor" href="#alternative-check-of-parameter-identifiability"></a> +</h3> +<p>The parameter check used in the <code>illparms</code> function is +based on a quadratic approximation of the likelihood surface near its +optimum, which is calculated using the Fisher Information Matrix (FIM). +An alternative way to check parameter identifiability <span class="citation">(Duchesne et al. 2021)</span> based on a multistart +approach has recently been implemented in mkin.</p> +<p>The graph below shows boxplots of the parameters obtained in 50 runs +of the saem algorithm with different parameter combinations, sampled +from the range of the parameters obtained for the individual datasets +fitted separately using nonlinear regression.</p> +<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">f_saem_dfop_tc_multi</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/multistart.html">multistart</a></span><span class="op">(</span><span class="va">f_saem</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span>, n <span class="op">=</span> <span class="fl">50</span>, cores <span class="op">=</span> <span class="fl">15</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/par.html" class="external-link">par</a></span><span class="op">(</span>mar <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">6.1</span>, <span class="fl">4.1</span>, <span class="fl">2.1</span>, <span class="fl">2.1</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/parplot.html">parplot</a></span><span class="op">(</span><span class="va">f_saem_dfop_tc_multi</span>, lpos <span class="op">=</span> <span class="st">"bottomright"</span>, ylim <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.3</span>, <span class="fl">10</span><span class="op">)</span>, las <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<div class="figure" style="text-align: center"> +<img src="2022_dmta_parent_files/figure-html/multistart-full-par-1.png" alt="Scaled parameters from the multistart runs, full model" width="960"><p class="caption"> +Scaled parameters from the multistart runs, full model +</p> +</div> +<p>The graph clearly confirms the lack of identifiability of the +variance of <code>k2</code> in the full model. The overparameterisation +of the model also indicates a lack of identifiability of the variance of +parameter <code>g</code>.</p> +<p>The parameter boxplots of the multistart runs with the reduced model +shown below indicate that all runs give similar results, regardless of +the starting parameters.</p> +<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">f_saem_dfop_tc_no_ranef_k2_multi</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/multistart.html">multistart</a></span><span class="op">(</span><span class="va">f_saem_dfop_tc_no_ranef_k2</span>,</span> +<span> n <span class="op">=</span> <span class="fl">50</span>, cores <span class="op">=</span> <span class="fl">15</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/par.html" class="external-link">par</a></span><span class="op">(</span>mar <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">6.1</span>, <span class="fl">4.1</span>, <span class="fl">2.1</span>, <span class="fl">2.1</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/parplot.html">parplot</a></span><span class="op">(</span><span class="va">f_saem_dfop_tc_no_ranef_k2_multi</span>, ylim <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.5</span>, <span class="fl">2</span><span class="op">)</span>, las <span class="op">=</span> <span class="fl">2</span>,</span> +<span> lpos <span class="op">=</span> <span class="st">"bottomright"</span><span class="op">)</span></span></code></pre></div> +<div class="figure" style="text-align: center"> +<img src="2022_dmta_parent_files/figure-html/multistart-reduced-par-1.png" alt="Scaled parameters from the multistart runs, reduced model" width="960"><p class="caption"> +Scaled parameters from the multistart runs, reduced model +</p> +</div> +<p>When only the parameters of the top 25% of the fits are shown (based +on a feature introduced in mkin 1.2.2 currently under development), the +scatter is even less as shown below.</p> +<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/par.html" class="external-link">par</a></span><span class="op">(</span>mar <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">6.1</span>, <span class="fl">4.1</span>, <span class="fl">2.1</span>, <span class="fl">2.1</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/parplot.html">parplot</a></span><span class="op">(</span><span class="va">f_saem_dfop_tc_no_ranef_k2_multi</span>, ylim <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.5</span>, <span class="fl">2</span><span class="op">)</span>, las <span class="op">=</span> <span class="fl">2</span>, llquant <span class="op">=</span> <span class="fl">0.25</span>,</span> +<span> lpos <span class="op">=</span> <span class="st">"bottomright"</span><span class="op">)</span></span></code></pre></div> +<div class="figure" style="text-align: center"> +<img src="2022_dmta_parent_files/figure-html/multistart-reduced-par-llquant-1.png" alt="Scaled parameters from the multistart runs, reduced model, fits with the top 25\% likelihood values" width="960"><p class="caption"> +Scaled parameters from the multistart runs, reduced model, fits with the +top 25% likelihood values +</p> +</div> +</div> +</div> +<div class="section level2"> +<h2 id="conclusions">Conclusions<a class="anchor" aria-label="anchor" href="#conclusions"></a> +</h2> +<p>Fitting the four parent degradation models SFO, FOMC, DFOP and HS as +part of hierarchical model fits with two different error models and +normal distributions of the transformed degradation parameters works +without technical problems. The biphasic models DFOP and HS gave the +best fit to the data, but the default parameter distribution model was +not fully identifiable. Removing the random effect for the second +kinetic rate constant of the DFOP model resulted in a reduced model that +was fully identifiable and showed the lowest values for the model +selection criteria AIC and BIC. The reliability of the identification of +all model parameters was confirmed using multiple starting values.</p> +</div> +<div class="section level2"> +<h2 id="acknowledgements">Acknowledgements<a class="anchor" aria-label="anchor" href="#acknowledgements"></a> +</h2> +<p>The helpful comments by Janina Wöltjen of the German Environment +Agency are gratefully acknowledged.</p> +</div> +<div class="section level2"> +<h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a> +</h2> +<div id="refs" class="references csl-bib-body hanging-indent"> +<div id="ref-duchesne_2021" class="csl-entry"> +Duchesne, Ronan, Anissa Guillemin, Olivier Gandrillon, and Fabien +Crauste. 2021. <span>“Practical Identifiability in the Frame of +Nonlinear Mixed Effects Models: The Example of the in Vitro +Erythropoiesis.”</span> <em>BMC Bioinformatics</em> 22 (478). <a href="https://doi.org/10.1186/s12859-021-04373-4" class="external-link">https://doi.org/10.1186/s12859-021-04373-4</a>. +</div> +</div> +</div> +<div class="section level2"> +<h2 id="appendix">Appendix<a class="anchor" aria-label="anchor" href="#appendix"></a> +</h2> +<div class="section level3"> +<h3 id="hierarchical-model-fit-listings">Hierarchical model fit listings<a class="anchor" aria-label="anchor" href="#hierarchical-model-fit-listings"></a> +</h3> +<caption> +Hierarchical mkin fit of the SFO model with error model const +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.4.2 +Date of fit: Fri Feb 14 08:13:11 2025 +Date of summary: Fri Feb 14 08:14:22 2025 + +Equations: +d_DMTA/dt = - k_DMTA * DMTA + +Data: +155 observations of 1 variable(s) grouped in 6 datasets + +Model predictions using solution type analytical + +Fitted in 0.869 s +Using 300, 100 iterations and 9 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + DMTA_0 k_DMTA +97.2953 0.0566 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + DMTA_0 k_DMTA +DMTA_0 97.3 0 +k_DMTA 0.0 1 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 796.3 795.3 -393.2 + +Optimised parameters: + est. lower upper +DMTA_0 97.28130 95.71113 98.8515 +k_DMTA 0.05665 0.02909 0.0842 +a.1 2.66442 2.35579 2.9731 +SD.DMTA_0 1.54776 0.15447 2.9411 +SD.k_DMTA 0.60690 0.26248 0.9513 + +Correlation: + DMTA_0 +k_DMTA 0.0168 + +Random effects: + est. lower upper +SD.DMTA_0 1.5478 0.1545 2.9411 +SD.k_DMTA 0.6069 0.2625 0.9513 + +Variance model: + est. lower upper +a.1 2.664 2.356 2.973 + +Estimated disappearance times: + DT50 DT90 +DMTA 12.24 40.65 + +</code></pre> +<p></p> +<caption> +Hierarchical mkin fit of the SFO model with error model tc +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.4.2 +Date of fit: Fri Feb 14 08:13:13 2025 +Date of summary: Fri Feb 14 08:14:22 2025 + +Equations: +d_DMTA/dt = - k_DMTA * DMTA + +Data: +155 observations of 1 variable(s) grouped in 6 datasets + +Model predictions using solution type analytical + +Fitted in 2.423 s +Using 300, 100 iterations and 9 chains + +Variance model: Two-component variance function + +Starting values for degradation parameters: + DMTA_0 k_DMTA +96.99175 0.05603 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + DMTA_0 k_DMTA +DMTA_0 96.99 0 +k_DMTA 0.00 1 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 798.3 797.1 -393.2 + +Optimised parameters: + est. lower upper +DMTA_0 97.271822 95.70316 98.84049 +k_DMTA 0.056638 0.02911 0.08417 +a.1 2.660081 2.27492 3.04525 +b.1 0.001665 -0.14451 0.14784 +SD.DMTA_0 1.545520 0.14301 2.94803 +SD.k_DMTA 0.606422 0.26227 0.95057 + +Correlation: + DMTA_0 +k_DMTA 0.0169 + +Random effects: + est. lower upper +SD.DMTA_0 1.5455 0.1430 2.9480 +SD.k_DMTA 0.6064 0.2623 0.9506 + +Variance model: + est. lower upper +a.1 2.660081 2.2749 3.0452 +b.1 0.001665 -0.1445 0.1478 + +Estimated disappearance times: + DT50 DT90 +DMTA 12.24 40.65 + +</code></pre> +<p></p> +<caption> +Hierarchical mkin fit of the FOMC model with error model const +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.4.2 +Date of fit: Fri Feb 14 08:13:11 2025 +Date of summary: Fri Feb 14 08:14:22 2025 + +Equations: +d_DMTA/dt = - (alpha/beta) * 1/((time/beta) + 1) * DMTA + +Data: +155 observations of 1 variable(s) grouped in 6 datasets + +Model predictions using solution type analytical + +Fitted in 1.228 s +Using 300, 100 iterations and 9 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + DMTA_0 alpha beta + 98.292 9.909 156.341 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + DMTA_0 alpha beta +DMTA_0 98.29 0 0 +alpha 0.00 1 0 +beta 0.00 0 1 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 734.2 732.7 -360.1 + +Optimised parameters: + est. lower upper +DMTA_0 98.3435 96.9033 99.784 +alpha 7.2007 2.5889 11.812 +beta 112.8745 34.8816 190.867 +a.1 2.0459 1.8054 2.286 +SD.DMTA_0 1.4795 0.2717 2.687 +SD.alpha 0.6396 0.1509 1.128 +SD.beta 0.6874 0.1587 1.216 + +Correlation: + DMTA_0 alpha +alpha -0.1125 +beta -0.1227 0.3632 + +Random effects: + est. lower upper +SD.DMTA_0 1.4795 0.2717 2.687 +SD.alpha 0.6396 0.1509 1.128 +SD.beta 0.6874 0.1587 1.216 + +Variance model: + est. lower upper +a.1 2.046 1.805 2.286 + +Estimated disappearance times: + DT50 DT90 DT50back +DMTA 11.41 42.53 12.8 + +</code></pre> +<p></p> +<caption> +Hierarchical mkin fit of the FOMC model with error model tc +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.4.2 +Date of fit: Fri Feb 14 08:13:13 2025 +Date of summary: Fri Feb 14 08:14:22 2025 + +Equations: +d_DMTA/dt = - (alpha/beta) * 1/((time/beta) + 1) * DMTA + +Data: +155 observations of 1 variable(s) grouped in 6 datasets + +Model predictions using solution type analytical + +Fitted in 2.87 s +Using 300, 100 iterations and 9 chains + +Variance model: Two-component variance function + +Starting values for degradation parameters: +DMTA_0 alpha beta +98.772 4.663 92.597 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + DMTA_0 alpha beta +DMTA_0 98.77 0 0 +alpha 0.00 1 0 +beta 0.00 0 1 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 720.7 719.1 -352.4 + +Optimised parameters: + est. lower upper +DMTA_0 99.10577 97.33296 100.87859 +alpha 5.46260 2.52199 8.40321 +beta 81.66080 30.46664 132.85497 +a.1 1.50219 1.25801 1.74636 +b.1 0.02893 0.02048 0.03739 +SD.DMTA_0 1.61887 -0.03843 3.27618 +SD.alpha 0.58145 0.17364 0.98925 +SD.beta 0.68205 0.21108 1.15302 + +Correlation: + DMTA_0 alpha +alpha -0.1321 +beta -0.1430 0.2467 + +Random effects: + est. lower upper +SD.DMTA_0 1.6189 -0.03843 3.2762 +SD.alpha 0.5814 0.17364 0.9892 +SD.beta 0.6821 0.21108 1.1530 + +Variance model: + est. lower upper +a.1 1.50219 1.25801 1.74636 +b.1 0.02893 0.02048 0.03739 + +Estimated disappearance times: + DT50 DT90 DT50back +DMTA 11.05 42.81 12.89 + +</code></pre> +<p></p> +<caption> +Hierarchical mkin fit of the DFOP model with error model const +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.4.2 +Date of fit: Fri Feb 14 08:13:12 2025 +Date of summary: Fri Feb 14 08:14:22 2025 + +Equations: +d_DMTA/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * + time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) + * DMTA + +Data: +155 observations of 1 variable(s) grouped in 6 datasets + +Model predictions using solution type analytical + +Fitted in 1.843 s +Using 300, 100 iterations and 9 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + DMTA_0 k1 k2 g +98.64383 0.09211 0.02999 0.76814 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + DMTA_0 k1 k2 g +DMTA_0 98.64 0 0 0 +k1 0.00 1 0 0 +k2 0.00 0 1 0 +g 0.00 0 0 1 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 711.8 710 -346.9 + +Optimised parameters: + est. lower upper +DMTA_0 98.092481 96.573899 99.61106 +k1 0.062499 0.030336 0.09466 +k2 0.009065 -0.005133 0.02326 +g 0.948967 0.862080 1.03586 +a.1 1.821671 1.604774 2.03857 +SD.DMTA_0 1.677785 0.472066 2.88350 +SD.k1 0.634962 0.270788 0.99914 +SD.k2 1.033498 -0.205994 2.27299 +SD.g 1.710046 0.428642 2.99145 + +Correlation: + DMTA_0 k1 k2 +k1 0.0246 +k2 0.0491 0.0953 +g -0.0552 -0.0889 -0.4795 + +Random effects: + est. lower upper +SD.DMTA_0 1.678 0.4721 2.8835 +SD.k1 0.635 0.2708 0.9991 +SD.k2 1.033 -0.2060 2.2730 +SD.g 1.710 0.4286 2.9914 + +Variance model: + est. lower upper +a.1 1.822 1.605 2.039 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +DMTA 11.79 42.8 12.88 11.09 76.46 + +</code></pre> +<p></p> +<caption> +Hierarchical mkin fit of the DFOP model with error model tc +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.4.2 +Date of fit: Fri Feb 14 08:13:14 2025 +Date of summary: Fri Feb 14 08:14:22 2025 + +Equations: +d_DMTA/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * + time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) + * DMTA + +Data: +155 observations of 1 variable(s) grouped in 6 datasets + +Model predictions using solution type analytical + +Fitted in 3.469 s +Using 300, 100 iterations and 9 chains + +Variance model: Two-component variance function + +Starting values for degradation parameters: + DMTA_0 k1 k2 g +98.71186 0.08675 0.01374 0.93491 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + DMTA_0 k1 k2 g +DMTA_0 98.71 0 0 0 +k1 0.00 1 0 0 +k2 0.00 0 1 0 +g 0.00 0 0 1 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 665.7 663.6 -322.9 + +Optimised parameters: + est. lower upper +DMTA_0 98.347470 96.380815 100.31413 +k1 0.064524 0.034279 0.09477 +k2 0.008304 0.005843 0.01076 +g 0.952128 0.909578 0.99468 +a.1 1.068907 0.883665 1.25415 +b.1 0.029265 0.022318 0.03621 +SD.DMTA_0 2.065796 0.427951 3.70364 +SD.k1 0.583703 0.251796 0.91561 +SD.k2 0.004167 -7.831228 7.83956 +SD.g 1.064450 0.397479 1.73142 + +Correlation: + DMTA_0 k1 k2 +k1 0.0223 +k2 0.0568 0.0394 +g -0.0464 -0.0269 -0.2713 + +Random effects: + est. lower upper +SD.DMTA_0 2.065796 0.4280 3.7036 +SD.k1 0.583703 0.2518 0.9156 +SD.k2 0.004167 -7.8312 7.8396 +SD.g 1.064450 0.3975 1.7314 + +Variance model: + est. lower upper +a.1 1.06891 0.88367 1.25415 +b.1 0.02927 0.02232 0.03621 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +DMTA 11.39 41.36 12.45 10.74 83.48 + +</code></pre> +<p></p> +<caption> +Hierarchical mkin fit of the HS model with error model const +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.4.2 +Date of fit: Fri Feb 14 08:13:12 2025 +Date of summary: Fri Feb 14 08:14:22 2025 + +Equations: +d_DMTA/dt = - ifelse(time <= tb, k1, k2) * DMTA + +Data: +155 observations of 1 variable(s) grouped in 6 datasets + +Model predictions using solution type analytical + +Fitted in 1.698 s +Using 300, 100 iterations and 9 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + DMTA_0 k1 k2 tb +97.82176 0.06931 0.02997 11.13945 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + DMTA_0 k1 k2 tb +DMTA_0 97.82 0 0 0 +k1 0.00 1 0 0 +k2 0.00 0 1 0 +tb 0.00 0 0 1 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 714 712.1 -348 + +Optimised parameters: + est. lower upper +DMTA_0 98.16102 96.47747 99.84456 +k1 0.07876 0.05261 0.10491 +k2 0.02227 0.01706 0.02747 +tb 13.99089 -7.40049 35.38228 +a.1 1.82305 1.60700 2.03910 +SD.DMTA_0 1.88413 0.56204 3.20622 +SD.k1 0.34292 0.10482 0.58102 +SD.k2 0.19851 0.01718 0.37985 +SD.tb 1.68168 0.58064 2.78272 + +Correlation: + DMTA_0 k1 k2 +k1 0.0142 +k2 0.0001 -0.0025 +tb 0.0165 -0.1256 -0.0301 + +Random effects: + est. lower upper +SD.DMTA_0 1.8841 0.56204 3.2062 +SD.k1 0.3429 0.10482 0.5810 +SD.k2 0.1985 0.01718 0.3798 +SD.tb 1.6817 0.58064 2.7827 + +Variance model: + est. lower upper +a.1 1.823 1.607 2.039 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +DMTA 8.801 67.91 20.44 8.801 31.13 + +</code></pre> +<p></p> +<caption> +Hierarchical mkin fit of the HS model with error model tc +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.4.2 +Date of fit: Fri Feb 14 08:13:13 2025 +Date of summary: Fri Feb 14 08:14:22 2025 + +Equations: +d_DMTA/dt = - ifelse(time <= tb, k1, k2) * DMTA + +Data: +155 observations of 1 variable(s) grouped in 6 datasets + +Model predictions using solution type analytical + +Fitted in 3.307 s +Using 300, 100 iterations and 9 chains + +Variance model: Two-component variance function + +Starting values for degradation parameters: + DMTA_0 k1 k2 tb +98.45190 0.07525 0.02576 19.19375 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + DMTA_0 k1 k2 tb +DMTA_0 98.45 0 0 0 +k1 0.00 1 0 0 +k2 0.00 0 1 0 +tb 0.00 0 0 1 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 667.1 665 -323.6 + +Optimised parameters: + est. lower upper +DMTA_0 97.76571 95.81350 99.71791 +k1 0.05855 0.03080 0.08630 +k2 0.02337 0.01664 0.03010 +tb 31.09638 29.38289 32.80987 +a.1 1.08835 0.90059 1.27611 +b.1 0.02964 0.02261 0.03667 +SD.DMTA_0 2.04877 0.42553 3.67200 +SD.k1 0.59166 0.25621 0.92711 +SD.k2 0.30698 0.09561 0.51835 +SD.tb 0.01274 -0.10915 0.13464 + +Correlation: + DMTA_0 k1 k2 +k1 0.0160 +k2 -0.0070 -0.0024 +tb -0.0668 -0.0103 -0.2013 + +Random effects: + est. lower upper +SD.DMTA_0 2.04877 0.42553 3.6720 +SD.k1 0.59166 0.25621 0.9271 +SD.k2 0.30698 0.09561 0.5183 +SD.tb 0.01274 -0.10915 0.1346 + +Variance model: + est. lower upper +a.1 1.08835 0.90059 1.27611 +b.1 0.02964 0.02261 0.03667 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +DMTA 11.84 51.71 15.57 11.84 29.66 + +</code></pre> +<p></p> +</div> +<div class="section level3"> +<h3 id="hierarchical-model-convergence-plots">Hierarchical model convergence plots<a class="anchor" aria-label="anchor" href="#hierarchical-model-convergence-plots"></a> +</h3> +<div class="figure" style="text-align: center"> +<img src="2022_dmta_parent_files/figure-html/convergence-saem-sfo-const-1.png" alt="Convergence plot for the NLHM SFO fit with constant variance" width="864"><p class="caption"> +Convergence plot for the NLHM SFO fit with constant variance +</p> +</div> +<div class="figure" style="text-align: center"> +<img src="2022_dmta_parent_files/figure-html/convergence-saem-sfo-tc-1.png" alt="Convergence plot for the NLHM SFO fit with two-component error" width="864"><p class="caption"> +Convergence plot for the NLHM SFO fit with two-component error +</p> +</div> +<div class="figure" style="text-align: center"> +<img src="2022_dmta_parent_files/figure-html/convergence-saem-fomc-const-1.png" alt="Convergence plot for the NLHM FOMC fit with constant variance" width="864"><p class="caption"> +Convergence plot for the NLHM FOMC fit with constant variance +</p> +</div> +<div class="figure" style="text-align: center"> +<img src="2022_dmta_parent_files/figure-html/convergence-saem-fomc-tc-1.png" alt="Convergence plot for the NLHM FOMC fit with two-component error" width="864"><p class="caption"> +Convergence plot for the NLHM FOMC fit with two-component error +</p> +</div> +<div class="figure" style="text-align: center"> +<img src="2022_dmta_parent_files/figure-html/convergence-saem-dfop-const-1.png" alt="Convergence plot for the NLHM DFOP fit with constant variance" width="864"><p class="caption"> +Convergence plot for the NLHM DFOP fit with constant variance +</p> +</div> +<div class="figure" style="text-align: center"> +<img src="2022_dmta_parent_files/figure-html/convergence-saem-dfop-tc-1.png" alt="Convergence plot for the NLHM DFOP fit with two-component error" width="864"><p