diff options
| author | Johannes Ranke <jranke@uni-bremen.de> | 2023-04-20 20:17:12 +0200 |
|---|---|---|
| committer | Johannes Ranke <jranke@uni-bremen.de> | 2023-04-20 20:17:12 +0200 |
| commit | 7b7c4bf493ba15824ea43bed764661678b4aca03 (patch) | |
| tree | 48de1e32327c36ee49fc476dc76ece8397ab55c6 /docs/articles | |
| parent | 842998b688037c007d8876d7e1110c929fe2374c (diff) | |
| parent | 9ae42bd20bc2543a94cf1581ba9820c2f9e3afbd (diff) | |
Merge branch 'v1.2.3_pkgdown'
Diffstat (limited to 'docs/articles')
92 files changed, 11684 insertions, 516 deletions
diff --git a/docs/articles/FOCUS_D.html b/docs/articles/FOCUS_D.html index 3c8ad547..0d2f56f5 100644 --- a/docs/articles/FOCUS_D.html +++ b/docs/articles/FOCUS_D.html @@ -33,14 +33,14 @@ </button> <span class="navbar-brand"> <a class="navbar-link" href="../index.html">mkin</a> - <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">1.2.0</span> + <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">1.2.3</span> </span> </div> <div id="navbar" class="navbar-collapse collapse"> <ul class="nav navbar-nav"> <li> - <a href="../reference/index.html">Functions and data</a> + <a href="../reference/index.html">Reference</a> </li> <li class="dropdown"> <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false"> @@ -52,6 +52,9 @@ <li> <a href="../articles/mkin.html">Introduction to mkin</a> </li> + <li class="divider"> + </li> +<li class="dropdown-header">Example evaluations with (generalised) nonlinear least squares</li> <li> <a href="../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a> </li> @@ -59,22 +62,31 @@ <a href="../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a> </li> <li> - <a href="../articles/web_only/dimethenamid_2018.html">Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models</a> + <a href="../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> + </li> + <li class="divider"> </li> +<li class="dropdown-header">Example evaluations with hierarchical models (nonlinear mixed-effects models)</li> <li> - <a href="../articles/web_only/multistart.html">Short demo of the multistart method</a> + <a href="../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a> </li> <li> - <a href="../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> + <a href="../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a> </li> <li> - <a href="../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> + <a href="../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a> </li> <li> - <a href="../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> + <a href="../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a> </li> <li> - <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> + <a href="../articles/web_only/multistart.html">Short demo of the multistart method</a> + </li> + <li class="divider"> + </li> +<li class="dropdown-header">Performance</li> + <li> + <a href="../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> </li> <li> <a href="../articles/web_only/benchmarks.html">Benchmark timings for mkin</a> @@ -82,6 +94,15 @@ <li> <a href="../articles/web_only/saem_benchmarks.html">Benchmark timings for saem.mmkin</a> </li> + <li class="divider"> + </li> +<li class="dropdown-header">Miscellaneous</li> + <li> + <a href="../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> + </li> + <li> + <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> + </li> </ul> </li> <li> @@ -105,13 +126,16 @@ - </header><script src="FOCUS_D_files/accessible-code-block-0.0.1/empty-anchor.js"></script><div class="row"> + </header><div class="row"> <div class="col-md-9 contents"> <div class="page-header toc-ignore"> - <h1 data-toc-skip>Example evaluation of FOCUS Example Dataset D</h1> - <h4 data-toc-skip class="author">Johannes Ranke</h4> + <h1 data-toc-skip>Example evaluation of FOCUS Example Dataset +D</h1> + <h4 data-toc-skip class="author">Johannes +Ranke</h4> - <h4 data-toc-skip class="date">Last change 31 January 2019 (rebuilt 2022-11-17)</h4> + <h4 data-toc-skip class="date">Last change 31 January 2019 +(rebuilt 2023-04-20)</h4> <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/FOCUS_D.rmd" class="external-link"><code>vignettes/FOCUS_D.rmd</code></a></small> <div class="hidden name"><code>FOCUS_D.rmd</code></div> @@ -120,7 +144,12 @@ -<p>This is just a very simple vignette showing how to fit a degradation model for a parent compound with one transformation product using <code>mkin</code>. After loading the library we look at the data. We have observed concentrations in the column named <code>value</code> at the times specified in column <code>time</code> for the two observed variables named <code>parent</code> and <code>m1</code>.</p> +<p>This is just a very simple vignette showing how to fit a degradation +model for a parent compound with one transformation product using +<code>mkin</code>. After loading the library we look at the data. We +have observed concentrations in the column named <code>value</code> at +the times specified in column <code>time</code> for the two observed +variables named <code>parent</code> and <code>m1</code>.</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>, quietly <span class="op">=</span> <span class="cn">TRUE</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="va">FOCUS_2006_D</span><span class="op">)</span></span></code></pre></div> @@ -169,8 +198,14 @@ <span><span class="co">## 42 m1 100 33.13</span></span> <span><span class="co">## 43 m1 120 25.15</span></span> <span><span class="co">## 44 m1 120 33.31</span></span></code></pre> -<p>Next we specify the degradation model: The parent compound degrades with simple first-order kinetics (SFO) to one metabolite named m1, which also degrades with SFO kinetics.</p> -<p>The call to mkinmod returns a degradation model. The differential equations represented in R code can be found in the character vector <code>$diffs</code> of the <code>mkinmod</code> object. If a C compiler (gcc) is installed and functional, the differential equation model will be compiled from auto-generated C code.</p> +<p>Next we specify the degradation model: The parent compound degrades +with simple first-order kinetics (SFO) to one metabolite named m1, which +also degrades with SFO kinetics.</p> +<p>The call to mkinmod returns a degradation model. The differential +equations represented in R code can be found in the character vector +<code>$diffs</code> of the <code>mkinmod</code> object. If a C compiler +(gcc) is installed and functional, the differential equation model will +be compiled from auto-generated C code.</p> <div class="sourceCode" id="cb3"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">SFO_SFO</span> <span class="op"><-</span> <span class="fu"><a href="../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>parent <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">"m1"</span><span class="op">)</span>, m1 <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 class="op">)</span></span></code></pre></div> <pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre> @@ -180,26 +215,32 @@ <span><span class="co">## "d_parent = - k_parent * parent" </span></span> <span><span class="co">## m1 </span></span> <span><span class="co">## "d_m1 = + f_parent_to_m1 * k_parent * parent - k_m1 * m1"</span></span></code></pre> -<p>We do the fitting without progress report (<code>quiet = TRUE</code>).</p> +<p>We do the fitting without progress report +(<code>quiet = TRUE</code>).</p> <div class="sourceCode" id="cb7"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">fit</span> <span class="op"><-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOCUS_2006_D</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, quiet = TRUE): Observations with value</span></span> -<span><span class="co">## of zero were removed from the data</span></span></code></pre> -<p>A plot of the fit including a residual plot for both observed variables is obtained using the <code>plot_sep</code> method for <code>mkinfit</code> objects, which shows separate graphs for all compounds and their residuals.</p> +<pre><code><span><span class="co">## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, quiet = TRUE): Observations with</span></span> +<span><span class="co">## value of zero were removed from the data</span></span></code></pre> +<p>A plot of the fit including a residual plot for both observed +variables is obtained using the <code>plot_sep</code> method for +<code>mkinfit</code> objects, which shows separate graphs for all +compounds and their residuals.</p> <div class="sourceCode" id="cb9"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="fu"><a href="../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">fit</span>, lpos <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">"topright"</span>, <span class="st">"bottomright"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> <p><img src="FOCUS_D_files/figure-html/plot-1.png" width="768"></p> -<p>Confidence intervals for the parameter estimates are obtained using the <code>mkinparplot</code> function.</p> +<p>Confidence intervals for the parameter estimates are obtained using +the <code>mkinparplot</code> function.</p> <div class="sourceCode" id="cb10"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="fu"><a href="../reference/mkinparplot.html">mkinparplot</a></span><span class="op">(</span><span class="va">fit</span><span class="op">)</span></span></code></pre></div> <p><img src="FOCUS_D_files/figure-html/plot_2-1.png" width="768"></p> -<p>A comprehensive report of the results is obtained using the <code>summary</code> method for <code>mkinfit</code> objects.</p> +<p>A comprehensive report of the results is obtained using the +<code>summary</code> method for <code>mkinfit</code> objects.</p> <div class="sourceCode" id="cb11"><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">fit</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## mkin version used for fitting: 1.2.0 </span></span> -<span><span class="co">## R version used for fitting: 4.2.2 </span></span> -<span><span class="co">## Date of fit: Thu Nov 17 14:04:21 2022 </span></span> -<span><span class="co">## Date of summary: Thu Nov 17 14:04:21 2022 </span></span> +<pre><code><span><span class="co">## mkin version used for fitting: 1.2.3 </span></span> +<span><span class="co">## R version used for fitting: 4.2.3 </span></span> +<span><span class="co">## Date of fit: Thu Apr 20 07:37:14 2023 </span></span> +<span><span class="co">## Date of summary: Thu Apr 20 07:37:14 2023 </span></span> <span><span class="co">## </span></span> <span><span class="co">## Equations:</span></span> <span><span class="co">## d_parent/dt = - k_parent * parent</span></span> @@ -207,7 +248,7 @@ <span><span class="co">## </span></span> <span><span class="co">## Model predictions using solution type analytical </span></span> <span><span class="co">## </span></span> -<span><span class="co">## Fitted using 401 model solutions performed in 0.154 s</span></span> +<span><span class="co">## Fitted using 401 model solutions performed in 0.047 s</span></span> <span><span class="co">## </span></span> <span><span class="co">## Error model: Constant variance </span></span> <span><span class="co">## </span></span> @@ -340,7 +381,7 @@ <div class="pkgdown"> <p></p> -<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p> +<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p> </div> </footer> diff --git a/docs/articles/FOCUS_D_files/figure-html/plot-1.png b/docs/articles/FOCUS_D_files/figure-html/plot-1.png Binary files differindex f0b51c1f..c0832a1a 100644 --- a/docs/articles/FOCUS_D_files/figure-html/plot-1.png +++ b/docs/articles/FOCUS_D_files/figure-html/plot-1.png diff --git a/docs/articles/FOCUS_D_files/figure-html/plot_2-1.png b/docs/articles/FOCUS_D_files/figure-html/plot_2-1.png Binary files differindex f6180470..02cfcfb4 100644 --- a/docs/articles/FOCUS_D_files/figure-html/plot_2-1.png +++ b/docs/articles/FOCUS_D_files/figure-html/plot_2-1.png diff --git a/docs/articles/FOCUS_L.html b/docs/articles/FOCUS_L.html index f02febc4..e47ed9d7 100644 --- a/docs/articles/FOCUS_L.html +++ b/docs/articles/FOCUS_L.html @@ -33,14 +33,14 @@ </button> <span class="navbar-brand"> <a class="navbar-link" href="../index.html">mkin</a> - <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">1.2.0</span> + <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">1.2.3</span> </span> </div> <div id="navbar" class="navbar-collapse collapse"> <ul class="nav navbar-nav"> <li> - <a href="../reference/index.html">Functions and data</a> + <a href="../reference/index.html">Reference</a> </li> <li class="dropdown"> <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false"> @@ -52,6 +52,9 @@ <li> <a href="../articles/mkin.html">Introduction to mkin</a> </li> + <li class="divider"> + </li> +<li class="dropdown-header">Example evaluations with (generalised) nonlinear least squares</li> <li> <a href="../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a> </li> @@ -59,22 +62,31 @@ <a href="../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a> </li> <li> - <a href="../articles/web_only/dimethenamid_2018.html">Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models</a> + <a href="../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> + </li> + <li class="divider"> </li> +<li class="dropdown-header">Example evaluations with hierarchical models (nonlinear mixed-effects models)</li> <li> - <a href="../articles/web_only/multistart.html">Short demo of the multistart method</a> + <a href="../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a> </li> <li> - <a href="../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> + <a href="../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a> </li> <li> - <a href="../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> + <a href="../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a> </li> <li> - <a href="../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> + <a href="../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a> </li> <li> - <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> + <a href="../articles/web_only/multistart.html">Short demo of the multistart method</a> + </li> + <li class="divider"> + </li> +<li class="dropdown-header">Performance</li> + <li> + <a href="../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> </li> <li> <a href="../articles/web_only/benchmarks.html">Benchmark timings for mkin</a> @@ -82,6 +94,15 @@ <li> <a href="../articles/web_only/saem_benchmarks.html">Benchmark timings for saem.mmkin</a> </li> + <li class="divider"> + </li> +<li class="dropdown-header">Miscellaneous</li> + <li> + <a href="../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> + </li> + <li> + <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> + </li> </ul> </li> <li> @@ -105,13 +126,16 @@ - </header><script src="FOCUS_L_files/accessible-code-block-0.0.1/empty-anchor.js"></script><div class="row"> + </header><div class="row"> <div class="col-md-9 contents"> <div class="page-header toc-ignore"> - <h1 data-toc-skip>Example evaluation of FOCUS Laboratory Data L1 to L3</h1> - <h4 data-toc-skip class="author">Johannes Ranke</h4> + <h1 data-toc-skip>Example evaluation of FOCUS Laboratory Data L1 +to L3</h1> + <h4 data-toc-skip class="author">Johannes +Ranke</h4> - <h4 data-toc-skip class="date">Last change 18 May 2022 (rebuilt 2022-11-17)</h4> + <h4 data-toc-skip class="date">Last change 18 May 2022 +(rebuilt 2023-04-20)</h4> <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/FOCUS_L.rmd" class="external-link"><code>vignettes/FOCUS_L.rmd</code></a></small> <div class="hidden name"><code>FOCUS_L.rmd</code></div> @@ -123,7 +147,8 @@ <div class="section level2"> <h2 id="laboratory-data-l1">Laboratory Data L1<a class="anchor" aria-label="anchor" href="#laboratory-data-l1"></a> </h2> -<p>The following code defines example dataset L1 from the FOCUS kinetics report, p. 284:</p> +<p>The following code defines example dataset L1 from the FOCUS kinetics +report, p. 284:</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="st"><a href="https://pkgdown.jrwb.de/mkin/">"mkin"</a></span>, quietly <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> <span><span class="va">FOCUS_2006_L1</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span></span> @@ -132,22 +157,29 @@ <span> <span class="fl">72.0</span>, <span class="fl">71.9</span>, <span class="fl">50.3</span>, <span class="fl">59.4</span>, <span class="fl">47.0</span>, <span class="fl">45.1</span>,</span> <span> <span class="fl">27.7</span>, <span class="fl">27.3</span>, <span class="fl">10.0</span>, <span class="fl">10.4</span>, <span class="fl">2.9</span>, <span class="fl">4.0</span><span class="op">)</span><span class="op">)</span></span> <span><span class="va">FOCUS_2006_L1_mkin</span> <span class="op"><-</span> <span class="fu"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span><span class="op">(</span><span class="va">FOCUS_2006_L1</span><span class="op">)</span></span></code></pre></div> -<p>Here we use the assumptions of simple first order (SFO), the case of declining rate constant over time (FOMC) and the case of two different phases of the kinetics (DFOP). For a more detailed discussion of the models, please see the FOCUS kinetics report.</p> -<p>Since mkin version 0.9-32 (July 2014), we can use shorthand notation like <code>"SFO"</code> for parent only degradation models. The following two lines fit the model and produce the summary report of the model fit. This covers the numerical analysis given in the FOCUS report.</p> +<p>Here we use the assumptions of simple first order (SFO), the case of +declining rate constant over time (FOMC) and the case of two different +phases of the kinetics (DFOP). For a more detailed discussion of the +models, please see the FOCUS kinetics report.</p> +<p>Since mkin version 0.9-32 (July 2014), we can use shorthand notation +like <code>"SFO"</code> for parent only degradation models. The +following two lines fit the model and produce the summary report of the +model fit. This covers the numerical analysis given in the FOCUS +report.</p> <div class="sourceCode" id="cb2"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">m.L1.SFO</span> <span class="op"><-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="va">FOCUS_2006_L1_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> <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">m.L1.SFO</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## mkin version used for fitting: 1.2.0 </span></span> -<span><span class="co">## R version used for fitting: 4.2.2 </span></span> -<span><span class="co">## Date of fit: Thu Nov 17 14:04:25 2022 </span></span> -<span><span class="co">## Date of summary: Thu Nov 17 14:04:25 2022 </span></span> +<pre><code><span><span class="co">## mkin version used for fitting: 1.2.3 </span></span> +<span><span class="co">## R version used for fitting: 4.2.3 </span></span> +<span><span class="co">## Date of fit: Thu Apr 20 07:37:15 2023 </span></span> +<span><span class="co">## Date of summary: Thu Apr 20 07:37:15 2023 </span></span> <span><span class="co">## </span></span> <span><span class="co">## Equations:</span></span> <span><span class="co">## d_parent/dt = - k_parent * parent</span></span> <span><span class="co">## </span></span> <span><span class="co">## Model predictions using solution type analytical </span></span> <span><span class="co">## </span></span> -<span><span class="co">## Fitted using 133 model solutions performed in 0.033 s</span></span> +<span><span class="co">## Fitted using 133 model solutions performed in 0.011 s</span></span> <span><span class="co">## </span></span> <span><span class="co">## Error model: Constant variance </span></span> <span><span class="co">## </span></span> @@ -221,7 +253,8 @@ <span><span class="co">## 21 parent 10.4 12.416 -2.0163</span></span> <span><span class="co">## 30 parent 2.9 5.251 -2.3513</span></span> <span><span class="co">## 30 parent 4.0 5.251 -1.2513</span></span></code></pre> -<p>A plot of the fit is obtained with the plot function for mkinfit objects.</p> +<p>A plot of the fit is obtained with the plot function for mkinfit +objects.</p> <div class="sourceCode" id="cb4"><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">m.L1.SFO</span>, show_errmin <span class="op">=</span> <span class="cn">TRUE</span>, main <span class="op">=</span> <span class="st">"FOCUS L1 - SFO"</span><span class="op">)</span></span></code></pre></div> <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-4-1.png" width="576"></p> @@ -241,19 +274,19 @@ <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">m.L1.FOMC</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div> <pre><code><span><span class="co">## Warning in sqrt(diag(covar)): NaNs produced</span></span></code></pre> <pre><code><span><span class="co">## Warning in sqrt(1/diag(V)): NaNs produced</span></span></code></pre> -<pre><code><span><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is</span></span> -<span><span class="co">## doubtful</span></span></code></pre> -<pre><code><span><span class="co">## mkin version used for fitting: 1.2.0 </span></span> -<span><span class="co">## R version used for fitting: 4.2.2 </span></span> -<span><span class="co">## Date of fit: Thu Nov 17 14:04:25 2022 </span></span> -<span><span class="co">## Date of summary: Thu Nov 17 14:04:25 2022 </span></span> +<pre><code><span><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result</span></span> +<span><span class="co">## is doubtful</span></span></code></pre> +<pre><code><span><span class="co">## mkin version used for fitting: 1.2.3 </span></span> +<span><span class="co">## R version used for fitting: 4.2.3 </span></span> +<span><span class="co">## Date of fit: Thu Apr 20 07:37:16 2023 </span></span> +<span><span class="co">## Date of summary: Thu Apr 20 07:37:16 2023 </span></span> <span><span class="co">## </span></span> <span><span class="co">## Equations:</span></span> <span><span class="co">## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent</span></span> <span><span class="co">## </span></span> <span><span class="co">## Model predictions using solution type analytical </span></span> <span><span class="co">## </span></span> -<span><span class="co">## Fitted using 369 model solutions performed in 0.08 s</span></span> +<span><span class="co">## Fitted using 369 model solutions performed in 0.025 s</span></span> <span><span class="co">## </span></span> <span><span class="co">## Error model: Constant variance </span></span> <span><span class="co">## </span></span> @@ -316,14 +349,40 @@ <span><span class="co">## Estimated disappearance times:</span></span> <span><span class="co">## DT50 DT90 DT50back</span></span> <span><span class="co">## parent 7.25 24.08 7.25</span></span></code></pre> -<p>We get a warning that the default optimisation algorithm <code>Port</code> did not converge, which is an indication that the model is overparameterised, <em>i.e.</em> contains too many parameters that are ill-defined as a consequence.</p> -<p>And in fact, due to the higher number of parameters, and the lower number of degrees of freedom of the fit, the <span class="math inline">\(\chi^2\)</span> error level is actually higher for the FOMC model (3.6%) than for the SFO model (3.4%). Additionally, the parameters <code>log_alpha</code> and <code>log_beta</code> internally fitted in the model have excessive confidence intervals, that span more than 25 orders of magnitude (!) when backtransformed to the scale of <code>alpha</code> and <code>beta</code>. Also, the t-test for significant difference from zero does not indicate such a significant difference, with p-values greater than 0.1, and finally, the parameter correlation of <code>log_alpha</code> and <code>log_beta</code> is 1.000, clearly indicating that the model is overparameterised.</p> -<p>The <span class="math inline">\(\chi^2\)</span> error levels reported in Appendix 3 and Appendix 7 to the FOCUS kinetics report are rounded to integer percentages and partly deviate by one percentage point from the results calculated by mkin. The reason for this is not known. However, mkin gives the same <span class="math inline">\(\chi^2\)</span> error levels as the kinfit package and the calculation routines of the kinfit package have been extensively compared to the results obtained by the KinGUI software, as documented in the kinfit package vignette. KinGUI was the first widely used standard package in this field. Also, the calculation of <span class="math inline">\(\chi^2\)</span> error levels was compared with KinGUII, CAKE and DegKin manager in a project sponsored by the German Umweltbundesamt <span class="citation">(Ranke 2014)</span>.