class="caption"> +Convergence plot for the NLHM DFOP fit with two-component error +</p> +</div> +<div class="figure" style="text-align: center"> +<img src="2022_dmta_parent_files/figure-html/convergence-saem-hs-const-1.png" alt="Convergence plot for the NLHM HS fit with constant variance" width="864"><p class="caption"> +Convergence plot for the NLHM HS fit with constant variance +</p> +</div> +<div class="figure" style="text-align: center"> +<img src="2022_dmta_parent_files/figure-html/convergence-saem-hs-tc-1.png" alt="Convergence plot for the NLHM HS fit with two-component error" width="864"><p class="caption"> +Convergence plot for the NLHM HS fit with two-component error +</p> +</div> +</div> +<div class="section level3"> +<h3 id="session-info">Session info<a class="anchor" aria-label="anchor" href="#session-info"></a> +</h3> +<pre><code>R version 4.4.2 (2024-10-31) +Platform: x86_64-pc-linux-gnu +Running under: Debian GNU/Linux 12 (bookworm) + +Matrix products: default +BLAS: /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.11.0 +LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.11.0 + +locale: + [1] LC_CTYPE=de_DE.UTF-8 LC_NUMERIC=C + [3] LC_TIME=de_DE.UTF-8 LC_COLLATE=de_DE.UTF-8 + [5] LC_MONETARY=de_DE.UTF-8 LC_MESSAGES=de_DE.UTF-8 + [7] LC_PAPER=de_DE.UTF-8 LC_NAME=C + [9] LC_ADDRESS=C LC_TELEPHONE=C +[11] LC_MEASUREMENT=de_DE.UTF-8 LC_IDENTIFICATION=C + +time zone: Europe/Berlin +tzcode source: system (glibc) + +attached base packages: +[1] parallel stats graphics grDevices utils datasets methods +[8] base + +other attached packages: +[1] 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_1.8.9 dplyr_1.1.4 compiler_4.4.2 + [5] tidyselect_1.2.1 gridExtra_2.3 jquerylib_0.1.4 systemfonts_1.1.0 + [9] scales_1.3.0 textshaping_0.4.1 yaml_2.3.10 fastmap_1.2.0 +[13] lattice_0.22-6 ggplot2_3.5.1 R6_2.5.1 generics_0.1.3 +[17] lmtest_0.9-40 MASS_7.3-61 htmlwidgets_1.6.4 tibble_3.2.1 +[21] desc_1.4.3 munsell_0.5.1 bslib_0.8.0 pillar_1.9.0 +[25] rlang_1.1.4 utf8_1.2.4 cachem_1.1.0 xfun_0.49 +[29] fs_1.6.5 sass_0.4.9 cli_3.6.3 pkgdown_2.1.1 +[33] magrittr_2.0.3 digest_0.6.37 grid_4.4.2 mclust_6.1.1 +[37] lifecycle_1.0.4 nlme_3.1-166 vctrs_0.6.5 evaluate_1.0.1 +[41] glue_1.8.0 codetools_0.2-20 ragg_1.3.3 zoo_1.8-12 +[45] fansi_1.0.6 colorspace_2.1-1 pkgconfig_2.0.3 tools_4.4.2 +[49] htmltools_0.5.8.1</code></pre> +</div> +<div class="section level3"> +<h3 id="hardware-info">Hardware info<a class="anchor" aria-label="anchor" href="#hardware-info"></a> +</h3> +<pre><code>CPU model: AMD Ryzen 9 7950X 16-Core Processor</code></pre> +<pre><code>MemTotal: 64927788 kB</code></pre> +</div> +</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/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-dfop-const-1.png b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-dfop-const-1.png Binary files differnew file mode 100644 index 00000000..91c027a5 --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-dfop-const-1.png diff --git a/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-dfop-tc-1.png b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-dfop-tc-1.png Binary files differnew file mode 100644 index 00000000..678b76e2 --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-dfop-tc-1.png diff --git a/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-dfop-tc-no-ranef-k2-1.png b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-dfop-tc-no-ranef-k2-1.png Binary files differnew file mode 100644 index 00000000..a3bc320e --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-dfop-tc-no-ranef-k2-1.png diff --git a/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-fomc-const-1.png b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-fomc-const-1.png Binary files differnew file mode 100644 index 00000000..da63e191 --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-fomc-const-1.png diff --git a/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-fomc-tc-1.png b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-fomc-tc-1.png Binary files differnew file mode 100644 index 00000000..00958654 --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-fomc-tc-1.png diff --git a/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-hs-const-1.png b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-hs-const-1.png Binary files differnew file mode 100644 index 00000000..72a996ac --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-hs-const-1.png diff --git a/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-hs-tc-1.png b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-hs-tc-1.png Binary files differnew file mode 100644 index 00000000..46cfa3f8 --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-hs-tc-1.png diff --git a/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-sfo-const-1.png b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-sfo-const-1.png Binary files differnew file mode 100644 index 00000000..6dc7a6e2 --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-sfo-const-1.png diff --git a/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-sfo-tc-1.png b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-sfo-tc-1.png Binary files differnew file mode 100644 index 00000000..8df26d78 --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-sfo-tc-1.png diff --git a/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/multistart-full-par-1.png b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/multistart-full-par-1.png Binary files differnew file mode 100644 index 00000000..f90b19e7 --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/multistart-full-par-1.png diff --git a/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/multistart-reduced-par-1.png b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/multistart-reduced-par-1.png Binary files differnew file mode 100644 index 00000000..f6f1e43d --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/multistart-reduced-par-1.png diff --git a/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/multistart-reduced-par-llquant-1.png b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/multistart-reduced-par-llquant-1.png Binary files differnew file mode 100644 index 00000000..ef6bc8bd --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/multistart-reduced-par-llquant-1.png diff --git a/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/plot-saem-dfop-tc-no-ranef-k2-1.png b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/plot-saem-dfop-tc-no-ranef-k2-1.png Binary files differnew file mode 100644 index 00000000..cd506f57 --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/plot-saem-dfop-tc-no-ranef-k2-1.png diff --git a/docs/dev/articles/prebuilt/2022_dmta_pathway.html b/docs/dev/articles/prebuilt/2022_dmta_pathway.html new file mode 100644 index 00000000..f7386a47 --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_dmta_pathway.html @@ -0,0 +1,2002 @@ +<!DOCTYPE html> +<!-- Generated by pkgdown: do not edit by hand --><html lang="en"> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> +<meta charset="utf-8"> +<meta http-equiv="X-UA-Compatible" content="IE=edge"> +<meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"> +<title>Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P • mkin</title> +<script src="../../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"> +<link href="../../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"> +<script src="../../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"> +<link href="../../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"> +<script src="../../deps/headroom-0.11.0/headroom.min.js"></script><script src="../../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../../deps/search-1.0.0/fuse.min.js"></script><script src="../../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../../pkgdown.js"></script><meta property="og:title" content="Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P"> +<meta name="robots" content="noindex"> +</head> +<body> + <a href="#main" class="visually-hidden-focusable">Skip to contents</a> + + + <nav class="navbar navbar-expand-lg fixed-top bg-light" data-bs-theme="default" aria-label="Site navigation"><div class="container"> + + <a class="navbar-brand me-2" href="../../index.html">mkin</a> + + <small class="nav-text text-info me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="In-development version">1.2.10</small> + + + <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation"> + <span class="navbar-toggler-icon"></span> + </button> + + <div id="navbar" class="collapse navbar-collapse ms-3"> + <ul class="navbar-nav me-auto"> +<li class="nav-item"><a class="nav-link" href="../../reference/index.html">Reference</a></li> +<li class="active nav-item dropdown"> + <button class="nav-link dropdown-toggle" type="button" id="dropdown-articles" data-bs-toggle="dropdown" aria-expanded="false" aria-haspopup="true">Articles</button> + <ul class="dropdown-menu" aria-labelledby="dropdown-articles"> +<li><a class="dropdown-item" href="../../articles/mkin.html">Introduction to mkin</a></li> + <li><hr class="dropdown-divider"></li> + <li><h6 class="dropdown-header" data-toc-skip>Example evaluations with (generalised) nonlinear least squares</h6></li> + <li><a class="dropdown-item" href="../../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a></li> + <li><a class="dropdown-item" href="../../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a></li> + <li><a class="dropdown-item" href="../../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a></li> + <li><hr class="dropdown-divider"></li> + <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/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> + <li><hr class="dropdown-divider"></li> + <li><h6 class="dropdown-header" data-toc-skip>Performance</h6></li> + <li><a class="dropdown-item" href="../../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a></li> + <li><a class="dropdown-item" href="../../articles/web_only/benchmarks.html">Benchmark timings for mkin</a></li> + <li><a class="dropdown-item" href="../../articles/web_only/saem_benchmarks.html">Benchmark timings for saem.mmkin</a></li> + <li><hr class="dropdown-divider"></li> + <li><h6 class="dropdown-header" data-toc-skip>Miscellaneous</h6></li> + <li><a class="dropdown-item" href="../../articles/twa.html">Calculation of time weighted average concentrations with mkin</a></li> + <li><a class="dropdown-item" href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a></li> + </ul> +</li> +<li class="nav-item"><a class="nav-link" href="../../coverage/coverage.html">Test coverage</a></li> +<li class="nav-item"><a class="nav-link" href="../../news/index.html">News</a></li> + </ul> +<ul class="navbar-nav"> +<li class="nav-item"><form class="form-inline" role="search"> + <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../../search.json"> +</form></li> +<li class="nav-item"><a class="external-link nav-link" href="https://github.com/jranke/mkin/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li> + </ul> +</div> + + + </div> +</nav><div class="container template-article"> + + + + +<div class="row"> + <main id="main" class="col-md-9"><div class="page-header"> + + <h1>Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</h1> + <h4 data-toc-skip class="author">Johannes +Ranke</h4> + + <h4 data-toc-skip class="date">Last change on 20 April 2023, +last compiled on 16 Februar 2025</h4> + + <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/prebuilt/2022_dmta_pathway.rmd" class="external-link"><code>vignettes/prebuilt/2022_dmta_pathway.rmd</code></a></small> + <div class="d-none name"><code>2022_dmta_pathway.rmd</code></div> + </div> + + + +<div class="section level2"> +<h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#introduction"></a> +</h2> +<p>The purpose of this document is to test demonstrate how nonlinear +hierarchical models (NLHM) based on the parent degradation models SFO, +FOMC, DFOP and HS, with parallel formation of two or more metabolites +can be fitted with the mkin package.</p> +<p>It was assembled in the course of work package 1.2 of Project Number +173340 (Application of nonlinear hierarchical models to the kinetic +evaluation of chemical degradation data) of the German Environment +Agency carried out in 2022 and 2023.</p> +<p>The mkin package is used in version 1.2.10, which is currently under +development. It contains the test data, and the functions used in the +evaluations. The <code>saemix</code> package is used as a backend for +fitting the NLHM, but is also loaded to make the convergence plot +function available.</p> +<p>This document is processed with the <code>knitr</code> package, which +also provides the <code>kable</code> function that is used to improve +the display of tabular data in R markdown documents. For parallel +processing, the <code>parallel</code> package is used.</p> +<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://pkgdown.jrwb.de/mkin/">mkin</a></span><span class="op">)</span></span> +<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://yihui.org/knitr/" class="external-link">knitr</a></span><span class="op">)</span></span> +<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">saemix</span><span class="op">)</span></span> +<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">parallel</span><span class="op">)</span></span> +<span><span class="va">n_cores</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/detectCores.html" class="external-link">detectCores</a></span><span class="op">(</span><span class="op">)</span></span> +<span></span> +<span><span class="co"># We need to start a new cluster after defining a compiled model that is</span></span> +<span><span class="co"># saved as a DLL to the user directory, therefore we define a function</span></span> +<span><span class="co"># This is used again after defining the pathway model</span></span> +<span><span class="va">start_cluster</span> <span class="op"><-</span> <span class="kw">function</span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span> <span class="op">{</span></span> +<span> <span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/Sys.info.html" class="external-link">Sys.info</a></span><span class="op">(</span><span class="op">)</span><span class="op">[</span><span class="st">"sysname"</span><span class="op">]</span> <span class="op">==</span> <span class="st">"Windows"</span><span class="op">)</span> <span class="op">{</span></span> +<span> <span class="va">ret</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makePSOCKcluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> +<span> <span class="op">}</span> <span class="kw">else</span> <span class="op">{</span></span> +<span> <span class="va">ret</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makeForkCluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> +<span> <span class="op">}</span></span> +<span> <span class="kw"><a href="https://rdrr.io/r/base/function.html" class="external-link">return</a></span><span class="op">(</span><span class="va">ret</span><span class="op">)</span></span> +<span><span class="op">}</span></span></code></pre></div> +</div> +<div class="section level2"> +<h2 id="data">Data<a class="anchor" aria-label="anchor" href="#data"></a> +</h2> +<p>The test data are available in the mkin package as an object of class +<code>mkindsg</code> (mkin dataset group) under the identifier +<code>dimethenamid_2018</code>. The following preprocessing steps are +done in this document.</p> +<ul> +<li>The data available for the enantiomer dimethenamid-P (DMTAP) are +renamed to have the same substance name as the data for the racemic +mixture dimethenamid (DMTA). The reason for this is that no difference +between their degradation behaviour was identified in the EU risk +assessment.</li> +<li>Unnecessary columns are discarded</li> +<li>The observation times of each dataset are multiplied with the +corresponding normalisation factor also available in the dataset, in +order to make it possible to describe all datasets with a single set of +parameters that are independent of temperature</li> +<li>Finally, datasets observed in the same soil (<code>Elliot 1</code> +and <code>Elliot 2</code>) are combined, resulting in dimethenamid +(DMTA) data from six soils.</li> +</ul> +<p>The following commented R code performs this preprocessing.</p> +<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="co"># Apply a function to each of the seven datasets in the mkindsg object to create a list</span></span> +<span><span class="va">dmta_ds</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">lapply</a></span><span class="op">(</span><span class="fl">1</span><span class="op">:</span><span class="fl">7</span>, <span class="kw">function</span><span class="op">(</span><span class="va">i</span><span class="op">)</span> <span class="op">{</span></span> +<span> <span class="va">ds_i</span> <span class="op"><-</span> <span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">ds</span><span class="op">[[</span><span class="va">i</span><span class="op">]</span><span class="op">]</span><span class="op">$</span><span class="va">data</span> <span class="co"># Get a dataset</span></span> +<span> <span class="va">ds_i</span><span class="op">[</span><span class="va">ds_i</span><span class="op">$</span><span class="va">name</span> <span class="op">==</span> <span class="st">"DMTAP"</span>, <span class="st">"name"</span><span class="op">]</span> <span class="op"><-</span> <span class="st">"DMTA"</span> <span class="co"># Rename DMTAP to DMTA</span></span> +<span> <span class="va">ds_i</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/subset.html" class="external-link">subset</a></span><span class="op">(</span><span class="va">ds_i</span>, select <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"name"</span>, <span class="st">"time"</span>, <span class="st">"value"</span><span class="op">)</span><span class="op">)</span> <span class="co"># Select data</span></span> +<span> <span class="va">ds_i</span><span class="op">$</span><span class="va">time</span> <span class="op"><-</span> <span class="va">ds_i</span><span class="op">$</span><span class="va">time</span> <span class="op">*</span> <span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">f_time_norm</span><span class="op">[</span><span class="va">i</span><span class="op">]</span> <span class="co"># Normalise time</span></span> +<span> <span class="va">ds_i</span> <span class="co"># Return the dataset</span></span> +<span><span class="op">}</span><span class="op">)</span></span> +<span></span> +<span><span class="co"># Use dataset titles as names for the list elements</span></span> +<span><span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">)</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</span><span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">ds</span>, <span class="kw">function</span><span class="op">(</span><span class="va">ds</span><span class="op">)</span> <span class="va">ds</span><span class="op">$</span><span class="va">title</span><span class="op">)</span></span> +<span></span> +<span><span class="co"># Combine data for Elliot soil to obtain a named list with six elements</span></span> +<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/cbind.html" class="external-link">rbind</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 1"</span><span class="op">]</span><span class="op">]</span>, <span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 2"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span> <span class="co">#</span></span> +<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 1"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="cn">NULL</span></span> +<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 2"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="cn">NULL</span></span></code></pre></div> +<p>The following tables show the 6 datasets.</p> +<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="kw">for</span> <span class="op">(</span><span class="va">ds_name</span> <span class="kw">in</span> <span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">)</span><span class="op">)</span> <span class="op">{</span></span> +<span> <span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span></span> +<span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="fu"><a href="../../reference/mkin_long_to_wide.html">mkin_long_to_wide</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">[[</span><span class="va">ds_name</span><span class="op">]</span><span class="op">]</span><span class="op">)</span>,</span> +<span> caption <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste</a></span><span class="op">(</span><span class="st">"Dataset"</span>, <span class="va">ds_name</span><span class="op">)</span>,</span> +<span> booktabs <span class="op">=</span> <span class="cn">TRUE</span>, row.names <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">)</span></span> +<span> <span class="fu"><a href="https://rdrr.io/r/base/cat.html" class="external-link">cat</a></span><span class="op">(</span><span class="st">"\n\\clearpage\n"</span><span class="op">)</span></span> +<span><span class="op">}</span></span></code></pre></div> +<table class="table"> +<caption>Dataset Calke</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">DMTA</th> +<th align="right">M23</th> +<th align="right">M27</th> +<th align="right">M31</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0</td> +<td align="right">95.8</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +</tr> +<tr class="even"> +<td align="right">0</td> +<td align="right">98.7</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +</tr> +<tr class="odd"> +<td align="right">14</td> +<td align="right">60.5</td> +<td align="right">4.1</td> +<td align="right">1.5</td> +<td align="right">2.0</td> +</tr> +<tr class="even"> +<td align="right">30</td> +<td align="right">39.1</td> +<td align="right">5.3</td> +<td align="right">2.4</td> +<td align="right">2.1</td> +</tr> +<tr class="odd"> +<td align="right">59</td> +<td align="right">15.2</td> +<td align="right">6.0</td> +<td align="right">3.2</td> +<td align="right">2.2</td> +</tr> +<tr class="even"> +<td align="right">120</td> +<td align="right">4.8</td> +<td align="right">4.3</td> +<td align="right">3.8</td> +<td align="right">1.8</td> +</tr> +<tr class="odd"> +<td align="right">120</td> +<td align="right">4.6</td> +<td align="right">4.1</td> +<td align="right">3.7</td> +<td align="right">2.1</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset Borstel</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">DMTA</th> +<th align="right">M23</th> +<th align="right">M27</th> +<th align="right">M31</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">100.5</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +</tr> +<tr class="even"> +<td align="right">0.000000</td> +<td align="right">99.6</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +</tr> +<tr class="odd"> +<td align="right">1.941295</td> +<td align="right">91.9</td> +<td align="right">0.4</td> +<td align="right">NA</td> +<td align="right">NA</td> +</tr> +<tr class="even"> +<td align="right">1.941295</td> +<td align="right">91.3</td> +<td align="right">0.5</td> +<td align="right">0.3</td> +<td align="right">0.1</td> +</tr> +<tr class="odd"> +<td align="right">6.794534</td> +<td align="right">81.8</td> +<td align="right">1.2</td> +<td align="right">0.8</td> +<td align="right">1.0</td> +</tr> +<tr class="even"> +<td align="right">6.794534</td> +<td align="right">82.1</td> +<td align="right">1.3</td> +<td align="right">0.9</td> +<td align="right">0.9</td> +</tr> +<tr class="odd"> +<td align="right">13.589067</td> +<td align="right">69.1</td> +<td align="right">2.8</td> +<td align="right">1.4</td> +<td align="right">2.0</td> +</tr> +<tr class="even"> +<td align="right">13.589067</td> +<td align="right">68.0</td> +<td align="right">2.0</td> +<td align="right">1.4</td> +<td align="right">2.5</td> +</tr> +<tr class="odd"> +<td align="right">27.178135</td> +<td align="right">51.4</td> +<td align="right">2.9</td> +<td align="right">2.7</td> +<td align="right">4.3</td> +</tr> +<tr class="even"> +<td align="right">27.178135</td> +<td align="right">51.4</td> +<td align="right">4.9</td> +<td align="right">2.6</td> +<td align="right">3.2</td> +</tr> +<tr class="odd"> +<td align="right">56.297565</td> +<td align="right">27.6</td> +<td align="right">12.2</td> +<td align="right">4.4</td> +<td align="right">4.3</td> +</tr> +<tr class="even"> +<td align="right">56.297565</td> +<td align="right">26.8</td> +<td align="right">12.2</td> +<td align="right">4.7</td> +<td align="right">4.8</td> +</tr> +<tr class="odd"> +<td align="right">86.387643</td> +<td align="right">15.7</td> +<td align="right">12.2</td> +<td align="right">5.4</td> +<td align="right">5.0</td> +</tr> +<tr class="even"> +<td align="right">86.387643</td> +<td align="right">15.3</td> +<td align="right">12.0</td> +<td align="right">5.2</td> +<td align="right">5.1</td> +</tr> +<tr class="odd"> +<td align="right">115.507073</td> +<td align="right">7.9</td> +<td align="right">10.4</td> +<td align="right">5.4</td> +<td align="right">4.3</td> +</tr> +<tr class="even"> +<td align="right">115.507073</td> +<td align="right">8.1</td> +<td align="right">11.6</td> +<td align="right">5.4</td> +<td align="right">4.4</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset Flaach</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">DMTA</th> +<th align="right">M23</th> +<th align="right">M27</th> +<th align="right">M31</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.0000000</td> +<td align="right">96.5</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +</tr> +<tr class="even"> +<td align="right">0.0000000</td> +<td align="right">96.8</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +</tr> +<tr class="odd"> +<td align="right">0.0000000</td> +<td align="right">97.0</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +</tr> +<tr class="even"> +<td align="right">0.6233856</td> +<td align="right">82.9</td> +<td align="right">0.7</td> +<td align="right">1.1</td> +<td align="right">0.3</td> +</tr> +<tr class="odd"> +<td align="right">0.6233856</td> +<td align="right">86.7</td> +<td align="right">0.7</td> +<td align="right">1.1</td> +<td align="right">0.3</td> +</tr> +<tr class="even"> +<td align="right">0.6233856</td> +<td align="right">87.4</td> +<td align="right">0.2</td> +<td align="right">0.3</td> +<td align="right">0.1</td> +</tr> +<tr class="odd"> +<td align="right">1.8701567</td> +<td align="right">72.8</td> +<td align="right">2.2</td> +<td align="right">2.6</td> +<td align="right">0.7</td> +</tr> +<tr class="even"> +<td align="right">1.8701567</td> +<td align="right">69.9</td> +<td align="right">1.8</td> +<td align="right">2.4</td> +<td align="right">0.6</td> +</tr> +<tr class="odd"> +<td align="right">1.8701567</td> +<td align="right">71.9</td> +<td align="right">1.6</td> +<td align="right">2.3</td> +<td align="right">0.7</td> +</tr> +<tr class="even"> +<td align="right">4.3636989</td> +<td align="right">51.4</td> +<td align="right">4.1</td> +<td align="right">5.0</td> +<td align="right">1.3</td> +</tr> +<tr class="odd"> +<td align="right">4.3636989</td> +<td align="right">52.9</td> +<td align="right">4.2</td> +<td align="right">5.9</td> +<td align="right">1.2</td> +</tr> +<tr class="even"> +<td align="right">4.3636989</td> +<td align="right">48.6</td> +<td align="right">4.2</td> +<td align="right">4.8</td> +<td align="right">1.4</td> +</tr> +<tr class="odd"> +<td align="right">8.7273979</td> +<td align="right">28.5</td> +<td align="right">7.5</td> +<td align="right">8.5</td> +<td align="right">2.4</td> +</tr> +<tr class="even"> +<td align="right">8.7273979</td> +<td align="right">27.3</td> +<td align="right">7.1</td> +<td align="right">8.5</td> +<td align="right">2.1</td> +</tr> +<tr class="odd"> +<td align="right">8.7273979</td> +<td align="right">27.5</td> +<td align="right">7.5</td> +<td align="right">8.3</td> +<td align="right">2.3</td> +</tr> +<tr class="even"> +<td align="right">13.0910968</td> +<td align="right">14.8</td> +<td align="right">8.4</td> +<td align="right">9.3</td> +<td align="right">3.3</td> +</tr> +<tr class="odd"> +<td align="right">13.0910968</td> +<td align="right">13.4</td> +<td align="right">6.8</td> +<td align="right">8.7</td> +<td align="right">2.4</td> +</tr> +<tr class="even"> +<td align="right">13.0910968</td> +<td align="right">14.4</td> +<td align="right">8.0</td> +<td align="right">9.1</td> +<td align="right">2.6</td> +</tr> +<tr class="odd"> +<td align="right">17.4547957</td> +<td align="right">7.7</td> +<td align="right">7.2</td> +<td align="right">8.6</td> +<td align="right">4.0</td> +</tr> +<tr class="even"> +<td align="right">17.4547957</td> +<td align="right">7.3</td> +<td align="right">7.2</td> +<td align="right">8.5</td> +<td align="right">3.6</td> +</tr> +<tr class="odd"> +<td align="right">17.4547957</td> +<td align="right">8.1</td> +<td align="right">6.9</td> +<td align="right">8.9</td> +<td align="right">3.3</td> +</tr> +<tr class="even"> +<td align="right">26.1821936</td> +<td align="right">2.0</td> +<td align="right">4.9</td> +<td align="right">8.1</td> +<td align="right">2.1</td> +</tr> +<tr class="odd"> +<td align="right">26.1821936</td> +<td align="right">1.5</td> +<td align="right">4.3</td> +<td align="right">7.7</td> +<td align="right">1.7</td> +</tr> +<tr class="even"> +<td align="right">26.1821936</td> +<td align="right">1.9</td> +<td align="right">4.5</td> +<td align="right">7.4</td> +<td align="right">1.8</td> +</tr> +<tr class="odd"> +<td align="right">34.9095915</td> +<td align="right">1.3</td> +<td align="right">3.8</td> +<td align="right">5.9</td> +<td align="right">1.6</td> +</tr> +<tr class="even"> +<td align="right">34.9095915</td> +<td align="right">1.0</td> +<td align="right">3.1</td> +<td align="right">6.0</td> +<td align="right">1.6</td> +</tr> +<tr class="odd"> +<td align="right">34.9095915</td> +<td align="right">1.1</td> +<td align="right">3.1</td> +<td align="right">5.9</td> +<td align="right">1.4</td> +</tr> +<tr class="even"> +<td align="right">43.6369893</td> +<td align="right">0.9</td> +<td align="right">2.7</td> +<td align="right">5.6</td> +<td align="right">1.8</td> +</tr> +<tr class="odd"> +<td align="right">43.6369893</td> +<td align="right">0.7</td> +<td align="right">2.3</td> +<td align="right">5.2</td> +<td align="right">1.5</td> +</tr> +<tr class="even"> +<td align="right">43.6369893</td> +<td align="right">0.7</td> +<td align="right">2.1</td> +<td align="right">5.6</td> +<td align="right">1.3</td> +</tr> +<tr class="odd"> +<td align="right">52.3643872</td> +<td align="right">0.6</td> +<td align="right">1.6</td> +<td align="right">4.3</td> +<td align="right">1.2</td> +</tr> +<tr class="even"> +<td align="right">52.3643872</td> +<td align="right">0.4</td> +<td align="right">1.1</td> +<td align="right">3.7</td> +<td align="right">0.9</td> +</tr> +<tr class="odd"> +<td align="right">52.3643872</td> +<td align="right">0.5</td> +<td align="right">1.3</td> +<td align="right">3.9</td> +<td align="right">1.1</td> +</tr> +<tr class="even"> +<td align="right">74.8062674</td> +<td align="right">0.4</td> +<td align="right">0.4</td> +<td align="right">2.5</td> +<td align="right">0.5</td> +</tr> +<tr class="odd"> +<td align="right">74.8062674</td> +<td align="right">0.3</td> +<td align="right">0.4</td> +<td align="right">2.4</td> +<td align="right">0.5</td> +</tr> +<tr class="even"> +<td align="right">74.8062674</td> +<td align="right">0.3</td> +<td align="right">0.3</td> +<td align="right">2.2</td> +<td align="right">0.3</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset BBA 2.2</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">DMTA</th> +<th align="right">M23</th> +<th align="right">M27</th> +<th align="right">M31</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.0000000</td> +<td align="right">98.09</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +</tr> +<tr class="even"> +<td align="right">0.0000000</td> +<td align="right">98.77</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +</tr> +<tr class="odd"> +<td align="right">0.7678922</td> +<td align="right">93.52</td> +<td align="right">0.36</td> +<td align="right">0.42</td> +<td align="right">0.36</td> +</tr> +<tr class="even"> +<td align="right">0.7678922</td> +<td align="right">92.03</td> +<td align="right">0.40</td> +<td align="right">0.47</td> +<td align="right">0.33</td> +</tr> +<tr class="odd"> +<td align="right">2.3036765</td> +<td align="right">88.39</td> +<td align="right">1.03</td> +<td align="right">0.71</td> +<td align="right">0.55</td> +</tr> +<tr class="even"> +<td align="right">2.3036765</td> +<td align="right">87.18</td> +<td align="right">1.07</td> +<td align="right">0.82</td> +<td align="right">0.64</td> +</tr> +<tr class="odd"> +<td align="right">5.3752452</td> +<td align="right">69.38</td> +<td align="right">3.60</td> +<td align="right">2.19</td> +<td align="right">1.94</td> +</tr> +<tr class="even"> +<td align="right">5.3752452</td> +<td align="right">71.06</td> +<td align="right">3.66</td> +<td align="right">2.28</td> +<td align="right">1.62</td> +</tr> +<tr class="odd"> +<td align="right">10.7504904</td> +<td align="right">45.21</td> +<td align="right">6.97</td> +<td align="right">5.45</td> +<td align="right">4.22</td> +</tr> +<tr class="even"> +<td align="right">10.7504904</td> +<td align="right">46.81</td> +<td align="right">7.22</td> +<td align="right">5.19</td> +<td align="right">4.37</td> +</tr> +<tr class="odd"> +<td align="right">16.1257355</td> +<td align="right">30.54</td> +<td align="right">8.65</td> +<td align="right">8.81</td> +<td align="right">6.31</td> +</tr> +<tr class="even"> +<td align="right">16.1257355</td> +<td align="right">30.07</td> +<td align="right">8.38</td> +<td align="right">7.93</td> +<td align="right">6.85</td> +</tr> +<tr class="odd"> +<td align="right">21.5009807</td> +<td align="right">21.60</td> +<td align="right">9.10</td> +<td align="right">10.25</td> +<td align="right">7.05</td> +</tr> +<tr class="even"> +<td align="right">21.5009807</td> +<td align="right">20.41</td> +<td align="right">8.63</td> +<td align="right">10.77</td> +<td align="right">6.84</td> +</tr> +<tr class="odd"> +<td align="right">32.2514711</td> +<td align="right">9.10</td> +<td align="right">7.63</td> +<td align="right">10.89</td> +<td align="right">6.53</td> +</tr> +<tr class="even"> +<td align="right">32.2514711</td> +<td align="right">9.70</td> +<td align="right">8.01</td> +<td align="right">10.85</td> +<td align="right">7.11</td> +</tr> +<tr class="odd"> +<td align="right">43.0019614</td> +<td align="right">6.58</td> +<td align="right">6.40</td> +<td align="right">10.41</td> +<td align="right">6.06</td> +</tr> +<tr class="even"> +<td align="right">43.0019614</td> +<td align="right">6.31</td> +<td align="right">6.35</td> +<td align="right">10.35</td> +<td align="right">6.05</td> +</tr> +<tr class="odd"> +<td align="right">53.7524518</td> +<td align="right">3.47</td> +<td align="right">5.35</td> +<td align="right">9.92</td> +<td align="right">5.50</td> +</tr> +<tr class="even"> +<td align="right">53.7524518</td> +<td align="right">3.52</td> +<td align="right">5.06</td> +<td align="right">9.42</td> +<td align="right">5.07</td> +</tr> +<tr class="odd"> +<td align="right">64.5029421</td> +<td align="right">3.40</td> +<td align="right">5.14</td> +<td align="right">9.15</td> +<td align="right">4.94</td> +</tr> +<tr class="even"> +<td align="right">64.5029421</td> +<td align="right">3.67</td> +<td align="right">5.91</td> +<td align="right">9.25</td> +<td align="right">4.39</td> +</tr> +<tr class="odd"> +<td align="right">91.3791680</td> +<td align="right">1.62</td> +<td align="right">3.35</td> +<td align="right">7.14</td> +<td align="right">3.64</td> +</tr> +<tr class="even"> +<td align="right">91.3791680</td> +<td align="right">1.62</td> +<td align="right">2.87</td> +<td align="right">7.13</td> +<td align="right">3.55</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset BBA 2.3</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">DMTA</th> +<th align="right">M23</th> +<th align="right">M27</th> +<th align="right">M31</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.0000000</td> +<td align="right">99.33</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +</tr> +<tr class="even"> +<td align="right">0.0000000</td> +<td align="right">97.44</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +</tr> +<tr class="odd"> +<td align="right">0.6733938</td> +<td align="right">93.73</td> +<td align="right">0.18</td> +<td align="right">0.50</td> +<td align="right">0.47</td> +</tr> +<tr class="even"> +<td align="right">0.6733938</td> +<td align="right">93.77</td> +<td align="right">0.18</td> +<td align="right">0.83</td> +<td align="right">0.34</td> +</tr> +<tr class="odd"> +<td align="right">2.0201814</td> +<td align="right">87.84</td> +<td align="right">0.52</td> +<td align="right">1.25</td> +<td align="right">1.00</td> +</tr> +<tr class="even"> +<td align="right">2.0201814</td> +<td align="right">89.82</td> +<td align="right">0.43</td> +<td align="right">1.09</td> +<td align="right">0.89</td> +</tr> +<tr class="odd"> +<td align="right">4.7137565</td> +<td align="right">71.61</td> +<td align="right">1.19</td> +<td align="right">3.28</td> +<td align="right">3.58</td> +</tr> +<tr class="even"> +<td align="right">4.7137565</td> +<td align="right">71.42</td> +<td align="right">1.11</td> +<td align="right">3.24</td> +<td align="right">3.41</td> +</tr> +<tr class="odd"> +<td align="right">9.4275131</td> +<td align="right">45.60</td> +<td align="right">2.26</td> +<td align="right">7.17</td> +<td align="right">8.74</td> +</tr> +<tr class="even"> +<td align="right">9.4275131</td> +<td align="right">45.42</td> +<td align="right">1.99</td> +<td align="right">7.91</td> +<td align="right">8.28</td> +</tr> +<tr class="odd"> +<td align="right">14.1412696</td> +<td align="right">31.12</td> +<td align="right">2.81</td> +<td align="right">10.15</td> +<td align="right">9.67</td> +</tr> +<tr class="even"> +<td align="right">14.1412696</td> +<td align="right">31.68</td> +<td align="right">2.83</td> +<td align="right">9.55</td> +<td align="right">8.95</td> +</tr> +<tr class="odd"> +<td align="right">18.8550262</td> +<td align="right">23.20</td> +<td align="right">3.39</td> +<td align="right">12.09</td> +<td align="right">10.34</td> +</tr> +<tr class="even"> +<td align="right">18.8550262</td> +<td align="right">24.13</td> +<td align="right">3.56</td> +<td align="right">11.89</td> +<td align="right">10.00</td> +</tr> +<tr class="odd"> +<td align="right">28.2825393</td> +<td align="right">9.43</td> +<td align="right">3.49</td> +<td align="right">13.32</td> +<td align="right">7.89</td> +</tr> +<tr class="even"> +<td align="right">28.2825393</td> +<td align="right">9.82</td> +<td align="right">3.28</td> +<td align="right">12.05</td> +<td align="right">8.13</td> +</tr> +<tr class="odd"> +<td align="right">37.7100523</td> +<td align="right">7.08</td> +<td align="right">2.80</td> +<td align="right">10.04</td> +<td align="right">5.06</td> +</tr> +<tr class="even"> +<td align="right">37.7100523</td> +<td align="right">8.64</td> +<td align="right">2.97</td> +<td align="right">10.78</td> +<td align="right">5.54</td> +</tr> +<tr class="odd"> +<td align="right">47.1375654</td> +<td align="right">4.41</td> +<td align="right">2.42</td> +<td align="right">9.32</td> +<td align="right">3.79</td> +</tr> +<tr class="even"> +<td align="right">47.1375654</td> +<td align="right">4.78</td> +<td align="right">2.51</td> +<td align="right">9.62</td> +<td align="right">4.11</td> +</tr> +<tr class="odd"> +<td align="right">56.5650785</td> +<td align="right">4.92</td> +<td align="right">2.22</td> +<td align="right">8.00</td> +<td align="right">3.11</td> +</tr> +<tr class="even"> +<td align="right">56.5650785</td> +<td align="right">5.08</td> +<td align="right">1.95</td> +<td align="right">8.45</td> +<td align="right">2.98</td> +</tr> +<tr class="odd"> +<td align="right">80.1338612</td> +<td align="right">2.13</td> +<td align="right">1.28</td> +<td align="right">5.71</td> +<td align="right">1.78</td> +</tr> +<tr class="even"> +<td align="right">80.1338612</td> +<td align="right">2.23</td> +<td align="right">0.99</td> +<td align="right">3.33</td> +<td align="right">1.55</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset Elliot</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">DMTA</th> +<th align="right">M23</th> +<th align="right">M27</th> +<th align="right">M31</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">97.5</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +</tr> +<tr class="even"> +<td align="right">0.000000</td> +<td align="right">100.7</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +</tr> +<tr class="odd"> +<td align="right">1.228478</td> +<td align="right">86.4</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +</tr> +<tr class="even"> +<td align="right">1.228478</td> +<td align="right">88.5</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">1.5</td> +</tr> +<tr class="odd"> +<td align="right">3.685435</td> +<td align="right">69.8</td> +<td align="right">2.8</td> +<td align="right">2.3</td> +<td align="right">5.0</td> +</tr> +<tr class="even"> +<td align="right">3.685435</td> +<td align="right">77.1</td> +<td align="right">1.7</td> +<td align="right">2.1</td> +<td align="right">2.4</td> +</tr> +<tr class="odd"> +<td align="right">8.599349</td> +<td align="right">59.0</td> +<td align="right">4.3</td> +<td align="right">4.0</td> +<td align="right">4.3</td> +</tr> +<tr class="even"> +<td align="right">8.599349</td> +<td align="right">54.2</td> +<td align="right">5.8</td> +<td align="right">3.4</td> +<td align="right">5.0</td> +</tr> +<tr class="odd"> +<td align="right">17.198697</td> +<td align="right">31.3</td> +<td align="right">8.2</td> +<td align="right">6.6</td> +<td align="right">8.0</td> +</tr> +<tr class="even"> +<td align="right">17.198697</td> +<td align="right">33.5</td> +<td align="right">5.2</td> +<td align="right">6.9</td> +<td align="right">7.7</td> +</tr> +<tr class="odd"> +<td