</p> +<p>We get a warning that the default optimisation algorithm +<code>Port</code> did not converge, which is an indication that the +model is overparameterised, <em>i.e.</em> contains too many parameters +that are ill-defined as a consequence.</p> +<p>And in fact, due to the higher number of parameters, and the lower +number of degrees of freedom of the fit, the <span class="math inline">\(\chi^2\)</span> error level is actually higher for +the FOMC model (3.6%) than for the SFO model (3.4%). Additionally, the +parameters <code>log_alpha</code> and <code>log_beta</code> internally +fitted in the model have excessive confidence intervals, that span more +than 25 orders of magnitude (!) when backtransformed to the scale of +<code>alpha</code> and <code>beta</code>. Also, the t-test for +significant difference from zero does not indicate such a significant +difference, with p-values greater than 0.1, and finally, the parameter +correlation of <code>log_alpha</code> and <code>log_beta</code> is +1.000, clearly indicating that the model is overparameterised.</p> +<p>The <span class="math inline">\(\chi^2\)</span> error levels reported +in Appendix 3 and Appendix 7 to the FOCUS kinetics report are rounded to +integer percentages and partly deviate by one percentage point from the +results calculated by mkin. The reason for this is not known. However, +mkin gives the same <span class="math inline">\(\chi^2\)</span> error +levels as the kinfit package and the calculation routines of the kinfit +package have been extensively compared to the results obtained by the +KinGUI software, as documented in the kinfit package vignette. KinGUI +was the first widely used standard package in this field. Also, the +calculation of <span class="math inline">\(\chi^2\)</span> error levels +was compared with KinGUII, CAKE and DegKin manager in a project +sponsored by the German Umweltbundesamt <span class="citation">(Ranke +2014)</span>.</p> </div> <div class="section level2"> <h2 id="laboratory-data-l2">Laboratory Data L2<a class="anchor" aria-label="anchor" href="#laboratory-data-l2"></a> </h2> -<p>The following code defines example dataset L2 from the FOCUS kinetics report, p. 287:</p> +<p>The following code defines example dataset L2 from the FOCUS kinetics +report, p. 287:</p> <div class="sourceCode" id="cb14"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">FOCUS_2006_L2</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span></span> <span> t <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/rep.html" class="external-link">rep</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="fl">0</span>, <span class="fl">1</span>, <span class="fl">3</span>, <span class="fl">7</span>, <span class="fl">14</span>, <span class="fl">28</span><span class="op">)</span>, each <span class="op">=</span> <span class="fl">2</span><span class="op">)</span>,</span> @@ -334,15 +393,28 @@ <div class="section level3"> <h3 id="sfo-fit-for-l2">SFO fit for L2<a class="anchor" aria-label="anchor" href="#sfo-fit-for-l2"></a> </h3> -<p>Again, the SFO model is fitted and the result is plotted. The residual plot can be obtained simply by adding the argument <code>show_residuals</code> to the plot command.</p> +<p>Again, the SFO model is fitted and the result is plotted. The +residual plot can be obtained simply by adding the argument +<code>show_residuals</code> to the plot command.</p> <div class="sourceCode" id="cb15"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">m.L2.SFO</span> <span class="op"><-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="va">FOCUS_2006_L2_mkin</span>, quiet<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span></span> <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">m.L2.SFO</span>, show_residuals <span class="op">=</span> <span class="cn">TRUE</span>, show_errmin <span class="op">=</span> <span class="cn">TRUE</span>,</span> <span> main <span class="op">=</span> <span class="st">"FOCUS L2 - SFO"</span><span class="op">)</span></span></code></pre></div> <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-8-1.png" width="672"></p> -<p>The <span class="math inline">\(\chi^2\)</span> error level of 14% suggests that the model does not fit very well. This is also obvious from the plots of the fit, in which we have included the residual plot.</p> -<p>In the FOCUS kinetics report, it is stated that there is no apparent systematic error observed from the residual plot up to the measured DT90 (approximately at day 5), and there is an underestimation beyond that point.</p> -<p>We may add that it is difficult to judge the random nature of the residuals just from the three samplings at days 0, 1 and 3. Also, it is not clear <em>a priori</em> why a consistent underestimation after the approximate DT90 should be irrelevant. However, this can be rationalised by the fact that the FOCUS fate models generally only implement SFO kinetics.</p> +<p>The <span class="math inline">\(\chi^2\)</span> error level of 14% +suggests that the model does not fit very well. This is also obvious +from the plots of the fit, in which we have included the residual +plot.</p> +<p>In the FOCUS kinetics report, it is stated that there is no apparent +systematic error observed from the residual plot up to the measured DT90 +(approximately at day 5), and there is an underestimation beyond that +point.</p> +<p>We may add that it is difficult to judge the random nature of the +residuals just from the three samplings at days 0, 1 and 3. Also, it is +not clear <em>a priori</em> why a consistent underestimation after the +approximate DT90 should be irrelevant. However, this can be rationalised +by the fact that the FOCUS fate models generally only implement SFO +kinetics.</p> </div> <div class="section level3"> <h3 id="fomc-fit-for-l2">FOMC fit for L2<a class="anchor" aria-label="anchor" href="#fomc-fit-for-l2"></a> @@ -355,17 +427,17 @@ <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-9-1.png" width="672"></p> <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">m.L2.FOMC</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## mkin version used for fitting: 1.2.0 </span></span> -<span><span class="co">## R version used for fitting: 4.2.2 </span></span> -<span><span class="co">## Date of fit: Thu Nov 17 14:04:26 2022 </span></span> -<span><span class="co">## Date of summary: Thu Nov 17 14:04:26 2022 </span></span> +<pre><code><span><span class="co">## mkin version used for fitting: 1.2.3 </span></span> +<span><span class="co">## R version used for fitting: 4.2.3 </span></span> +<span><span class="co">## Date of fit: Thu Apr 20 07:37:16 2023 </span></span> +<span><span class="co">## Date of summary: Thu Apr 20 07:37:16 2023 </span></span> <span><span class="co">## </span></span> <span><span class="co">## Equations:</span></span> <span><span class="co">## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent</span></span> <span><span class="co">## </span></span> <span><span class="co">## Model predictions using solution type analytical </span></span> <span><span class="co">## </span></span> -<span><span class="co">## Fitted using 239 model solutions performed in 0.048 s</span></span> +<span><span class="co">## Fitted using 239 model solutions performed in 0.015 s</span></span> <span><span class="co">## </span></span> <span><span class="co">## Error model: Constant variance </span></span> <span><span class="co">## </span></span> @@ -423,7 +495,10 @@ <span><span class="co">## Estimated disappearance times:</span></span> <span><span class="co">## DT50 DT90 DT50back</span></span> <span><span class="co">## parent 0.8092 5.356 1.612</span></span></code></pre> -<p>The error level at which the <span class="math inline">\(\chi^2\)</span> test passes is much lower in this case. Therefore, the FOMC model provides a better description of the data, as less experimental error has to be assumed in order to explain the data.</p> +<p>The error level at which the <span class="math inline">\(\chi^2\)</span> test passes is much lower in this +case. Therefore, the FOMC model provides a better description of the +data, as less experimental error has to be assumed in order to explain +the data.</p> </div> <div class="section level3"> <h3 id="dfop-fit-for-l2">DFOP fit for L2<a class="anchor" aria-label="anchor" href="#dfop-fit-for-l2"></a> @@ -436,10 +511,10 @@ <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-10-1.png" width="672"></p> <div class="sourceCode" id="cb20"><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">m.L2.DFOP</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## mkin version used for fitting: 1.2.0 </span></span> -<span><span class="co">## R version used for fitting: 4.2.2 </span></span> -<span><span class="co">## Date of fit: Thu Nov 17 14:04:27 2022 </span></span> -<span><span class="co">## Date of summary: Thu Nov 17 14:04:27 2022 </span></span> +<pre><code><span><span class="co">## mkin version used for fitting: 1.2.3 </span></span> +<span><span class="co">## R version used for fitting: 4.2.3 </span></span> +<span><span class="co">## Date of fit: Thu Apr 20 07:37:16 2023 </span></span> +<span><span class="co">## Date of summary: Thu Apr 20 07:37:16 2023 </span></span> <span><span class="co">## </span></span> <span><span class="co">## Equations:</span></span> <span><span class="co">## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *</span></span> @@ -448,7 +523,7 @@ <span><span class="co">## </span></span> <span><span class="co">## Model predictions using solution type analytical </span></span> <span><span class="co">## </span></span> -<span><span class="co">## Fitted using 581 model solutions performed in 0.128 s</span></span> +<span><span class="co">## Fitted using 581 model solutions performed in 0.04 s</span></span> <span><span class="co">## </span></span> <span><span class="co">## Error model: Constant variance </span></span> <span><span class="co">## </span></span> @@ -511,13 +586,15 @@ <span><span class="co">## Estimated disappearance times:</span></span> <span><span class="co">## DT50 DT90 DT50back DT50_k1 DT50_k2</span></span> <span><span class="co">## parent 0.5335 5.311 1.599 0.03084 2.058</span></span></code></pre> -<p>Here, the DFOP model is clearly the best-fit model for dataset L2 based on the chi^2 error level criterion.</p> +<p>Here, the DFOP model is clearly the best-fit model for dataset L2 +based on the chi^2 error level criterion.</p> </div> </div> <div class="section level2"> <h2 id="laboratory-data-l3">Laboratory Data L3<a class="anchor" aria-label="anchor" href="#laboratory-data-l3"></a> </h2> -<p>The following code defines example dataset L3 from the FOCUS kinetics report, p. 290.</p> +<p>The following code defines example dataset L3 from the FOCUS kinetics +report, p. 290.</p> <div class="sourceCode" id="cb22"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">FOCUS_2006_L3</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span></span> <span> t <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</span>, <span class="fl">3</span>, <span class="fl">7</span>, <span class="fl">14</span>, <span class="fl">30</span>, <span class="fl">60</span>, <span class="fl">91</span>, <span class="fl">120</span><span class="op">)</span>,</span> @@ -526,26 +603,35 @@ <div class="section level3"> <h3 id="fit-multiple-models">Fit multiple models<a class="anchor" aria-label="anchor" href="#fit-multiple-models"></a> </h3> -<p>As of mkin version 0.9-39 (June 2015), we can fit several models to one or more datasets in one call to the function <code>mmkin</code>. The datasets have to be passed in a list, in this case a named list holding only the L3 dataset prepared above.</p> +<p>As of mkin version 0.9-39 (June 2015), we can fit several models to +one or more datasets in one call to the function <code>mmkin</code>. The +datasets have to be passed in a list, in this case a named list holding +only the L3 dataset prepared above.</p> <div class="sourceCode" id="cb23"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="co"># Only use one core here, not to offend the CRAN checks</span></span> <span><span class="va">mm.L3</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="op">)</span>, cores <span class="op">=</span> <span class="fl">1</span>,</span> <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="st">"FOCUS L3"</span> <span class="op">=</span> <span class="va">FOCUS_2006_L3_mkin</span><span class="op">)</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> <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">mm.L3</span><span class="op">)</span></span></code></pre></div> <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-12-1.png" width="700"></p> -<p>The <span class="math inline">\(\chi^2\)</span> error level of 21% as well as the plot suggest that the SFO model does not fit very well. The FOMC model performs better, with an error level at which the <span class="math inline">\(\chi^2\)</span> test passes of 7%. Fitting the four parameter DFOP model further reduces the <span class="math inline">\(\chi^2\)</span> error level considerably.</p> +<p>The <span class="math inline">\(\chi^2\)</span> error level of 21% as +well as the plot suggest that the SFO model does not fit very well. The +FOMC model performs better, with an error level at which the <span class="math inline">\(\chi^2\)</span> test passes of 7%. Fitting the +four parameter DFOP model further reduces the <span class="math inline">\(\chi^2\)</span> error level considerably.</p> </div> <div class="section level3"> <h3 id="accessing-mmkin-objects">Accessing mmkin objects<a class="anchor" aria-label="anchor" href="#accessing-mmkin-objects"></a> </h3> -<p>The objects returned by mmkin are arranged like a matrix, with models as a row index and datasets as a column index.</p> -<p>We can extract the summary and plot for <em>e.g.</em> the DFOP fit, using square brackets for indexing which will result in the use of the summary and plot functions working on mkinfit objects.</p> +<p>The objects returned by mmkin are arranged like a matrix, with models +as a row index and datasets as a column index.</p> +<p>We can extract the summary and plot for <em>e.g.</em> the DFOP fit, +using square brackets for indexing which will result in the use of the +summary and plot functions working on mkinfit objects.</p> <div class="sourceCode" id="cb24"><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">mm.L3</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="fl">1</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## mkin version used for fitting: 1.2.0 </span></span> -<span><span class="co">## R version used for fitting: 4.2.2 </span></span> -<span><span class="co">## Date of fit: Thu Nov 17 14:04:27 2022 </span></span> -<span><span class="co">## Date of summary: Thu Nov 17 14:04:28 2022 </span></span> +<pre><code><span><span class="co">## mkin version used for fitting: 1.2.3 </span></span> +<span><span class="co">## R version used for fitting: 4.2.3 </span></span> +<span><span class="co">## Date of fit: Thu Apr 20 07:37:17 2023 </span></span> +<span><span class="co">## Date of summary: Thu Apr 20 07:37:17 2023 </span></span> <span><span class="co">## </span></span> <span><span class="co">## Equations:</span></span> <span><span class="co">## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *</span></span> @@ -554,7 +640,7 @@ <span><span class="co">## </span></span> <span><span class="co">## Model predictions using solution type analytical </span></span> <span><span class="co">## </span></span> -<span><span class="co">## Fitted using 376 model solutions performed in 0.078 s</span></span> +<span><span class="co">## Fitted using 376 model solutions performed in 0.024 s</span></span> <span><span class="co">## </span></span> <span><span class="co">## Error model: Constant variance </span></span> <span><span class="co">## </span></span> @@ -631,20 +717,30 @@ <div class="sourceCode" id="cb26"><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">mm.L3</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="fl">1</span><span class="op">]</span><span class="op">]</span>, show_errmin <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-13-1.png" width="700"></p> -<p>Here, a look to the model plot, the confidence intervals of the parameters and the correlation matrix suggest that the parameter estimates are reliable, and the DFOP model can be used as the best-fit model based on the <span class="math inline">\(\chi^2\)</span> error level criterion for laboratory data L3.</p> -<p>This is also an example where the standard t-test for the parameter <code>g_ilr</code> is misleading, as it tests for a significant difference from zero. In this case, zero appears to be the correct value for this parameter, and the confidence interval for the backtransformed parameter <code>g</code> is quite narrow.</p> +<p>Here, a look to the model plot, the confidence intervals of the +parameters and the correlation matrix suggest that the parameter +estimates are reliable, and the DFOP model can be used as the best-fit +model based on the <span class="math inline">\(\chi^2\)</span> error +level criterion for laboratory data L3.</p> +<p>This is also an example where the standard t-test for the parameter +<code>g_ilr</code> is misleading, as it tests for a significant +difference from zero. In this case, zero appears to be the correct value +for this parameter, and the confidence interval for the backtransformed +parameter <code>g</code> is quite narrow.</p> </div> </div> <div class="section level2"> <h2 id="laboratory-data-l4">Laboratory Data L4<a class="anchor" aria-label="anchor" href="#laboratory-data-l4"></a> </h2> -<p>The following code defines example dataset L4 from the FOCUS kinetics report, p. 293:</p> +<p>The following code defines example dataset L4 from the FOCUS kinetics +report, p. 293:</p> <div class="sourceCode" id="cb27"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">FOCUS_2006_L4</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span></span> <span> t <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</span>, <span class="fl">3</span>, <span class="fl">7</span>, <span class="fl">14</span>, <span class="fl">30</span>, <span class="fl">60</span>, <span class="fl">91</span>, <span class="fl">120</span><span class="op">)</span>,</span> <span> parent <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">96.6</span>, <span class="fl">96.3</span>, <span class="fl">94.3</span>, <span class="fl">88.8</span>, <span class="fl">74.9</span>, <span class="fl">59.9</span>, <span class="fl">53.5</span>, <span class="fl">49.0</span><span class="op">)</span><span class="op">)</span></span> <span><span class="va">FOCUS_2006_L4_mkin</span> <span class="op"><-</span> <span class="fu"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span><span class="op">(</span><span class="va">FOCUS_2006_L4</span><span class="op">)</span></span></code></pre></div> -<p>Fits of the SFO and FOMC models, plots and summaries are produced below:</p> +<p>Fits of the SFO and FOMC models, plots and summaries are produced +below:</p> <div class="sourceCode" id="cb28"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="co"># Only use one core here, not to offend the CRAN checks</span></span> <span><span class="va">mm.L4</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="op">)</span>, cores <span class="op">=</span> <span class="fl">1</span>,</span> @@ -652,20 +748,24 @@ <span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> <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">mm.L4</span><span class="op">)</span></span></code></pre></div> <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-15-1.png" width="700"></p> -<p>The <span class="math inline">\(\chi^2\)</span> error level of 3.3% as well as the plot suggest that the SFO model fits very well. The error level at which the <span class="math inline">\(\chi^2\)</span> test passes is slightly lower for the FOMC model. However, the difference appears negligible.</p> +<p>The <span class="math inline">\(\chi^2\)</span> error level of 3.3% +as well as the plot suggest that the SFO model fits very well. The error +level at which the <span class="math inline">\(\chi^2\)</span> test +passes is slightly lower for the FOMC model. However, the difference +appears negligible.</p> <div class="sourceCode" id="cb29"><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">mm.L4</span><span class="op">[[</span><span class="st">"SFO"</span>, <span class="fl">1</span><span class="op">]</span><span class="op">]</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## mkin version used for fitting: 1.2.0 </span></span> -<span><span class="co">## R version used for fitting: 4.2.2 </span></span> -<span><span class="co">## Date of fit: Thu Nov 17 14:04:28 2022 </span></span> -<span><span class="co">## Date of summary: Thu Nov 17 14:04:29 2022 </span></span> +<pre><code><span><span class="co">## mkin version used for fitting: 1.2.3 </span></span> +<span><span class="co">## R version used for fitting: 4.2.3 </span></span> +<span><span class="co">## Date of fit: Thu Apr 20 07:37:17 2023 </span></span> +<span><span class="co">## Date of summary: Thu Apr 20 07:37:17 2023 </span></span> <span><span class="co">## </span></span> <span><span class="co">## Equations:</span></span> <span><span class="co">## d_parent/dt = - k_parent * parent</span></span> <span><span class="co">## </span></span> <span><span class="co">## Model predictions using solution type analytical </span></span> <span><span class="co">## </span></span> -<span><span class="co">## Fitted using 142 model solutions performed in 0.029 s</span></span> +<span><span class="co">## Fitted using 142 model solutions performed in 0.009 s</span></span> <span><span class="co">## </span></span> <span><span class="co">## Error model: Constant variance </span></span> <span><span class="co">## </span></span> @@ -720,17 +820,17 @@ <span><span class="co">## parent 106 352</span></span></code></pre> <div class="sourceCode" id="cb31"><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">mm.L4</span><span class="op">[[</span><span class="st">"FOMC"</span>, <span class="fl">1</span><span class="op">]</span><span class="op">]</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## mkin version used for fitting: 1.2.0 </span></span> -<span><span class="co">## R version used for fitting: 4.2.2 </span></span> -<span><span class="co">## Date of fit: Thu Nov 17 14:04:28 2022 </span></span> -<span><span class="co">## Date of summary: Thu Nov 17 14:04:29 2022 </span></span> +<pre><code><span><span class="co">## mkin version used for fitting: 1.2.3 </span></span> +<span><span class="co">## R version used for fitting: 4.2.3 </span></span> +<span><span class="co">## Date of fit: Thu Apr 20 07:37:17 2023 </span></span> +<span><span class="co">## Date of summary: Thu Apr 20 07:37:17 2023 </span></span> <span><span class="co">## </span></span> <span><span class="co">## Equations:</span></span> <span><span class="co">## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent</span></span> <span><span class="co">## </span></span> <span><span class="co">## Model predictions using solution type analytical </span></span> <span><span class="co">## </span></span> -<span><span class="co">## Fitted using 224 model solutions performed in 0.046 s</span></span> +<span><span class="co">## Fitted using 224 model solutions performed in 0.014 s</span></span> <span><span class="co">## </span></span> <span><span class="co">## Error model: Constant variance </span></span> <span><span class="co">## </span></span> @@ -792,9 +892,11 @@ <div class="section level2"> <h2 class="unnumbered" id="references">References<a class="anchor" aria-label="anchor" href="#references"></a> </h2> -<div id="refs" class="references hanging-indent"> -<div id="ref-ranke2014"> -<p>Ranke, Johannes. 2014. “Prüfung und Validierung von Modellierungssoftware als Alternative zu ModelMaker 4.0.” Umweltbundesamt Projektnummer 27452.</p> +<div id="refs" class="references csl-bib-body hanging-indent"> +<div id="ref-ranke2014" class="csl-entry"> +Ranke, Johannes. 2014. <span>“<span class="nocase">Prüfung und +Validierung von Modellierungssoftware als Alternative zu ModelMaker +4.0</span>.”