align="right">25.798046</td> +<td align="right">19.6</td> +<td align="right">5.1</td> +<td align="right">8.2</td> +<td align="right">7.8</td> +</tr> +<tr class="even"> +<td align="right">25.798046</td> +<td align="right">20.9</td> +<td align="right">6.1</td> +<td align="right">8.8</td> +<td align="right">6.5</td> +</tr> +<tr class="odd"> +<td align="right">34.397395</td> +<td align="right">13.3</td> +<td align="right">6.0</td> +<td align="right">9.7</td> +<td align="right">8.0</td> +</tr> +<tr class="even"> +<td align="right">34.397395</td> +<td align="right">15.8</td> +<td align="right">6.0</td> +<td align="right">8.8</td> +<td align="right">7.4</td> +</tr> +<tr class="odd"> +<td align="right">51.596092</td> +<td align="right">6.7</td> +<td align="right">5.0</td> +<td align="right">8.3</td> +<td align="right">6.9</td> +</tr> +<tr class="even"> +<td align="right">51.596092</td> +<td align="right">8.7</td> +<td align="right">4.2</td> +<td align="right">9.2</td> +<td align="right">9.0</td> +</tr> +<tr class="odd"> +<td align="right">68.794789</td> +<td align="right">8.8</td> +<td align="right">3.9</td> +<td align="right">9.3</td> +<td align="right">5.5</td> +</tr> +<tr class="even"> +<td align="right">68.794789</td> +<td align="right">8.7</td> +<td align="right">2.9</td> +<td align="right">8.5</td> +<td align="right">6.1</td> +</tr> +<tr class="odd"> +<td align="right">103.192184</td> +<td align="right">6.0</td> +<td align="right">1.9</td> +<td align="right">8.6</td> +<td align="right">6.1</td> +</tr> +<tr class="even"> +<td align="right">103.192184</td> +<td align="right">4.4</td> +<td align="right">1.5</td> +<td align="right">6.0</td> +<td align="right">4.0</td> +</tr> +<tr class="odd"> +<td align="right">146.188928</td> +<td align="right">3.3</td> +<td align="right">2.0</td> +<td align="right">5.6</td> +<td align="right">3.1</td> +</tr> +<tr class="even"> +<td align="right">146.188928</td> +<td align="right">2.8</td> +<td align="right">2.3</td> +<td align="right">4.5</td> +<td align="right">2.9</td> +</tr> +<tr class="odd"> +<td align="right">223.583066</td> +<td align="right">1.4</td> +<td align="right">1.2</td> +<td align="right">4.1</td> +<td align="right">1.8</td> +</tr> +<tr class="even"> +<td align="right">223.583066</td> +<td align="right">1.8</td> +<td align="right">1.9</td> +<td align="right">3.9</td> +<td align="right">2.6</td> +</tr> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">93.4</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +</tr> +<tr class="even"> +<td align="right">0.000000</td> +<td align="right">103.2</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +</tr> +<tr class="odd"> +<td align="right">1.228478</td> +<td align="right">89.2</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">1.3</td> +</tr> +<tr class="even"> +<td align="right">1.228478</td> +<td align="right">86.6</td> +<td align="right">NA</td> +<td align="right">NA</td> +<td align="right">NA</td> +</tr> +<tr class="odd"> +<td align="right">3.685435</td> +<td align="right">78.2</td> +<td align="right">2.6</td> +<td align="right">1.0</td> +<td align="right">3.1</td> +</tr> +<tr class="even"> +<td align="right">3.685435</td> +<td align="right">78.1</td> +<td align="right">2.4</td> +<td align="right">2.6</td> +<td align="right">2.3</td> +</tr> +<tr class="odd"> +<td align="right">8.599349</td> +<td align="right">55.6</td> +<td align="right">5.5</td> +<td align="right">4.5</td> +<td align="right">3.4</td> +</tr> +<tr class="even"> +<td align="right">8.599349</td> +<td align="right">53.0</td> +<td align="right">5.6</td> +<td align="right">4.6</td> +<td align="right">4.3</td> +</tr> +<tr class="odd"> +<td align="right">17.198697</td> +<td align="right">33.7</td> +<td align="right">7.3</td> +<td align="right">7.6</td> +<td align="right">7.8</td> +</tr> +<tr class="even"> +<td align="right">17.198697</td> +<td align="right">33.2</td> +<td align="right">6.5</td> +<td align="right">6.7</td> +<td align="right">8.7</td> +</tr> +<tr class="odd"> +<td align="right">25.798046</td> +<td align="right">20.9</td> +<td align="right">5.8</td> +<td align="right">8.7</td> +<td align="right">7.7</td> +</tr> +<tr class="even"> +<td align="right">25.798046</td> +<td align="right">19.9</td> +<td align="right">7.7</td> +<td align="right">7.6</td> +<td align="right">6.5</td> +</tr> +<tr class="odd"> +<td align="right">34.397395</td> +<td align="right">18.2</td> +<td align="right">7.8</td> +<td align="right">8.0</td> +<td align="right">6.3</td> +</tr> +<tr class="even"> +<td align="right">34.397395</td> +<td align="right">12.7</td> +<td align="right">7.3</td> +<td align="right">8.6</td> +<td align="right">8.7</td> +</tr> +<tr class="odd"> +<td align="right">51.596092</td> +<td align="right">7.8</td> +<td align="right">7.0</td> +<td align="right">7.4</td> +<td align="right">5.7</td> +</tr> +<tr class="even"> +<td align="right">51.596092</td> +<td align="right">9.0</td> +<td align="right">6.3</td> +<td align="right">7.2</td> +<td align="right">4.2</td> +</tr> +<tr class="odd"> +<td align="right">68.794789</td> +<td align="right">11.4</td> +<td align="right">4.3</td> +<td align="right">10.3</td> +<td align="right">3.2</td> +</tr> +<tr class="even"> +<td align="right">68.794789</td> +<td align="right">9.0</td> +<td align="right">3.8</td> +<td align="right">9.4</td> +<td align="right">4.2</td> +</tr> +<tr class="odd"> +<td align="right">103.192184</td> +<td align="right">3.9</td> +<td align="right">2.6</td> +<td align="right">6.5</td> +<td align="right">3.8</td> +</tr> +<tr class="even"> +<td align="right">103.192184</td> +<td align="right">4.4</td> +<td align="right">2.8</td> +<td align="right">6.9</td> +<td align="right">4.0</td> +</tr> +<tr class="odd"> +<td align="right">146.188928</td> +<td align="right">2.6</td> +<td align="right">1.6</td> +<td align="right">4.6</td> +<td align="right">4.5</td> +</tr> +<tr class="even"> +<td align="right">146.188928</td> +<td align="right">3.4</td> +<td align="right">1.1</td> +<td align="right">4.5</td> +<td align="right">4.5</td> +</tr> +<tr class="odd"> +<td align="right">223.583066</td> +<td align="right">2.0</td> +<td align="right">1.4</td> +<td align="right">4.3</td> +<td align="right">3.8</td> +</tr> +<tr class="even"> +<td align="right">223.583066</td> +<td align="right">1.7</td> +<td align="right">1.3</td> +<td align="right">4.2</td> +<td align="right">2.3</td> +</tr> +</tbody> +</table> +</div> +<div class="section level2"> +<h2 id="separate-evaluations">Separate evaluations<a class="anchor" aria-label="anchor" href="#separate-evaluations"></a> +</h2> +<p>As a first step to obtain suitable starting parameters for the NLHM +fits, we do separate fits of several variants of the pathway model used +previously <span class="citation">(Ranke et al. 2021)</span>, varying +the kinetic model for the parent compound. Because the SFORB model often +provides faster convergence than the DFOP model, and can sometimes be +fitted where the DFOP model results in errors, it is included in the set +of parent models tested here.</p> +<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="kw">if</span> <span class="op">(</span><span class="op">!</span><span class="fu"><a href="https://rdrr.io/r/base/files2.html" class="external-link">dir.exists</a></span><span class="op">(</span><span class="st">"dmta_dlls"</span><span class="op">)</span><span class="op">)</span> <span class="fu"><a href="https://rdrr.io/r/base/files2.html" class="external-link">dir.create</a></span><span class="op">(</span><span class="st">"dmta_dlls"</span><span class="op">)</span></span> +<span><span class="va">m_sfo_path_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> +<span> DMTA <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"M23"</span>, <span class="st">"M27"</span>, <span class="st">"M31"</span><span class="op">)</span><span class="op">)</span>,</span> +<span> M23 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> +<span> M27 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> +<span> M31 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M27"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> +<span> name <span class="op">=</span> <span class="st">"m_sfo_path"</span>, dll_dir <span class="op">=</span> <span class="st">"dmta_dlls"</span>,</span> +<span> unload <span class="op">=</span> <span class="cn">TRUE</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span>,</span> +<span> quiet <span class="op">=</span> <span class="cn">TRUE</span></span> +<span><span class="op">)</span></span> +<span><span class="va">m_fomc_path_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> +<span> DMTA <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"FOMC"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"M23"</span>, <span class="st">"M27"</span>, <span class="st">"M31"</span><span class="op">)</span><span class="op">)</span>,</span> +<span> M23 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> +<span> M27 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> +<span> M31 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M27"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> +<span> name <span class="op">=</span> <span class="st">"m_fomc_path"</span>, dll_dir <span class="op">=</span> <span class="st">"dmta_dlls"</span>,</span> +<span> unload <span class="op">=</span> <span class="cn">TRUE</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span>,</span> +<span> quiet <span class="op">=</span> <span class="cn">TRUE</span></span> +<span><span class="op">)</span></span> +<span><span class="va">m_dfop_path_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> +<span> DMTA <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"DFOP"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"M23"</span>, <span class="st">"M27"</span>, <span class="st">"M31"</span><span class="op">)</span><span class="op">)</span>,</span> +<span> M23 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> +<span> M27 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> +<span> M31 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M27"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> +<span> name <span class="op">=</span> <span class="st">"m_dfop_path"</span>, dll_dir <span class="op">=</span> <span class="st">"dmta_dlls"</span>,</span> +<span> unload <span class="op">=</span> <span class="cn">TRUE</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span>,</span> +<span> quiet <span class="op">=</span> <span class="cn">TRUE</span></span> +<span><span class="op">)</span></span> +<span><span class="va">m_sforb_path_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> +<span> DMTA <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"M23"</span>, <span class="st">"M27"</span>, <span class="st">"M31"</span><span class="op">)</span><span class="op">)</span>,</span> +<span> M23 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> +<span> M27 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> +<span> M31 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M27"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> +<span> name <span class="op">=</span> <span class="st">"m_sforb_path"</span>, dll_dir <span class="op">=</span> <span class="st">"dmta_dlls"</span>,</span> +<span> unload <span class="op">=</span> <span class="cn">TRUE</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span>,</span> +<span> quiet <span class="op">=</span> <span class="cn">TRUE</span></span> +<span><span class="op">)</span></span> +<span><span class="va">m_hs_path_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> +<span> DMTA <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"HS"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"M23"</span>, <span class="st">"M27"</span>, <span class="st">"M31"</span><span class="op">)</span><span class="op">)</span>,</span> +<span> M23 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> +<span> M27 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> +<span> M31 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M27"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> +<span> name <span class="op">=</span> <span class="st">"m_hs_path"</span>, dll_dir <span class="op">=</span> <span class="st">"dmta_dlls"</span>,</span> +<span> unload <span class="op">=</span> <span class="cn">TRUE</span>, overwrite <span class="op">=</span> <span class="cn">TRUE</span>,</span> +<span> quiet <span class="op">=</span> <span class="cn">TRUE</span></span> +<span><span class="op">)</span></span> +<span><span class="va">cl</span> <span class="op"><-</span> <span class="fu">start_cluster</span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> +<span></span> +<span><span class="va">deg_mods_1</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span></span> +<span> sfo_path_1 <span class="op">=</span> <span class="va">m_sfo_path_1</span>,</span> +<span> fomc_path_1 <span class="op">=</span> <span class="va">m_fomc_path_1</span>,</span> +<span> dfop_path_1 <span class="op">=</span> <span class="va">m_dfop_path_1</span>,</span> +<span> sforb_path_1 <span class="op">=</span> <span class="va">m_sforb_path_1</span>,</span> +<span> hs_path_1 <span class="op">=</span> <span class="va">m_hs_path_1</span><span class="op">)</span></span> +<span></span> +<span><span class="va">sep_1_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span></span> +<span> <span class="va">deg_mods_1</span>,</span> +<span> <span class="va">dmta_ds</span>,</span> +<span> error_model <span class="op">=</span> <span class="st">"const"</span>,</span> +<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> +<span></span> +<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">sep_1_const</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">Calke</th> +<th align="left">Borstel</th> +<th align="left">Flaach</th> +<th align="left">BBA 2.2</th> +<th align="left">BBA 2.3</th> +<th align="left">Elliot</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">sfo_path_1</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">fomc_path_1</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">dfop_path_1</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">sforb_path_1</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">hs_path_1</td> +<td align="left">C</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">C</td> +<td align="left">C</td> +</tr> +</tbody> +</table> +<p>All separate pathway fits with SFO or FOMC for the parent and +constant variance converged (status OK). Most fits with DFOP or SFORB +for the parent converged as well. The fits with HS for the parent did +not converge with default settings.</p> +<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">sep_1_tc</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">sep_1_const</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">sep_1_tc</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">Calke</th> +<th align="left">Borstel</th> +<th align="left">Flaach</th> +<th align="left">BBA 2.2</th> +<th align="left">BBA 2.3</th> +<th align="left">Elliot</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">sfo_path_1</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">fomc_path_1</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">dfop_path_1</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">sforb_path_1</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">hs_path_1</td> +<td align="left">C</td> +<td align="left">C</td> +<td align="left">C</td> +<td align="left">C</td> +<td align="left">C</td> +<td align="left">C</td> +</tr> +</tbody> +</table> +<p>With the two-component error model, the set of fits with convergence +problems is slightly different, with convergence problems appearing for +different data sets when applying the DFOP and SFORB model and some +additional convergence problems when using the FOMC model for the +parent.</p> +</div> +<div class="section level2"> +<h2 id="hierarchichal-model-fits">Hierarchichal model fits<a class="anchor" aria-label="anchor" href="#hierarchichal-model-fits"></a> +</h2> +<p>The following code fits two sets of the corresponding hierarchical +models to the data, one assuming constant variance, and one assuming +two-component error.</p> +<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">saem_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mhmkin.html">mhmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">sep_1_const</span>, <span class="va">sep_1_tc</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<p>The run time for these fits was around two hours on five year old +hardware. After a recent hardware upgrade these fits complete in less +than twenty minutes.</p> +<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">sfo_path_1</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">fomc_path_1</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">dfop_path_1</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">sforb_path_1</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">hs_path_1</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<p>According to the <code>status</code> function, all fits terminated +successfully.</p> +<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">npar</th> +<th align="right">AIC</th> +<th align="right">BIC</th> +<th align="right">Lik</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">sfo_path_1 const</td> +<td align="right">17</td> +<td align="right">2291.8</td> +<td align="right">2288.3</td> +<td align="right">-1128.9</td> +</tr> +<tr class="even"> +<td align="left">sfo_path_1 tc</td> +<td align="right">18</td> +<td align="right">2276.4</td> +<td align="right">2272.7</td> +<td align="right">-1120.2</td> +</tr> +<tr class="odd"> +<td align="left">fomc_path_1 const</td> +<td align="right">19</td> +<td align="right">2095.9</td> +<td align="right">2091.9</td> +<td align="right">-1028.9</td> +</tr> +<tr class="even"> +<td align="left">fomc_path_1 tc</td> +<td align="right">20</td> +<td align="right">1939.0</td> +<td align="right">1934.8</td> +<td align="right">-949.5</td> +</tr> +<tr class="odd"> +<td align="left">dfop_path_1 const</td> +<td align="right">21</td> +<td align="right">2039.7</td> +<td align="right">2035.3</td> +<td align="right">-998.8</td> +</tr> +<tr class="even"> +<td align="left">sforb_path_1 const</td> +<td align="right">21</td> +<td align="right">2017.7</td> +<td align="right">2013.4</td> +<td align="right">-987.9</td> +</tr> +<tr class="odd"> +<td align="left">hs_path_1 const</td> +<td align="right">21</td> +<td align="right">2023.7</td> +<td align="right">2019.3</td> +<td align="right">-990.9</td> +</tr> +<tr class="even"> +<td align="left">dfop_path_1 tc</td> +<td align="right">22</td> +<td align="right">1881.7</td> +<td align="right">1877.1</td> +<td align="right">-918.9</td> +</tr> +<tr class="odd"> +<td align="left">sforb_path_1 tc</td> +<td align="right">22</td> +<td align="right">1832.7</td> +<td align="right">1828.1</td> +<td align="right">-894.3</td> +</tr> +<tr class="even"> +<td align="left">hs_path_1 tc</td> +<td align="right">22</td> +<td align="right">1831.6</td> +<td align="right">1827.0</td> +<td align="right">-893.8</td> +</tr> +</tbody> +</table> +<p>When the goodness-of-fit of the models is compared, a warning is +obtained, indicating that the likelihood of the pathway fit with SFORB +for the parent compound and constant variance could not be calculated +with importance sampling (method ‘is’). As this is the default method on +which all AIC and BIC comparisons are based, this variant is not +included in the model comparison table. Comparing the goodness-of-fit of +the remaining models, HS model model with two-component error provides +the best fit. However, for batch experiments performed with constant +conditions such as the experiments evaluated here, there is no reason to +assume a discontinuity, so the SFORB model is preferable from a +mechanistic viewpoint. In addition, the information criteria AIC and BIC +are very similar for HS and SFORB. Therefore, the SFORB model is +selected here for further refinements.</p> +<div class="section level3"> +<h3 id="parameter-identifiability-based-on-the-fisher-information-matrix">Parameter identifiability based on the Fisher Information +Matrix<a class="anchor" aria-label="anchor" href="#parameter-identifiability-based-on-the-fisher-information-matrix"></a> +</h3> +<p>Using the <code>illparms</code> function, ill-defined statistical +model parameters such as standard deviations of the degradation +parameters in the population and error model parameters can be +found.</p> +<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">sfo_path_1</td> +<td align="left"></td> +<td align="left">sd(DMTA_0)</td> +</tr> +<tr class="even"> +<td align="left">fomc_path_1</td> +<td align="left"></td> +<td align="left">sd(DMTA_0)</td> +</tr> +<tr class="odd"> +<td align="left">dfop_path_1</td> +<td align="left"></td> +<td align="left"></td> +</tr> +<tr class="even"> +<td align="left">sforb_path_1</td> +<td align="left">sd(log_k_DMTA_bound_free)</td> +<td align="left">sd(log_k_DMTA_bound_free)</td> +</tr> +<tr class="odd"> +<td align="left">hs_path_1</td> +<td align="left"></td> +<td align="left">sd(log_tb)</td> +</tr> +</tbody> +</table> +<p>When using constant variance, no ill-defined variance parameters are +identified with the <code>illparms</code> function in any of the +degradation models. When using the two-component error model, there is +one ill-defined variance parameter in all variants except for the +variant using DFOP for the parent compound.