</span> Umweltbundesamt Projektnummer 27452. </div> </div> </div> @@ -817,7 +919,7 @@ <div class="pkgdown"> <p></p> -<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p> +<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p> </div> </footer> diff --git a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-10-1.png b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-10-1.png Binary files differindex b2bff18f..11706305 100644 --- a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-10-1.png +++ b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-10-1.png diff --git a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-12-1.png b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-12-1.png Binary files differindex d613c035..daa488a3 100644 --- a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-12-1.png +++ b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-12-1.png diff --git a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-13-1.png b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-13-1.png Binary files differindex 8387a272..5caea744 100644 --- a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-13-1.png +++ b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-13-1.png diff --git a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-15-1.png b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-15-1.png Binary files differindex 74f0fc48..0dc9d57d 100644 --- a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-15-1.png +++ b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-15-1.png diff --git a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-4-1.png b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-4-1.png Binary files differindex 1c56cb20..13344b25 100644 --- a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-4-1.png +++ b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-4-1.png diff --git a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-5-1.png b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-5-1.png Binary files differindex 4247131e..ec234b6e 100644 --- a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-5-1.png +++ b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-5-1.png diff --git a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-6-1.png b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-6-1.png Binary files differindex b6130527..c3f55dd6 100644 --- a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-6-1.png +++ b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-6-1.png diff --git a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-8-1.png b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-8-1.png Binary files differindex dea51d58..d3551b47 100644 --- a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-8-1.png +++ b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-8-1.png diff --git a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-9-1.png b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-9-1.png Binary files differindex 05460304..5f8afc00 100644 --- a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-9-1.png +++ b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-9-1.png diff --git a/docs/articles/index.html b/docs/articles/index.html index f4f6d557..991f8994 100644 --- a/docs/articles/index.html +++ b/docs/articles/index.html @@ -17,13 +17,13 @@ </button> <span class="navbar-brand"> <a class="navbar-link" href="../index.html">mkin</a> - <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">1.2.1</span> + <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">1.2.3.1</span> </span> </div> <div id="navbar" class="navbar-collapse collapse"> <ul class="nav navbar-nav"><li> - <a href="../reference/index.html">Functions and data</a> + <a href="../reference/index.html">Reference</a> </li> <li class="dropdown"> <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false"> @@ -34,6 +34,8 @@ <ul class="dropdown-menu" role="menu"><li> <a href="../articles/mkin.html">Introduction to mkin</a> </li> + <li class="divider"> + <li class="dropdown-header">Example evaluations with (generalised) nonlinear least squares</li> <li> <a href="../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a> </li> @@ -41,22 +43,29 @@ <a href="../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a> </li> <li> - <a href="../articles/web_only/dimethenamid_2018.html">Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models</a> + <a href="../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> </li> + <li class="divider"> + <li class="dropdown-header">Example evaluations with hierarchical models (nonlinear mixed-effects models)</li> <li> - <a href="../articles/web_only/multistart.html">Short demo of the multistart method</a> + <a href="../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a> </li> <li> - <a href="../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> + <a href="../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a> </li> <li> - <a href="../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> + <a href="../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a> </li> <li> - <a href="../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> + <a href="../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a> </li> <li> - <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> + <a href="../articles/web_only/multistart.html">Short demo of the multistart method</a> + </li> + <li class="divider"> + <li class="dropdown-header">Performance</li> + <li> + <a href="../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> </li> <li> <a href="../articles/web_only/benchmarks.html">Benchmark timings for mkin</a> @@ -64,6 +73,14 @@ <li> <a href="../articles/web_only/saem_benchmarks.html">Benchmark timings for saem.mmkin</a> </li> + <li class="divider"> + <li class="dropdown-header">Miscellaneous</li> + <li> + <a href="../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> + </li> + <li> + <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> + </li> </ul></li> <li> <a href="../news/index.html">News</a> @@ -96,6 +113,12 @@ <dd> </dd><dt><a href="mkin.html">Introduction to mkin</a></dt> <dd> + </dd><dt><a href="prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a></dt> + <dd> + </dd><dt><a href="prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a></dt> + <dd> + </dd><dt><a href="prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a></dt> + <dd> </dd><dt><a href="twa.html">Calculation of time weighted average concentrations with mkin</a></dt> <dd> </dd><dt><a href="web_only/FOCUS_Z.html">Example evaluation of FOCUS dataset Z</a></dt> @@ -122,7 +145,7 @@ </div> <div class="pkgdown"> - <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p> + <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p> </div> </footer></div> diff --git a/docs/articles/mkin.html b/docs/articles/mkin.html index da499501..88c63bef 100644 --- a/docs/articles/mkin.html +++ b/docs/articles/mkin.html @@ -33,14 +33,14 @@ </button> <span class="navbar-brand"> <a class="navbar-link" href="../index.html">mkin</a> - <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">1.2.0</span> + <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">1.2.3</span> </span> </div> <div id="navbar" class="navbar-collapse collapse"> <ul class="nav navbar-nav"> <li> - <a href="../reference/index.html">Functions and data</a> + <a href="../reference/index.html">Reference</a> </li> <li class="dropdown"> <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false"> @@ -52,6 +52,9 @@ <li> <a href="../articles/mkin.html">Introduction to mkin</a> </li> + <li class="divider"> + </li> +<li class="dropdown-header">Example evaluations with (generalised) nonlinear least squares</li> <li> <a href="../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a> </li> @@ -59,22 +62,31 @@ <a href="../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a> </li> <li> - <a href="../articles/web_only/dimethenamid_2018.html">Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models</a> + <a href="../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> + </li> + <li class="divider"> </li> +<li class="dropdown-header">Example evaluations with hierarchical models (nonlinear mixed-effects models)</li> <li> - <a href="../articles/web_only/multistart.html">Short demo of the multistart method</a> + <a href="../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a> </li> <li> - <a href="../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> + <a href="../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a> </li> <li> - <a href="../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> + <a href="../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a> </li> <li> - <a href="../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> + <a href="../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a> </li> <li> - <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> + <a href="../articles/web_only/multistart.html">Short demo of the multistart method</a> + </li> + <li class="divider"> + </li> +<li class="dropdown-header">Performance</li> + <li> + <a href="../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> </li> <li> <a href="../articles/web_only/benchmarks.html">Benchmark timings for mkin</a> @@ -82,6 +94,15 @@ <li> <a href="../articles/web_only/saem_benchmarks.html">Benchmark timings for saem.mmkin</a> </li> + <li class="divider"> + </li> +<li class="dropdown-header">Miscellaneous</li> + <li> + <a href="../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> + </li> + <li> + <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> + </li> </ul> </li> <li> @@ -105,13 +126,15 @@ - </header><script src="mkin_files/accessible-code-block-0.0.1/empty-anchor.js"></script><div class="row"> + </header><div class="row"> <div class="col-md-9 contents"> <div class="page-header toc-ignore"> <h1 data-toc-skip>Introduction to mkin</h1> - <h4 data-toc-skip class="author">Johannes Ranke</h4> + <h4 data-toc-skip class="author">Johannes +Ranke</h4> - <h4 data-toc-skip class="date">Last change 15 February 2021 (rebuilt 2022-11-17)</h4> + <h4 data-toc-skip class="date">Last change 15 February 2021 +(rebuilt 2023-04-20)</h4> <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/mkin.rmd" class="external-link"><code>vignettes/mkin.rmd</code></a></small> <div class="hidden name"><code>mkin.rmd</code></div> @@ -120,11 +143,21 @@ -<p><a href="https://www.jrwb.de" class="external-link">Wissenschaftlicher Berater, Kronacher Str. 12, 79639 Grenzach-Wyhlen, Germany</a><br> Privatdozent at the University of Freiburg</p> +<p><a href="https://www.jrwb.de" class="external-link">Wissenschaftlicher Berater, Kronacher +Str. 12, 79639 Grenzach-Wyhlen, Germany</a><br> Privatdozent at the +University of Freiburg</p> <div class="section level2"> <h2 id="abstract">Abstract<a class="anchor" aria-label="anchor" href="#abstract"></a> </h2> -<p>In the regulatory evaluation of chemical substances like plant protection products (pesticides), biocides and other chemicals, degradation data play an important role. For the evaluation of pesticide degradation experiments, detailed guidance has been developed, based on nonlinear optimisation. The <code>R</code> add-on package <code>mkin</code> implements fitting some of the models recommended in this guidance from within R and calculates some statistical measures for data series within one or more compartments, for parent and metabolites.</p> +<p>In the regulatory evaluation of chemical substances like plant +protection products (pesticides), biocides and other chemicals, +degradation data play an important role. For the evaluation of pesticide +degradation experiments, detailed guidance has been developed, based on +nonlinear optimisation. The <code>R</code> add-on package +<code>mkin</code> implements fitting some of the models recommended in +this guidance from within R and calculates some statistical measures for +data series within one or more compartments, for parent and +metabolites.</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="st"><a href="https://pkgdown.jrwb.de/mkin/">"mkin"</a></span>, quietly <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> <span><span class="co"># Define the kinetic model</span></span> @@ -159,95 +192,248 @@ <div class="section level2"> <h2 id="background">Background<a class="anchor" aria-label="anchor" href="#background"></a> </h2> -<p>The <code>mkin</code> package <span class="citation">(Ranke 2021)</span> implements the approach to degradation kinetics recommended in the kinetics report provided by the FOrum for Co-ordination of pesticide fate models and their USe <span class="citation">(FOCUS Work Group on Degradation Kinetics 2006, 2014)</span>. It covers data series describing the decline of one compound, data series with transformation products (commonly termed metabolites) and data series for more than one compartment. It is possible to include back reactions. Therefore, equilibrium reactions and equilibrium partitioning can be specified, although this often leads to an overparameterisation of the model.</p> -<p>When the first <code>mkin</code> code was published in 2010, the most commonly used tools for fitting more complex kinetic degradation models to experimental data were KinGUI <span class="citation">(Schäfer et al. 2007)</span>, a MATLAB based tool with a graphical user interface that was specifically tailored to the task and included some output as proposed by the FOCUS Kinetics Workgroup, and ModelMaker, a general purpose compartment based tool providing infrastructure for fitting dynamic simulation models based on differential equations to data.</p> -<p>The ‘mkin’ code was first uploaded to the BerliOS development platform. When this was taken down, the version control history was imported into the R-Forge site (see <em>e.g.</em> <a href="https://cgit.jrwb.de/mkin/commit/?id=30cbb4092f6d2d3beff5800603374a0d009ad770" class="external-link">the initial commit on 11 May 2010</a>), where the code is still being updated.</p> -<p>At that time, the R package <code>FME</code> (Flexible Modelling Environment) <span class="citation">(Soetaert and Petzoldt 2010)</span> was already available, and provided a good basis for developing a package specifically tailored to the task. The remaining challenge was to make it as easy as possible for the users (including the author of this vignette) to specify the system of differential equations and to include the output requested by the FOCUS guidance, such as the <span class="math inline">\(\chi^2\)</span> error level as defined in this guidance.</p> -<p>Also, <code>mkin</code> introduced using analytical solutions for parent only kinetics for improved optimization speed. Later, Eigenvalue based solutions were introduced to <code>mkin</code> for the case of linear differential equations (<em>i.e.</em> where the FOMC or DFOP models were not used for the parent compound), greatly improving the optimization speed for these cases. This, has become somehow obsolete, as the use of compiled code described below gives even faster execution times.</p> -<p>The possibility to specify back-reactions and a biphasic model (SFORB) for metabolites were present in <code>mkin</code> from the very beginning.</p> +<p>The <code>mkin</code> package <span class="citation">(J. Ranke +2021)</span> implements the approach to degradation kinetics recommended +in the kinetics report provided by the FOrum for Co-ordination of +pesticide fate models and their USe <span class="citation">(FOCUS Work +Group on Degradation Kinetics 2006, 2014)</span>. It covers data series +describing the decline of one compound, data series with transformation +products (commonly termed metabolites) and data series for more than one +compartment. It is possible to include back reactions. Therefore, +equilibrium reactions and equilibrium partitioning can be specified, +although this often leads to an overparameterisation of the model.</p> +<p>When the first <code>mkin</code> code was published in 2010, the most +commonly used tools for fitting more complex kinetic degradation models +to experimental data were KinGUI <span class="citation">(Schäfer et al. +2007)</span>, a MATLAB based tool with a graphical user interface that +was specifically tailored to the task and included some output as +proposed by the FOCUS Kinetics Workgroup, and ModelMaker, a general +purpose compartment based tool providing infrastructure for fitting +dynamic simulation models based on differential equations to data.</p> +<p>The ‘mkin’ code was first uploaded to the BerliOS development +platform. When this was taken down, the version control history was +imported into the R-Forge site (see <em>e.g.</em> <a href="https://cgit.jrwb.de/mkin/commit/?id=30cbb4092f6d2d3beff5800603374a0d009ad770" class="external-link">the +initial commit on 11 May 2010</a>), where the code is still being +updated.</p> +<p>At that time, the R package <code>FME</code> (Flexible Modelling +Environment) <span class="citation">(Soetaert and Petzoldt 2010)</span> +was already available, and provided a good basis for developing a +package specifically tailored to the task. The remaining challenge was +to make it as easy as possible for the users (including the author of +this vignette) to specify the system of differential equations and to +include the output requested by the FOCUS guidance, such as the <span class="math inline">\(\chi^2\)</span> error level as defined in this +guidance.</p> +<p>Also, <code>mkin</code> introduced using analytical solutions for +parent only kinetics for improved optimization speed. Later, Eigenvalue +based solutions were introduced to <code>mkin</code> for the case of +linear differential equations (<em>i.e.</em> where the FOMC or DFOP +models were not used for the parent compound), greatly improving the +optimization speed for these cases. This, has become somehow obsolete, +as the use of compiled code described below gives even faster execution +times.</p> +<p>The possibility to specify back-reactions and a biphasic model +(SFORB) for metabolites were present in <code>mkin</code> from the very +beginning.</p> <div class="section level3"> <h3 id="derived-software-tools">Derived software tools<a class="anchor" aria-label="anchor" href="#derived-software-tools"></a> </h3> -<p>Soon after the publication of <code>mkin</code>, two derived tools were published, namely KinGUII (developed at Bayer Crop Science) and CAKE (commissioned to Tessella by Syngenta), which added a graphical user interface (GUI), and added fitting by iteratively reweighted least squares (IRLS) and characterisation of likely parameter distributions by Markov Chain Monte Carlo (MCMC) sampling.</p> -<p>CAKE focuses on a smooth use experience, sacrificing some flexibility in the model definition, originally allowing only two primary metabolites in parallel. The current version 3.4 of CAKE released in May 2020 uses a scheme for up to six metabolites in a flexible arrangement and supports biphasic modelling of metabolites, but does not support back-reactions (non-instantaneous equilibria).</p> -<p>KinGUI offers an even more flexible widget for specifying complex kinetic models. Back-reactions (non-instantaneous equilibria) were supported early on, but until 2014, only simple first-order models could be specified for transformation products. Starting with KinGUII version 2.1, biphasic modelling of metabolites was also available in KinGUII.</p> -<p>A further graphical user interface (GUI) that has recently been brought to a decent degree of maturity is the browser based GUI named <code>gmkin</code>. Please see its <a href="https://pkgdown.jrwb.de/gmkin/" class="external-link">documentation page</a> and <a href="https://pkgdown.jrwb.de/gmkin/articles/gmkin_manual.html" class="external-link">manual</a> for further information.</p> -<p>A comparison of scope, usability and numerical results obtained with these tools has been recently been published by <span class="citation">Ranke, Wöltjen, and Meinecke (2018)</span>.</p> +<p>Soon after the publication of <code>mkin</code>, two derived tools +were published, namely KinGUII (developed at Bayer Crop Science) and +CAKE (commissioned to Tessella by Syngenta), which added a graphical +user interface (GUI), and added fitting by iteratively reweighted least +squares (IRLS) and characterisation of likely parameter distributions by +Markov Chain Monte Carlo (MCMC) sampling.</p> +<p>CAKE focuses on a smooth use experience, sacrificing some flexibility +in the model definition, originally allowing only two primary +metabolites in parallel. The current version 3.4 of CAKE released in May +2020 uses a scheme for up to six metabolites in a flexible arrangement +and supports biphasic modelling of metabolites, but does not support +back-reactions (non-instantaneous equilibria).</p> +<p>KinGUI offers an even more flexible widget for specifying complex +kinetic models. Back-reactions (non-instantaneous equilibria) were +supported early on, but until 2014, only simple first-order models could +be specified for transformation products. Starting with KinGUII version +2.1, biphasic modelling of metabolites was also available in +KinGUII.</p> +<p>A further graphical user interface (GUI) that has recently been +brought to a decent degree of maturity is the browser based GUI named +<code>gmkin</code>. Please see its <a href="https://pkgdown.jrwb.de/gmkin/" class="external-link">documentation page</a> and <a href="https://pkgdown.jrwb.de/gmkin/articles/gmkin_manual.html" class="external-link">manual</a> +for further information.</p> +<p>A comparison of scope, usability and numerical results obtained with +these tools has been recently been published by <span class="citation">Johannes Ranke, Wöltjen, and Meinecke +(2018)</span>.</p> </div> </div> <div class="section level2"> <h2 id="unique-features">Unique features<a class="anchor" aria-label="anchor" href="#unique-features"></a> </h2> -<p>Currently, the main unique features available in <code>mkin</code> are</p> +<p>Currently, the main unique features available in <code>mkin</code> +are</p> <ul> -<li>the <a href="https://pkgdown.jrwb.de/mkin/articles/web_only/compiled_models.html">speed increase</a> by using compiled code when a compiler is present,</li> -<li>parallel model fitting on multicore machines using the <a href="https://pkgdown.jrwb.de/mkin/reference/mmkin.html"><code>mmkin</code> function</a>,</li> -<li>the estimation of parameter confidence intervals based on transformed parameters (see below) and</li> -<li>the possibility to use the <a href="https://pkgdown.jrwb.de/mkin/reference/sigma_twocomp.html">two-component error model</a> +<li>the <a href="https://pkgdown.jrwb.de/mkin/articles/web_only/compiled_models.html">speed +increase</a> by using compiled code when a compiler is present,</li> +<li>parallel model fitting on multicore machines using the <a href="https://pkgdown.jrwb.de/mkin/reference/mmkin.html"><code>mmkin</code> +function</a>,</li> +<li>the estimation of parameter confidence intervals based on +transformed parameters (see below) and</li> +<li>the possibility to use the <a href="https://pkgdown.jrwb.de/mkin/reference/sigma_twocomp.html">two-component +error model</a> </li> </ul> -<p>The iteratively reweighted least squares fitting of different variances for each variable as introduced by <span class="citation">Gao et al. (2011)</span> has been available in mkin since <a href="https://pkgdown.jrwb.de/mkin/news/index.html#mkin-0-9-22-2013-10-26">version 0.9-22</a>. With <a href="https://pkgdown.jrwb.de/mkin/news/index.html#mkin-0-9-49-5-2019-07-04">release 0.9.49.5</a>, the IRLS algorithm has been complemented by direct or step-wise maximisation of the likelihood function, which makes it possible not only to fit the variance by variable error model but also a <a href="https://pkgdown.jrwb.de/mkin/reference/sigma_twocomp.html">two-component error model</a> inspired by error models developed in analytical chemistry <span class="citation">(Ranke and Meinecke 2019)</span>.</p> +<p>The iteratively reweighted least squares fitting of different +variances for each variable as introduced by <span class="citation">Gao +et al. (2011)</span> has been available in mkin since <a href="https://pkgdown.jrwb.de/mkin/news/index.html#mkin-0-9-22-2013-10-26">version +0.9-22</a>. With <a href="https://pkgdown.jrwb.de/mkin/news/index.html#mkin-0-9-49-5-2019-07-04">release +0.9.49.5</a>, the IRLS algorithm has been complemented by direct or +step-wise maximisation of the likelihood function, which makes it +possible not only to fit the variance by variable error model but also a +<a href="https://pkgdown.jrwb.de/mkin/reference/sigma_twocomp.html">two-component +error model</a> inspired by error models developed in analytical +chemistry <span class="citation">(Johannes Ranke and Meinecke +2019)</span>.