</p> +<p>For the selected combination of the SFORB pathway model with +two-component error, the random effect for the rate constant from +reversibly bound DMTA to the free DMTA (<code>k_DMTA_bound_free</code>) +is not well-defined. Therefore, the fit is updated without assuming a +random effect for this parameter.</p> +<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">saem_sforb_path_1_tc_reduced</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">[[</span><span class="st">"sforb_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span>,</span> +<span> no_random_effect <span class="op">=</span> <span class="st">"log_k_DMTA_bound_free"</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">saem_sforb_path_1_tc_reduced</span><span class="op">)</span></span></code></pre></div> +<p>As expected, no ill-defined parameters remain. The model comparison +below shows that the reduced model is preferable.</p> +<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">[[</span><span class="st">"sforb_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span>, <span class="va">saem_sforb_path_1_tc_reduced</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">npar</th> +<th align="right">AIC</th> +<th align="right">BIC</th> +<th align="right">Lik</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">saem_sforb_path_1_tc_reduced</td> +<td align="right">21</td> +<td align="right">1830.4</td> +<td align="right">1826.0</td> +<td align="right">-894.2</td> +</tr> +<tr class="even"> +<td align="left">saem_1[[“sforb_path_1”, “tc”]]</td> +<td align="right">22</td> +<td align="right">1832.7</td> +<td align="right">1828.1</td> +<td align="right">-894.3</td> +</tr> +</tbody> +</table> +<p>The convergence plot of the refined fit is shown below.</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/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">saem_sforb_path_1_tc_reduced</span><span class="op">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></span></code></pre></div> +<p><img src="2022_dmta_pathway_files/figure-html/saem-sforb-path-1-tc-reduced-convergence-1.png" width="700" style="display: block; margin: auto;"></p> +<p>For some parameters, for example for <code>f_DMTA_ilr_1</code> and +<code>f_DMTA_ilr_2</code>, i.e. for two of the parameters determining +the formation fractions of the parallel formation of the three +metabolites, some movement of the parameters is still visible in the +second phase of the algorithm. However, the amplitude of this movement +is in the range of the amplitude towards the end of the first phase. +Therefore, it is likely that an increase in iterations would not improve +the parameter estimates very much, and it is proposed that the fit is +acceptable. No numeric convergence criterion is implemented in +saemix.</p> +</div> +<div class="section level3"> +<h3 id="alternative-check-of-parameter-identifiability">Alternative check of parameter identifiability<a class="anchor" aria-label="anchor" href="#alternative-check-of-parameter-identifiability"></a> +</h3> +<p>As an alternative check of parameter identifiability <span class="citation">(Duchesne et al. 2021)</span>, multistart runs were +performed on the basis of the refined fit shown above.</p> +<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">saem_sforb_path_1_tc_reduced_multi</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/multistart.html">multistart</a></span><span class="op">(</span><span class="va">saem_sforb_path_1_tc_reduced</span>,</span> +<span> n <span class="op">=</span> <span class="fl">32</span>, cores <span class="op">=</span> <span class="fl">10</span><span class="op">)</span></span></code></pre></div> +<pre><code> + (subscript) logical subscript too long</code></pre> +<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">saem_sforb_path_1_tc_reduced_multi</span><span class="op">)</span></span></code></pre></div> +<pre><code><multistart> object with 32 fits: + E OK + 7 25 +OK: Fit terminated successfully +E: Error</code></pre> +<p>Out of the 32 fits that were initiated, only 17 terminated without an +error. The reason for this is that the wide variation of starting +parameters in combination with the parameter variation that is used in +the SAEM algorithm leads to parameter combinations for the degradation +model that the numerical integration routine cannot cope with. Because +of this variation of initial parameters, some of the model fits take up +to two times more time than the original fit.</p> +<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/par.html" class="external-link">par</a></span><span class="op">(</span>mar <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">12.1</span>, <span class="fl">4.1</span>, <span class="fl">2.1</span>, <span class="fl">2.1</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/parplot.html">parplot</a></span><span class="op">(</span><span class="va">saem_sforb_path_1_tc_reduced_multi</span>, ylim <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.5</span>, <span class="fl">2</span><span class="op">)</span>, las <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<div class="figure" style="text-align: center"> +<img src="2022_dmta_pathway_files/figure-html/unnamed-chunk-2-1.png" alt="Parameter boxplots for the multistart runs that succeeded" width="960"><p class="caption"> +Parameter boxplots for the multistart runs that succeeded +</p> +</div> +<p>However, visual analysis of the boxplot of the parameters obtained in +the successful fits confirms that the results are sufficiently +independent of the starting parameters, and there are no remaining +ill-defined parameters.</p> +</div> +</div> +<div class="section level2"> +<h2 id="plots-of-selected-fits">Plots of selected fits<a class="anchor" aria-label="anchor" href="#plots-of-selected-fits"></a> +</h2> +<p>The SFORB pathway fits with full and reduced parameter distribution +model are shown below.</p> +<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">[[</span><span class="st">"sforb_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> +<div class="figure" style="text-align: center"> +<img src="2022_dmta_pathway_files/figure-html/unnamed-chunk-3-1.png" alt="SFORB pathway fit with two-component error" width="700"><p class="caption"> +SFORB pathway fit with two-component error +</p> +</div> +<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">saem_sforb_path_1_tc_reduced</span><span class="op">)</span></span></code></pre></div> +<div class="figure" style="text-align: center"> +<img src="2022_dmta_pathway_files/figure-html/unnamed-chunk-4-1.png" alt="SFORB pathway fit with two-component error, reduced parameter model" width="700"><p class="caption"> +SFORB pathway fit with two-component error, reduced parameter model +</p> +</div> +<p>Plots of the remaining fits and listings for all successful fits are +shown in the Appendix.</p> +<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">stopCluster</a></span><span class="op">(</span><span class="va">cl</span><span class="op">)</span></span></code></pre></div> +</div> +<div class="section level2"> +<h2 id="conclusions">Conclusions<a class="anchor" aria-label="anchor" href="#conclusions"></a> +</h2> +<p>Pathway fits with SFO, FOMC, DFOP, SFORB and HS models for the parent +compound could be successfully performed.</p> +</div> +<div class="section level2"> +<h2 id="acknowledgements">Acknowledgements<a class="anchor" aria-label="anchor" href="#acknowledgements"></a> +</h2> +<p>The helpful comments by Janina Wöltjen of the German Environment +Agency on earlier versions of this document are gratefully +acknowledged.</p> +</div> +<div class="section level2"> +<h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a> +</h2> +<div id="refs" class="references csl-bib-body hanging-indent"> +<div id="ref-duchesne_2021" class="csl-entry"> +Duchesne, Ronan, Anissa Guillemin, Olivier Gandrillon, and Fabien +Crauste. 2021. <span>“Practical Identifiability in the Frame of +Nonlinear Mixed Effects Models: The Example of the in Vitro +Erythropoiesis.”</span> <em>BMC Bioinformatics</em> 22 (478). <a href="https://doi.org/10.1186/s12859-021-04373-4" class="external-link">https://doi.org/10.1186/s12859-021-04373-4</a>. +</div> +<div id="ref-ranke2021" class="csl-entry"> +Ranke, Johannes, Janina Wöltjen, Jana Schmidt, and Emmanuelle Comets. +2021. <span>“Taking Kinetic Evaluations of Degradation Data to the Next +Level with Nonlinear Mixed-Effects Models.”</span> <em>Environments</em> +8 (8). <a href="https://doi.org/10.3390/environments8080071" class="external-link">https://doi.org/10.3390/environments8080071</a>. +</div> +</div> +</div> +<div class="section level2"> +<h2 id="appendix">Appendix<a class="anchor" aria-label="anchor" href="#appendix"></a> +</h2> +<div class="section level3"> +<h3 id="plots-of-hierarchical-fits-not-selected-for-refinement">Plots of hierarchical fits not selected for refinement<a class="anchor" aria-label="anchor" href="#plots-of-hierarchical-fits-not-selected-for-refinement"></a> +</h3> +<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">[[</span><span class="st">"sfo_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> +<div class="figure" style="text-align: center"> +<img src="2022_dmta_pathway_files/figure-html/unnamed-chunk-6-1.png" alt="SFO pathway fit with two-component error" width="700"><p class="caption"> +SFO pathway fit with two-component error +</p> +</div> +<div class="sourceCode" id="cb22"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">[[</span><span class="st">"fomc_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> +<div class="figure" style="text-align: center"> +<img src="2022_dmta_pathway_files/figure-html/unnamed-chunk-7-1.png" alt="FOMC pathway fit with two-component error" width="700"><p class="caption"> +FOMC pathway fit with two-component error +</p> +</div> +<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">saem_1</span><span class="op">[[</span><span class="st">"sforb_path_1"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> +<div class="figure" style="text-align: center"> +<img src="2022_dmta_pathway_files/figure-html/unnamed-chunk-8-1.png" alt="HS pathway fit with two-component error" width="700"><p class="caption"> +HS pathway fit with two-component error +</p> +</div> +</div> +<div class="section level3"> +<h3 id="hierarchical-model-fit-listings">Hierarchical model fit listings<a class="anchor" aria-label="anchor" href="#hierarchical-model-fit-listings"></a> +</h3> +<div class="section level4"> +<h4 id="fits-with-random-effects-for-all-degradation-parameters">Fits with random effects for all degradation parameters<a class="anchor" aria-label="anchor" href="#fits-with-random-effects-for-all-degradation-parameters"></a> +</h4> + +</div> +<div class="section level4"> +<h4 id="improved-fit-of-the-sforb-pathway-model-with-two-component-error">Improved fit of the SFORB pathway model with two-component +error<a class="anchor" aria-label="anchor" href="#improved-fit-of-the-sforb-pathway-model-with-two-component-error"></a> +</h4> + +</div> +</div> +<div class="section level3"> +<h3 id="session-info">Session info<a class="anchor" aria-label="anchor" href="#session-info"></a> +</h3> +<pre><code>R version 4.4.2 (2024-10-31) +Platform: x86_64-pc-linux-gnu +Running under: Debian GNU/Linux 12 (bookworm) + +Matrix products: default +BLAS: /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.11.0 +LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.11.0 + +locale: + [1] LC_CTYPE=de_DE.UTF-8 LC_NUMERIC=C + [3] LC_TIME=de_DE.UTF-8 LC_COLLATE=de_DE.UTF-8 + [5] LC_MONETARY=de_DE.UTF-8 LC_MESSAGES=de_DE.UTF-8 + [7] LC_PAPER=de_DE.UTF-8 LC_NAME=C + [9] LC_ADDRESS=C LC_TELEPHONE=C +[11] LC_MEASUREMENT=de_DE.UTF-8 LC_IDENTIFICATION=C + +time zone: Europe/Berlin +tzcode source: system (glibc) + +attached base packages: +[1] parallel stats graphics grDevices utils datasets methods +[8] base + +other attached packages: +[1] 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] sass_0.4.9 utf8_1.2.4 generics_0.1.3 lattice_0.22-6 + [5] digest_0.6.37 magrittr_2.0.3 evaluate_1.0.1 grid_4.4.2 + [9] fastmap_1.2.0 jsonlite_1.8.9 processx_3.8.4 pkgbuild_1.4.5 +[13] deSolve_1.40 mclust_6.1.1 ps_1.8.1 gridExtra_2.3 +[17] fansi_1.0.6 scales_1.3.0 codetools_0.2-20 textshaping_0.4.1 +[21] jquerylib_0.1.4 cli_3.6.3 rlang_1.1.4 munsell_0.5.1 +[25] cachem_1.1.0 yaml_2.3.10 inline_0.3.20 tools_4.4.2 +[29] dplyr_1.1.4 colorspace_2.1-1 ggplot2_3.5.1 vctrs_0.6.5 +[33] R6_2.5.1 zoo_1.8-12 lifecycle_1.0.4 fs_1.6.5 +[37] htmlwidgets_1.6.4 MASS_7.3-61 ragg_1.3.3 pkgconfig_2.0.3 +[41] desc_1.4.3 callr_3.7.6 pkgdown_2.1.1 pillar_1.9.0 +[45] bslib_0.8.0 gtable_0.3.6 glue_1.8.0 systemfonts_1.1.0 +[49] xfun_0.49 tibble_3.2.1 lmtest_0.9-40 tidyselect_1.2.1 +[53] htmltools_0.5.8.1 nlme_3.1-166 compiler_4.4.2 </code></pre> +</div> +<div class="section level3"> +<h3 id="hardware-info">Hardware info<a class="anchor" aria-label="anchor" href="#hardware-info"></a> +</h3> +<pre><code>CPU model: AMD Ryzen 9 7950X 16-Core Processor</code></pre> +<pre><code>MemTotal: 64927788 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/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/saem-sforb-path-1-tc-reduced-convergence-1.png b/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/saem-sforb-path-1-tc-reduced-convergence-1.png Binary files differnew file mode 100644 index 00000000..0facfbe5 --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/saem-sforb-path-1-tc-reduced-convergence-1.png diff --git a/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-2-1.png b/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-2-1.png Binary files differnew file mode 100644 index 00000000..4e363872 --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-2-1.png diff --git a/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-3-1.png b/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-3-1.png Binary files differnew file mode 100644 index 00000000..562d8d9d --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-3-1.png diff --git a/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-4-1.png b/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-4-1.png Binary files differnew file mode 100644 index 00000000..7bf4aa4a --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-4-1.png diff --git a/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-6-1.png b/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-6-1.png Binary files differnew file mode 100644 index 00000000..602c1138 --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-6-1.png diff --git a/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-7-1.png b/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-7-1.png Binary files differnew file mode 100644 index 00000000..8db8e11c --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-7-1.png diff --git a/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-8-1.png b/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-8-1.png Binary files differnew file mode 100644 index 00000000..562d8d9d --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-8-1.png diff --git a/docs/dev/articles/prebuilt/2023_mesotrione_parent.html b/docs/dev/articles/prebuilt/2023_mesotrione_parent.html new file mode 100644 index 00000000..501639b6 --- /dev/null +++ b/docs/dev/articles/prebuilt/2023_mesotrione_parent.html @@ -0,0 +1,2499 @@ +<!DOCTYPE html> +<!-- Generated by pkgdown: do not edit by hand --><html lang="en"> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> +<meta charset="utf-8"> +<meta http-equiv="X-UA-Compatible" content="IE=edge"> +<meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"> +<title>Testing covariate modelling in hierarchical parent degradation kinetics with residue data on mesotrione • mkin</title> +<script src="../../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"> +<link href="../../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"> +<script src="../../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"> +<link href="../../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"> +<script src="../../deps/headroom-0.11.0/headroom.min.js"></script><script src="../../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../../deps/search-1.0.0/fuse.min.js"></script><script src="../../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../../pkgdown.js"></script><meta property="og:title" content="Testing covariate modelling in hierarchical parent degradation kinetics with residue data on mesotrione"> +<meta name="robots" content="noindex"> +</head> +<body> + <a href="#main" class="visually-hidden-focusable">Skip to contents</a> + + + <nav class="navbar navbar-expand-lg fixed-top bg-light" data-bs-theme="default" aria-label="Site navigation"><div class="container"> + + <a class="navbar-brand me-2" href="../../index.html">mkin</a> + + <small class="nav-text text-info me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="In-development version">1.2.10</small> + + + <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation"> + <span class="navbar-toggler-icon"></span> + </button> + + <div id="navbar" class="collapse navbar-collapse ms-3"> + <ul class="navbar-nav me-auto"> +<li class="nav-item"><a class="nav-link" href="../../reference/index.html">Reference</a></li> +<li class="active nav-item dropdown"> + <button class="nav-link dropdown-toggle" type="button" id="dropdown-articles" data-bs-toggle="dropdown" aria-expanded="false" aria-haspopup="true">Articles</button> + <ul class="dropdown-menu" aria-labelledby="dropdown-articles"> +<li><a class="dropdown-item" href="../../articles/mkin.html">Introduction to mkin</a></li> + <li><hr class="dropdown-divider"></li> + <li><h6 class="dropdown-header" data-toc-skip>Example evaluations with (generalised) nonlinear least squares</h6></li> + <li><a class="dropdown-item" href="../../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a></li> + <li><a class="dropdown-item" href="../../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a></li> + <li><a class="dropdown-item" href="../../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a></li> + <li><hr class="dropdown-divider"></li> + <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/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> + <li><hr class="dropdown-divider"></li> + <li><h6 class="dropdown-header" data-toc-skip>Performance</h6></li> + <li><a class="dropdown-item" href="../../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a></li> + <li><a class="dropdown-item" href="../../articles/web_only/benchmarks.html">Benchmark timings for mkin</a></li> + <li><a class="dropdown-item" href="../../articles/web_only/saem_benchmarks.html">Benchmark timings for saem.mmkin</a></li> + <li><hr class="dropdown-divider"></li> + <li><h6 class="dropdown-header" data-toc-skip>Miscellaneous</h6></li> + <li><a class="dropdown-item" href="../../articles/twa.html">Calculation of time weighted average concentrations with mkin</a></li> + <li><a class="dropdown-item" href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a></li> + </ul> +</li> +<li class="nav-item"><a class="nav-link" href="../../coverage/coverage.html">Test coverage</a></li> +<li class="nav-item"><a class="nav-link" href="../../news/index.html">News</a></li> + </ul> +<ul class="navbar-nav"> +<li class="nav-item"><form class="form-inline" role="search"> + <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../../search.json"> +</form></li> +<li class="nav-item"><a class="external-link nav-link" href="https://github.com/jranke/mkin/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li> + </ul> +</div> + + + </div> +</nav><div class="container template-article"> + + + + +<div class="row"> + <main id="main" class="col-md-9"><div class="page-header"> + + <h1>Testing covariate modelling in hierarchical parent degradation kinetics with residue data on mesotrione</h1> + <h4 data-toc-skip class="author">Johannes +Ranke</h4> + + <h4 data-toc-skip class="date">Last change on 4 August 2023, +last compiled on 16 Februar 2025</h4> + + <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/prebuilt/2023_mesotrione_parent.rmd" class="external-link"><code>vignettes/prebuilt/2023_mesotrione_parent.rmd</code></a></small> + <div class="d-none name"><code>2023_mesotrione_parent.rmd</code></div> + </div> + + + +<div class="section level2"> +<h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#introduction"></a> +</h2> +<p>The purpose of this document is to test demonstrate how nonlinear +hierarchical models (NLHM) based on the parent degradation models SFO, +FOMC, DFOP and HS can be fitted with the mkin package, also considering +the influence of covariates like soil pH on different degradation +parameters. Because in some other case studies, the SFORB +parameterisation of biexponential decline has shown some advantages over +the DFOP parameterisation, SFORB was included in the list of tested +models as well.