</p> </div> <div class="section level2"> <h2 id="internal-parameter-transformations">Internal parameter transformations<a class="anchor" aria-label="anchor" href="#internal-parameter-transformations"></a> </h2> -<p>For rate constants, the log transformation is used, as proposed by Bates and Watts <span class="citation">(1988, 77, 149)</span>. Approximate intervals are constructed for the transformed rate constants <span class="citation">(compare Bates and Watts 1988, 135)</span>, <em>i.e.</em> for their logarithms. Confidence intervals for the rate constants are then obtained using the appropriate backtransformation using the exponential function.</p> -<p>In the first version of <code>mkin</code> allowing for specifying models using formation fractions, a home-made reparameterisation was used in order to ensure that the sum of formation fractions would not exceed unity.</p> -<p>This method is still used in the current version of KinGUII (v2.1 from April 2014), with a modification that allows for fixing the pathway to sink to zero. CAKE uses penalties in the objective function in order to enforce this constraint.</p> -<p>In 2012, an alternative reparameterisation of the formation fractions was proposed together with René Lehmann <span class="citation">(Ranke and Lehmann 2012)</span>, based on isometric logratio transformation (ILR). The aim was to improve the validity of the linear approximation of the objective function during the parameter estimation procedure as well as in the subsequent calculation of parameter confidence intervals. In the current version of mkin, a logit transformation is used for parameters that are bound between 0 and 1, such as the g parameter of the DFOP model.</p> +<p>For rate constants, the log transformation is used, as proposed by +Bates and Watts <span class="citation">(1988, 77, 149)</span>. +Approximate intervals are constructed for the transformed rate constants +<span class="citation">(compare Bates and Watts 1988, 135)</span>, +<em>i.e.</em> for their logarithms. Confidence intervals for the rate +constants are then obtained using the appropriate backtransformation +using the exponential function.</p> +<p>In the first version of <code>mkin</code> allowing for specifying +models using formation fractions, a home-made reparameterisation was +used in order to ensure that the sum of formation fractions would not +exceed unity.</p> +<p>This method is still used in the current version of KinGUII (v2.1 +from April 2014), with a modification that allows for fixing the pathway +to sink to zero. CAKE uses penalties in the objective function in order +to enforce this constraint.</p> +<p>In 2012, an alternative reparameterisation of the formation fractions +was proposed together with René Lehmann <span class="citation">(J. Ranke +and Lehmann 2012)</span>, based on isometric logratio transformation +(ILR). The aim was to improve the validity of the linear approximation +of the objective function during the parameter estimation procedure as +well as in the subsequent calculation of parameter confidence intervals. +In the current version of mkin, a logit transformation is used for +parameters that are bound between 0 and 1, such as the g parameter of +the DFOP model.</p> <div class="section level3"> <h3 id="confidence-intervals-based-on-transformed-parameters">Confidence intervals based on transformed parameters<a class="anchor" aria-label="anchor" href="#confidence-intervals-based-on-transformed-parameters"></a> </h3> -<p>In the first attempt at providing improved parameter confidence intervals introduced to <code>mkin</code> in 2013, confidence intervals obtained from FME on the transformed parameters were simply all backtransformed one by one to yield asymmetric confidence intervals for the backtransformed parameters.</p> -<p>However, while there is a 1:1 relation between the rate constants in the model and the transformed parameters fitted in the model, the parameters obtained by the isometric logratio transformation are calculated from the set of formation fractions that quantify the paths to each of the compounds formed from a specific parent compound, and no such 1:1 relation exists.</p> -<p>Therefore, parameter confidence intervals for formation fractions obtained with this method only appear valid for the case of a single transformation product, where currently the logit transformation is used for the formation fraction.</p> -<p>The confidence intervals obtained by backtransformation for the cases where a 1:1 relation between transformed and original parameter exist are considered by the author of this vignette to be more accurate than those obtained using a re-estimation of the Hessian matrix after backtransformation, as implemented in the FME package.</p> +<p>In the first attempt at providing improved parameter confidence +intervals introduced to <code>mkin</code> in 2013, confidence intervals +obtained from FME on the transformed parameters were simply all +backtransformed one by one to yield asymmetric confidence intervals for +the backtransformed parameters.</p> +<p>However, while there is a 1:1 relation between the rate constants in +the model and the transformed parameters fitted in the model, the +parameters obtained by the isometric logratio transformation are +calculated from the set of formation fractions that quantify the paths +to each of the compounds formed from a specific parent compound, and no +such 1:1 relation exists.</p> +<p>Therefore, parameter confidence intervals for formation fractions +obtained with this method only appear valid for the case of a single +transformation product, where currently the logit transformation is used +for the formation fraction.</p> +<p>The confidence intervals obtained by backtransformation for the cases +where a 1:1 relation between transformed and original parameter exist +are considered by the author of this vignette to be more accurate than +those obtained using a re-estimation of the Hessian matrix after +backtransformation, as implemented in the FME package.</p> </div> <div class="section level3"> <h3 id="parameter-t-test-based-on-untransformed-parameters">Parameter t-test based on untransformed parameters<a class="anchor" aria-label="anchor" href="#parameter-t-test-based-on-untransformed-parameters"></a> </h3> -<p>The standard output of many nonlinear regression software packages includes the results from a test for significant difference from zero for all parameters. Such a test is also recommended to check the validity of rate constants in the FOCUS guidance <span class="citation">(FOCUS Work Group on Degradation Kinetics 2014, 96ff)</span>.</p> -<p>It has been argued that the precondition for this test, <em>i.e.</em> normal distribution of the estimator for the parameters, is not fulfilled in the case of nonlinear regression <span class="citation">(Ranke and Lehmann 2015)</span>. However, this test is commonly used by industry, consultants and national authorities in order to decide on the reliability of parameter estimates, based on the FOCUS guidance mentioned above. Therefore, the results of this one-sided t-test are included in the summary output from <code>mkin</code>.</p> -<p>As it is not reasonable to test for significant difference of the transformed parameters (<em>e.g.</em> <span class="math inline">\(log(k)\)</span>) from zero, the t-test is calculated based on the model definition before parameter transformation, <em>i.e.</em> in a similar way as in packages that do not apply such an internal parameter transformation. A note is included in the <code>mkin</code> output, pointing to the fact that the t-test is based on the unjustified assumption of normal distribution of the parameter estimators.</p> +<p>The standard output of many nonlinear regression software packages +includes the results from a test for significant difference from zero +for all parameters. Such a test is also recommended to check the +validity of rate constants in the FOCUS guidance <span class="citation">(FOCUS Work Group on Degradation Kinetics 2014, +96ff)</span>.</p> +<p>It has been argued that the precondition for this test, <em>i.e.</em> +normal distribution of the estimator for the parameters, is not +fulfilled in the case of nonlinear regression <span class="citation">(J. +Ranke and Lehmann 2015)</span>. However, this test is commonly used by +industry, consultants and national authorities in order to decide on the +reliability of parameter estimates, based on the FOCUS guidance +mentioned above. Therefore, the results of this one-sided t-test are +included in the summary output from <code>mkin</code>.</p> +<p>As it is not reasonable to test for significant difference of the +transformed parameters (<em>e.g.</em> <span class="math inline">\(log(k)\)</span>) from zero, the t-test is +calculated based on the model definition before parameter +transformation, <em>i.e.</em> in a similar way as in packages that do +not apply such an internal parameter transformation. A note is included +in the <code>mkin</code> output, pointing to the fact that the t-test is +based on the unjustified assumption of normal distribution of the +parameter estimators.</p> </div> </div> <div class="section level2"> <h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a> </h2> <!-- vim: set foldmethod=syntax: --> -<div id="refs" class="references hanging-indent"> -<div id="ref-bates1988"> -<p>Bates, D., and D. Watts. 1988. <em>Nonlinear Regression and Its Applications</em>. Wiley-Interscience.</p> +<div id="refs" class="references csl-bib-body hanging-indent"> +<div id="ref-bates1988" class="csl-entry"> +Bates, D., and D. Watts. 1988. <em>Nonlinear Regression and Its +Applications</em>. Wiley-Interscience. </div> -<div id="ref-FOCUS2006"> -<p>FOCUS Work Group on Degradation Kinetics. 2006. <em>Guidance Document on Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in Eu Registration. Report of the Focus Work Group on Degradation Kinetics</em>. <a href="http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics" class="external-link">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>.</p> +<div id="ref-FOCUS2006" class="csl-entry"> +FOCUS Work Group on Degradation Kinetics. 2006. <em>Guidance Document on +Estimating Persistence and Degradation Kinetics from Environmental Fate +Studies on Pesticides in EU Registration. Report of the FOCUS Work Group +on Degradation Kinetics</em>. <a href="http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics" class="external-link">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>. </div> -<div id="ref-FOCUSkinetics2014"> -<p>———. 2014. <em>Generic Guidance for Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in Eu Registration</em>. 1.1 ed. <a href="http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics" class="external-link">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>.</p> +<div id="ref-FOCUSkinetics2014" class="csl-entry"> +———. 2014. <em>Generic Guidance for Estimating Persistence and +Degradation Kinetics from Environmental Fate Studies on Pesticides in EU +Registration</em>. 1.1 ed. <a href="http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics" class="external-link">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>. </div> -<div id="ref-gao11"> -<p>Gao, Z., J. W. Green, J. Vanderborght, and W. Schmitt. 2011. “Improving Uncertainty Analysis in Kinetic Evaluations Using Iteratively Reweighted Least Squares.” Journal. <em>Environmental Science and Technology</em> 45: 4429–37.</p> +<div id="ref-gao11" class="csl-entry"> +Gao, Z., J. W. Green, J. Vanderborght, and W. Schmitt. 2011. +<span>“Improving Uncertainty Analysis in Kinetic Evaluations Using +Iteratively Reweighted Least Squares.”</span> Journal. <em>Environmental +Science and Technology</em> 45: 4429–37. </div> -<div id="ref-pkg:mkin"> -<p>Ranke, J. 2021. <em>‘mkin‘: Kinetic Evaluation of Chemical Degradation Data</em>. <a href="https://CRAN.R-project.org/package=mkin" class="external-link">https://CRAN.R-project.org/package=mkin</a>.</p> +<div id="ref-pkg:mkin" class="csl-entry"> +Ranke, J. 2021. <em>‘<span class="nocase">mkin</span>‘: +<span>K</span>inetic Evaluation of Chemical Degradation Data</em>. <a href="https://CRAN.R-project.org/package=mkin" class="external-link">https://CRAN.R-project.org/package=mkin</a>. </div> -<div id="ref-ranke2012"> -<p>Ranke, J., and R. Lehmann. 2012. “Parameter Reliability in Kinetic Evaluation of Environmental Metabolism Data - Assessment and the Influence of Model Specification.” In <em>SETAC World 20-24 May</em>. Berlin. <a href="https://jrwb.de/posters/Poster_SETAC_2012_Kinetic_parameter_uncertainty_model_parameterization_Lehmann_Ranke.pdf" class="external-link">https://jrwb.de/posters/Poster_SETAC_2012_Kinetic_parameter_uncertainty_model_parameterization_Lehmann_Ranke.pdf</a>.</p> +<div id="ref-ranke2012" class="csl-entry"> +Ranke, J., and R. Lehmann. 2012. <span>“Parameter Reliability in Kinetic +Evaluation of Environmental Metabolism Data - Assessment and the +Influence of Model Specification.”</span> In <em>SETAC World 20-24 +May</em>. Berlin. <a href="https://jrwb.de/posters/Poster_SETAC_2012_Kinetic_parameter_uncertainty_model_parameterization_Lehmann_Ranke.pdf" class="external-link">https://jrwb.de/posters/Poster_SETAC_2012_Kinetic_parameter_uncertainty_model_parameterization_Lehmann_Ranke.pdf</a>. </div> -<div id="ref-ranke2015"> -<p>———. 2015. “To T-Test or Not to T-Test, That Is the Question.” In <em>XV Symposium on Pesticide Chemistry 2-4 September 2015</em>. Piacenza. <a href="https://jrwb.de/posters/piacenza_2015.pdf" class="external-link">https://jrwb.de/posters/piacenza_2015.pdf</a>.</p> +<div id="ref-ranke2015" class="csl-entry"> +———. 2015. <span>“To t-Test or Not to t-Test, That Is the +Question.”</span> In <em>XV Symposium on Pesticide Chemistry 2-4 +September 2015</em>. Piacenza. <a href="https://jrwb.de/posters/piacenza_2015.pdf" class="external-link">https://jrwb.de/posters/piacenza_2015.pdf</a>. </div> -<div id="ref-ranke2019"> -<p>Ranke, Johannes, and Stefan Meinecke. 2019. “Error Models for the Kinetic Evaluation of Chemical Degradation Data.” <em>Environments</em> 6 (12). <a href="https://doi.org/10.3390/environments6120124" class="external-link">https://doi.org/10.3390/environments6120124</a>.</p> +<div id="ref-ranke2019" class="csl-entry"> +Ranke, Johannes, and Stefan Meinecke. 2019. <span>“Error Models for the +Kinetic Evaluation of Chemical Degradation Data.”</span> +<em>Environments</em> 6 (12). <a href="https://doi.org/10.3390/environments6120124" class="external-link">https://doi.org/10.3390/environments6120124</a>. </div> -<div id="ref-ranke2018"> -<p>Ranke, Johannes, Janina Wöltjen, and Stefan Meinecke. 2018. “Comparison of Software Tools for Kinetic Evaluation of Chemical Degradation Data.” <em>Environmental Sciences Europe</em> 30 (1): 17. <a href="https://doi.org/10.1186/s12302-018-0145-1" class="external-link">https://doi.org/10.1186/s12302-018-0145-1</a>.</p> +<div id="ref-ranke2018" class="csl-entry"> +Ranke, Johannes, Janina Wöltjen, and Stefan Meinecke. 2018. +<span>“Comparison of Software Tools for Kinetic Evaluation of Chemical +Degradation Data.”</span> <em>Environmental Sciences Europe</em> 30 (1): +17. <a href="https://doi.org/10.1186/s12302-018-0145-1" class="external-link">https://doi.org/10.1186/s12302-018-0145-1</a>. </div> -<div id="ref-schaefer2007"> -<p>Schäfer, D., B. Mikolasch, P. Rainbird, and B. Harvey. 2007. “KinGUI: A New Kinetic Software Tool for Evaluations According to FOCUS Degradation Kinetics.” In <em>Proceedings of the Xiii Symposium Pesticide Chemistry</em>, edited by Del Re A. A. M., Capri E., Fragoulis G., and Trevisan M., 916–23. Piacenza.</p> +<div id="ref-schaefer2007" class="csl-entry"> +Schäfer, D., B. Mikolasch, P. Rainbird, and B. Harvey. 2007. +<span>“<span>KinGUI</span>: A New Kinetic Software Tool for Evaluations +According to <span>FOCUS</span> Degradation Kinetics.”</span> In +<em>Proceedings of the XIII Symposium Pesticide Chemistry</em>, edited +by Del Re A. A. M., Capri E., Fragoulis G., and Trevisan M., 916–23. +Piacenza. </div> -<div id="ref-soetaert2010"> -<p>Soetaert, Karline, and Thomas Petzoldt. 2010. “Inverse Modelling, Sensitivity and Monte Carlo Analysis in R Using Package FME.” <em>Journal of Statistical Software</em> 33 (3): 1–28. <a href="https://doi.org/10.18637/jss.v033.i03" class="external-link">https://doi.org/10.18637/jss.v033.i03</a>.</p> +<div id="ref-soetaert2010" class="csl-entry"> +Soetaert, Karline, and Thomas Petzoldt. 2010. <span>“Inverse Modelling, +Sensitivity and Monte Carlo Analysis in <span>R</span> Using Package +<span>FME</span>.”</span> <em>Journal of Statistical Software</em> 33 +(3): 1–28. <a href="https://doi.org/10.18637/jss.v033.i03" class="external-link">https://doi.org/10.18637/jss.v033.i03</a>. </div> </div> </div> @@ -270,7 +456,7 @@ <div class="pkgdown"> <p></p> -<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p> +<p>Site built with <a 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SOP Attachment examples</a> + </li> + </ul> +</li> +<li> + <a href="../../news/index.html">News</a> +</li> + </ul> +<ul class="nav navbar-nav navbar-right"> +<li> + <a href="https://github.com/jranke/mkin/" class="external-link"> + <span class="fab fa-github fa-lg"></span> + + </a> +</li> + </ul> +</div> +<!--/.nav-collapse --> + </div> +<!--/.container --> +</div> +<!--/.navbar --> + + + + </header><div class="row"> + <div class="col-md-9 contents"> + <div class="page-header toc-ignore"> + <h1 data-toc-skip>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 20 April 2023, +last compiled on 20 April 2023</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="hidden 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 1.2.3 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">700.1</td> +<td align="right">696.2</td> +<td align="right">-340.1</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">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">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">C</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">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">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</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">Fth, 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">Fth, FO</td> +<td align="left">Fth, FO</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">NA</td> +</tr> +</tbody> +</table> +<p>The model comparison below suggests 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="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">2692.8</td> +<td align="right">2686.6</td> +<td align="right">-1330.4</td> +</tr> +<tr class="even"> +<td align="left">sfo_path_1 tc</td> +<td align="right">17</td> +<td align="right">2657.7</td> +<td align="right">2651.1</td> +<td align="right">-1311.9</td> +</tr> +<tr class="odd"> +<td align="left">fomc_path_1 const</td> +<td align="right">18</td> +<td align="right">2427.8</td> +<td align="right">2420.8</td> +<td align="right">-1195.9</td> +</tr> +<tr class="even"> +<td align="left">fomc_path_1 tc</td> +<td align="right">19</td> +<td align="right">2423.4</td> +<td align="right">2416.0</td> +<td align="right">-1192.7</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">2427.3</td> +<td align="right">2419.5</td> +<td align="right">-1193.7</td> +</tr> +<tr class="even"> +<td align="left">dfop_path_1 tc</td> +<td align="right">20</td> +<td align="right">2398.0</td> +<td align="right">2390.2</td> +<td align="right">-1179.0</td> +</tr> +<tr class="odd"> +<td align="left">sforb_path_1 tc</td> +<td align="right">20</td> +<td align="right">2399.8</td> +<td align="right">2392.0</td> +<td align="right">-1179.9</td> +</tr> +<tr class="even"> +<td align="left">hs_path_1 tc</td> +<td align="right">21</td> +<td align="right">2422.3</td> +<td align="right">2414.1</td> +<td align="right">-1190.2</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="cb16"><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="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">"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="cb18"><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="cb19"><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">C</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="cb20"><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">C</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 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="cb21"><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="cb22"><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">OK</td> +<td align="left">FO</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.</p> +<div class="sourceCode" id="cb23"><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">sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)</td> +<td align="left">NA</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 both fits, 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="cb24"><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="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 const</td> +<td align="right">20</td> +<td align="right">2308.3</td> +<td align="right">2300.5</td> +<td align="right">-1134.2</td> +</tr> +<tr class="even"> +<td align="left">fomc_path_2 tc</td> +<td align="right">21</td> +<td align="right">2248.3</td> +<td align="right">2240.1</td> +<td align="right">-1103.2</td> +</tr> +<tr class="odd"> +<td align="left">dfop_path_2 const</td> +<td align="right">22</td> +<td align="right">2289.6</td> +<td align="right">2281.0</td> +<td align="right">-1122.8</td> +</tr> +<tr class="even"> +<td align="left">sforb_path_2 const</td> +<td align="right">22</td> +<td align="right">2284.1</td> +<td align="right">2275.5</td> +<td align="right">-1120.0</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">2240.4</td> +<td align="right">2231.8</td> +<td align="right">-1098.2</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="cb25"><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="cb26"><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="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">"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="cb28"><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="cb29"><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="cb30"><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="cb31"><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="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">2250.9</td> +<td align="right">2243.5</td> +<td align="right">-1106.5</td> +</tr> +<tr class="even"> +<td align="left">dfop_path_2 const</td> +<td align="right">20</td> +<td align="right">2281.7</td> +<td align="right">2273.9</td> +<td align="right">-1120.8</td> +</tr> +<tr class="odd"> +<td align="left">sforb_path_2 const</td> +<td align="right">20</td> +<td align="right">2279.5</td> +<td align="right">2271.7</td> +<td align="right">-1119.7</td> +</tr> +<tr class="even"> +<td align="left">dfop_path_2 tc</td> +<td align="right">20</td> +<td align="right">2231.5</td> +<td align="right">2223.7</td> +<td align="right">-1095.8</td> +</tr> +<tr class="odd"> +<td align="left">sforb_path_2 tc</td> +<td align="right">20</td> +<td align="right">2235.7</td> +<td align="right">2227.9</td> +<td align="right">-1097.9</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="cb32"><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="cb33"><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="cb34"><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="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">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: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 07:44:55 2023 +Date of summary: Thu Apr 20 20:01:30 2023 + +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 431.793 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 22.5404 10.4289 + +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 8.684 0.00 +f_JCZ38_qlogis 0.0000 0.000 13.48 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2693 2687 -1330 + +Optimised parameters: + est. lower upper +cyan_0 95.0946 NA NA +log_k_cyan -3.8544 NA NA +log_k_JCZ38 -3.0402 NA NA +log_k_J9Z38 -5.0109 NA NA +log_k_JSE76 -5.2857 NA NA +f_cyan_ilr_1 0.8069 NA NA +f_cyan_ilr_2 16.6623 NA NA +f_JCZ38_qlogis 1.3602 NA NA +a.1 4.8326 NA NA +SD.log_k_cyan 0.5842 NA NA +SD.log_k_JCZ38 1.2680 NA NA +SD.log_k_J9Z38 0.3626 NA NA +SD.log_k_JSE76 0.5244 NA NA +SD.f_cyan_ilr_1 0.2752 NA NA +SD.f_cyan_ilr_2 2.3556 NA NA +SD.f_JCZ38_qlogis 0.2400 NA NA + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_cyan 