</p> +<p>The mkin package is used in version 1.2.10, which is contains the +functions that were used for the evaluations. The <code>saemix</code> +package is used as a backend for fitting the NLHM, but is also loaded to +make the convergence plot function available.</p> +<p>This document is processed with the <code>knitr</code> package, which +also provides the <code>kable</code> function that is used to improve +the display of tabular data in R markdown documents. For parallel +processing, the <code>parallel</code> package is used.</p> +<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://pkgdown.jrwb.de/mkin/">mkin</a></span><span class="op">)</span></span> +<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://yihui.org/knitr/" class="external-link">knitr</a></span><span class="op">)</span></span> +<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">saemix</span><span class="op">)</span></span> +<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">parallel</span><span class="op">)</span></span> +<span><span class="va">n_cores</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/detectCores.html" class="external-link">detectCores</a></span><span class="op">(</span><span class="op">)</span></span> +<span><span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/Sys.info.html" class="external-link">Sys.info</a></span><span class="op">(</span><span class="op">)</span><span class="op">[</span><span class="st">"sysname"</span><span class="op">]</span> <span class="op">==</span> <span class="st">"Windows"</span><span class="op">)</span> <span class="op">{</span></span> +<span> <span class="va">cl</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makePSOCKcluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> +<span><span class="op">}</span> <span class="kw">else</span> <span class="op">{</span></span> +<span> <span class="va">cl</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makeForkCluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> +<span><span class="op">}</span></span></code></pre></div> +<div class="section level3"> +<h3 id="test-data">Test data<a class="anchor" aria-label="anchor" href="#test-data"></a> +</h3> +<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">data_file</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.file.html" class="external-link">system.file</a></span><span class="op">(</span></span> +<span> <span class="st">"testdata"</span>, <span class="st">"mesotrione_soil_efsa_2016.xlsx"</span>, package <span class="op">=</span> <span class="st">"mkin"</span><span class="op">)</span></span> +<span><span class="va">meso_ds</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/read_spreadsheet.html">read_spreadsheet</a></span><span class="op">(</span><span class="va">data_file</span>, parent_only <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<p>The following tables show the covariate data and the 18 datasets that +were read in from the spreadsheet file.</p> +<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">pH</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/attr.html" class="external-link">attr</a></span><span class="op">(</span><span class="va">meso_ds</span>, <span class="st">"covariates"</span><span class="op">)</span></span> +<span><span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="va">pH</span>, caption <span class="op">=</span> <span class="st">"Covariate data"</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<caption>Covariate data</caption> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">pH</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">Richmond</td> +<td align="right">6.2</td> +</tr> +<tr class="even"> +<td align="left">Richmond 2</td> +<td align="right">6.2</td> +</tr> +<tr class="odd"> +<td align="left">ERTC</td> +<td align="right">6.4</td> +</tr> +<tr class="even"> +<td align="left">Toulouse</td> +<td align="right">7.7</td> +</tr> +<tr class="odd"> +<td align="left">Picket Piece</td> +<td align="right">7.1</td> +</tr> +<tr class="even"> +<td align="left">721</td> +<td align="right">5.6</td> +</tr> +<tr class="odd"> +<td align="left">722</td> +<td align="right">5.7</td> +</tr> +<tr class="even"> +<td align="left">723</td> +<td align="right">5.4</td> +</tr> +<tr class="odd"> +<td align="left">724</td> +<td align="right">4.8</td> +</tr> +<tr class="even"> +<td align="left">725</td> +<td align="right">5.8</td> +</tr> +<tr class="odd"> +<td align="left">727</td> +<td align="right">5.1</td> +</tr> +<tr class="even"> +<td align="left">728</td> +<td align="right">5.9</td> +</tr> +<tr class="odd"> +<td align="left">729</td> +<td align="right">5.6</td> +</tr> +<tr class="even"> +<td align="left">730</td> +<td align="right">5.3</td> +</tr> +<tr class="odd"> +<td align="left">731</td> +<td align="right">6.1</td> +</tr> +<tr class="even"> +<td align="left">732</td> +<td align="right">5.0</td> +</tr> +<tr class="odd"> +<td align="left">741</td> +<td align="right">5.7</td> +</tr> +<tr class="even"> +<td align="left">742</td> +<td align="right">7.2</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="kw">for</span> <span class="op">(</span><span class="va">ds_name</span> <span class="kw">in</span> <span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">meso_ds</span><span class="op">)</span><span class="op">)</span> <span class="op">{</span></span> +<span> <span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span></span> +<span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="fu"><a href="../../reference/mkin_long_to_wide.html">mkin_long_to_wide</a></span><span class="op">(</span><span class="va">meso_ds</span><span class="op">[[</span><span class="va">ds_name</span><span class="op">]</span><span class="op">]</span><span class="op">)</span>,</span> +<span> caption <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste</a></span><span class="op">(</span><span class="st">"Dataset"</span>, <span class="va">ds_name</span><span class="op">)</span>,</span> +<span> booktabs <span class="op">=</span> <span class="cn">TRUE</span>, row.names <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="op">}</span></span></code></pre></div> +<table class="table"> +<caption>Dataset Richmond</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">91.00</td> +</tr> +<tr class="even"> +<td align="right">1.179050</td> +<td align="right">86.70</td> +</tr> +<tr class="odd"> +<td align="right">3.537149</td> +<td align="right">73.60</td> +</tr> +<tr class="even"> +<td align="right">7.074299</td> +<td align="right">61.50</td> +</tr> +<tr class="odd"> +<td align="right">10.611448</td> +<td align="right">55.70</td> +</tr> +<tr class="even"> +<td align="right">15.327647</td> +<td align="right">47.70</td> +</tr> +<tr class="odd"> +<td align="right">17.685747</td> +<td align="right">39.50</td> +</tr> +<tr class="even"> +<td align="right">24.760046</td> +<td align="right">29.80</td> +</tr> +<tr class="odd"> +<td align="right">35.371494</td> +<td align="right">19.60</td> +</tr> +<tr class="even"> +<td align="right">68.384889</td> +<td align="right">5.67</td> +</tr> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">97.90</td> +</tr> +<tr class="even"> +<td align="right">1.179050</td> +<td align="right">96.40</td> +</tr> +<tr class="odd"> +<td align="right">3.537149</td> +<td align="right">89.10</td> +</tr> +<tr class="even"> +<td align="right">7.074299</td> +<td align="right">74.40</td> +</tr> +<tr class="odd"> +<td align="right">10.611448</td> +<td align="right">57.40</td> +</tr> +<tr class="even"> +<td align="right">15.327647</td> +<td align="right">46.30</td> +</tr> +<tr class="odd"> +<td align="right">18.864797</td> +<td align="right">35.50</td> +</tr> +<tr class="even"> +<td align="right">27.118146</td> +<td align="right">27.20</td> +</tr> +<tr class="odd"> +<td align="right">35.371494</td> +<td align="right">19.10</td> +</tr> +<tr class="even"> +<td align="right">74.280138</td> +<td align="right">6.50</td> +</tr> +<tr class="odd"> +<td align="right">108.472582</td> +<td align="right">3.40</td> +</tr> +<tr class="even"> +<td align="right">142.665027</td> +<td align="right">2.20</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset Richmond 2</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">96.0</td> +</tr> +<tr class="even"> +<td align="right">2.422004</td> +<td align="right">82.4</td> +</tr> +<tr class="odd"> +<td align="right">5.651343</td> +<td align="right">71.2</td> +</tr> +<tr class="even"> +<td align="right">8.073348</td> +<td align="right">53.1</td> +</tr> +<tr class="odd"> +<td align="right">11.302687</td> +<td align="right">48.5</td> +</tr> +<tr class="even"> +<td align="right">16.954030</td> +<td align="right">33.4</td> +</tr> +<tr class="odd"> +<td align="right">22.605373</td> +<td align="right">24.2</td> +</tr> +<tr class="even"> +<td align="right">45.210746</td> +<td align="right">11.9</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset ERTC</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">99.9</td> +</tr> +<tr class="even"> +<td align="right">2.755193</td> +<td align="right">80.0</td> +</tr> +<tr class="odd"> +<td align="right">6.428782</td> +<td align="right">42.1</td> +</tr> +<tr class="even"> +<td align="right">9.183975</td> +<td align="right">50.1</td> +</tr> +<tr class="odd"> +<td align="right">12.857565</td> +<td align="right">28.4</td> +</tr> +<tr class="even"> +<td align="right">19.286347</td> +<td align="right">39.8</td> +</tr> +<tr class="odd"> +<td align="right">25.715130</td> +<td align="right">29.9</td> +</tr> +<tr class="even"> +<td align="right">51.430259</td> +<td align="right">2.5</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset Toulouse</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">96.8</td> +</tr> +<tr class="even"> +<td align="right">2.897983</td> +<td align="right">63.3</td> +</tr> +<tr class="odd"> +<td align="right">6.761960</td> +<td align="right">22.3</td> +</tr> +<tr class="even"> +<td align="right">9.659942</td> +<td align="right">16.6</td> +</tr> +<tr class="odd"> +<td align="right">13.523919</td> +<td align="right">16.1</td> +</tr> +<tr class="even"> +<td align="right">20.285879</td> +<td align="right">17.2</td> +</tr> +<tr class="odd"> +<td align="right">27.047838</td> +<td align="right">1.8</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset Picket Piece</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">102.0</td> +</tr> +<tr class="even"> +<td align="right">2.841195</td> +<td align="right">73.7</td> +</tr> +<tr class="odd"> +<td align="right">6.629454</td> +<td align="right">35.5</td> +</tr> +<tr class="even"> +<td align="right">9.470649</td> +<td align="right">31.8</td> +</tr> +<tr class="odd"> +<td align="right">13.258909</td> +<td align="right">18.0</td> +</tr> +<tr class="even"> +<td align="right">19.888364</td> +<td align="right">3.7</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 721</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">86.4</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">61.4</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">49.8</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">41.0</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">35.1</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 722</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">90.3</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">52.1</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">37.4</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">21.2</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">14.3</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 723</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">89.3</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">70.8</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">51.1</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">42.7</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">26.7</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 724</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">89.4</td> +</tr> +<tr class="even"> +<td align="right">9.008208</td> +<td align="right">65.2</td> +</tr> +<tr class="odd"> +<td align="right">18.016415</td> +<td align="right">55.8</td> +</tr> +<tr class="even"> +<td align="right">27.024623</td> +<td align="right">46.0</td> +</tr> +<tr class="odd"> +<td align="right">36.032831</td> +<td align="right">41.7</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 725</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">89.0</td> +</tr> +<tr class="even"> +<td align="right">10.99058</td> +<td align="right">35.4</td> +</tr> +<tr class="odd"> +<td align="right">21.98116</td> +<td align="right">18.6</td> +</tr> +<tr class="even"> +<td align="right">32.97174</td> +<td align="right">11.6</td> +</tr> +<tr class="odd"> +<td align="right">43.96232</td> +<td align="right">7.6</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 727</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">91.3</td> +</tr> +<tr class="even"> +<td align="right">10.96104</td> +<td align="right">63.2</td> +</tr> +<tr class="odd"> +<td align="right">21.92209</td> +<td align="right">51.1</td> +</tr> +<tr class="even"> +<td align="right">32.88313</td> +<td align="right">42.0</td> +</tr> +<tr class="odd"> +<td align="right">43.84417</td> +<td align="right">40.8</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 728</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">91.8</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">43.6</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">22.0</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">15.9</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">8.8</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 729</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">91.6</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">60.5</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">43.5</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">28.4</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">20.5</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 730</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">92.7</td> +</tr> +<tr class="even"> +<td align="right">11.07446</td> +<td align="right">58.9</td> +</tr> +<tr class="odd"> +<td align="right">22.14893</td> +<td align="right">44.0</td> +</tr> +<tr class="even"> +<td align="right">33.22339</td> +<td align="right">46.0</td> +</tr> +<tr class="odd"> +<td align="right">44.29785</td> +<td align="right">29.3</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 731</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">92.1</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">64.4</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">45.3</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">33.6</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">23.5</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 732</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">90.3</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">58.2</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">40.1</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">33.1</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">25.8</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 741</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">90.3</td> +</tr> +<tr class="even"> +<td align="right">10.84712</td> +<td align="right">68.7</td> +</tr> +<tr class="odd"> +<td align="right">21.69424</td> +<td align="right">58.0</td> +</tr> +<tr class="even"> +<td align="right">32.54136</td> +<td align="right">52.2</td> +</tr> +<tr class="odd"> +<td align="right">43.38848</td> +<td align="right">48.0</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 742</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">92.0</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">60.9</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">36.2</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">18.3</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">8.7</td> +</tr> +</tbody> +</table> +</div> +</div> +<div class="section level2"> +<h2 id="separate-evaluations">Separate evaluations<a class="anchor" aria-label="anchor" href="#separate-evaluations"></a> +</h2> +<p>In order to obtain suitable starting parameters for the NLHM fits, +separate fits of the five models to the data for each soil are generated +using the <code>mmkin</code> function from the mkin package. In a first +step, constant variance is assumed. Convergence is checked with the +<code>status</code> function.</p> +<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">deg_mods</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>, <span class="st">"SFORB"</span>, <span class="st">"HS"</span><span class="op">)</span></span> +<span><span class="va">f_sep_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span></span> +<span> <span class="va">deg_mods</span>,</span> +<span> <span class="va">meso_ds</span>,</span> +<span> error_model <span class="op">=</span> <span class="st">"const"</span>,</span> +<span> cluster <span class="op">=</span> <span class="va">cl</span>,</span> +<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span>, <span class="fl">1</span><span class="op">:</span><span class="fl">5</span><span class="op">]</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">Richmond</th> +<th align="left">Richmond 2</th> +<th align="left">ERTC</th> +<th align="left">Toulouse</th> +<th align="left">Picket Piece</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span>, <span class="fl">6</span><span class="op">:</span><span class="fl">18</span><span class="op">]</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<colgroup> +<col width="10%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +</colgroup> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">721</th> +<th align="left">722</th> +<th align="left">723</th> +<th align="left">724</th> +<th align="left">725</th> +<th align="left">727</th> +<th align="left">728</th> +<th align="left">729</th> +<th align="left">730</th> +<th align="left">731</th> +<th align="left">732</th> +<th align="left">741</th> +<th align="left">742</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<p>In the tables above, OK indicates convergence and C indicates failure +to converge. Most separate fits with constant variance converged, with +the exception of two FOMC fits, one SFORB fit and one HS fit.</p> +<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">f_sep_tc</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_sep_const</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_tc</span><span class="op">[</span>, <span class="fl">1</span><span class="op">:</span><span class="fl">5</span><span class="op">]</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">Richmond</th> +<th align="left">Richmond 2</th> +<th align="left">ERTC</th> +<th align="left">Toulouse</th> +<th align="left">Picket Piece</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_tc</span><span class="op">[</span>, <span class="fl">6</span><span class="op">:</span><span class="fl">18</span><span class="op">]</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<colgroup> +<col width="10%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +</colgroup> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">721</th> +<th align="left">722</th> +<th align="left">723</th> +<th align="left">724</th> +<th align="left">725</th> +<th align="left">727</th> +<th align="left">728</th> +<th align="left">729</th> +<th align="left">730</th> +<th align="left">731</th> +<th align="left">732</th> +<th align="left">741</th> +<th align="left">742</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<p>With the two-component error model, the set of fits that did not +converge is larger, with convergence problems appearing for a number of +non-SFO fits.</p> +</div> +<div class="section level2"> +<h2 id="hierarchical-model-fits-without-covariate-effect">Hierarchical model fits without covariate effect<a class="anchor" aria-label="anchor" href="#hierarchical-model-fits-without-covariate-effect"></a> +</h2> +<p>The following code fits hierarchical kinetic models for the ten +combinations of the five different degradation models with the two +different error models in parallel.</p> +<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">f_saem_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mhmkin.html">mhmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">f_sep_const</span>, <span class="va">f_sep_tc</span><span class="op">)</span>, cluster <span class="op">=</span> <span class="va">cl</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<p>All fits terminate without errors (status OK).