0.5842 NA NA +SD.log_k_JCZ38 1.2680 NA NA +SD.log_k_J9Z38 0.3626 NA NA +SD.log_k_JSE76 0.5244 NA NA +SD.f_cyan_ilr_1 0.2752 NA NA +SD.f_cyan_ilr_2 2.3556 NA NA +SD.f_JCZ38_qlogis 0.2400 NA NA + +Variance model: + est. lower upper +a.1 4.833 NA NA + +Backtransformed parameters: + est. lower upper +cyan_0 95.094581 NA NA +k_cyan 0.021186 NA NA +k_JCZ38 0.047825 NA NA +k_J9Z38 0.006665 NA NA +k_JSE76 0.005063 NA NA +f_cyan_to_JCZ38 0.757885 NA NA +f_cyan_to_J9Z38 0.242115 NA NA +f_JCZ38_to_JSE76 0.795792 NA NA + +Resulting formation fractions: + ff +cyan_JCZ38 7.579e-01 +cyan_J9Z38 2.421e-01 +cyan_sink 5.877e-10 +JCZ38_JSE76 7.958e-01 +JCZ38_sink 2.042e-01 + +Estimated disappearance times: + DT50 DT90 +cyan 32.72 108.68 +JCZ38 14.49 48.15 +J9Z38 103.99 345.46 +JSE76 136.90 454.76 + +</code></pre> +<p></p> +<caption> +Hierarchical SFO path 1 fit with two-component error +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 07:44:53 2023 +Date of summary: Thu Apr 20 20:01:30 2023 + +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 429.526 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 20.0030 15.1336 + +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 7.334 0.00 +f_JCZ38_qlogis 0.0000 0.000 11.78 + +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 94.72923 NA NA +log_k_cyan -3.91670 NA NA +log_k_JCZ38 -3.12917 NA NA +log_k_J9Z38 -5.06070 NA NA +log_k_JSE76 -5.09254 NA NA +f_cyan_ilr_1 0.81116 NA NA +f_cyan_ilr_2 39.97850 NA NA +f_JCZ38_qlogis 3.09728 NA NA +a.1 3.95044 NA NA +b.1 0.07998 NA NA +SD.log_k_cyan 0.58855 NA NA +SD.log_k_JCZ38 1.29753 NA NA +SD.log_k_J9Z38 0.62851 NA NA +SD.log_k_JSE76 0.37235 NA NA +SD.f_cyan_ilr_1 0.37346 NA NA +SD.f_cyan_ilr_2 1.41667 NA NA +SD.f_JCZ38_qlogis 1.81467 NA NA + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_cyan 0.5886 NA NA +SD.log_k_JCZ38 1.2975 NA NA +SD.log_k_J9Z38 0.6285 NA NA +SD.log_k_JSE76 0.3724 NA NA +SD.f_cyan_ilr_1 0.3735 NA NA +SD.f_cyan_ilr_2 1.4167 NA NA +SD.f_JCZ38_qlogis 1.8147 NA NA + +Variance model: + est. lower upper +a.1 3.95044 NA NA +b.1 0.07998 NA NA + +Backtransformed parameters: + est. lower upper +cyan_0 94.729229 NA NA +k_cyan 0.019907 NA NA +k_JCZ38 0.043754 NA NA +k_J9Z38 0.006341 NA NA +k_JSE76 0.006142 NA NA +f_cyan_to_JCZ38 0.758991 NA NA +f_cyan_to_J9Z38 0.241009 NA NA +f_JCZ38_to_JSE76 0.956781 NA NA + +Resulting formation fractions: + ff +cyan_JCZ38 0.75899 +cyan_J9Z38 0.24101 +cyan_sink 0.00000 +JCZ38_JSE76 0.95678 +JCZ38_sink 0.04322 + +Estimated disappearance times: + DT50 DT90 +cyan 34.82 115.67 +JCZ38 15.84 52.63 +J9Z38 109.31 363.12 +JSE76 112.85 374.87 + +</code></pre> +<p></p> +<caption> +Hierarchical FOMC path 1 fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 07:45:50 2023 +Date of summary: Thu Apr 20 20:01:30 2023 + +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 477.996 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 + 7.3870 15.7604 -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 12.33 0.00 0.0000 0.0000 +f_JCZ38_qlogis 0.00 20.42 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_0 101.0225 98.306270 103.7387 +log_k_JCZ38 -3.3786 -4.770657 -1.9866 +log_k_J9Z38 -5.2603 -5.902085 -4.6186 +log_k_JSE76 -6.1427 -7.318336 -4.9671 +f_cyan_ilr_1 0.7437 0.421215 1.0663 +f_cyan_ilr_2 0.9108 0.267977 1.5537 +f_JCZ38_qlogis 2.0487 0.524897 3.5724 +log_alpha -0.2268 -0.618049 0.1644 +log_beta 2.8986 2.700701 3.0964 +a.1 3.4058 3.169913 3.6416 +SD.cyan_0 2.5279 0.454190 4.6016 +SD.log_k_JCZ38 1.5636 0.572824 2.5543 +SD.log_k_J9Z38 0.5316 -0.004405 1.0677 +SD.log_k_JSE76 0.9903 0.106325 1.8742 +SD.f_cyan_ilr_1 0.3464 0.112066 0.5807 +SD.f_cyan_ilr_2 0.2804 -0.393900 0.9546 +SD.f_JCZ38_qlogis 0.9416 -0.152986 2.0362 +SD.log_alpha 0.4273 0.161044 0.6936 + +Correlation: + cyan_0 l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 log_lph +log_k_JCZ38 -0.0156 +log_k_J9Z38 -0.0493 0.0073 +log_k_JSE76 -0.0329 0.0018 0.0069 +f_cyan_ilr_1 -0.0086 0.0180 -0.1406 0.0012 +f_cyan_ilr_2 -0.2629 0.0779 0.2826 0.0274 0.0099 +f_JCZ38_qlogis 0.0713 -0.0747 -0.0505 0.1169 -0.1022 -0.4893 +log_alpha -0.0556 0.0120 0.0336 0.0193 0.0036 0.0840 -0.0489 +log_beta -0.2898 0.0460 0.1305 0.0768 0.0190 0.4071 -0.1981 0.2772 + +Random effects: + est. lower upper +SD.cyan_0 2.5279 0.454190 4.6016 +SD.log_k_JCZ38 1.5636 0.572824 2.5543 +SD.log_k_J9Z38 0.5316 -0.004405 1.0677 +SD.log_k_JSE76 0.9903 0.106325 1.8742 +SD.f_cyan_ilr_1 0.3464 0.112066 0.5807 +SD.f_cyan_ilr_2 0.2804 -0.393900 0.9546 +SD.f_JCZ38_qlogis 0.9416 -0.152986 2.0362 +SD.log_alpha 0.4273 0.161044 0.6936 + +Variance model: + est. lower upper +a.1 3.406 3.17 3.642 + +Backtransformed parameters: + est. lower upper +cyan_0 1.010e+02 9.831e+01 1.037e+02 +k_JCZ38 3.409e-02 8.475e-03 1.372e-01 +k_J9Z38 5.194e-03 2.734e-03 9.867e-03 +k_JSE76 2.149e-03 6.633e-04 6.963e-03 +f_cyan_to_JCZ38 6.481e-01 NA NA +f_cyan_to_J9Z38 2.264e-01 NA NA +f_JCZ38_to_JSE76 8.858e-01 6.283e-01 9.727e-01 +alpha 7.971e-01 5.390e-01 1.179e+00 +beta 1.815e+01 1.489e+01 2.212e+01 + +Resulting formation fractions: + ff +cyan_JCZ38 0.6481 +cyan_J9Z38 0.2264 +cyan_sink 0.1255 +JCZ38_JSE76 0.8858 +JCZ38_sink 0.1142 + +Estimated disappearance times: + DT50 DT90 DT50back +cyan 25.15 308.01 92.72 +JCZ38 20.33 67.54 NA +J9Z38 133.46 443.35 NA +JSE76 322.53 1071.42 NA + +</code></pre> +<p></p> +<caption> +Hierarchical FOMC path 1 fit with two-component error +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 07:45:45 2023 +Date of summary: Thu Apr 20 20:01:30 2023 + +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 480.648 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 + 101.13827 -3.32493 -5.08921 -5.93478 0.71330 + f_cyan_ilr_2 f_JCZ38_qlogis log_alpha log_beta + 10.05989 12.79248 -0.09621 3.10646 + +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 5.643 0.000 0.000 0.00 0.0000 +log_k_JCZ38 0.000 2.319 0.000 0.00 0.0000 +log_k_J9Z38 0.000 0.000 1.731 0.00 0.0000 +log_k_JSE76 0.000 0.000 0.000 1.86 0.0000 +f_cyan_ilr_1 0.000 0.000 0.000 0.00 0.7186 +f_cyan_ilr_2 0.000 0.000 0.000 0.00 0.0000 +f_JCZ38_qlogis 0.000 0.000 0.000 0.00 0.0000 +log_alpha 0.000 0.000 0.000 0.00 0.0000 +log_beta 0.000 0.000 0.000 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 12.49 0.00 0.0000 0.0000 +f_JCZ38_qlogis 0.00 20.19 0.0000 0.0000 +log_alpha 0.00 0.00 0.3142 0.0000 +log_beta 0.00 0.00 0.0000 0.7331 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2423 2416 -1193 + +Optimised parameters: + est. lower upper +cyan_0 100.57649 NA NA +log_k_JCZ38 -3.46250 NA NA +log_k_J9Z38 -5.24442 NA NA +log_k_JSE76 -5.75229 NA NA +f_cyan_ilr_1 0.68480 NA NA +f_cyan_ilr_2 0.61670 NA NA +f_JCZ38_qlogis 87.97407 NA NA +log_alpha -0.15699 NA NA +log_beta 3.01540 NA NA +a.1 3.11518 NA NA +b.1 0.04445 NA NA +SD.log_k_JCZ38 1.40732 NA NA +SD.log_k_J9Z38 0.56510 NA NA +SD.log_k_JSE76 0.72067 NA NA +SD.f_cyan_ilr_1 0.31199 NA NA +SD.f_cyan_ilr_2 0.36894 NA NA +SD.f_JCZ38_qlogis 6.92892 NA NA +SD.log_alpha 0.25662 NA NA +SD.log_beta 0.35845 NA NA + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_JCZ38 1.4073 NA NA +SD.log_k_J9Z38 0.5651 NA NA +SD.log_k_JSE76 0.7207 NA NA +SD.f_cyan_ilr_1 0.3120 NA NA +SD.f_cyan_ilr_2 0.3689 NA NA +SD.f_JCZ38_qlogis 6.9289 NA NA +SD.log_alpha 0.2566 NA NA +SD.log_beta 0.3585 NA NA + +Variance model: + est. lower upper +a.1 3.11518 NA NA +b.1 0.04445 NA NA + +Backtransformed parameters: + est. lower upper +cyan_0 1.006e+02 NA NA +k_JCZ38 3.135e-02 NA NA +k_J9Z38 5.277e-03 NA NA +k_JSE76 3.175e-03 NA NA +f_cyan_to_JCZ38 5.991e-01 NA NA +f_cyan_to_J9Z38 2.275e-01 NA NA +f_JCZ38_to_JSE76 1.000e+00 NA NA +alpha 8.547e-01 NA NA +beta 2.040e+01 NA NA + +Resulting formation fractions: + ff +cyan_JCZ38 0.5991 +cyan_J9Z38 0.2275 +cyan_sink 0.1734 +JCZ38_JSE76 1.0000 +JCZ38_sink 0.0000 + +Estimated disappearance times: + DT50 DT90 DT50back +cyan 25.50 281.29 84.68 +JCZ38 22.11 73.44 NA +J9Z38 131.36 436.35 NA +JSE76 218.28 725.11 NA + +</code></pre> +<p></p> +<caption> +Hierarchical DFOP path 1 fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 07:46:41 2023 +Date of summary: Thu Apr 20 20:01:30 2023 + +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 528.713 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 + 102.0644 -3.4008 -5.0024 -5.8613 0.6855 + f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 g_qlogis + 1.2365 13.7245 -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 16.11 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_0 102.6079 NA NA +log_k_JCZ38 -3.4855 NA NA +log_k_J9Z38 -5.1686 NA NA +log_k_JSE76 -5.6697 NA NA +f_cyan_ilr_1 0.6714 NA NA +f_cyan_ilr_2 0.4986 NA NA +f_JCZ38_qlogis 55.4760 NA NA +log_k1 -1.8409 NA NA +log_k2 -4.4915 NA NA +g_qlogis -0.6403 NA NA +a.1 3.2387 NA NA +SD.log_k_JCZ38 1.4524 NA NA +SD.log_k_J9Z38 0.5151 NA NA +SD.log_k_JSE76 0.6514 NA NA +SD.f_cyan_ilr_1 0.3023 NA NA +SD.f_cyan_ilr_2 0.2959 NA NA +SD.f_JCZ38_qlogis 1.9984 NA NA +SD.log_k1 0.5188 NA NA +SD.log_k2 0.3894 NA NA +SD.g_qlogis 0.8579 NA NA + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_JCZ38 1.4524 NA NA +SD.log_k_J9Z38 0.5151 NA NA +SD.log_k_JSE76 0.6514 NA NA +SD.f_cyan_ilr_1 0.3023 NA NA +SD.f_cyan_ilr_2 0.2959 NA NA +SD.f_JCZ38_qlogis 1.9984 NA NA +SD.log_k1 0.5188 NA NA +SD.log_k2 0.3894 NA NA +SD.g_qlogis 0.8579 NA NA + +Variance model: + est. lower upper +a.1 3.239 NA NA + +Backtransformed parameters: + est. lower upper +cyan_0 1.026e+02 NA NA +k_JCZ38 3.064e-02 NA NA +k_J9Z38 5.692e-03 NA NA +k_JSE76 3.449e-03 NA NA +f_cyan_to_JCZ38 5.798e-01 NA NA +f_cyan_to_J9Z38 2.243e-01 NA NA +f_JCZ38_to_JSE76 1.000e+00 NA NA +k1 1.587e-01 NA NA +k2 1.120e-02 NA NA +g 3.452e-01 NA NA + +Resulting formation fractions: + ff +cyan_JCZ38 0.5798 +cyan_J9Z38 0.2243 +cyan_sink 0.1958 +JCZ38_JSE76 1.0000 +JCZ38_sink 0.0000 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +cyan 25.21 167.73 50.49 4.368 61.87 +JCZ38 22.62 75.15 NA NA NA +J9Z38 121.77 404.50 NA NA NA +JSE76 200.98 667.64 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: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 07:49:05 2023 +Date of summary: Thu Apr 20 20:01:30 2023 + +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 673.139 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 + 6.7799 13.7245 -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 0.6838 +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 11.77 0.00 0.0000 0.0000 0.000 +f_JCZ38_qlogis 0.00 16.11 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_0 100.8076 NA NA +log_k_JCZ38 -3.4684 NA NA +log_k_J9Z38 -5.0844 NA NA +log_k_JSE76 -5.5743 NA NA +f_cyan_ilr_1 0.6669 NA NA +f_cyan_ilr_2 0.7912 NA NA +f_JCZ38_qlogis 84.1825 NA NA +log_k1 -2.1671 NA NA +log_k2 -4.5447 NA NA +g_qlogis -0.5631 NA NA +a.1 2.9627 NA NA +b.1 0.0444 NA NA +SD.log_k_JCZ38 1.4044 NA NA +SD.log_k_J9Z38 0.6410 NA NA +SD.log_k_JSE76 0.5391 NA NA +SD.f_cyan_ilr_1 0.3203 NA NA +SD.f_cyan_ilr_2 0.5038 NA NA +SD.f_JCZ38_qlogis 3.5865 NA NA +SD.log_k2 0.3119 NA NA +SD.g_qlogis 0.8276 NA NA + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_JCZ38 1.4044 NA NA +SD.log_k_J9Z38 0.6410 NA NA +SD.log_k_JSE76 0.5391 NA NA +SD.f_cyan_ilr_1 0.3203 NA NA +SD.f_cyan_ilr_2 0.5038 NA NA +SD.f_JCZ38_qlogis 3.5865 NA NA +SD.log_k2 0.3119 NA NA +SD.g_qlogis 0.8276 NA NA + +Variance model: + est. lower upper +a.1 2.9627 NA NA +b.1 0.0444 NA NA + +Backtransformed parameters: + est. lower upper +cyan_0 1.008e+02 NA NA +k_JCZ38 3.117e-02 NA NA +k_J9Z38 6.193e-03 NA NA +k_JSE76 3.794e-03 NA NA +f_cyan_to_JCZ38 6.149e-01 NA NA +f_cyan_to_J9Z38 2.395e-01 NA NA +f_JCZ38_to_JSE76 1.000e+00 NA NA +k1 1.145e-01 NA NA +k2 1.062e-02 NA NA +g 3.628e-01 NA NA + +Resulting formation fractions: + ff +cyan_JCZ38 0.6149 +cyan_J9Z38 0.2395 +cyan_sink 0.1456 +JCZ38_JSE76 1.0000 +JCZ38_sink 0.0000 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +cyan 26.26 174.32 52.47 6.053 65.25 +JCZ38 22.24 73.88 NA NA NA +J9Z38 111.93 371.82 NA NA NA +JSE76 182.69 606.88 NA NA NA + +</code></pre> +<p></p> +<caption> +Hierarchical SFORB path 1 fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 07:46:35 2023 +Date of summary: Thu Apr 20 20:01:30 2023 + +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 531.17 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 + 13.7418 + +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 16.14 + +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_0 102.7803 NA NA +log_k_cyan_free -2.8068 NA NA +log_k_cyan_free_bound -2.5714 NA NA +log_k_cyan_bound_free -3.4426 NA NA +log_k_JCZ38 -3.4994 NA NA +log_k_J9Z38 -5.1148 NA NA +log_k_JSE76 -5.6335 NA NA +f_cyan_ilr_1 0.6597 NA NA +f_cyan_ilr_2 0.5132 NA NA +f_JCZ38_qlogis 37.2090 NA NA +a.1 3.2367 NA NA +SD.log_k_cyan_free 0.3161 NA NA +SD.log_k_cyan_free_bound 0.8103 NA NA +SD.log_k_cyan_bound_free 0.5554 NA NA +SD.log_k_JCZ38 1.4858 NA NA +SD.log_k_J9Z38 0.5859 NA NA +SD.log_k_JSE76 0.6195 NA NA +SD.f_cyan_ilr_1 0.3118 NA NA +SD.f_cyan_ilr_2 0.3344 NA NA +SD.f_JCZ38_qlogis 0.5518 NA NA + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_cyan_free 0.3161 NA NA +SD.log_k_cyan_free_bound 0.8103 NA NA +SD.log_k_cyan_bound_free 0.5554 NA NA +SD.log_k_JCZ38 1.4858 NA NA +SD.log_k_J9Z38 0.5859 NA NA +SD.log_k_JSE76 0.6195 NA NA +SD.f_cyan_ilr_1 0.3118 NA NA +SD.f_cyan_ilr_2 0.3344 NA NA +SD.f_JCZ38_qlogis 0.5518 NA NA + +Variance model: + est. lower upper +a.1 3.237 NA NA + +Backtransformed parameters: + est. lower upper +cyan_free_0 1.028e+02 NA NA +k_cyan_free 6.040e-02 NA NA +k_cyan_free_bound 7.643e-02 NA NA +k_cyan_bound_free 3.198e-02 NA NA +k_JCZ38 3.022e-02 NA NA +k_J9Z38 6.007e-03 NA NA +k_JSE76 3.576e-03 NA NA +f_cyan_free_to_JCZ38 5.787e-01 NA NA +f_cyan_free_to_J9Z38 2.277e-01 NA NA +f_JCZ38_to_JSE76 1.000e+00 NA NA + +Estimated Eigenvalues of SFORB model(s): +cyan_b1 cyan_b2 cyan_g +0.15646 0.01235 0.33341 + +Resulting formation fractions: + ff +cyan_free_JCZ38 0.5787 +cyan_free_J9Z38 0.2277 +cyan_free_sink 0.1936 +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 24.48 153.7 46.26 4.43 56.15 +JCZ38 22.94 76.2 NA NA NA +J9Z38 115.39 383.3 NA NA NA +JSE76 193.84 643.9 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: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 07:49:08 2023 +Date of summary: Thu Apr 20 20:01:30 2023 + +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 675.659 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 6.8139 + f_JCZ38_qlogis + 13.7419 + +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 11.84 0.00 +f_JCZ38_qlogis 0.0000 0.00 16.14 + +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_0 100.69983 NA NA +log_k_cyan_free -3.11584 NA NA +log_k_cyan_free_bound -3.15216 NA NA +log_k_cyan_bound_free -3.65986 NA NA +log_k_JCZ38 -3.47811 NA NA +log_k_J9Z38 -5.08835 NA NA +log_k_JSE76 -5.55514 NA NA +f_cyan_ilr_1 0.66764 NA NA +f_cyan_ilr_2 0.78329 NA NA +f_JCZ38_qlogis 25.35245 NA NA +a.1 2.99088 NA NA +b.1 0.04346 NA NA +SD.log_k_cyan_free 0.48797 NA NA +SD.log_k_cyan_bound_free 0.27243 NA NA +SD.log_k_JCZ38 1.42450 NA NA +SD.log_k_J9Z38 0.63496 NA NA +SD.log_k_JSE76 0.55951 NA NA +SD.f_cyan_ilr_1 0.32687 NA NA +SD.f_cyan_ilr_2 0.48056 NA NA +SD.f_JCZ38_qlogis 0.43818 NA NA + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_cyan_free 0.4880 NA NA +SD.log_k_cyan_bound_free 0.2724 NA NA +SD.log_k_JCZ38 1.4245 NA NA +SD.log_k_J9Z38 0.6350 NA NA +SD.log_k_JSE76 0.5595 NA NA +SD.f_cyan_ilr_1 0.3269 NA NA +SD.f_cyan_ilr_2 0.4806 NA NA +SD.f_JCZ38_qlogis 0.4382 NA NA + +Variance model: + est. lower upper +a.1 2.99088 NA NA +b.1 0.04346 NA NA + +Backtransformed parameters: + est. lower upper +cyan_free_0 1.007e+02 NA NA +k_cyan_free 4.434e-02 NA NA +k_cyan_free_bound 4.276e-02 NA NA +k_cyan_bound_free 2.574e-02 NA NA +k_JCZ38 3.087e-02 NA NA +k_J9Z38 6.168e-03 NA NA +k_JSE76 3.868e-03 NA NA +f_cyan_free_to_JCZ38 6.143e-01 NA NA +f_cyan_free_to_J9Z38 2.389e-01 NA NA +f_JCZ38_to_JSE76 1.000e+00 NA NA + +Estimated Eigenvalues of SFORB model(s): +cyan_b1 cyan_b2 cyan_g +0.10161 0.01123 0.36636 + +Resulting formation fractions: + ff +cyan_free_JCZ38 6.143e-01 +cyan_free_J9Z38 2.389e-01 +cyan_free_sink 1.468e-01 +cyan_free 1.000e+00 +JCZ38_JSE76 1.000e+00 +JCZ38_sink 9.763e-12 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 +cyan 25.91 164.4 49.49 6.822 61.72 +JCZ38 22.46 74.6 NA NA NA +J9Z38 112.37 373.3 NA NA NA +JSE76 179.22 595.4 NA NA NA + +</code></pre> +<p></p> +<caption> +Hierarchical HS path 1 fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 07:46:30 2023 +Date of summary: Thu Apr 20 20:01:30 2023 + +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 525.846 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 + 102.8738 -3.4490 -4.9348 -5.5989 0.6469 + f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 log_tb + 1.2854 9.7193 -2.9084 -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 5.409 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 1.006 0.0000 +f_cyan_ilr_1 0.000 0.00 0.00 0.000 0.6371 +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 2.167 0.00 0.0000 0.0000 0.0000 +f_JCZ38_qlogis 0.000 10.22 0.0000 0.0000 0.0000 +log_k1 0.000 0.00 0.7003 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 0.6774 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2427 2420 -1194 + +Optimised parameters: + est. lower upper +cyan_0 101.84849 NA NA +log_k_JCZ38 -3.47365 NA NA +log_k_J9Z38 -5.10562 NA NA +log_k_JSE76 -5.60318 NA NA +f_cyan_ilr_1 0.66127 NA NA +f_cyan_ilr_2 0.60283 NA NA +f_JCZ38_qlogis 45.06408 NA NA +log_k1 -3.10124 NA NA +log_k2 -4.39028 NA NA +log_tb 2.32256 NA NA +a.1 3.32683 NA NA +SD.log_k_JCZ38 1.41427 NA NA +SD.log_k_J9Z38 0.54767 NA NA +SD.log_k_JSE76 0.62147 NA NA +SD.f_cyan_ilr_1 0.30189 NA NA +SD.f_cyan_ilr_2 0.34960 NA NA +SD.f_JCZ38_qlogis 0.04644 NA NA +SD.log_k1 0.39534 NA NA +SD.log_k2 0.43468 NA NA +SD.log_tb 0.60781 NA NA + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_JCZ38 1.41427 NA NA +SD.log_k_J9Z38 0.54767 NA NA +SD.log_k_JSE76 0.62147 NA NA +SD.f_cyan_ilr_1 0.30189 NA NA +SD.f_cyan_ilr_2 0.34960 NA NA +SD.f_JCZ38_qlogis 0.04644 NA NA +SD.log_k1 0.39534 NA NA +SD.log_k2 0.43468 NA NA +SD.log_tb 0.60781 NA NA + +Variance model: + est. lower upper +a.1 3.327 NA NA + +Backtransformed parameters: + est. lower upper +cyan_0 1.018e+02 NA NA +k_JCZ38 3.100e-02 NA NA +k_J9Z38 6.063e-03 NA NA +k_JSE76 3.686e-03 NA NA +f_cyan_to_JCZ38 5.910e-01 NA NA +f_cyan_to_J9Z38 2.320e-01 NA NA +f_JCZ38_to_JSE76 1.000e+00 NA NA +k1 4.499e-02 NA NA +k2 1.240e-02 NA NA +tb 1.020e+01 NA NA + +Resulting formation fractions: + ff +cyan_JCZ38 0.591 +cyan_J9Z38 0.232 +cyan_sink 0.177 +JCZ38_JSE76 1.000 +JCZ38_sink 0.000 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +cyan 29.09 158.91 47.84 15.41 55.91 +JCZ38 22.36 74.27 NA NA NA +J9Z38 114.33 379.80 NA NA NA +JSE76 188.04 624.66 NA NA NA + +</code></pre> +<p></p> +<caption> +Hierarchical HS path 1 fit with two-component error +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 07:46:19 2023 +Date of summary: Thu Apr 20 20:01:30 2023 + +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 514.968 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 + 101.168 -3.358 -4.941 -5.794 0.676 + f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 log_tb + 5.740 13.863 -3.147 -4.262 2.173 + +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 5.79 0.000 0.000 0.000 0.0000 +log_k_JCZ38 0.00 2.271 0.000 0.000 0.0000 +log_k_J9Z38 0.00 0.000 1.614 0.000 0.0000 +log_k_JSE76 0.00 0.000 0.000 1.264 0.0000 +f_cyan_ilr_1 0.00 0.000 0.000 0.000 0.6761 +f_cyan_ilr_2 0.00 0.000 0.000 0.000 0.0000 +f_JCZ38_qlogis 0.00 0.000 0.000 0.000 0.0000 +log_k1 0.00 0.000 0.000 0.000 0.0000 +log_k2 0.00 0.000 0.000 0.000 0.0000 +log_tb 0.00 0.000 0.000 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 0.000 +log_k_JCZ38 0.000 0.00 0.0000 0.0000 0.000 +log_k_J9Z38 0.000 0.00 0.0000 0.0000 0.000 +log_k_JSE76 0.000 0.00 0.0000 0.0000 0.000 +f_cyan_ilr_1 0.000 0.00 0.0000 0.0000 0.000 +f_cyan_ilr_2 9.572 0.00 0.0000 0.0000 0.000 +f_JCZ38_qlogis 0.000 19.19 0.0000 0.0000 0.000 +log_k1 0.000 0.00 0.8705 0.0000 0.000 +log_k2 0.000 0.00 0.0000 0.9288 0.000 +log_tb 0.000 0.00 0.0000 0.0000 1.065 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2422 2414 -1190 + +Optimised parameters: + est. lower upper +cyan_0 100.9521 NA NA +log_k_JCZ38 -3.4629 NA NA +log_k_J9Z38 -5.0346 NA NA +log_k_JSE76 -5.5722 NA NA +f_cyan_ilr_1 0.6560 NA NA +f_cyan_ilr_2 0.7983 NA NA +f_JCZ38_qlogis 42.7949 NA NA +log_k1 -3.1721 NA NA +log_k2 -4.4039 NA NA +log_tb 2.3994 NA NA +a.1 3.0586 NA NA +b.1 0.0380 NA NA +SD.log_k_JCZ38 1.3754 NA NA +SD.log_k_J9Z38 0.6703 NA NA +SD.log_k_JSE76 0.5876 NA NA +SD.f_cyan_ilr_1 0.3272 NA NA +SD.f_cyan_ilr_2 0.5300 NA NA +SD.f_JCZ38_qlogis 6.4465 NA NA +SD.log_k1 0.4135 NA NA +SD.log_k2 0.4182 NA NA +SD.log_tb 0.6035 NA NA + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_JCZ38 1.3754 NA NA +SD.log_k_J9Z38 0.6703 NA NA +SD.log_k_JSE76 0.5876 NA NA +SD.f_cyan_ilr_1 0.3272 NA NA +SD.f_cyan_ilr_2 0.5300 NA NA +SD.f_JCZ38_qlogis 6.4465 NA NA +SD.log_k1 0.4135 NA NA +SD.log_k2 0.4182 NA NA +SD.log_tb 0.6035 NA NA + +Variance model: + est. lower upper +a.1 3.059 NA NA +b.1 0.038 NA NA + +Backtransformed parameters: + est. lower upper +cyan_0 1.010e+02 NA NA +k_JCZ38 3.134e-02 NA NA +k_J9Z38 6.509e-03 NA NA +k_JSE76 3.802e-03 NA NA +f_cyan_to_JCZ38 6.127e-01 NA NA +f_cyan_to_J9Z38 2.423e-01 NA NA +f_JCZ38_to_JSE76 1.000e+00 NA NA +k1 4.191e-02 NA NA +k2 1.223e-02 NA NA +tb 1.102e+01 NA NA + +Resulting formation fractions: + ff +cyan_JCZ38 0.6127 +cyan_J9Z38 0.2423 +cyan_sink 0.1449 +JCZ38_JSE76 1.0000 +JCZ38_sink 0.0000 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +cyan 29.94 161.54 48.63 16.54 56.68 +JCZ38 22.12 73.47 NA NA NA +J9Z38 106.50 353.77 NA NA NA +JSE76 182.30 605.60 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 constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 07:58:00 2023 +Date of summary: Thu Apr 20 20:01:30 2023 + +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 522.351 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 + 101.8173 -1.8998 -5.1449 -2.5415 0.6705 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta + 4.4669 16.1281 13.3327 -0.2314 2.8738 + +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 5.742 0.000 0.000 0.00 0.0000 +log_k_JCZ38 0.000 1.402 0.000 0.00 0.0000 +log_k_J9Z38 0.000 0.000 1.718 0.00 0.0000 +log_k_JSE76 0.000 0.000 0.000 3.57 0.0000 +f_cyan_ilr_1 0.000 0.000 0.000 0.00 0.5926 +f_cyan_ilr_2 0.000 0.000 0.000 0.00 0.0000 +f_JCZ38_qlogis 0.000 0.000 0.000 0.00 0.0000 +f_JSE76_qlogis 0.000 0.000 0.000 0.00 0.0000 +log_alpha 0.000 0.000 0.000 0.00 0.0000 +log_beta 0.000 0.000 0.000 0.00 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 10.56 0.00 0.00 0.0000 0.0000 +f_JCZ38_qlogis 0.00 12.04 0.00 0.0000 0.0000 +f_JSE76_qlogis 0.00 0.00 15.26 0.0000 0.0000 +log_alpha 0.00 0.00 0.00 0.4708 0.0000 +log_beta 0.00 0.00 0.00 0.0000 0.4432 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2308 2301 -1134 + +Optimised parameters: + est. lower upper +cyan_0 101.9586 99.22024 104.69700 +log_k_JCZ38 -2.4861 -3.17661 -1.79560 +log_k_J9Z38 -5.3926 -6.08842 -4.69684 +log_k_JSE76 -3.1193 -4.12904 -2.10962 +f_cyan_ilr_1 0.7368 0.42085 1.05276 +f_cyan_ilr_2 0.6196 0.06052 1.17861 +f_JCZ38_qlogis 4.8970 -4.68003 14.47398 +f_JSE76_qlogis 4.4066 -1.02087 9.83398 +log_alpha -0.3021 -0.68264 0.07838 +log_beta 2.7438 2.57970 2.90786 +a.1 2.9008 2.69920 3.10245 +SD.cyan_0 2.7081 0.64216 4.77401 +SD.log_k_JCZ38 0.7043 0.19951 1.20907 +SD.log_k_J9Z38 0.6248 0.05790 1.19180 +SD.log_k_JSE76 1.0750 0.33157 1.81839 +SD.f_cyan_ilr_1 0.3429 0.11688 0.56892 +SD.f_cyan_ilr_2 0.4774 0.09381 0.86097 +SD.f_JCZ38_qlogis 1.5565 -7.83970 10.95279 +SD.f_JSE76_qlogis 1.6871 -1.25577 4.63000 +SD.log_alpha 0.4216 0.15913 0.68405 + +Correlation: + cyan_0 l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76 +log_k_JCZ38 -0.0167 +log_k_J9Z38 -0.0307 0.0057 +log_k_JSE76 -0.0032 0.1358 0.0009 +f_cyan_ilr_1 -0.0087 0.0206 -0.1158 -0.0009 +f_cyan_ilr_2 -0.1598 0.0690 0.1770 0.0002 -0.0007 +f_JCZ38_qlogis 0.0966 -0.1132 -0.0440 0.0182 -0.1385 -0.4583 +f_JSE76_qlogis -0.0647 0.1157 0.0333 -0.0026 0.1110 0.3620 -0.8586 +log_alpha -0.0389 0.0113 0.0209 0.0021 0.0041 0.0451 -0.0605 0.0412 +log_beta -0.2508 0.0533 0.0977 0.0098 0.0220 0.2741 -0.2934 0.1999 + 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 0.2281 + +Random effects: + est. lower upper +SD.cyan_0 2.7081 0.64216 4.7740 +SD.log_k_JCZ38 0.7043 0.19951 1.2091 +SD.log_k_J9Z38 0.6248 0.05790 1.1918 +SD.log_k_JSE76 1.0750 0.33157 1.8184 +SD.f_cyan_ilr_1 0.3429 0.11688 0.5689 +SD.f_cyan_ilr_2 0.4774 0.09381 0.8610 +SD.f_JCZ38_qlogis 1.5565 -7.83970 10.9528 +SD.f_JSE76_qlogis 1.6871 -1.25577 4.6300 +SD.log_alpha 0.4216 0.15913 0.6840 + +Variance model: + est. lower upper +a.1 2.901 2.699 3.102 + +Backtransformed parameters: + est. lower upper +cyan_0 101.95862 99.220240 1.047e+02 +k_JCZ38 0.08323 0.041727 1.660e-01 +k_J9Z38 0.00455 0.002269 9.124e-03 +k_JSE76 0.04419 0.016098 1.213e-01 +f_cyan_to_JCZ38 0.61318 NA NA +f_cyan_to_J9Z38 0.21630 NA NA +f_JCZ38_to_JSE76 0.99259 0.009193 1.000e+00 +f_JSE76_to_JCZ38 0.98795 0.264857 9.999e-01 +alpha 0.73924 0.505281 1.082e+00 +beta 15.54568 13.193194 1.832e+01 + +Resulting formation fractions: + ff +cyan_JCZ38 0.613182 +cyan_J9Z38 0.216298 +cyan_sink 0.170519 +JCZ38_JSE76 0.992586 +JCZ38_sink 0.007414 +JSE76_JCZ38 0.987950 +JSE76_sink 0.012050 + +Estimated disappearance times: + DT50 DT90 DT50back +cyan 24.157 334.68 100.7 +JCZ38 8.328 27.66 NA +J9Z38 152.341 506.06 NA +JSE76 15.687 52.11 NA + +</code></pre> +<p></p> +<caption> +Hierarchical FOMC path 2 fit with two-component error +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 07:57:52 2023 +Date of summary: Thu Apr 20 20:01:30 2023 + +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 514.301 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 + 101.9028 -1.9055 -5.0249 -2.5646 0.6807 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta + 4.8883 16.0676 9.3923 -0.1346 3.0364 + +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 6.321 0.000 0.000 0.000 0.0000 +log_k_JCZ38 0.000 1.392 0.000 0.000 0.0000 +log_k_J9Z38 0.000 0.000 1.561 0.000 0.0000 +log_k_JSE76 0.000 0.000 0.000 3.614 0.0000 +f_cyan_ilr_1 0.000 0.000 0.000 0.000 0.6339 +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 10.41 0.00 0.00 0.0000 0.0000 +f_JCZ38_qlogis 0.00 12.24 0.00 0.0000 0.0000 +f_JSE76_qlogis 0.00 0.00 15.13 0.0000 0.0000 +log_alpha 0.00 0.00 0.00 0.3701 0.0000 +log_beta 0.00 0.00 0.00 0.0000 0.5662 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2248 2240 -1103 + +Optimised parameters: + est. lower upper +cyan_0 101.55545 9.920e+01 1.039e+02 +log_k_JCZ38 -2.37354 -2.928e+00 -1.819e+00 +log_k_J9Z38 -5.14736 -5.960e+00 -4.335e+00 +log_k_JSE76 -3.07802 -4.243e+00 -1.913e+00 +f_cyan_ilr_1 0.71263 3.655e-01 1.060e+00 +f_cyan_ilr_2 0.95202 2.701e-01 1.634e+00 +f_JCZ38_qlogis 3.58473 1.251e+00 5.919e+00 +f_JSE76_qlogis 19.03623 -1.037e+07 1.037e+07 +log_alpha -0.15297 -4.490e-01 1.431e-01 +log_beta 2.99230 2.706e+00 3.278e+00 +a.1 2.04816 NA NA +b.1 0.06886 NA NA +SD.log_k_JCZ38 0.56174 NA NA +SD.log_k_J9Z38 0.86509 NA NA +SD.log_k_JSE76 1.28450 NA NA +SD.f_cyan_ilr_1 0.38705 NA NA +SD.f_cyan_ilr_2 0.54153 NA NA +SD.f_JCZ38_qlogis 1.65311 NA NA +SD.f_JSE76_qlogis 7.51468 NA NA +SD.log_alpha 0.31586 NA NA +SD.log_beta 0.24696 NA NA + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_JCZ38 0.5617 NA NA +SD.log_k_J9Z38 0.8651 NA NA +SD.log_k_JSE76 1.2845 NA NA +SD.f_cyan_ilr_1 0.3870 NA NA +SD.f_cyan_ilr_2 0.5415 NA NA +SD.f_JCZ38_qlogis 1.6531 NA NA +SD.f_JSE76_qlogis 7.5147 NA NA +SD.log_alpha 0.3159 NA NA +SD.log_beta 0.2470 NA NA + +Variance model: + est. lower upper +a.1 2.04816 NA NA +b.1 0.06886 NA NA + +Backtransformed parameters: + est. lower upper +cyan_0 1.016e+02 99.20301 103.9079 +k_JCZ38 9.315e-02 0.05349 0.1622 +k_J9Z38 5.815e-03 0.00258 0.0131 +k_JSE76 4.605e-02 0.01436 0.1477 +f_cyan_to_JCZ38 6.438e-01 NA NA +f_cyan_to_J9Z38 2.350e-01 NA NA +f_JCZ38_to_JSE76 9.730e-01 0.77745 0.9973 +f_JSE76_to_JCZ38 1.000e+00 0.00000 1.0000 +alpha 8.582e-01 0.63824 1.1538 +beta 1.993e+01 14.97621 26.5262 + +Resulting formation fractions: + ff +cyan_JCZ38 6.438e-01 +cyan_J9Z38 2.350e-01 +cyan_sink 1.212e-01 +JCZ38_JSE76 9.730e-01 +JCZ38_sink 2.700e-02 +JSE76_JCZ38 1.000e+00 +JSE76_sink 5.403e-09 + +Estimated disappearance times: + DT50 DT90 DT50back +cyan 24.771 271.70 81.79 +JCZ38 7.441 24.72 NA +J9Z38 119.205 395.99 NA +JSE76 15.052 50.00 NA + +</code></pre> +<p></p> +<caption> +Hierarchical DFOP path 2 fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 07:58:43 2023 +Date of summary: Thu Apr 20 20:01:30 2023 + +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 565.562 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 + 102.4358 -2.3107 -5.3123 -3.7120 0.6753 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 + 1.1462 12.4095 12.3630 -1.9317 -4.4557 + g_qlogis + -0.5648 + +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 4.594 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 0.0 0.000 0.0000 +log_k_JCZ38 0.000 0.00 0.0 0.000 0.0000 +log_k_J9Z38 0.000 0.00 0.0 0.000 0.0000 +log_k_JSE76 0.000 0.00 0.0 0.000 0.0000 +f_cyan_ilr_1 0.000 0.00 0.0 0.000 0.0000 +f_cyan_ilr_2 1.797 0.00 0.0 0.000 0.0000 +f_JCZ38_qlogis 0.000 13.85 0.0 0.000 0.0000 +f_JSE76_qlogis 0.000 0.00 14.1 0.000 0.0000 +log_k1 0.000 0.00 0.0 1.106 0.0000 +log_k2 0.000 0.00 0.0 0.000 0.6141 +g_qlogis 0.000 0.00 0.0 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 + 2290 2281 -1123 + +Optimised parameters: + est. lower upper +cyan_0 102.6903 101.44420 103.9365 +log_k_JCZ38 -2.4018 -2.98058 -1.8230 +log_k_J9Z38 -5.1865 -5.92931 -4.4437 +log_k_JSE76 -3.0784 -4.25226 -1.9045 +f_cyan_ilr_1 0.7157 0.37625 1.0551 +f_cyan_ilr_2 0.7073 0.20136 1.2132 +f_JCZ38_qlogis 4.6797 0.43240 8.9269 +f_JSE76_qlogis 5.0080 -1.01380 11.0299 +log_k1 -1.9620 -2.62909 -1.2949 +log_k2 -4.4894 -4.94958 -4.0292 +g_qlogis -0.4658 -1.34443 0.4129 +a.1 2.7158 2.52576 2.9059 +SD.log_k_JCZ38 0.5818 0.15679 1.0067 +SD.log_k_J9Z38 0.7421 0.16751 1.3167 +SD.log_k_JSE76 1.2841 0.43247 2.1356 +SD.f_cyan_ilr_1 0.3748 0.13040 0.6192 +SD.f_cyan_ilr_2 0.4550 0.08396 0.8261 +SD.f_JCZ38_qlogis 2.0862 -0.73390 4.9062 +SD.f_JSE76_qlogis 1.9585 -3.14773 7.0647 +SD.log_k1 0.7389 0.25761 1.2201 +SD.log_k2 0.5132 0.18143 0.8450 +SD.g_qlogis 0.9870 0.35773 1.6164 + +Correlation: + cyan_0 l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76 +log_k_JCZ38 -0.0170 +log_k_J9Z38 -0.0457 0.0016 +log_k_JSE76 -0.0046 0.1183 0.0005 +f_cyan_ilr_1 0.0079 0.0072 -0.0909 0.0003 +f_cyan_ilr_2 -0.3114 0.0343 0.1542 0.0023 -0.0519 +f_JCZ38_qlogis 0.0777 -0.0601 -0.0152 0.0080 -0.0520 -0.2524 +f_JSE76_qlogis -0.0356 0.0817 0.0073 0.0051 0.0388 0.1959 -0.6236 +log_k1 0.0848 -0.0028 0.0010 -0.0010 -0.0014 -0.0245 0.0121 -0.0177 +log_k2 0.0274 -0.0001 0.0075 0.0000 -0.0023 -0.0060 0.0000 -0.0130 +g_qlogis 0.0159 0.0002 -0.0095 0.0002 0.0029 -0.0140 -0.0001 0.0149 + 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 0.0280 +g_qlogis -0.0278 -0.0310 + +Random effects: + est. lower upper +SD.log_k_JCZ38 0.5818 0.15679 1.0067 +SD.log_k_J9Z38 0.7421 0.16751 1.3167 +SD.log_k_JSE76 1.2841 0.43247 2.1356 +SD.f_cyan_ilr_1 0.3748 0.13040 0.6192 +SD.f_cyan_ilr_2 0.4550 0.08396 0.8261 +SD.f_JCZ38_qlogis 2.0862 -0.73390 4.9062 +SD.f_JSE76_qlogis 1.9585 -3.14773 7.0647 +SD.log_k1 0.7389 0.25761 1.2201 +SD.log_k2 0.5132 0.18143 0.8450 +SD.g_qlogis 0.9870 0.35773 1.6164 + +Variance model: + est. lower upper +a.1 2.716 2.526 2.906 + +Backtransformed parameters: + est. lower upper +cyan_0 1.027e+02 1.014e+02 103.93649 +k_JCZ38 9.056e-02 5.076e-02 0.16154 +k_J9Z38 5.591e-03 2.660e-03 0.01175 +k_JSE76 4.603e-02 1.423e-02 0.14890 +f_cyan_to_JCZ38 6.184e-01 NA NA +f_cyan_to_J9Z38 2.248e-01 NA NA +f_JCZ38_to_JSE76 9.908e-01 6.064e-01 0.99987 +f_JSE76_to_JCZ38 9.934e-01 2.662e-01 0.99998 +k1 1.406e-01 7.214e-02 0.27393 +k2 1.123e-02 7.086e-03 0.01779 +g 3.856e-01 2.068e-01 0.60177 + +Resulting formation fractions: + ff +cyan_JCZ38 0.618443 +cyan_J9Z38 0.224770 +cyan_sink 0.156787 +JCZ38_JSE76 0.990803 +JCZ38_sink 0.009197 +JSE76_JCZ38 0.993360 +JSE76_sink 0.006640 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +cyan 21.674 161.70 48.68 4.931 61.74 +JCZ38 7.654 25.43 NA NA NA +J9Z38 123.966 411.81 NA NA NA +JSE76 15.057 50.02 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: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 08:01:24 2023 +Date of summary: Thu Apr 20 20:01:30 2023 + +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 726.501 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 + 101.7523 -1.5948 -5.0119 -2.2723 0.6719 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 + 5.1681 12.8238 12.4130 -2.0057 -4.5526 + g_qlogis + -0.5805 + +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 5.627 0.000 0.000 0.000 0.0000 +log_k_JCZ38 0.000 2.327 0.000 0.000 0.0000 +log_k_J9Z38 0.000 0.000 1.664 0.000 0.0000 +log_k_JSE76 0.000 0.000 0.000 4.566 0.0000 +f_cyan_ilr_1 0.000 0.000 0.000 0.000 0.6519 +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_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 f_JSE76_qlogis log_k1 log_k2 +cyan_0 0.0 0.00 0.00 0.0000 0.0000 +log_k_JCZ38 0.0 0.00 0.00 0.0000 0.0000 +log_k_J9Z38 0.0 0.00 0.00 0.0000 0.0000 +log_k_JSE76 0.0 0.00 0.00 0.0000 0.0000 +f_cyan_ilr_1 0.0 0.00 0.00 0.0000 0.0000 +f_cyan_ilr_2 10.1 0.00 0.00 0.0000 0.0000 +f_JCZ38_qlogis 0.0 13.99 0.00 0.0000 0.0000 +f_JSE76_qlogis 0.0 0.00 14.15 0.0000 0.0000 +log_k1 0.0 0.00 0.00 0.8452 0.0000 +log_k2 0.0 0.00 0.00 0.0000 0.5968 +g_qlogis 0.0 0.00 0.00 0.0000 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 1.691 + +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_0 101.10667 9.903e+01 103.18265 +log_k_JCZ38 -2.49437 -3.297e+00 -1.69221 +log_k_J9Z38 -5.08171 -5.875e+00 -4.28846 +log_k_JSE76 -3.20072 -4.180e+00 -2.22163 +f_cyan_ilr_1 0.71059 3.639e-01 1.05727 +f_cyan_ilr_2 1.15398 2.981e-01 2.00984 +f_JCZ38_qlogis 3.18027 1.056e+00 5.30452 +f_JSE76_qlogis 5.61578 -2.505e+01 36.28077 +log_k1 -2.38875 -2.517e+00 -2.26045 +log_k2 -4.67246 -4.928e+00 -4.41715 +g_qlogis -0.28231 -1.135e+00 0.57058 +a.1 2.08190 1.856e+00 2.30785 +b.1 0.06114 5.015e-02 0.07214 +SD.log_k_JCZ38 0.84622 2.637e-01 1.42873 +SD.log_k_J9Z38 0.84564 2.566e-01 1.43464 +SD.log_k_JSE76 1.04385 3.242e-01 1.76351 +SD.f_cyan_ilr_1 0.38568 1.362e-01 0.63514 +SD.f_cyan_ilr_2 0.68046 7.166e-02 1.28925 +SD.f_JCZ38_qlogis 1.25244 -4.213e-02 2.54700 +SD.f_JSE76_qlogis 0.28202 -1.515e+03 1515.87968 +SD.log_k2 0.25749 7.655e-02 0.43843 +SD.g_qlogis 0.94535 3.490e-01 1.54174 + +Correlation: + cyan_0 l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76 +log_k_JCZ38 -0.0086 +log_k_J9Z38 -0.0363 -0.0007 +log_k_JSE76 0.0015 0.1210 -0.0017 +f_cyan_ilr_1 -0.0048 0.0095 -0.0572 0.0030 +f_cyan_ilr_2 -0.4788 0.0328 0.1143 0.0027 -0.0316 +f_JCZ38_qlogis 0.0736 -0.0664 -0.0137 0.0145 -0.0444 -0.2175 +f_JSE76_qlogis -0.0137 0.0971 0.0035 0.0009 0.0293 0.1333 -0.6767 +log_k1 0.2345 -0.0350 -0.0099 -0.0113 -0.0126 -0.1652 0.1756 -0.2161 +log_k2 0.0440 -0.0133 0.0199 -0.0040 -0.0097 -0.0119 0.0604 -0.1306 +g_qlogis 0.0438 0.0078 -0.0123 0.0029 0.0046 -0.0363 -0.0318 0.0736 + 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 0.3198 +g_qlogis -0.1666 -0.0954 + +Random effects: + est. lower upper +SD.log_k_JCZ38 0.8462 2.637e-01 1.4287 +SD.log_k_J9Z38 0.8456 2.566e-01 1.4346 +SD.log_k_JSE76 1.0439 3.242e-01 1.7635 +SD.f_cyan_ilr_1 0.3857 1.362e-01 0.6351 +SD.f_cyan_ilr_2 0.6805 7.166e-02 1.2893 +SD.f_JCZ38_qlogis 1.2524 -4.213e-02 2.5470 +SD.f_JSE76_qlogis 0.2820 -1.515e+03 1515.8797 +SD.log_k2 0.2575 7.655e-02 0.4384 +SD.g_qlogis 0.9453 3.490e-01 1.5417 + +Variance model: + est. lower upper +a.1 2.08190 1.85595 2.30785 +b.1 0.06114 0.05015 0.07214 + +Backtransformed parameters: + est. lower upper +cyan_0 1.011e+02 9.903e+01 103.18265 +k_JCZ38 8.255e-02 3.701e-02 0.18411 +k_J9Z38 6.209e-03 2.809e-03 0.01373 +k_JSE76 4.073e-02 1.530e-02 0.10843 +f_cyan_to_JCZ38 6.608e-01 NA NA +f_cyan_to_J9Z38 2.419e-01 NA NA +f_JCZ38_to_JSE76 9.601e-01 7.419e-01 0.99506 +f_JSE76_to_JCZ38 9.964e-01 1.322e-11 1.00000 +k1 9.174e-02 8.070e-02 0.10430 +k2 9.349e-03 7.243e-03 0.01207 +g 4.299e-01 2.432e-01 0.63890 + +Resulting formation fractions: + ff +cyan_JCZ38 0.660808 +cyan_J9Z38 0.241904 +cyan_sink 0.097288 +JCZ38_JSE76 0.960085 +JCZ38_sink 0.039915 +JSE76_JCZ38 0.996373 +JSE76_sink 0.003627 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +cyan 24.359 186.18 56.05 7.555 74.14 +JCZ38 8.397 27.89 NA NA NA +J9Z38 111.631 370.83 NA NA NA +JSE76 17.017 56.53 NA NA NA + +</code></pre> +<p></p> +<caption> +Hierarchical SFORB path 2 fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 07:58:46 2023 +Date of summary: Thu Apr 20 20:01:30 2023 + +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 568.562 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 + 102.4394 -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 + 13.2672 13.3538 + +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 0.00 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 0.6349 0.000 0.00 0.00 +f_cyan_ilr_2 0.0000 1.797 0.00 0.00 +f_JCZ38_qlogis 0.0000 0.000 13.84 0.00 +f_JSE76_qlogis 0.0000 0.000 0.00 14.66 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2284 2275 -1120 + +Optimised parameters: + est. lower upper +cyan_free_0 102.7730 1.015e+02 1.041e+02 +log_k_cyan_free -2.8530 -3.167e+00 -2.539e+00 +log_k_cyan_free_bound -2.7326 -3.543e+00 -1.922e+00 +log_k_cyan_bound_free -3.5582 -4.126e+00 -2.990e+00 +log_k_JCZ38 -2.3810 -2.921e+00 -1.841e+00 +log_k_J9Z38 -5.2301 -5.963e+00 -4.497e+00 +log_k_JSE76 -3.0286 -4.286e+00 -1.771e+00 +f_cyan_ilr_1 0.7081 3.733e-01 1.043e+00 +f_cyan_ilr_2 0.5847 7.846e-03 1.162e+00 +f_JCZ38_qlogis 9.5676 -1.323e+03 1.342e+03 +f_JSE76_qlogis 3.7042 7.254e-02 7.336e+00 +a.1 2.7222 2.532e+00 2.913e+00 +SD.log_k_cyan_free 0.3338 1.086e-01 5.589e-01 +SD.log_k_cyan_free_bound 0.8888 3.023e-01 1.475e+00 +SD.log_k_cyan_bound_free 0.6220 2.063e-01 1.038e+00 +SD.log_k_JCZ38 0.5221 1.334e-01 9.108e-01 +SD.log_k_J9Z38 0.7104 1.371e-01 1.284e+00 +SD.log_k_JSE76 1.3837 4.753e-01 2.292e+00 +SD.f_cyan_ilr_1 0.3620 1.248e-01 5.992e-01 +SD.f_cyan_ilr_2 0.4259 8.145e-02 7.704e-01 +SD.f_JCZ38_qlogis 3.5332 -1.037e+05 1.037e+05 +SD.f_JSE76_qlogis 1.6990 -2.771e-01 3.675e+00 + +Correlation: + cyn_f_0 lg_k_c_ lg_k_cyn_f_ lg_k_cyn_b_ l__JCZ3 l__J9Z3 +log_k_cyan_free 0.2126 +log_k_cyan_free_bound 0.0894 0.0871 +log_k_cyan_bound_free 0.0033 0.0410 0.0583 +log_k_JCZ38 -0.0708 -0.0280 -0.0147 0.0019 +log_k_J9Z38 -0.0535 -0.0138 0.0012 0.0148 0.0085 +log_k_JSE76 -0.0066 -0.0030 -0.0021 -0.0005 0.1090 0.0010 +f_cyan_ilr_1 -0.0364 -0.0157 -0.0095 -0.0015 0.0458 -0.0960 +f_cyan_ilr_2 -0.3814 -0.1104 -0.0423 0.0146 0.1540 0.1526 +f_JCZ38_qlogis 0.2507 0.0969 0.0482 -0.0097 -0.2282 -0.0363 +f_JSE76_qlogis -0.1648 -0.0710 -0.0443 -0.0087 0.2002 0.0226 + 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 0.0001 +f_cyan_ilr_2 0.0031 0.0586 +f_JCZ38_qlogis 0.0023 -0.1867 -0.6255 +f_JSE76_qlogis 0.0082 0.1356 0.4519 -0.7951 + +Random effects: + est. lower upper +SD.log_k_cyan_free 0.3338 1.086e-01 5.589e-01 +SD.log_k_cyan_free_bound 0.8888 3.023e-01 1.475e+00 +SD.log_k_cyan_bound_free 0.6220 2.063e-01 1.038e+00 +SD.log_k_JCZ38 0.5221 1.334e-01 9.108e-01 +SD.log_k_J9Z38 0.7104 1.371e-01 1.284e+00 +SD.log_k_JSE76 1.3837 4.753e-01 2.292e+00 +SD.f_cyan_ilr_1 0.3620 1.248e-01 5.992e-01 +SD.f_cyan_ilr_2 0.4259 8.145e-02 7.704e-01 +SD.f_JCZ38_qlogis 3.5332 -1.037e+05 1.037e+05 +SD.f_JSE76_qlogis 1.6990 -2.771e-01 3.675e+00 + +Variance model: + est. lower upper +a.1 2.722 2.532 2.913 + +Backtransformed parameters: + est. lower upper +cyan_free_0 1.028e+02 1.015e+02 104.06475 +k_cyan_free 5.767e-02 4.213e-02 0.07894 +k_cyan_free_bound 6.505e-02 2.892e-02 0.14633 +k_cyan_bound_free 2.849e-02 1.614e-02 0.05028 +k_JCZ38 9.246e-02 5.390e-02 0.15859 +k_J9Z38 5.353e-03 2.572e-03 0.01114 +k_JSE76 4.838e-02 1.376e-02 0.17009 +f_cyan_free_to_JCZ38 6.011e-01 5.028e-01 0.83792 +f_cyan_free_to_J9Z38 2.208e-01 5.028e-01 0.83792 +f_JCZ38_to_JSE76 9.999e-01 0.000e+00 1.00000 +f_JSE76_to_JCZ38 9.760e-01 5.181e-01 0.99935 + +Estimated Eigenvalues of SFORB model(s): +cyan_b1 cyan_b2 cyan_g +0.13942 0.01178 0.35948 + +Resulting formation fractions: + ff +cyan_free_JCZ38 6.011e-01 +cyan_free_J9Z38 2.208e-01 +cyan_free_sink 1.780e-01 +cyan_free 1.000e+00 +JCZ38_JSE76 9.999e-01 +JCZ38_sink 6.996e-05 +JSE76_JCZ38 9.760e-01 +JSE76_sink 2.403e-02 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 +cyan 23.390 157.60 47.44 4.971 58.82 +JCZ38 7.497 24.90 NA NA NA +J9Z38 129.482 430.13 NA NA NA +JSE76 14.326 47.59 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: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 08:01:30 2023 +Date of summary: Thu Apr 20 20:01:30 2023 + +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 732.212 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 + 101.751 -2.837 -3.016 +log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 + -3.660 -2.299 -5.313 + log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 + -3.699 0.672 5.873 + f_JCZ38_qlogis f_JSE76_qlogis + 13.216 13.338 + +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 0.00 0.00 0.00 +log_k_cyan_free 0.0000 0.00 0.00 0.00 +log_k_cyan_free_bound 0.0000 0.00 0.00 0.00 +log_k_cyan_bound_free 0.0000 0.00 0.00 0.00 +log_k_JCZ38 0.0000 0.00 0.00 0.00 +log_k_J9Z38 0.0000 0.00 0.00 0.00 +log_k_JSE76 0.0000 0.00 0.00 0.00 +f_cyan_ilr_1 0.6519 0.00 0.00 0.00 +f_cyan_ilr_2 0.0000 10.78 0.00 0.00 +f_JCZ38_qlogis 0.0000 0.00 13.96 0.00 +f_JSE76_qlogis 0.0000 0.00 0.00 14.69 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2240 2232 -1098 + +Optimised parameters: + est. lower upper +cyan_free_0 101.10205 98.99221 103.2119 +log_k_cyan_free -3.16929 -3.61395 -2.7246 +log_k_cyan_free_bound -3.38259 -3.63022 -3.1350 +log_k_cyan_bound_free -3.81075 -4.13888 -3.4826 +log_k_JCZ38 -2.42057 -3.00756 -1.8336 +log_k_J9Z38 -5.07501 -5.85138 -4.2986 +log_k_JSE76 -3.12442 -4.21277 -2.0361 +f_cyan_ilr_1 0.70577 0.35788 1.0537 +f_cyan_ilr_2 1.14824 0.15810 2.1384 +f_JCZ38_qlogis 3.52245 0.43257 6.6123 +f_JSE76_qlogis 5.65140 -21.22295 32.5257 +a.1 2.07062 1.84329 2.2980 +b.1 0.06227 0.05124 0.0733 +SD.log_k_cyan_free 0.49468 0.18566 0.8037 +SD.log_k_cyan_bound_free 0.28972 0.07188 0.5076 +SD.log_k_JCZ38 0.58852 0.16800 1.0090 +SD.log_k_J9Z38 0.82500 0.24730 1.4027 +SD.log_k_JSE76 1.19201 0.40313 1.9809 +SD.f_cyan_ilr_1 0.38534 0.13640 0.6343 +SD.f_cyan_ilr_2 0.72463 0.10076 1.3485 +SD.f_JCZ38_qlogis 1.38223 -0.20997 2.9744 +SD.f_JSE76_qlogis 2.07989 -72.53027 76.6901 + +Correlation: + cyn_f_0 lg_k_c_ lg_k_cyn_f_ lg_k_cyn_b_ l__JCZ3 l__J9Z3 +log_k_cyan_free 0.1117 +log_k_cyan_free_bound 0.1763 0.1828 +log_k_cyan_bound_free 0.0120 0.0593 0.5030 +log_k_JCZ38 -0.0459 -0.0230 -0.0931 -0.0337 +log_k_J9Z38 -0.0381 -0.0123 -0.0139 0.0237 0.0063 +log_k_JSE76 -0.0044 -0.0038 -0.0175 -0.0072 0.1120 0.0003 +f_cyan_ilr_1 -0.0199 -0.0087 -0.0407 -0.0233 0.0268 -0.0552 +f_cyan_ilr_2 -0.4806 -0.1015 -0.2291 -0.0269 0.1156 0.1113 +f_JCZ38_qlogis 0.1805 0.0825 0.3085 0.0963 -0.1674 -0.0314 +f_JSE76_qlogis -0.1586 -0.0810 -0.3560 -0.1563 0.2025 0.0278 + 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 0.0024 +f_cyan_ilr_2 0.0087 0.0172 +f_JCZ38_qlogis -0.0016 -0.1047 -0.4656 +f_JSE76_qlogis 0.0119 0.1034 0.4584 -0.8137 + +Random effects: + est. lower upper +SD.log_k_cyan_free 0.4947 0.18566 0.8037 +SD.log_k_cyan_bound_free 0.2897 0.07188 0.5076 +SD.log_k_JCZ38 0.5885 0.16800 1.0090 +SD.log_k_J9Z38 0.8250 0.24730 1.4027 +SD.log_k_JSE76 1.1920 0.40313 1.9809 +SD.f_cyan_ilr_1 0.3853 0.13640 0.6343 +SD.f_cyan_ilr_2 0.7246 0.10076 1.3485 +SD.f_JCZ38_qlogis 1.3822 -0.20997 2.9744 +SD.f_JSE76_qlogis 2.0799 -72.53027 76.6901 + +Variance model: + est. lower upper +a.1 2.07062 1.84329 2.2980 +b.1 0.06227 0.05124 0.0733 + +Backtransformed parameters: + est. lower upper +cyan_free_0 1.011e+02 9.899e+01 103.21190 +k_cyan_free 4.203e-02 2.695e-02 0.06557 +k_cyan_free_bound 3.396e-02 2.651e-02 0.04350 +k_cyan_bound_free 2.213e-02 1.594e-02 0.03073 +k_JCZ38 8.887e-02 4.941e-02 0.15984 +k_J9Z38 6.251e-03 2.876e-03 0.01359 +k_JSE76 4.396e-02 1.481e-02 0.13054 +f_cyan_free_to_JCZ38 6.590e-01 5.557e-01 0.95365 +f_cyan_free_to_J9Z38 2.429e-01 5.557e-01 0.95365 +f_JCZ38_to_JSE76 9.713e-01 6.065e-01 0.99866 +f_JSE76_to_JCZ38 9.965e-01 6.067e-10 1.00000 + +Estimated Eigenvalues of SFORB model(s): +cyan_b1 cyan_b2 cyan_g +0.08749 0.01063 0.40855 + +Resulting formation fractions: + ff +cyan_free_JCZ38 0.65905 +cyan_free_J9Z38 0.24291 +cyan_free_sink 0.09805 +cyan_free 1.00000 +JCZ38_JSE76 0.97132 +JCZ38_sink 0.02868 +JSE76_JCZ38 0.99650 +JSE76_sink 0.00350 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 +cyan 24.91 167.16 50.32 7.922 65.19 +JCZ38 7.80 25.91 NA NA NA +J9Z38 110.89 368.36 NA NA NA +JSE76 15.77 52.38 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: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 08:15:01 2023 +Date of summary: Thu Apr 20 20:01:31 2023 + +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 808.728 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 + 101.9028 -1.9055 -5.0249 -2.5646 0.6807 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta + 4.8883 16.0676 9.3923 -0.1346 3.0364 + +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 6.321 0.000 0.000 0.000 0.0000 +log_k_JCZ38 0.000 1.392 0.000 0.000 0.0000 +log_k_J9Z38 0.000 0.000 1.561 0.000 0.0000 +log_k_JSE76 0.000 0.000 0.000 3.614 0.0000 +f_cyan_ilr_1 0.000 0.000 0.000 0.000 0.6339 +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 10.41 0.00 0.00 0.0000 0.0000 +f_JCZ38_qlogis 0.00 12.24 0.00 0.0000 0.0000 +f_JSE76_qlogis 0.00 0.00 15.13 0.0000 0.0000 +log_alpha 0.00 0.00 0.00 0.3701 0.0000 +log_beta 0.00 0.00 0.00 0.0000 0.5662 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2251 2244 -1106 + +Optimised parameters: + est. lower upper +cyan_0 101.05768 NA NA +log_k_JCZ38 -2.73252 NA NA +log_k_J9Z38 -5.07399 NA NA +log_k_JSE76 -3.52863 NA NA +f_cyan_ilr_1 0.72176 NA NA +f_cyan_ilr_2 1.34610 NA NA +f_JCZ38_qlogis 2.08337 NA NA +f_JSE76_qlogis 1590.31880 NA NA +log_alpha -0.09336 NA NA +log_beta 3.10191 NA NA +a.1 2.08557 1.85439 2.31675 +b.1 0.06998 0.05800 0.08197 +SD.log_k_JCZ38 1.20053 0.43329 1.96777 +SD.log_k_J9Z38 0.85854 0.26708 1.45000 +SD.log_k_JSE76 0.62528 0.16061 1.08995 +SD.f_cyan_ilr_1 0.35190 0.12340 0.58039 +SD.f_cyan_ilr_2 0.85385 0.15391 1.55378 +SD.log_alpha 0.28971 0.08718 0.49225 +SD.log_beta 0.31614 0.05938 0.57290 + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_JCZ38 1.2005 0.43329 1.9678 +SD.log_k_J9Z38 0.8585 0.26708 1.4500 +SD.log_k_JSE76 0.6253 0.16061 1.0900 +SD.f_cyan_ilr_1 0.3519 0.12340 0.5804 +SD.f_cyan_ilr_2 0.8538 0.15391 1.5538 +SD.log_alpha 0.2897 0.08718 0.4923 +SD.log_beta 0.3161 0.05938 0.5729 + +Variance model: + est. lower upper +a.1 2.08557 1.854 2.31675 +b.1 0.06998 0.058 0.08197 + +Backtransformed parameters: + est. lower upper +cyan_0 1.011e+02 NA NA +k_JCZ38 6.506e-02 NA NA +k_J9Z38 6.257e-03 NA NA +k_JSE76 2.935e-02 NA NA +f_cyan_to_JCZ38 6.776e-01 NA NA +f_cyan_to_J9Z38 2.442e-01 NA NA +f_JCZ38_to_JSE76 8.893e-01 NA NA +f_JSE76_to_JCZ38 1.000e+00 NA NA +alpha 9.109e-01 NA NA +beta 2.224e+01 NA NA + +Resulting formation fractions: + ff +cyan_JCZ38 0.67761 +cyan_J9Z38 0.24417 +cyan_sink 0.07822 +JCZ38_JSE76 0.88928 +JCZ38_sink 0.11072 +JSE76_JCZ38 1.00000 +JSE76_sink 0.00000 + +Estimated disappearance times: + DT50 DT90 DT50back +cyan 25.36 256.37 77.18 +JCZ38 10.65 35.39 NA +J9Z38 110.77 367.98 NA +JSE76 23.62 78.47 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: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 08:16:32 2023 +Date of summary: Thu Apr 20 20:01:31 2023 + +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 900.061 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 + 102.4358 -2.3107 -5.3123 -3.7120 0.6753 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 + 1.1462 12.4095 12.3630 -1.9317 -4.4557 + g_qlogis + -0.5648 + +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 4.594 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 0.0 0.000 0.0000 +log_k_JCZ38 0.000 0.00 0.0 0.000 0.0000 +log_k_J9Z38 0.000 0.00 0.0 0.000 0.0000 +log_k_JSE76 0.000 0.00 0.0 0.000 0.0000 +f_cyan_ilr_1 0.000 0.00 0.0 0.000 0.0000 +f_cyan_ilr_2 1.797 0.00 0.0 0.000 0.0000 +f_JCZ38_qlogis 0.000 13.85 0.0 0.000 0.0000 +f_JSE76_qlogis 0.000 0.00 14.1 0.000 0.0000 +log_k1 0.000 0.00 0.0 1.106 0.0000 +log_k2 0.000 0.00 0.0 0.000 0.6141 +g_qlogis 0.000 0.00 0.0 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_0 102.5254 NA NA +log_k_JCZ38 -2.9358 NA NA +log_k_J9Z38 -5.1424 NA NA +log_k_JSE76 -3.6458 NA NA +f_cyan_ilr_1 0.6957 NA NA +f_cyan_ilr_2 0.6635 NA NA +f_JCZ38_qlogis 4984.8163 NA NA +f_JSE76_qlogis 1.9415 NA NA +log_k1 -1.9456 NA NA +log_k2 -4.4705 NA NA +g_qlogis -0.5117 NA NA +a.1 2.7455 2.55392 2.9370 +SD.log_k_JCZ38 1.3163 0.47635 2.1563 +SD.log_k_J9Z38 0.7162 0.16133 1.2711 +SD.log_k_JSE76 0.6457 0.15249 1.1390 +SD.f_cyan_ilr_1 0.3424 0.11714 0.5677 +SD.f_cyan_ilr_2 0.4524 0.09709 0.8077 +SD.log_k1 0.7353 0.25445 1.2161 +SD.log_k2 0.5137 0.18206 0.8453 +SD.g_qlogis 0.9857 0.35651 1.6148 + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_JCZ38 1.3163 0.47635 2.1563 +SD.log_k_J9Z38 0.7162 0.16133 1.2711 +SD.log_k_JSE76 0.6457 0.15249 1.1390 +SD.f_cyan_ilr_1 0.3424 0.11714 0.5677 +SD.f_cyan_ilr_2 0.4524 0.09709 0.8077 +SD.log_k1 0.7353 0.25445 1.2161 +SD.log_k2 0.5137 0.18206 0.8453 +SD.g_qlogis 0.9857 0.35651 1.6148 + +Variance model: + est. lower upper +a.1 2.745 2.554 2.937 + +Backtransformed parameters: + est. lower upper +cyan_0 1.025e+02 NA NA +k_JCZ38 5.309e-02 NA NA +k_J9Z38 5.844e-03 NA NA +k_JSE76 2.610e-02 NA NA +f_cyan_to_JCZ38 6.079e-01 NA NA +f_cyan_to_J9Z38 2.272e-01 NA NA +f_JCZ38_to_JSE76 1.000e+00 NA NA +f_JSE76_to_JCZ38 8.745e-01 NA NA +k1 1.429e-01 NA NA +k2 1.144e-02 NA NA +g 3.748e-01 NA NA + +Resulting formation fractions: + ff +cyan_JCZ38 0.6079 +cyan_J9Z38 0.2272 +cyan_sink 0.1649 +JCZ38_JSE76 1.0000 +JCZ38_sink 0.0000 +JSE76_JCZ38 0.8745 +JSE76_sink 0.1255 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +cyan 22.29 160.20 48.22 4.85 60.58 +JCZ38 13.06 43.37 NA NA NA +J9Z38 118.61 394.02 NA NA NA +JSE76 26.56 88.22 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: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 08:16:47 2023 +Date of summary: Thu Apr 20 20:01:31 2023 + +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 914.763 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 + 101.7523 -1.5948 -5.0119 -2.2723 0.6719 + f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2 + 5.1681 12.8238 12.4130 -2.0057 -4.5526 + g_qlogis + -0.5805 + +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 5.627 0.000 0.000 0.000 0.0000 +log_k_JCZ38 0.000 2.327 0.000 0.000 0.0000 +log_k_J9Z38 0.000 0.000 1.664 0.000 0.0000 +log_k_JSE76 0.000 0.000 0.000 4.566 0.0000 +f_cyan_ilr_1 0.000 0.000 0.000 0.000 0.6519 +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_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 f_JSE76_qlogis log_k1 log_k2 +cyan_0 0.0 0.00 0.00 0.0000 0.0000 +log_k_JCZ38 0.0 0.00 0.00 0.0000 0.0000 +log_k_J9Z38 0.0 0.00 0.00 0.0000 0.0000 +log_k_JSE76 0.0 0.00 0.00 0.0000 0.0000 +f_cyan_ilr_1 0.0 0.00 0.00 0.0000 0.0000 +f_cyan_ilr_2 10.1 0.00 0.00 0.0000 0.0000 +f_JCZ38_qlogis 0.0 13.99 0.00 0.0000 0.0000 +f_JSE76_qlogis 0.0 0.00 14.15 0.0000 0.0000 +log_k1 0.0 0.00 0.00 0.8452 0.0000 +log_k2 0.0 0.00 0.00 0.0000 0.5968 +g_qlogis 0.0 0.00 0.00 0.0000 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 1.691 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2232 2224 -1096 + +Optimised parameters: + est. lower upper +cyan_0 101.20051 NA NA +log_k_JCZ38 -2.93542 NA NA +log_k_J9Z38 -5.03151 NA NA +log_k_JSE76 -3.67679 NA NA +f_cyan_ilr_1 0.67290 NA NA +f_cyan_ilr_2 0.99787 NA NA +f_JCZ38_qlogis 348.32484 NA NA +f_JSE76_qlogis 1.87846 NA NA +log_k1 -2.32738 NA NA +log_k2 -4.61295 NA NA +g_qlogis -0.38342 NA NA +a.1 2.06184 1.83746 2.28622 +b.1 0.06329 0.05211 0.07447 +SD.log_k_JCZ38 1.29042 0.47468 2.10617 +SD.log_k_J9Z38 0.84235 0.25903 1.42566 +SD.log_k_JSE76 0.56930 0.13934 0.99926 +SD.f_cyan_ilr_1 0.35183 0.12298 0.58068 +SD.f_cyan_ilr_2 0.77269 0.17908 1.36631 +SD.log_k2 0.28549 0.09210 0.47888 +SD.g_qlogis 0.93830 0.34568 1.53093 + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_JCZ38 1.2904 0.4747 2.1062 +SD.log_k_J9Z38 0.8423 0.2590 1.4257 +SD.log_k_JSE76 0.5693 0.1393 0.9993 +SD.f_cyan_ilr_1 0.3518 0.1230 0.5807 +SD.f_cyan_ilr_2 0.7727 0.1791 1.3663 +SD.log_k2 0.2855 0.0921 0.4789 +SD.g_qlogis 0.9383 0.3457 1.5309 + +Variance model: + est. lower upper +a.1 2.06184 1.83746 2.28622 +b.1 0.06329 0.05211 0.07447 + +Backtransformed parameters: + est. lower upper +cyan_0 1.012e+02 NA NA +k_JCZ38 5.311e-02 NA NA +k_J9Z38 6.529e-03 NA NA +k_JSE76 2.530e-02 NA NA +f_cyan_to_JCZ38 6.373e-01 NA NA +f_cyan_to_J9Z38 2.461e-01 NA NA +f_JCZ38_to_JSE76 1.000e+00 NA NA +f_JSE76_to_JCZ38 8.674e-01 NA NA +k1 9.755e-02 NA NA +k2 9.922e-03 NA NA +g 4.053e-01 NA NA + +Resulting formation fractions: + ff +cyan_JCZ38 0.6373 +cyan_J9Z38 0.2461 +cyan_sink 0.1167 +JCZ38_JSE76 1.0000 +JCZ38_sink 0.0000 +JSE76_JCZ38 0.8674 +JSE76_sink 0.1326 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +cyan 24.93 179.68 54.09 7.105 69.86 +JCZ38 13.05 43.36 NA NA NA +J9Z38 106.16 352.67 NA NA NA +JSE76 27.39 91.00 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: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 08:16:33 2023 +Date of summary: Thu Apr 20 20:01:31 2023 + +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 901.179 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 + 102.4394 -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 + 13.2672 13.3538 + +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 0.00 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 0.6349 0.000 0.00 0.00 +f_cyan_ilr_2 0.0000 1.797 0.00 0.00 +f_JCZ38_qlogis 0.0000 0.000 13.84 0.00 +f_JSE76_qlogis 0.0000 0.000 0.00 14.66 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2279 2272 -1120 + +Optimised parameters: + est. lower upper +cyan_free_0 102.5621 NA NA +log_k_cyan_free -2.8531 NA NA +log_k_cyan_free_bound -2.6916 NA NA +log_k_cyan_bound_free -3.5032 NA NA +log_k_JCZ38 -2.9436 NA NA +log_k_J9Z38 -5.1140 NA NA +log_k_JSE76 -3.6472 NA NA +f_cyan_ilr_1 0.6887 NA NA +f_cyan_ilr_2 0.6874 NA NA +f_JCZ38_qlogis 4063.6389 NA NA +f_JSE76_qlogis 1.9556 NA NA +a.1 2.7460 2.55451 2.9376 +SD.log_k_cyan_free 0.3131 0.09841 0.5277 +SD.log_k_cyan_free_bound 0.8850 0.29909 1.4710 +SD.log_k_cyan_bound_free 0.6167 0.20391 1.0295 +SD.log_k_JCZ38 1.3555 0.49101 2.2200 +SD.log_k_J9Z38 0.7200 0.16166 1.2783 +SD.log_k_JSE76 0.6252 0.14619 1.1042 +SD.f_cyan_ilr_1 0.3386 0.11447 0.5627 +SD.f_cyan_ilr_2 0.4699 0.09810 0.8417 + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_cyan_free 0.3131 0.09841 0.5277 +SD.log_k_cyan_free_bound 0.8850 0.29909 1.4710 +SD.log_k_cyan_bound_free 0.6167 0.20391 1.0295 +SD.log_k_JCZ38 1.3555 0.49101 2.2200 +SD.log_k_J9Z38 0.7200 0.16166 1.2783 +SD.log_k_JSE76 0.6252 0.14619 1.1042 +SD.f_cyan_ilr_1 0.3386 0.11447 0.5627 +SD.f_cyan_ilr_2 0.4699 0.09810 0.8417 + +Variance model: + est. lower upper +a.1 2.746 2.555 2.938 + +Backtransformed parameters: + est. lower upper +cyan_free_0 1.026e+02 NA NA +k_cyan_free 5.767e-02 NA NA +k_cyan_free_bound 6.777e-02 NA NA +k_cyan_bound_free 3.010e-02 NA NA +k_JCZ38 5.267e-02 NA NA +k_J9Z38 6.012e-03 NA NA +k_JSE76 2.606e-02 NA NA +f_cyan_free_to_JCZ38 6.089e-01 NA NA +f_cyan_free_to_J9Z38 2.299e-01 NA NA +f_JCZ38_to_JSE76 1.000e+00 NA NA +f_JSE76_to_JCZ38 8.761e-01 NA NA + +Estimated Eigenvalues of SFORB model(s): +cyan_b1 cyan_b2 cyan_g + 0.1434 0.0121 0.3469 + +Resulting formation fractions: + ff +cyan_free_JCZ38 0.6089 +cyan_free_J9Z38 0.2299 +cyan_free_sink 0.1612 +cyan_free 1.0000 +JCZ38_JSE76 1.0000 +JCZ38_sink 0.0000 +JSE76_JCZ38 0.8761 +JSE76_sink 0.1239 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 +cyan 23.94 155.06 46.68 4.832 57.28 +JCZ38 13.16 43.71 NA NA NA +J9Z38 115.30 383.02 NA NA NA +JSE76 26.59 88.35 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: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 08:16:19 2023 +Date of summary: Thu Apr 20 20:01:31 2023 + +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 887.343 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 + 101.751 -2.837 -3.016 +log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 + -3.660 -2.299 -5.313 + log_k_JSE76 f_cyan_ilr_1 f_cyan_ilr_2 + -3.699 0.672 5.873 + f_JCZ38_qlogis f_JSE76_qlogis + 13.216 13.338 + +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 0.00 0.00 0.00 +log_k_cyan_free 0.0000 0.00 0.00 0.00 +log_k_cyan_free_bound 0.0000 0.00 0.00 0.00 +log_k_cyan_bound_free 0.0000 0.00 0.00 0.00 +log_k_JCZ38 0.0000 0.00 0.00 0.00 +log_k_J9Z38 0.0000 0.00 0.00 0.00 +log_k_JSE76 0.0000 0.00 0.00 0.00 +f_cyan_ilr_1 0.6519 0.00 0.00 0.00 +f_cyan_ilr_2 0.0000 10.78 0.00 0.00 +f_JCZ38_qlogis 0.0000 0.00 13.96 0.00 +f_JSE76_qlogis 0.0000 0.00 0.00 14.69 + +Starting values for error model parameters: +a.1 b.1 + 1 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 2236 2228 -1098 + +Optimised parameters: + est. lower upper +cyan_free_0 100.72760 NA NA +log_k_cyan_free -3.18281 NA NA +log_k_cyan_free_bound -3.37924 NA NA +log_k_cyan_bound_free -3.77107 NA NA +log_k_JCZ38 -2.92811 NA NA +log_k_J9Z38 -5.02759 NA NA +log_k_JSE76 -3.65835 NA NA +f_cyan_ilr_1 0.67390 NA NA +f_cyan_ilr_2 1.15106 NA NA +f_JCZ38_qlogis 827.82299 NA NA +f_JSE76_qlogis 1.83064 NA NA +a.1 2.06921 1.84443 2.29399 +b.1 0.06391 0.05267 0.07515 +SD.log_k_cyan_free 0.50518 0.18962 0.82075 +SD.log_k_cyan_bound_free 0.30991 0.08170 0.53813 +SD.log_k_JCZ38 1.26661 0.46578 2.06744 +SD.log_k_J9Z38 0.88272 0.27813 1.48730 +SD.log_k_JSE76 0.53050 0.12561 0.93538 +SD.f_cyan_ilr_1 0.35547 0.12461 0.58633 +SD.f_cyan_ilr_2 0.91446 0.20131 1.62761 + +Correlation is not available + +Random effects: + est. lower upper +SD.log_k_cyan_free 0.5052 0.1896 0.8207 +SD.log_k_cyan_bound_free 0.3099 0.0817 0.5381 +SD.log_k_JCZ38 1.2666 0.4658 2.0674 +SD.log_k_J9Z38 0.8827 0.2781 1.4873 +SD.log_k_JSE76 0.5305 0.1256 0.9354 +SD.f_cyan_ilr_1 0.3555 0.1246 0.5863 +SD.f_cyan_ilr_2 0.9145 0.2013 1.6276 + +Variance model: + est. lower upper +a.1 2.06921 1.84443 2.29399 +b.1 0.06391 0.05267 0.07515 + +Backtransformed parameters: + est. lower upper +cyan_free_0 1.007e+02 NA NA +k_cyan_free 4.147e-02 NA NA +k_cyan_free_bound 3.407e-02 NA NA +k_cyan_bound_free 2.303e-02 NA NA +k_JCZ38 5.350e-02 NA NA +k_J9Z38 6.555e-03 NA NA +k_JSE76 2.578e-02 NA NA +f_cyan_free_to_JCZ38 6.505e-01 NA NA +f_cyan_free_to_J9Z38 2.508e-01 NA NA +f_JCZ38_to_JSE76 1.000e+00 NA NA +f_JSE76_to_JCZ38 8.618e-01 NA NA + +Estimated Eigenvalues of SFORB model(s): +cyan_b1 cyan_b2 cyan_g +0.08768 0.01089 0.39821 + +Resulting formation fractions: + ff +cyan_free_JCZ38 0.65053 +cyan_free_J9Z38 0.25082 +cyan_free_sink 0.09864 +cyan_free 1.00000 +JCZ38_JSE76 1.00000 +JCZ38_sink 0.00000 +JSE76_JCZ38 0.86184 +JSE76_sink 0.13816 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_cyan_b1 DT50_cyan_b2 +cyan 25.32 164.79 49.61 7.906 63.64 +JCZ38 12.96 43.04 NA NA NA +J9Z38 105.75 351.29 NA NA NA +JSE76 26.89 89.33 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 4.2.3 (2023-03-15) +Platform: x86_64-pc-linux-gnu (64-bit) +Running under: Debian GNU/Linux 12 (bookworm) + +Matrix products: default +BLAS: /usr/lib/x86_64-linux-gnu/openblas-serial/libblas.so.3 +LAPACK: /usr/lib/x86_64-linux-gnu/openblas-serial/libopenblas-r0.3.21.so + +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 + +attached base packages: +[1] parallel stats graphics grDevices utils datasets methods +[8] base + +other attached packages: +[1] saemix_3.2 npde_3.3 knitr_1.42 mkin_1.2.3 + +loaded via a namespace (and not attached): + [1] pillar_1.9.0 bslib_0.4.2 compiler_4.2.3 jquerylib_0.1.4 + [5] tools_4.2.3 mclust_6.0.0 digest_0.6.31 tibble_3.2.1 + [9] jsonlite_1.8.4 evaluate_0.20 memoise_2.0.1 lifecycle_1.0.3 +[13] nlme_3.1-162 gtable_0.3.3 lattice_0.21-8 pkgconfig_2.0.3 +[17] rlang_1.1.0 DBI_1.1.3 cli_3.6.1 yaml_2.3.7 +[21] pkgdown_2.0.7 xfun_0.38 fastmap_1.1.1 gridExtra_2.3 +[25] dplyr_1.1.1 stringr_1.5.0 generics_0.1.3 desc_1.4.2 +[29] fs_1.6.1 vctrs_0.6.1 sass_0.4.5 systemfonts_1.0.4 +[33] tidyselect_1.2.0 rprojroot_2.0.3 lmtest_0.9-40 grid_4.2.3 +[37] inline_0.3.19 glue_1.6.2 R6_2.5.1 textshaping_0.3.6 +[41] fansi_1.0.4 rmarkdown_2.21 purrr_1.0.1 ggplot2_3.4.2 +[45] magrittr_2.0.3 scales_1.2.1 htmltools_0.5.5 colorspace_2.1-0 +[49] ragg_1.2.5 utf8_1.2.3 stringi_1.7.12 munsell_0.5.0 +[53] cachem_1.0.7 zoo_1.8-12 </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: 64936316 kB</code></pre> +</div> +</div> + </div> + + <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar"> + + <nav id="toc" data-toggle="toc"><h2 data-toc-skip>Contents</h2> + </nav> +</div> + +</div> + + + + <footer><div class="copyright"> + <p></p> +<p>Developed by Johannes Ranke.</p> +</div> + +<div class="pkgdown"> + <p></p> +<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p> +</div> + + </footer> +</div> + + + + + + + </body> +</html> diff --git a/docs/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-13-1.png b/docs/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-13-1.png Binary files differnew file mode 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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 20 April 2023</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="hidden 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 1.2.3. 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">C</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">C</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">720.4</td> +<td align="right">718.8</td> +<td align="right">-352.2</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">665.5</td> +<td align="right">663.4</td> +<td align="right">-322.8</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="37%"> +<col width="6%"> +<col width="8%"> +<col width="8%"> +<col width="9%"> +<col width="9%"> +<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">663.8</td> +<td align="right">661.9</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">665.5</td> +<td align="right">663.4</td> +<td align="right">-322.8</td> +<td align="right">0.2809</td> +<td align="right">1</td> +<td align="right">0.5961</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: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 14:07:09 2023 +Date of summary: Thu Apr 20 14:07:10 2023 + +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 4.175 s +Using 300, 100 iterations and 9 chains + +Variance model: Two-component variance function + +Starting values for degradation parameters: + DMTA_0 k1 k2 g +98.759266 0.087034 0.009933 0.930827 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + DMTA_0 k1 k2 g +DMTA_0 98.76 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 + 663.8 661.9 -322.9 + +Optimised parameters: + est. lower upper +DMTA_0 98.228939 96.285869 100.17201 +k1 0.064063 0.033477 0.09465 +k2 0.008297 0.005824 0.01077 +g 0.953821 0.914328 0.99331 +a.1 1.068479 0.869538 1.26742 +b.1 0.029424 0.022406 0.03644 +SD.DMTA_0 2.030437 0.404824 3.65605 +SD.k1 0.594692 0.256660 0.93272 +SD.g 1.006754 0.361327 1.65218 + +Correlation: + DMTA_0 k1 k2 +k1 0.0218 +k2 0.0556 0.0355 +g -0.0516 -0.0284 -0.2800 + +Random effects: + est. lower upper +SD.DMTA_0 2.0304 0.4048 3.6560 +SD.k1 0.5947 0.2567 0.9327 +SD.g 1.0068 0.3613 1.6522 + +Variance model: + est. lower upper +a.1 1.06848 0.86954 1.26742 +b.1 0.02942 0.02241 0.03644 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +DMTA 11.45 41.4 12.46 10.82 83.54</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: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 14:07:02 2023 +Date of summary: Thu Apr 20 14:08:16 2023 + +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 0.982 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: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 14:07:03 2023 +Date of summary: Thu Apr 20 14:08:16 2023 + +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 2.398 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 95.703157 98.84049 +k_DMTA 0.056638 0.029110 0.08417 +a.1 2.660081 2.230398 3.08976 +b.1 0.001665 -0.006911 0.01024 +SD.DMTA_0 1.545520 0.145035 2.94601 +SD.k_DMTA 0.606422 0.262274 0.95057 + +Correlation: + DMTA_0 +k_DMTA 0.0169 + +Random effects: + est. lower upper +SD.DMTA_0 1.5455 0.1450 2.9460 +SD.k_DMTA 0.6064 0.2623 0.9506 + +Variance model: + est. lower upper +a.1 2.660081 2.230398 3.08976 +b.1 0.001665 -0.006911 0.01024 + +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: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 14:07:02 2023 +Date of summary: Thu Apr 20 14:08:16 2023 + +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 1.398 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 112.8746 34.8816 190.868 +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: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 14:07:04 2023 +Date of summary: Thu Apr 20 14:08:16 2023 + +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 3.044 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 + 720.4 718.8 -352.2 + +Optimised parameters: + est. lower upper +DMTA_0 98.99136 97.26011 100.72261 +alpha 5.86312 2.57485 9.15138 +beta 88.55571 29.20889 147.90254 +a.1 1.51063 1.24384 1.77741 +b.1 0.02824 0.02040 0.03609 +SD.DMTA_0 1.57436 -0.04867 3.19739 +SD.alpha 0.59871 0.17132 1.02611 +SD.beta 0.72994 0.22849 1.23139 + +Correlation: + DMTA_0 alpha +alpha -0.1363 +beta -0.1414 0.2542 + +Random effects: + est. lower upper +SD.DMTA_0 1.5744 -0.04867 3.197 +SD.alpha 0.5987 0.17132 1.026 +SD.beta 0.7299 0.22849 1.231 + +Variance model: + est. lower upper +a.1 1.51063 1.2438 1.77741 +b.1 0.02824 0.0204 0.03609 + +Estimated disappearance times: + DT50 DT90 DT50back +DMTA 11.11 42.6 12.82 + +</code></pre> +<p></p> +<caption> +Hierarchical mkin fit of the DFOP model with error model const +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 14:07:02 2023 +Date of summary: Thu Apr 20 14:08:16 2023 + +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 1.838 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 96.573898 99.61106 +k1 0.062499 0.030336 0.09466 +k2 0.009065 -0.005133 0.02326 +g 0.948967 0.862079 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: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 14:07:04 2023 +Date of summary: Thu Apr 20 14:08:16 2023 + +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 3.297 s +Using 300, 100 iterations and 9 chains + +Variance model: Two-component variance function + +Starting values for degradation parameters: + DMTA_0 k1 k2 g +98.759266 0.087034 0.009933 0.930827 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + DMTA_0 k1 k2 g +DMTA_0 98.76 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 + 665.5 663.4 -322.8 + +Optimised parameters: + est. lower upper +DMTA_0 98.377019 96.447952 100.30609 +k1 0.064843 0.034607 0.09508 +k2 0.008895 0.006368 0.01142 +g 0.949696 0.903815 0.99558 +a.1 1.065241 0.865754 1.26473 +b.1 0.029340 0.022336 0.03634 +SD.DMTA_0 2.007754 0.387982 3.62753 +SD.k1 0.580473 0.250286 0.91066 +SD.k2 0.006105 -4.920337 4.93255 +SD.g 1.097149 0.412779 1.78152 + +Correlation: + DMTA_0 k1 k2 +k1 0.0235 +k2 0.0595 0.0424 +g -0.0470 -0.0278 -0.2731 + +Random effects: + est. lower upper +SD.DMTA_0 2.007754 0.3880 3.6275 +SD.k1 0.580473 0.2503 0.9107 +SD.k2 0.006105 -4.9203 4.9325 +SD.g 1.097149 0.4128 1.7815 + +Variance model: + est. lower upper +a.1 1.06524 0.86575 1.26473 +b.1 0.02934 0.02234 0.03634 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +DMTA 11.36 41.32 12.44 10.69 77.92 + +</code></pre> +<p></p> +<caption> +Hierarchical mkin fit of the HS model with error model const +</caption> +<pre><code> +saemix version used for fitting: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 14:07:03 2023 +Date of summary: Thu Apr 20 14:08:16 2023 + +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 1.972 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: 3.2 +mkin version used for pre-fitting: 1.2.3 +R version used for fitting: 4.2.3 +Date of fit: Thu Apr 20 14:07:04 2023 +Date of summary: Thu Apr 20 14:08:16 2023 + +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 3.378 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 97.76570 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 0.88590 1.29080 +b.1 0.02964 0.02257 0.03671 +SD.DMTA_0 2.04877 0.42607 3.67147 +SD.k1 0.59166 0.25621 0.92711 +SD.k2 0.30698 0.09561 0.51835 +SD.tb 0.01274 -0.10914 0.13462 + +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 0.42607 3.6715 +SD.k1 0.59166 0.25621 0.9271 +SD.k2 0.30698 0.09561 0.5183 +SD.tb 0.01274 -0.10914 0.1346 + +Variance model: + est. lower upper +a.1 1.08835 0.88590 1.29080 +b.1 0.02964 0.02257 0.03671 + +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 4.2.3 (2023-03-15) +Platform: x86_64-pc-linux-gnu (64-bit) +Running under: Debian GNU/Linux 12 (bookworm) + +Matrix products: default +BLAS: /usr/lib/x86_64-linux-gnu/openblas-serial/libblas.so.3 +LAPACK: /usr/lib/x86_64-linux-gnu/openblas-serial/libopenblas-r0.3.21.so + +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 + +attached base packages: +[1] parallel stats graphics grDevices utils datasets methods +[8] base + +other attached packages: +[1] saemix_3.2 npde_3.3 knitr_1.42 mkin_1.2.3 + +loaded via a namespace (and not attached): + [1] highr_0.10 pillar_1.9.0 bslib_0.4.2 compiler_4.2.3 + [5] jquerylib_0.1.4 tools_4.2.3 mclust_6.0.0 digest_0.6.31 + [9] tibble_3.2.1 jsonlite_1.8.4 evaluate_0.20 memoise_2.0.1 +[13] lifecycle_1.0.3 nlme_3.1-162 gtable_0.3.3 lattice_0.21-8 +[17] pkgconfig_2.0.3 rlang_1.1.0 DBI_1.1.3 cli_3.6.1 +[21] yaml_2.3.7 pkgdown_2.0.7 xfun_0.38 fastmap_1.1.1 +[25] gridExtra_2.3 dplyr_1.1.1 stringr_1.5.0 generics_0.1.3 +[29] desc_1.4.2 fs_1.6.1 vctrs_0.6.1 sass_0.4.5 +[33] systemfonts_1.0.4 tidyselect_1.2.0 rprojroot_2.0.3 lmtest_0.9-40 +[37] grid_4.2.3 glue_1.6.2 R6_2.5.1 textshaping_0.3.6 +[41] fansi_1.0.4 rmarkdown_2.21 purrr_1.0.1 ggplot2_3.4.2 +[45] magrittr_2.0.3 codetools_0.2-19 scales_1.2.1 htmltools_0.5.5 +[49] colorspace_2.1-0 ragg_1.2.5 utf8_1.2.3 stringi_1.7.12 +[53] munsell_0.5.0 cachem_1.0.7 zoo_1.8-12 </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: 64936316 kB</code></pre> +</div> +</div> + </div> + + <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar"> + + <nav id="toc" data-toggle="toc"><h2 data-toc-skip>Contents</h2> + </nav> +</div> + +</div> + + + + <footer><div class="copyright"> + <p></p> +<p>Developed by Johannes Ranke.</p> +</div> + +<div class="pkgdown"> + <p></p> +<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p> +</div> + + </footer> +</div> + + + + + + + </body> +</html> diff --git a/docs/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-dfop-const-1.png b/docs/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-dfop-const-1.png Binary files differnew file mode 100644 index 00000000..3f145074 --- /dev/null +++ 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<li> + <a href="../../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a> + </li> + <li> + <a href="../../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a> + </li> + <li> + <a href="../../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a> + </li> + <li> + <a href="../../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a> + </li> + <li> + <a href="../../articles/web_only/multistart.html">Short demo of the multistart method</a> + </li> + <li class="divider"> + </li> +<li class="dropdown-header">Performance</li> + <li> + <a href="../../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> + </li> + <li> + <a 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data-toc-skip>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 20 April 2023</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="hidden 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 1.2.3, 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">C</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">C</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">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</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">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">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="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">OK</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> +<pre><code>Warning in FUN(X[[i]], ...): Could not obtain log likelihood with 'is' method +for sforb_path_1 const</code></pre> +<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">2276.3</td> +<td align="right">2272.5</td> +<td align="right">-1120.1</td> +</tr> +<tr class="odd"> +<td align="left">fomc_path_1 const</td> +<td align="right">19</td> +<td align="right">2099.0</td> +<td align="right">2095.0</td> +<td align="right">-1030.5</td> +</tr> +<tr class="even"> +<td align="left">fomc_path_1 tc</td> +<td align="right">20</td> +<td align="right">1939.6</td> +<td align="right">1935.5</td> +<td align="right">-949.8</td> +</tr> +<tr class="odd"> +<td align="left">dfop_path_1 const</td> +<td align="right">21</td> +<td align="right">2038.8</td> +<td align="right">2034.4</td> +<td align="right">-998.4</td> +</tr> +<tr class="even"> +<td align="left">hs_path_1 const</td> +<td align="right">21</td> +<td align="right">2024.2</td> +<td align="right">2019.8</td> +<td align="right">-991.1</td> +</tr> +<tr class="odd"> +<td align="left">dfop_path_1 tc</td> +<td align="right">22</td> +<td align="right">1879.8</td> +<td align="right">1875.2</td> +<td align="right">-917.9</td> +</tr> +<tr class="even"> +<td align="left">sforb_path_1 tc</td> +<td align="right">22</td> +<td align="right">1832.9</td> +<td align="right">1828.3</td> +<td align="right">-894.4</td> +</tr> +<tr class="odd"> +<td align="left">hs_path_1 tc</td> +<td align="right">22</td> +<td align="right">1831.4</td> +<td align="right">1826.8</td> +<td align="right">-893.7</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="cb10"><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"></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="cb11"><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="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">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">1830.3</td> +<td align="right">1825.9</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">1832.9</td> +<td align="right">1828.3</td> +<td align="right">-894.4</td> +</tr> +</tbody> +</table> +<p>The convergence plot of the refined fit is shown below.