</p> +<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">npar</th> +<th align="right">AIC</th> +<th align="right">BIC</th> +<th align="right">Lik</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO const</td> +<td align="right">5</td> +<td align="right">800.0</td> +<td align="right">804.5</td> +<td align="right">-395.0</td> +</tr> +<tr class="even"> +<td align="left">SFO tc</td> +<td align="right">6</td> +<td align="right">801.9</td> +<td align="right">807.2</td> +<td align="right">-394.9</td> +</tr> +<tr class="odd"> +<td align="left">FOMC const</td> +<td align="right">7</td> +<td align="right">787.4</td> +<td align="right">793.6</td> +<td align="right">-386.7</td> +</tr> +<tr class="even"> +<td align="left">FOMC tc</td> +<td align="right">8</td> +<td align="right">788.9</td> +<td align="right">796.1</td> +<td align="right">-386.5</td> +</tr> +<tr class="odd"> +<td align="left">DFOP const</td> +<td align="right">9</td> +<td align="right">787.6</td> +<td align="right">795.6</td> +<td align="right">-384.8</td> +</tr> +<tr class="even"> +<td align="left">SFORB const</td> +<td align="right">9</td> +<td align="right">787.4</td> +<td align="right">795.4</td> +<td align="right">-384.7</td> +</tr> +<tr class="odd"> +<td align="left">HS const</td> +<td align="right">9</td> +<td align="right">781.9</td> +<td align="right">789.9</td> +<td align="right">-382.0</td> +</tr> +<tr class="even"> +<td align="left">DFOP tc</td> +<td align="right">10</td> +<td align="right">787.4</td> +<td align="right">796.3</td> +<td align="right">-383.7</td> +</tr> +<tr class="odd"> +<td align="left">SFORB tc</td> +<td align="right">10</td> +<td align="right">795.8</td> +<td align="right">804.7</td> +<td align="right">-387.9</td> +</tr> +<tr class="even"> +<td align="left">HS tc</td> +<td align="right">10</td> +<td align="right">783.7</td> +<td align="right">792.7</td> +<td align="right">-381.9</td> +</tr> +</tbody> +</table> +<p>The model comparisons show that the fits with constant variance are +consistently preferable to the corresponding fits with two-component +error for these data. This is confirmed by the fact that the parameter +<code>b.1</code> (the relative standard deviation in the fits obtained +with the saemix package), is ill-defined in all fits.</p> +<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<colgroup> +<col width="6%"> +<col width="44%"> +<col width="49%"> +</colgroup> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">sd(meso_0)</td> +<td align="left">sd(meso_0), b.1</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">sd(meso_0), sd(log_beta)</td> +<td align="left">sd(meso_0), sd(log_beta), b.1</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">sd(meso_0), sd(log_k1)</td> +<td align="left">sd(meso_0), sd(g_qlogis), b.1</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">sd(meso_free_0), sd(log_k_meso_free_bound)</td> +<td align="left">sd(meso_free_0), sd(log_k_meso_free_bound), b.1</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">sd(meso_0)</td> +<td align="left">sd(meso_0), b.1</td> +</tr> +</tbody> +</table> +<p>For obtaining fits with only well-defined random effects, we update +the set of fits, excluding random effects that were ill-defined +according to the <code>illparms</code> function.</p> +<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">f_saem_2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_saem_1</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<p>The updated fits terminate without errors.</p> +<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left"></td> +<td align="left">b.1</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left"></td> +<td align="left">b.1</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left"></td> +<td align="left">b.1</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left"></td> +<td align="left">b.1</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left"></td> +<td align="left">b.1</td> +</tr> +</tbody> +</table> +<p>No ill-defined errors remain in the fits with constant variance.</p> +</div> +<div class="section level2"> +<h2 id="hierarchical-model-fits-with-covariate-effect">Hierarchical model fits with covariate effect<a class="anchor" aria-label="anchor" href="#hierarchical-model-fits-with-covariate-effect"></a> +</h2> +<p>In the following sections, hierarchical fits including a model for +the influence of pH on selected degradation parameters are shown for all +parent models. Constant variance is selected as the error model based on +the fits without covariate effects. Random effects that were ill-defined +in the fits without pH influence are excluded. A potential influence of +the soil pH is only included for parameters with a well-defined random +effect, because experience has shown that only for such parameters a +significant pH effect could be found.</p> +<div class="section level3"> +<h3 id="sfo">SFO<a class="anchor" aria-label="anchor" href="#sfo"></a> +</h3> +<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">sfo_pH</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="st">"meso_0"</span>, covariates <span class="op">=</span> <span class="va">pH</span>,</span> +<span> covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_k_meso</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">sfo_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_0</td> +<td align="right">91.35</td> +<td align="right">89.27</td> +<td align="right">93.43</td> +</tr> +<tr class="even"> +<td align="left">log_k_meso</td> +<td align="right">-6.66</td> +<td align="right">-7.97</td> +<td align="right">-5.35</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_k_meso)</td> +<td align="right">0.59</td> +<td align="right">0.37</td> +<td align="right">0.81</td> +</tr> +<tr class="even"> +<td align="left">a.1</td> +<td align="right">5.48</td> +<td align="right">4.71</td> +<td align="right">6.24</td> +</tr> +<tr class="odd"> +<td align="left">SD.log_k_meso</td> +<td align="right">0.35</td> +<td align="right">0.23</td> +<td align="right">0.47</td> +</tr> +</tbody> +</table> +<p>The parameter showing the pH influence in the above table is +<code>beta_pH(log_k_meso)</code>. Its confidence interval does not +include zero, indicating that the influence of soil pH on the log of the +degradation rate constant is significantly greater than zero.</p> +<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"SFO"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span>, <span class="va">sfo_pH</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets + + npar AIC BIC Lik Chisq Df Pr(>Chisq) +f_saem_2[["SFO", "const"]] 4 797.56 801.12 -394.78 +sfo_pH 5 783.09 787.54 -386.54 16.473 1 4.934e-05 *** +--- +Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre> +<p>The comparison with the SFO fit without covariate effect confirms +that considering the soil pH improves the model, both by comparison of +AIC and BIC and by the likelihood ratio test.</p> +<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">sfo_pH</span><span class="op">)</span></span></code></pre></div> +<p><img src="2023_mesotrione_parent_files/figure-html/unnamed-chunk-8-1.png" width="700" style="display: block; margin: auto;"></p> +<p>Endpoints for a model with covariates are by default calculated for +the median of the covariate values. This quantile can be adapted, or a +specific covariate value can be given as shown below.</p> +<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">sfo_pH</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +50% 5.75 + +$distimes + DT50 DT90 +meso 18.52069 61.52441</code></pre> +<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">sfo_pH</span>, covariate_quantile <span class="op">=</span> <span class="fl">0.9</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +90% 7.13 + +$distimes + DT50 DT90 +meso 8.237019 27.36278</code></pre> +<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">sfo_pH</span>, covariates <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>pH <span class="op">=</span> <span class="fl">7.0</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +User 7 + +$distimes + DT50 DT90 +meso 8.89035 29.5331</code></pre> +</div> +<div class="section level3"> +<h3 id="fomc">FOMC<a class="anchor" aria-label="anchor" href="#fomc"></a> +</h3> +<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">fomc_pH</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"FOMC"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="st">"meso_0"</span>, covariates <span class="op">=</span> <span class="va">pH</span>,</span> +<span> covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_alpha</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb28"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">fomc_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_0</td> +<td align="right">92.84</td> +<td align="right">90.75</td> +<td align="right">94.93</td> +</tr> +<tr class="even"> +<td align="left">log_alpha</td> +<td align="right">-2.21</td> +<td align="right">-3.49</td> +<td align="right">-0.92</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_alpha)</td> +<td align="right">0.58</td> +<td align="right">0.37</td> +<td align="right">0.79</td> +</tr> +<tr class="even"> +<td align="left">log_beta</td> +<td align="right">4.21</td> +<td align="right">3.44</td> +<td align="right">4.99</td> +</tr> +<tr class="odd"> +<td align="left">a.1</td> +<td align="right">5.03</td> +<td align="right">4.32</td> +<td align="right">5.73</td> +</tr> +<tr class="even"> +<td align="left">SD.log_alpha</td> +<td align="right">0.00</td> +<td align="right">-23.77</td> +<td align="right">23.78</td> +</tr> +<tr class="odd"> +<td align="left">SD.log_beta</td> +<td align="right">0.37</td> +<td align="right">0.01</td> +<td align="right">0.74</td> +</tr> +</tbody> +</table> +<p>As in the case of SFO, the confidence interval of the slope parameter +(here <code>beta_pH(log_alpha)</code>) quantifying the influence of soil +pH does not include zero, and the model comparison clearly indicates +that the model with covariate influence is preferable. However, the +random effect for <code>alpha</code> is not well-defined any more after +inclusion of the covariate effect (the confidence interval of +<code>SD.log_alpha</code> includes zero).</p> +<div class="sourceCode" id="cb29"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">fomc_pH</span><span class="op">)</span></span></code></pre></div> +<pre><code>[1] "sd(log_alpha)"</code></pre> +<p>Therefore, the model is updated without this random effect, and no +ill-defined parameters remain.</p> +<div class="sourceCode" id="cb31"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">fomc_pH_2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">fomc_pH</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_0"</span>, <span class="st">"log_alpha"</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">fomc_pH_2</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb32"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"FOMC"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span>, <span class="va">fomc_pH</span>, <span class="va">fomc_pH_2</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets + + npar AIC BIC Lik Chisq Df Pr(>Chisq) +f_saem_2[["FOMC", "const"]] 5 783.25 787.71 -386.63 +fomc_pH_2 6 767.49 772.83 -377.75 17.762 1 2.503e-05 *** +fomc_pH 7 770.07 776.30 -378.04 0.000 1 1 +--- +Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre> +<p>Model comparison indicates that including pH dependence significantly +improves the fit, and that the reduced model with covariate influence +results in the most preferable FOMC fit.</p> +<div class="sourceCode" id="cb34"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">fomc_pH_2</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_0</td> +<td align="right">93.05</td> +<td align="right">90.98</td> +<td align="right">95.13</td> +</tr> +<tr class="even"> +<td align="left">log_alpha</td> +<td align="right">-2.91</td> +<td align="right">-4.18</td> +<td align="right">-1.63</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_alpha)</td> +<td align="right">0.66</td> +<td align="right">0.44</td> +<td align="right">0.87</td> +</tr> +<tr class="even"> +<td align="left">log_beta</td> +<td align="right">3.95</td> +<td align="right">3.29</td> +<td align="right">4.62</td> +</tr> +<tr class="odd"> +<td align="left">a.1</td> +<td align="right">4.98</td> +<td align="right">4.28</td> +<td align="right">5.68</td> +</tr> +<tr class="even"> +<td align="left">SD.log_beta</td> +<td align="right">0.40</td> +<td align="right">0.26</td> +<td align="right">0.54</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb35"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">fomc_pH_2</span><span class="op">)</span></span></code></pre></div> +<p><img src="2023_mesotrione_parent_files/figure-html/unnamed-chunk-14-1.png" width="700" style="display: block; margin: auto;"></p> +<div class="sourceCode" id="cb36"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">fomc_pH_2</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +50% 5.75 + +$distimes + DT50 DT90 DT50back +meso 17.30248 82.91343 24.95943</code></pre> +<div class="sourceCode" id="cb38"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">fomc_pH_2</span>, covariates <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>pH <span class="op">=</span> <span class="fl">7</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +User 7 + +$distimes + DT50 DT90 DT50back +meso 6.986239 27.02927 8.136621</code></pre> +</div> +<div class="section level3"> +<h3 id="dfop">DFOP<a class="anchor" aria-label="anchor" href="#dfop"></a> +</h3> +<p>In the DFOP fits without covariate effects, random effects for two +degradation parameters (<code>k2</code> and <code>g</code>) were +identifiable.</p> +<div class="sourceCode" id="cb40"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_0</td> +<td align="right">93.61</td> +<td align="right">91.58</td> +<td align="right">95.63</td> +</tr> +<tr class="even"> +<td align="left">log_k1</td> +<td align="right">-1.53</td> +<td align="right">-2.27</td> +<td align="right">-0.79</td> +</tr> +<tr class="odd"> +<td align="left">log_k2</td> +<td align="right">-3.42</td> +<td align="right">-3.73</td> +<td align="right">-3.11</td> +</tr> +<tr class="even"> +<td align="left">g_qlogis</td> +<td align="right">-1.67</td> +<td align="right">-2.57</td> +<td align="right">-0.77</td> +</tr> +<tr class="odd"> +<td align="left">a.1</td> +<td align="right">4.74</td> +<td align="right">4.02</td> +<td align="right">5.45</td> +</tr> +<tr class="even"> +<td align="left">SD.log_k2</td> +<td align="right">0.60</td> +<td align="right">0.38</td> +<td align="right">0.81</td> +</tr> +<tr class="odd"> +<td align="left">SD.g_qlogis</td> +<td align="right">0.94</td> +<td align="right">0.33</td> +<td align="right">1.54</td> +</tr> +</tbody> +</table> +<p>A fit with pH dependent degradation parameters was obtained by +excluding the same random effects as in the refined DFOP fit without +covariate influence, and including covariate models for the two +identifiable parameters <code>k2</code> and <code>g</code>.</p> +<div class="sourceCode" id="cb41"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">dfop_pH</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_0"</span>, <span class="st">"log_k1"</span><span class="op">)</span>,</span> +<span> covariates <span class="op">=</span> <span class="va">pH</span>,</span> +<span> covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_k2</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">g_qlogis</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<p>The corresponding parameters for the influence of soil pH are +<code>beta_pH(log_k2)</code> for the influence of soil pH on +<code>k2</code>, and <code>beta_pH(g_qlogis)</code> for its influence on +<code>g</code>.</p> +<div class="sourceCode" id="cb42"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">dfop_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_0</td> +<td align="right">92.84</td> +<td align="right">90.85</td> +<td align="right">94.84</td> +</tr> +<tr class="even"> +<td align="left">log_k1</td> +<td align="right">-2.82</td> +<td align="right">-3.09</td> +<td align="right">-2.54</td> +</tr> +<tr class="odd"> +<td align="left">log_k2</td> +<td align="right">-11.48</td> +<td align="right">-15.32</td> +<td align="right">-7.64</td> +</tr> +<tr class="even"> +<td align="left">beta_pH(log_k2)</td> +<td align="right">1.31</td> +<td align="right">0.69</td> +<td align="right">1.92</td> +</tr> +<tr class="odd"> +<td align="left">g_qlogis</td> +<td align="right">3.13</td> +<td align="right">0.47</td> +<td align="right">5.80</td> +</tr> +<tr class="even"> +<td align="left">beta_pH(g_qlogis)</td> +<td align="right">-0.57</td> +<td align="right">-1.04</td> +<td align="right">-0.09</td> +</tr> +<tr class="odd"> +<td align="left">a.1</td> +<td align="right">4.96</td> +<td align="right">4.26</td> +<td align="right">5.65</td> +</tr> +<tr class="even"> +<td align="left">SD.log_k2</td> +<td align="right">0.76</td> +<td align="right">0.47</td> +<td align="right">1.05</td> +</tr> +<tr class="odd"> +<td align="left">SD.g_qlogis</td> +<td align="right">0.01</td> +<td align="right">-9.96</td> +<td align="right">9.97</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb43"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">dfop_pH</span><span class="op">)</span></span></code></pre></div> +<pre><code>[1] "sd(g_qlogis)"</code></pre> +<p>Confidence intervals for neither of them include zero, indicating a +significant difference from zero. However, the random effect for +<code>g</code> is now ill-defined. The fit is updated without this +ill-defined random effect.</p> +<div class="sourceCode" id="cb45"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">dfop_pH_2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">dfop_pH</span>,</span> +<span> no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_0"</span>, <span class="st">"log_k1"</span>, <span class="st">"g_qlogis"</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">dfop_pH_2</span><span class="op">)</span></span></code></pre></div> +<pre><code>[1] "beta_pH(g_qlogis)"</code></pre> +<p>Now, the slope parameter for the pH effect on <code>g</code> is +ill-defined. Therefore, another attempt is made without the +corresponding covariate model.</p> +<div class="sourceCode" id="cb47"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">dfop_pH_3</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_0"</span>, <span class="st">"log_k1"</span><span class="op">)</span>,</span> +<span> covariates <span class="op">=</span> <span class="va">pH</span>,</span> +<span> covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_k2</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">dfop_pH_3</span><span class="op">)</span></span></code></pre></div> +<pre><code>[1] "sd(g_qlogis)"</code></pre> +<p>As the random effect for <code>g</code> is again ill-defined, the fit +is repeated without it.</p> +<div class="sourceCode" id="cb49"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">dfop_pH_4</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">dfop_pH_3</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_0"</span>, <span class="st">"log_k1"</span>, <span class="st">"g_qlogis"</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">dfop_pH_4</span><span class="op">)</span></span></code></pre></div> +<p>While no ill-defined parameters remain, model comparison suggests +that the previous model <code>dfop_pH_2</code> with two pH dependent +parameters is preferable, based on information criteria as well as based +on the likelihood ratio test.</p> +<div class="sourceCode" id="cb50"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span>, <span class="va">dfop_pH</span>, <span class="va">dfop_pH_2</span>, <span class="va">dfop_pH_3</span>, <span class="va">dfop_pH_4</span><span class="op">)</span></span></code></pre></div> +<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets + + npar AIC BIC Lik +f_saem_2[["DFOP", "const"]] 7 782.94 789.18 -384.47 +dfop_pH_4 7 767.35 773.58 -376.68 +dfop_pH_2 8 765.14 772.26 -374.57 +dfop_pH_3 8 769.00 776.12 -376.50 +dfop_pH 9 769.10 777.11 -375.55</code></pre> +<div class="sourceCode" id="cb52"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">dfop_pH_2</span>, <span class="va">dfop_pH_4</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets + + npar AIC BIC Lik Chisq Df Pr(>Chisq) +dfop_pH_4 7 767.35 773.58 -376.68 +dfop_pH_2 8 765.14 772.26 -374.57 4.2153 1 0.04006 * +--- +Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre> +<p>When focussing on parameter identifiability using the test if the +confidence interval includes zero, <code>dfop_pH_4</code> would still be +the preferred model. However, it should be kept in mind that parameter +confidence intervals are constructed using a simple linearisation of the +likelihood. As the confidence interval of the random effect for +<code>g</code> only marginally includes zero, it is suggested that this +is acceptable, and that <code>dfop_pH_2</code> can be considered the +most preferable model.</p> +<div class="sourceCode" id="cb54"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">dfop_pH_2</span><span class="op">)</span></span></code></pre></div> +<p><img src="2023_mesotrione_parent_files/figure-html/unnamed-chunk-19-1.png" width="700" style="display: block; margin: auto;"></p> +<div class="sourceCode" id="cb55"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">dfop_pH_2</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +50% 5.75 + +$distimes + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 18.36876 73.51841 22.13125 4.191901 23.98672</code></pre> +<div class="sourceCode" id="cb57"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">dfop_pH_2</span>, covariates <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>pH <span class="op">=</span> <span class="fl">7</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +User 7 + +$distimes + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 8.346428 28.34437 8.532507 4.191901 8.753618</code></pre> +</div> +<div class="section level3"> +<h3 id="sforb">SFORB<a class="anchor" aria-label="anchor" href="#sforb"></a> +</h3> +<div class="sourceCode" id="cb59"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">sforb_pH</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"SFORB"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_free_0"</span>, <span class="st">"log_k_meso_free_bound"</span><span class="op">)</span>,</span> +<span> covariates <span class="op">=</span> <span class="va">pH</span>,</span> +<span> covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_k_meso_free</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">log_k_meso_bound_free</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb60"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">sforb_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_free_0</td> +<td align="right">93.42</td> +<td align="right">91.32</td> +<td align="right">95.52</td> +</tr> +<tr class="even"> +<td align="left">log_k_meso_free</td> +<td align="right">-5.37</td> +<td align="right">-6.94</td> +<td align="right">-3.81</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_k_meso_free)</td> +<td align="right">0.42</td> +<td align="right">0.18</td> +<td align="right">0.67</td> +</tr> +<tr class="even"> +<td align="left">log_k_meso_free_bound</td> +<td align="right">-3.49</td> +<td align="right">-4.92</td> +<td align="right">-2.05</td> +</tr> +<tr class="odd"> +<td align="left">log_k_meso_bound_free</td> +<td align="right">-9.98</td> +<td align="right">-19.22</td> +<td align="right">-0.74</td> +</tr> +<tr class="even"> +<td align="left">beta_pH(log_k_meso_bound_free)</td> +<td align="right">1.23</td> +<td align="right">-0.21</td> +<td align="right">2.67</td> +</tr> +<tr class="odd"> +<td align="left">a.1</td> +<td align="right">4.90</td> +<td align="right">4.18</td> +<td align="right">5.63</td> +</tr> +<tr class="even"> +<td align="left">SD.log_k_meso_free</td> +<td align="right">0.35</td> +<td align="right">0.23</td> +<td align="right">0.47</td> +</tr> +<tr class="odd"> +<td align="left">SD.log_k_meso_bound_free</td> +<td align="right">0.13</td> +<td align="right">-1.95</td> +<td align="right">2.20</td> +</tr> +</tbody> +</table> +<p>The confidence interval of +<code>beta_pH(log_k_meso_bound_free)</code> includes zero, indicating +that the influence of soil pH on <code>k_meso_bound_free</code> cannot +reliably be quantified. Also, the confidence interval for the random +effect on this parameter (<code>SD.log_k_meso_bound_free</code>) +includes zero.</p> +<p>Using the <code>illparms</code> function, these ill-defined +parameters can be found more conveniently.</p> +<div class="sourceCode" id="cb61"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">sforb_pH</span><span class="op">)</span></span></code></pre></div> +<pre><code>[1] "sd(log_k_meso_bound_free)" "beta_pH(log_k_meso_bound_free)"</code></pre> +<p>To remove the ill-defined parameters, a second variant of the SFORB +model with pH influence is fitted. No ill-defined parameters remain.</p> +<div class="sourceCode" id="cb63"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">sforb_pH_2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">sforb_pH</span>,</span> +<span> no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_free_0"</span>, <span class="st">"log_k_meso_free_bound"</span>, <span class="st">"log_k_meso_bound_free"</span><span class="op">)</span>,</span> +<span> covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_k_meso_free</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">sforb_pH_2</span><span class="op">)</span></span></code></pre></div> +<p>The model comparison of the SFORB fits includes the refined model +without covariate effect, and both versions of the SFORB fit with +covariate effect.</p> +<div class="sourceCode" id="cb64"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"SFORB"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span>, <span class="va">sforb_pH</span>, <span class="va">sforb_pH_2</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets + + npar AIC BIC Lik Chisq Df Pr(>Chisq) +f_saem_2[["SFORB", "const"]] 7 783.40 789.63 -384.70 +sforb_pH_2 7 770.94 777.17 -378.47 12.4616 0 +sforb_pH 9 768.81 776.83 -375.41 6.1258 2 0.04675 * +--- +Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre> +<p>The first model including pH influence is preferable based on +information criteria and the likelihood ratio test. However, as it is +not fully identifiable, the second model is selected.</p> +<div class="sourceCode" id="cb66"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">sforb_pH_2</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_free_0</td> +<td align="right">93.32</td> +<td align="right">91.16</td> +<td align="right">95.48</td> +</tr> +<tr class="even"> +<td align="left">log_k_meso_free</td> +<td align="right">-6.15</td> +<td align="right">-7.43</td> +<td align="right">-4.86</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_k_meso_free)</td> +<td align="right">0.54</td> +<td align="right">0.33</td> +<td align="right">0.75</td> +</tr> +<tr class="even"> +<td align="left">log_k_meso_free_bound</td> +<td align="right">-3.80</td> +<td align="right">-5.20</td> +<td align="right">-2.40</td> +</tr> +<tr class="odd"> +<td align="left">log_k_meso_bound_free</td> +<td align="right">-2.95</td> +<td align="right">-4.26</td> +<td align="right">-1.64</td> +</tr> +<tr class="even"> +<td align="left">a.1</td> +<td align="right">5.08</td> +<td align="right">4.38</td> +<td align="right">5.79</td> +</tr> +<tr class="odd"> +<td align="left">SD.log_k_meso_free</td> +<td align="right">0.33</td> +<td align="right">0.22</td> +<td align="right">0.45</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb67"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">sforb_pH_2</span><span class="op">)</span></span></code></pre></div> +<p><img src="2023_mesotrione_parent_files/figure-html/unnamed-chunk-25-1.png" width="700" style="display: block; margin: auto;"></p> +<div class="sourceCode" id="cb68"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">sforb_pH_2</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +50% 5.75 + +$ff +meso_free + 1 + +$SFORB + meso_b1 meso_b2 meso_g +0.09735824 0.02631699 0.31602120 + +$distimes + DT50 DT90 DT50back DT50_meso_b1 DT50_meso_b2 +meso 16.86549 73.15824 22.02282 7.119554 26.33839</code></pre> +<div class="sourceCode" id="cb70"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">sforb_pH_2</span>, covariates <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>pH <span class="op">=</span> <span class="fl">7</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +User 7 + +$ff +meso_free + 1 + +$SFORB + meso_b1 meso_b2 meso_g +0.13315233 0.03795988 0.61186191 + +$distimes + DT50 DT90 DT50back DT50_meso_b1 DT50_meso_b2 +meso 7.932495 36.93311 11.11797 5.205671 18.26</code></pre> +</div> +<div class="section level3"> +<h3 id="hs">HS<a class="anchor" aria-label="anchor" href="#hs"></a> +</h3> +<div class="sourceCode" id="cb72"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">hs_pH</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"HS"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_0"</span><span class="op">)</span>,</span> +<span> covariates <span class="op">=</span> <span class="va">pH</span>,</span> +<span> covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_k1</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">log_k2</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">log_tb</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb73"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">hs_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_0</td> +<td align="right">93.33</td> +<td align="right">91.47</td> +<td align="right">95.19</td> +</tr> +<tr class="even"> +<td align="left">log_k1</td> +<td align="right">-5.81</td> +<td align="right">-7.27</td> +<td align="right">-4.36</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_k1)</td> +<td align="right">0.47</td> +<td align="right">0.23</td> +<td align="right">0.72</td> +</tr> +<tr class="even"> +<td align="left">log_k2</td> +<td align="right">-6.80</td> +<td align="right">-8.76</td> +<td align="right">-4.83</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_k2)</td> +<td align="right">0.54</td> +<td align="right">0.21</td> +<td align="right">0.87</td> +</tr> +<tr class="even"> +<td align="left">log_tb</td> +<td align="right">3.25</td> +<td align="right">1.25</td> +<td align="right">5.25</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_tb)</td> +<td align="right">-0.10</td> +<td align="right">-0.43</td> +<td align="right">0.23</td> +</tr> +<tr class="even"> +<td align="left">a.1</td> +<td align="right">4.49</td> +<td align="right">3.78</td> +<td align="right">5.21</td> +</tr> +<tr class="odd"> +<td align="left">SD.log_k1</td> +<td align="right">0.37</td> +<td align="right">0.24</td> +<td align="right">0.51</td> +</tr> +<tr class="even"> +<td align="left">SD.log_k2</td> +<td align="right">0.29</td> +<td align="right">0.10</td> +<td align="right">0.48</td> +</tr> +<tr class="odd"> +<td align="left">SD.log_tb</td> +<td align="right">0.25</td> +<td align="right">-0.07</td> +<td align="right">0.57</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb74"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">hs_pH</span><span class="op">)</span></span></code></pre></div> +<pre><code>[1] "sd(log_tb)" "beta_pH(log_tb)"</code></pre> +<p>According to the output of the <code>illparms</code> function, the +random effect on the break time <code>tb</code> cannot reliably be +quantified, neither can the influence of soil pH on <code>tb</code>. The +fit is repeated without the corresponding covariate model, and no +ill-defined parameters remain.</p> +<div class="sourceCode" id="cb76"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">hs_pH_2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">hs_pH</span>, covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_k1</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">log_k2</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">hs_pH_2</span><span class="op">)</span></span></code></pre></div> +<p>Model comparison confirms that this model is preferable to the fit +without covariate influence, and also to the first version with +covariate influence.</p> +<div class="sourceCode" id="cb77"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"HS"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span>, <span class="va">hs_pH</span>, <span class="va">hs_pH_2</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets + + npar AIC BIC Lik Chisq Df Pr(>Chisq) +f_saem_2[["HS", "const"]] 8 780.08 787.20 -382.04 +hs_pH_2 10 766.47 775.37 -373.23 17.606 2 0.0001503 *** +hs_pH 11 769.80 779.59 -373.90 0.000 1 1.0000000 +--- +Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre> +<div class="sourceCode" id="cb79"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">hs_pH_2</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_0</td> +<td align="right">93.33</td> +<td align="right">91.50</td> +<td align="right">95.15</td> +</tr> +<tr class="even"> +<td align="left">log_k1</td> +<td align="right">-5.68</td> +<td align="right">-7.09</td> +<td align="right">-4.27</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_k1)</td> +<td align="right">0.46</td> +<td align="right">0.22</td> +<td align="right">0.69</td> +</tr> +<tr class="even"> +<td align="left">log_k2</td> +<td align="right">-6.61</td> +<td align="right">-8.34</td> +<td align="right">-4.88</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_k2)</td> +<td align="right">0.50</td> +<td align="right">0.21</td> +<td align="right">0.79</td> +</tr> +<tr class="even"> +<td align="left">log_tb</td> +<td align="right">2.70</td> +<td align="right">2.33</td> +<td align="right">3.08</td> +</tr> +<tr class="odd"> +<td align="left">a.1</td> +<td align="right">4.45</td> +<td align="right">3.74</td> +<td align="right">5.16</td> +</tr> +<tr class="even"> +<td align="left">SD.log_k1</td> +<td align="right">0.36</td> +<td align="right">0.22</td> +<td align="right">0.49</td> +</tr> +<tr class="odd"> +<td align="left">SD.log_k2</td> +<td align="right">0.23</td> +<td align="right">0.02</td> +<td align="right">0.43</td> +</tr> +<tr class="even"> +<td align="left">SD.log_tb</td> +<td align="right">0.55</td> +<td align="right">0.25</td> +<td align="right">0.85</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb80"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">hs_pH_2</span><span class="op">)</span></span></code></pre></div> +<p><img src="2023_mesotrione_parent_files/figure-html/unnamed-chunk-30-1.png" width="700" style="display: block; margin: auto;"></p> +<div class="sourceCode" id="cb81"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">hs_pH_2</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +50% 5.75 + +$distimes + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 14.68725 82.45287 24.82079 14.68725 29.29299</code></pre> +<div class="sourceCode" id="cb83"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">hs_pH_2</span>, covariates <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>pH <span class="op">=</span> <span class="fl">7</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +User 7 + +$distimes + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 8.298536 38.85371 11.69613 8.298536 15.71561</code></pre> +</div> +<div class="section level3"> +<h3 id="comparison-across-parent-models">Comparison across parent models<a class="anchor" aria-label="anchor" href="#comparison-across-parent-models"></a> +</h3> +<p>After model reduction for all models with pH influence, they are +compared with each other.</p> +<div class="sourceCode" id="cb85"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">sfo_pH</span>, <span class="va">fomc_pH_2</span>, <span class="va">dfop_pH_2</span>, <span class="va">dfop_pH_4</span>, <span class="va">sforb_pH_2</span>, <span class="va">hs_pH_2</span><span class="op">)</span></span></code></pre></div> +<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets + + npar AIC BIC Lik +sfo_pH 5 783.09 787.54 -386.54 +fomc_pH_2 6 767.49 772.83 -377.75 +dfop_pH_4 7 767.35 773.58 -376.68 +sforb_pH_2 7 770.94 777.17 -378.47 +dfop_pH_2 8 765.14 772.26 -374.57 +hs_pH_2 10 766.47 775.37 -373.23</code></pre> +<p>The DFOP model with pH influence on <code>k2</code> and +<code>g</code> and a random effect only on <code>k2</code> is finally +selected as the best fit.</p> +<p>The endpoints resulting from this model are listed below. Please +refer to the Appendix for a detailed listing.</p> +<div class="sourceCode" id="cb87"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">dfop_pH_2</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +50% 5.75 + +$distimes + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 18.36876 73.51841 22.13125 4.191901 23.98672</code></pre> +<div class="sourceCode" id="cb89"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">dfop_pH_2</span>, covariates <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>pH <span class="op">=</span> <span class="fl">7</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +User 7 + +$distimes + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 8.346428 28.34437 8.532507 4.191901 8.753618</code></pre> +</div> +</div> +<div class="section level2"> +<h2 id="conclusions">Conclusions<a class="anchor" aria-label="anchor" href="#conclusions"></a> +</h2> +<p>These evaluations demonstrate that covariate effects can be included +for all types of parent degradation models. These models can then be +further refined to make them fully identifiable.</p> +</div> +<div class="section level2"> +<h2 id="appendix">Appendix<a class="anchor" aria-label="anchor" href="#appendix"></a> +</h2> +<div class="section level3"> +<h3 id="hierarchical-fit-listings">Hierarchical fit listings<a class="anchor" aria-label="anchor" href="#hierarchical-fit-listings"></a> +</h3> +<div class="section level4"> +<h4 id="fits-without-covariate-effects">Fits without covariate effects<a class="anchor" aria-label="anchor" href="#fits-without-covariate-effects"></a> +</h4> + +</div> +<div class="section level4"> +<h4 id="fits-with-covariate-effects">Fits with covariate effects<a class="anchor" aria-label="anchor" href="#fits-with-covariate-effects"></a> +</h4> + +</div> +</div> +<div class="section level3"> +<h3 id="session-info">Session info<a class="anchor" aria-label="anchor" href="#session-info"></a> +</h3> +<pre><code>R version 4.4.2 (2024-10-31) +Platform: x86_64-pc-linux-gnu +Running under: Debian GNU/Linux 12 (bookworm) + +Matrix products: default +BLAS: /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.11.0 +LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.11.0 + +locale: + [1] LC_CTYPE=de_DE.UTF-8 LC_NUMERIC=C + [3] LC_TIME=de_DE.UTF-8 LC_COLLATE=de_DE.UTF-8 + [5] LC_MONETARY=de_DE.UTF-8 LC_MESSAGES=de_DE.UTF-8 + [7] LC_PAPER=de_DE.UTF-8 LC_NAME=C + [9] LC_ADDRESS=C LC_TELEPHONE=C +[11] LC_MEASUREMENT=de_DE.UTF-8 LC_IDENTIFICATION=C + +time zone: Europe/Berlin +tzcode source: system (glibc) + +attached base packages: +[1] parallel stats graphics grDevices utils datasets methods +[8] base + +other attached packages: +[1] saemix_3.3 npde_3.5 knitr_1.49 mkin_1.2.10 + +loaded via a namespace (and not attached): + [1] gtable_0.3.6 jsonlite_1.8.9 dplyr_1.1.4 compiler_4.4.2 + [5] tidyselect_1.2.1 gridExtra_2.3 jquerylib_0.1.4 systemfonts_1.1.0 + [9] scales_1.3.0 textshaping_0.4.1 yaml_2.3.10 fastmap_1.2.0 +[13] lattice_0.22-6 ggplot2_3.5.1 R6_2.5.1 generics_0.1.3 +[17] lmtest_0.9-40 MASS_7.3-61 htmlwidgets_1.6.4 tibble_3.2.1 +[21] desc_1.4.3 munsell_0.5.1 bslib_0.8.0 pillar_1.9.0 +[25] rlang_1.1.4 utf8_1.2.4 cachem_1.1.0 xfun_0.49 +[29] fs_1.6.5 sass_0.4.9 cli_3.6.3 pkgdown_2.1.1 +[33] magrittr_2.0.3 digest_0.6.37 grid_4.4.2 mclust_6.1.1 +[37] lifecycle_1.0.4 nlme_3.1-166 vctrs_0.6.5 evaluate_1.0.1 +[41] glue_1.8.0 ragg_1.3.3 zoo_1.8-12 fansi_1.0.6 +[45] colorspace_2.1-1 rmarkdown_2.29 pkgconfig_2.0.3 tools_4.4.2 +[49] htmltools_0.5.8.1</code></pre> +</div> +<div class="section level3"> +<h3 id="hardware-info">Hardware info<a class="anchor" aria-label="anchor" href="#hardware-info"></a> +</h3> +<pre><code>CPU model: AMD Ryzen 9 7950X 16-Core Processor</code></pre> +<pre><code>MemTotal: 64927788 kB</code></pre> +</div> +</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/dev/articles/prebuilt/2023_mesotrione_parent_files/figure-html/unnamed-chunk-14-1.png b/docs/dev/articles/prebuilt/2023_mesotrione_parent_files/figure-html/unnamed-chunk-14-1.png Binary files differnew file mode 100644 index 00000000..719bf0e9 --- /dev/null +++ b/docs/dev/articles/prebuilt/2023_mesotrione_parent_files/figure-html/unnamed-chunk-14-1.png diff --git a/docs/dev/articles/prebuilt/2023_mesotrione_parent_files/figure-html/unnamed-chunk-19-1.png b/docs/dev/articles/prebuilt/2023_mesotrione_parent_files/figure-html/unnamed-chunk-19-1.png Binary files differnew file mode 100644 index 00000000..6afcac48 --- /dev/null +++ b/docs/dev/articles/prebuilt/2023_mesotrione_parent_files/figure-html/unnamed-chunk-19-1.png diff --git a/docs/dev/articles/prebuilt/2023_mesotrione_parent_files/figure-html/unnamed-chunk-25-1.png b/docs/dev/articles/prebuilt/2023_mesotrione_parent_files/figure-html/unnamed-chunk-25-1.png Binary files differnew file mode 100644 index 00000000..50253fb1 --- /dev/null +++ b/docs/dev/articles/prebuilt/2023_mesotrione_parent_files/figure-html/unnamed-chunk-25-1.png diff --git a/docs/dev/articles/prebuilt/2023_mesotrione_parent_files/figure-html/unnamed-chunk-30-1.png b/docs/dev/articles/prebuilt/2023_mesotrione_parent_files/figure-html/unnamed-chunk-30-1.png Binary files differnew file mode 100644 index 00000000..c8b77724 --- /dev/null +++ b/docs/dev/articles/prebuilt/2023_mesotrione_parent_files/figure-html/unnamed-chunk-30-1.png diff --git a/docs/dev/articles/prebuilt/2023_mesotrione_parent_files/figure-html/unnamed-chunk-8-1.png b/docs/dev/articles/prebuilt/2023_mesotrione_parent_files/figure-html/unnamed-chunk-8-1.png Binary files differnew file mode 100644 index 00000000..8fa204a3 --- /dev/null +++ b/docs/dev/articles/prebuilt/2023_mesotrione_parent_files/figure-html/unnamed-chunk-8-1.png |