</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">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="cb14"><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> +<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 +15 17 +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 4.2.3 (2023-03-15) +Platform: x86_64-pc-linux-gnu (64-bit) +Running under: Debian GNU/Linux 12 (bookworm) + +Matrix products: default +BLAS: /usr/lib/x86_64-linux-gnu/openblas-serial/libblas.so.3 +LAPACK: /usr/lib/x86_64-linux-gnu/openblas-serial/libopenblas-r0.3.21.so + +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 + +attached base packages: +[1] parallel stats graphics grDevices utils datasets methods +[8] base + +other attached packages: +[1] saemix_3.2 npde_3.3 knitr_1.42 mkin_1.2.3 + +loaded via a namespace (and not attached): + [1] deSolve_1.35 zoo_1.8-12 tidyselect_1.2.0 xfun_0.38 + [5] bslib_0.4.2 purrr_1.0.1 lattice_0.21-8 colorspace_2.1-0 + [9] vctrs_0.6.1 generics_0.1.3 htmltools_0.5.5 yaml_2.3.7 +[13] utf8_1.2.3 rlang_1.1.0 pkgbuild_1.4.0 pkgdown_2.0.7 +[17] jquerylib_0.1.4 pillar_1.9.0 glue_1.6.2 DBI_1.1.3 +[21] lifecycle_1.0.3 stringr_1.5.0 munsell_0.5.0 gtable_0.3.3 +[25] ragg_1.2.5 codetools_0.2-19 memoise_2.0.1 evaluate_0.20 +[29] inline_0.3.19 callr_3.7.3 fastmap_1.1.1 ps_1.7.4 +[33] lmtest_0.9-40 fansi_1.0.4 highr_0.10 scales_1.2.1 +[37] cachem_1.0.7 desc_1.4.2 jsonlite_1.8.4 systemfonts_1.0.4 +[41] fs_1.6.1 textshaping_0.3.6 gridExtra_2.3 ggplot2_3.4.2 +[45] digest_0.6.31 stringi_1.7.12 processx_3.8.0 dplyr_1.1.1 +[49] grid_4.2.3 rprojroot_2.0.3 cli_3.6.1 tools_4.2.3 +[53] magrittr_2.0.3 sass_0.4.5 tibble_3.2.1 crayon_1.5.2 +[57] pkgconfig_2.0.3 prettyunits_1.1.1 rmarkdown_2.21 R6_2.5.1 +[61] mclust_6.0.0 nlme_3.1-162 compiler_4.2.3 </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: 64936316 kB</code></pre> +</div> +</div> + </div> + + <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar"> + + <nav id="toc" data-toggle="toc"><h2 data-toc-skip>Contents</h2> + </nav> +</div> + +</div> + + + + <footer><div class="copyright"> + <p></p> +<p>Developed by Johannes Ranke.</p> +</div> + +<div class="pkgdown"> + <p></p> +<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p> +</div> + + </footer> +</div> + + + + + + + </body> +</html> diff --git a/docs/articles/prebuilt/2022_dmta_pathway_files/figure-html/saem-sforb-path-1-tc-reduced-convergence-1.png b/docs/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..206c424d --- /dev/null +++ b/docs/articles/prebuilt/2022_dmta_pathway_files/figure-html/saem-sforb-path-1-tc-reduced-convergence-1.png diff --git a/docs/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-2-1.png b/docs/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-2-1.png Binary files 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index 41340e88..c8c91bcb 100644 --- a/docs/articles/twa.html +++ b/docs/articles/twa.html @@ -33,14 +33,14 @@ </button> <span class="navbar-brand"> <a class="navbar-link" href="../index.html">mkin</a> - <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">1.2.0</span> + <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">1.2.3</span> </span> </div> <div id="navbar" class="navbar-collapse collapse"> <ul class="nav navbar-nav"> <li> - <a href="../reference/index.html">Functions and data</a> + <a href="../reference/index.html">Reference</a> </li> <li class="dropdown"> <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false"> @@ -52,6 +52,9 @@ <li> <a href="../articles/mkin.html">Introduction to mkin</a> </li> + <li class="divider"> + </li> +<li class="dropdown-header">Example evaluations with (generalised) nonlinear least squares</li> <li> <a href="../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a> </li> @@ -59,22 +62,31 @@ <a href="../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a> </li> <li> - <a href="../articles/web_only/dimethenamid_2018.html">Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models</a> + <a href="../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> + </li> + <li class="divider"> </li> +<li class="dropdown-header">Example evaluations with hierarchical models (nonlinear mixed-effects models)</li> <li> - <a href="../articles/web_only/multistart.html">Short demo of the multistart method</a> + <a href="../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a> </li> <li> - <a href="../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> + <a href="../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a> </li> <li> - <a href="../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> + <a href="../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a> </li> <li> - <a href="../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> + <a href="../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a> </li> <li> - <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> + <a href="../articles/web_only/multistart.html">Short demo of the multistart method</a> + </li> + <li class="divider"> + </li> +<li class="dropdown-header">Performance</li> + <li> + <a href="../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> </li> <li> <a href="../articles/web_only/benchmarks.html">Benchmark timings for mkin</a> @@ -82,6 +94,15 @@ <li> <a href="../articles/web_only/saem_benchmarks.html">Benchmark timings for saem.mmkin</a> </li> + <li class="divider"> + </li> +<li class="dropdown-header">Miscellaneous</li> + <li> + <a href="../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> + </li> + <li> + <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> + </li> </ul> </li> <li> @@ -105,13 +126,16 @@ - </header><script src="twa_files/accessible-code-block-0.0.1/empty-anchor.js"></script><div class="row"> + </header><div class="row"> <div class="col-md-9 contents"> <div class="page-header toc-ignore"> - <h1 data-toc-skip>Calculation of time weighted average concentrations with mkin</h1> - <h4 data-toc-skip class="author">Johannes Ranke</h4> + <h1 data-toc-skip>Calculation of time weighted average +concentrations with mkin</h1> + <h4 data-toc-skip class="author">Johannes +Ranke</h4> - <h4 data-toc-skip class="date">Last change 18 September 2019 (rebuilt 2022-11-17)</h4> + <h4 data-toc-skip class="date">Last change 18 September 2019 +(rebuilt 2023-04-20)</h4> <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/twa.rmd" class="external-link"><code>vignettes/twa.rmd</code></a></small> <div class="hidden name"><code>twa.rmd</code></div> @@ -120,13 +144,25 @@ -<p>Since version 0.9.45.1 of the ‘mkin’ package, a function for calculating time weighted average concentrations for decline kinetics (<em>i.e.</em> only for the compound applied in the experiment) is included. Strictly speaking, they are maximum moving window time weighted average concentrations, <em>i.e.</em> the maximum time weighted average concentration that can be found when moving a time window of a specified width over the decline curve.</p> -<p>Time weighted average concentrations for the SFO, FOMC and the DFOP model are calculated using the formulas given in the FOCUS kinetics guidance <span class="citation">(FOCUS Work Group on Degradation Kinetics 2014, 251)</span>:</p> +<p>Since version 0.9.45.1 of the ‘mkin’ package, a function for +calculating time weighted average concentrations for decline kinetics +(<em>i.e.</em> only for the compound applied in the experiment) is +included. Strictly speaking, they are maximum moving window time +weighted average concentrations, <em>i.e.</em> the maximum time weighted +average concentration that can be found when moving a time window of a +specified width over the decline curve.</p> +<p>Time weighted average concentrations for the SFO, FOMC and the DFOP +model are calculated using the formulas given in the FOCUS kinetics +guidance <span class="citation">(FOCUS Work Group on Degradation +Kinetics 2014, 251)</span>:</p> <p>SFO:</p> -<p><span class="math display">\[c_\textrm{twa} = c_0 \frac{\left( 1 - e^{- k t} \right)}{ k t} \]</span></p> +<p><span class="math display">\[c_\textrm{twa} = c_0 \frac{\left( 1 - +e^{- k t} \right)}{ k t} \]</span></p> <p>FOMC:</p> -<p><span class="math display">\[c_\textrm{twa} = c_0 \frac{\beta}{t (1 - \alpha)} - \left( \left(\frac{t}{\beta} + 1 \right)^{1 - \alpha} - 1 \right) \]</span></p> +<p><span class="math display">\[c_\textrm{twa} = c_0 \frac{\beta}{t (1 - +\alpha)} + \left( \left(\frac{t}{\beta} + 1 \right)^{1 - \alpha} +- 1 \right) \]</span></p> <p>DFOP:</p> <p><span class="math display">\[c_\textrm{twa} = \frac{c_0}{t} \left( \frac{g}{k_1} \left( 1 - e^{- k_1 t} \right) + @@ -134,15 +170,25 @@ <p>HS for <span class="math inline">\(t > t_b\)</span>:</p> <p><span class="math display">\[c_\textrm{twa} = \frac{c_0}{t} \left( \frac{1}{k_1} \left( 1 - e^{- k_1 t_b} \right) + - \frac{e^{- k_1 t_b}}{k_2} \left( 1 - e^{- k_2 (t - t_b)} \right) \right) \]</span></p> -<p>Often, the ratio between the time weighted average concentration <span class="math inline">\(c_\textrm{twa}\)</span> and the initial concentration <span class="math inline">\(c_0\)</span></p> -<p><span class="math display">\[f_\textrm{twa} = \frac{c_\textrm{twa}}{c_0}\]</span></p> -<p>is needed. This can be calculated from the fitted initial concentration <span class="math inline">\(c_0\)</span> and the time weighted average concentration <span class="math inline">\(c_\textrm{twa}\)</span>, or directly from the model parameters using the following formulas:</p> + \frac{e^{- k_1 t_b}}{k_2} \left( 1 - e^{- k_2 (t - t_b)} +\right) \right) \]</span></p> +<p>Often, the ratio between the time weighted average concentration +<span class="math inline">\(c_\textrm{twa}\)</span> and the initial +concentration <span class="math inline">\(c_0\)</span></p> +<p><span class="math display">\[f_\textrm{twa} = +\frac{c_\textrm{twa}}{c_0}\]</span></p> +<p>is needed. This can be calculated from the fitted initial +concentration <span class="math inline">\(c_0\)</span> and the time +weighted average concentration <span class="math inline">\(c_\textrm{twa}\)</span>, or directly from the +model parameters using the following formulas:</p> <p>SFO:</p> -<p><span class="math display">\[f_\textrm{twa} = \frac{\left( 1 - e^{- k t} \right)}{k t} \]</span></p> +<p><span class="math display">\[f_\textrm{twa} = \frac{\left( 1 - e^{- k +t} \right)}{k t} \]</span></p> <p>FOMC:</p> -<p><span class="math display">\[f_\textrm{twa} = \frac{\beta}{t (1 - \alpha)} - \left( \left(\frac{t}{\beta} + 1 \right)^{1 - \alpha} - 1 \right) \]</span></p> +<p><span class="math display">\[f_\textrm{twa} = \frac{\beta}{t (1 - +\alpha)} + \left( \left(\frac{t}{\beta} + 1 \right)^{1 - \alpha} +- 1 \right) \]</span></p> <p>DFOP:</p> <p><span class="math display">\[f_\textrm{twa} = \frac{1}{t} \left( \frac{g}{k_1} \left( 1 - e^{- k_1 t} \right) + @@ -150,11 +196,19 @@ <p>HS for <span class="math inline">\(t > t_b\)</span>:</p> <p><span class="math display">\[f_\textrm{twa} = \frac{1}{t} \left( \frac{1}{k_1} \left( 1 - e^{- k_1 t_b} \right) + - \frac{e^{- k_1 t_b}}{k_2} \left( 1 - e^{- k_2 (t - t_b)} \right) \right) \]</span></p> -<p>Note that a method for calculating maximum moving window time weighted average concentrations for a model fitted by ‘mkinfit’ or from parent decline model parameters is included in the <code><a href="../reference/max_twa_parent.html">max_twa_parent()</a></code> function. If the same is needed for metabolites, the function <code><a href="https://pkgdown.jrwb.de/pfm/reference/max_twa.html" class="external-link">pfm::max_twa()</a></code> from the ‘pfm’ package can be used.</p> -<div id="refs" class="references hanging-indent"> -<div id="ref-FOCUSkinetics2014"> -<p>FOCUS Work Group on Degradation Kinetics. 2014. <em>Generic Guidance for Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in Eu Registration</em>. 1.1 ed. <a href="http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics" class="external-link">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>.</p> + \frac{e^{- k_1 t_b}}{k_2} \left( 1 - e^{- k_2 (t - t_b)} +\right) \right) \]</span></p> +<p>Note that a method for calculating maximum moving window time +weighted average concentrations for a model fitted by ‘mkinfit’ or from +parent decline model parameters is included in the +<code><a href="../reference/max_twa_parent.html">max_twa_parent()</a></code> function. If the same is needed for +metabolites, the function <code><a href="https://pkgdown.jrwb.de/pfm/reference/max_twa.html" class="external-link">pfm::max_twa()</a></code> from the ‘pfm’ +package can be used.</p> +<div id="refs" class="references csl-bib-body hanging-indent"> +<div id="ref-FOCUSkinetics2014" class="csl-entry"> +FOCUS Work Group on Degradation Kinetics. 2014. <em>Generic Guidance for +Estimating Persistence and Degradation Kinetics from Environmental Fate +Studies on Pesticides in EU Registration</em>. 1.1 ed. <a href="http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics" class="external-link">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>. </div> </div> </div> @@ -174,7 +228,7 @@ <div class="pkgdown"> <p></p> -<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p> +<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p> </div> </footer> diff --git a/docs/articles/web_only/FOCUS_Z.html b/docs/articles/web_only/FOCUS_Z.html index ea20ecd9..9602adb5 100644 --- a/docs/articles/web_only/FOCUS_Z.html +++ b/docs/articles/web_only/FOCUS_Z.html @@ -33,14 +33,14 @@ </button> <span class="navbar-brand"> <a class="navbar-link" href="../../index.html">mkin</a> - <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">1.2.0</span> + <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">1.2.3</span> </span> </div> <div id="navbar" class="navbar-collapse collapse"> <ul class="nav navbar-nav"> <li> - <a href="../../reference/index.html">Functions and data</a> + <a href="../../reference/index.html">Reference</a> </li> <li class="dropdown"> <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false"> @@ -52,6 +52,9 @@ <li> <a href="../../articles/mkin.html">Introduction to mkin</a> </li> + <li class="divider"> + </li> +<li class="dropdown-header">Example evaluations with (generalised) nonlinear least squares</li> <li> <a href="../../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a> </li> @@ -59,22 +62,31 @@ <a href="../../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a> </li> <li> - <a href="../../articles/web_only/dimethenamid_2018.html">Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models</a> + <a href="../../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> + </li> + <li class="divider"> </li> +<li class="dropdown-header">Example evaluations with hierarchical models (nonlinear mixed-effects models)</li> <li> - <a href="../../articles/web_only/multistart.html">Short demo of the multistart method</a> + <a href="../../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a> </li> <li> - <a href="../../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> + <a href="../../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a> </li> <li> - <a href="../../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> + <a href="../../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a> </li> <li> - <a href="../../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> + <a href="../../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a> </li> <li> - <a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> + <a href="../../articles/web_only/multistart.html">Short demo of the multistart method</a> + </li> + <li class="divider"> + </li> +<li class="dropdown-header">Performance</li> + <li> + <a href="../../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> </li> <li> <a href="../../articles/web_only/benchmarks.html">Benchmark timings for mkin</a> @@ -82,6 +94,15 @@ <li> <a href="../../articles/web_only/saem_benchmarks.html">Benchmark timings for saem.mmkin</a> </li> + <li class="divider"> + </li> +<li class="dropdown-header">Miscellaneous</li> + <li> + <a href="../../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> + </li> + <li> + <a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> + </li> </ul> </li> <li> @@ -105,13 +126,15 @@ - </header><script src="FOCUS_Z_files/accessible-code-block-0.0.1/empty-anchor.js"></script><div class="row"> + </header><div class="row"> <div class="col-md-9 contents"> <div class="page-header toc-ignore"> <h1 data-toc-skip>Example evaluation of FOCUS dataset Z</h1> - <h4 data-toc-skip class="author">Johannes Ranke</h4> + <h4 data-toc-skip class="author">Johannes +Ranke</h4> - <h4 data-toc-skip class="date">Last change 16 January 2018 (rebuilt 2022-11-17)</h4> + <h4 data-toc-skip class="date">Last change 16 January 2018 +(rebuilt 2023-04-20)</h4> <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/FOCUS_Z.rmd" class="external-link"><code>vignettes/web_only/FOCUS_Z.rmd</code></a></small> <div class="hidden name"><code>FOCUS_Z.rmd</code></div> @@ -120,11 +143,15 @@ -<p><a href="http://www.jrwb.de" class="external-link">Wissenschaftlicher Berater, Kronacher Str. 12, 79639 Grenzach-Wyhlen, Germany</a><br><a href="http://chem.uft.uni-bremen.de/ranke" class="external-link">Privatdozent at the University of Bremen</a></p> +<p><a href="http://www.jrwb.de" class="external-link">Wissenschaftlicher Berater, Kronacher +Str. 12, 79639 Grenzach-Wyhlen, Germany</a><br><a href="http://chem.uft.uni-bremen.de/ranke" class="external-link">Privatdozent at the +University of Bremen</a></p> <div class="section level2"> <h2 id="the-data">The data<a class="anchor" aria-label="anchor" href="#the-data"></a> </h2> -<p>The following code defines the example dataset from Appendix 7 to the FOCUS kinetics report <span class="citation">(FOCUS Work Group on Degradation Kinetics 2014, 354)</span>.</p> +<p>The following code defines the example dataset from Appendix 7 to the +FOCUS kinetics report <span class="citation">(FOCUS Work Group on +Degradation Kinetics 2014, 354)</span>.</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>, quietly <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> <span><span class="va">LOD</span> <span class="op">=</span> <span class="fl">0.5</span></span> @@ -145,7 +172,11 @@ <div class="section level2"> <h2 id="parent-and-one-metabolite">Parent and one metabolite<a class="anchor" aria-label="anchor" href="#parent-and-one-metabolite"></a> </h2> -<p>The next step is to set up the models used for the kinetic analysis. As the simultaneous fit of parent and the first metabolite is usually straightforward, Step 1 (SFO for parent only) is skipped here. We start with the model 2a, with formation and decline of metabolite Z1 and the pathway from parent directly to sink included (default in mkin).</p> +<p>The next step is to set up the models used for the kinetic analysis. +As the simultaneous fit of parent and the first metabolite is usually +straightforward, Step 1 (SFO for parent only) is skipped here. We start +with the model 2a, with formation and decline of metabolite Z1 and the +pathway from parent directly to sink included (default in mkin).</p> <div class="sourceCode" id="cb2"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">Z.2a</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <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">"Z1"</span><span class="op">)</span>,</span> <span> Z1 <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 class="op">)</span></span></code></pre></div> @@ -158,15 +189,21 @@ <code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.2a</span><span class="op">)</span></span></code></pre></div> <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png" width="700"></p> <div class="sourceCode" id="cb7"><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">m.Z.2a</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></code></pre></div> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.2a</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></code></pre></div> <pre><code><span><span class="co">## Estimate se_notrans t value Pr(>t) Lower Upper</span></span> <span><span class="co">## Z0_0 97.01488 3.301084 29.3888 3.2971e-21 91.66556 102.3642</span></span> <span><span class="co">## k_Z0 2.23601 0.207078 10.7979 3.3309e-11 1.95303 2.5600</span></span> <span><span class="co">## k_Z1 0.48212 0.063265 7.6207 2.8154e-08 0.40341 0.5762</span></span> <span><span class="co">## f_Z0_to_Z1 1.00000 0.094764 10.5525 5.3560e-11 0.00000 1.0000</span></span> <span><span class="co">## sigma 4.80411 0.635638 7.5579 3.2592e-08 3.52677 6.0815</span></span></code></pre> -<p>As obvious from the parameter summary (the component of the summary), the kinetic rate constant from parent compound Z to sink is very small and the t-test for this parameter suggests that it is not significantly different from zero. This suggests, in agreement with the analysis in the FOCUS kinetics report, to simplify the model by removing the pathway to sink.</p> -<p>A similar result can be obtained when formation fractions are used in the model formulation:</p> +<p>As obvious from the parameter summary (the component of the summary), +the kinetic rate constant from parent compound Z to sink is very small +and the t-test for this parameter suggests that it is not significantly +different from zero. This suggests, in agreement with the analysis in +the FOCUS kinetics report, to simplify the model by removing the pathway +to sink.</p> +<p>A similar result can be obtained when formation fractions are used in +the model formulation:</p> <div class="sourceCode" id="cb9"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">Z.2a.ff</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <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">"Z1"</span><span class="op">)</span>,</span> <span> Z1 <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> @@ -180,16 +217,24 @@ <code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.2a.ff</span><span class="op">)</span></span></code></pre></div> <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png" width="700"></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">m.Z.2a.ff</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></code></pre></div> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.2a.ff</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></code></pre></div> <pre><code><span><span class="co">## Estimate se_notrans t value Pr(>t) Lower Upper</span></span> <span><span class="co">## Z0_0 97.01488 3.301084 29.3888 3.2971e-21 91.66556 102.3642</span></span> <span><span class="co">## k_Z0 2.23601 0.207078 10.7979 3.3309e-11 1.95303 2.5600</span></span> <span><span class="co">## k_Z1 0.48212 0.063265 7.6207 2.8154e-08 0.40341 0.5762</span></span> <span><span class="co">## f_Z0_to_Z1 1.00000 0.094764 10.5525 5.3560e-11 0.00000 1.0000</span></span> <span><span class="co">## sigma 4.80411 0.635638 7.5579 3.2592e-08 3.52677 6.0815</span></span></code></pre> -<p>Here, the ilr transformed formation fraction fitted in the model takes a very large value, and the backtransformed formation fraction from parent Z to Z1 is practically unity. Here, the covariance matrix used for the calculation of confidence intervals is not returned as the model is overparameterised.</p> -<p>A simplified model is obtained by removing the pathway to the sink. </p> -<p>In the following, we use the parameterisation with formation fractions in order to be able to compare with the results in the FOCUS guidance, and as it makes it easier to use parameters obtained in a previous fit when adding a further metabolite.</p> +<p>Here, the ilr transformed formation fraction fitted in the model +takes a very large value, and the backtransformed formation fraction +from parent Z to Z1 is practically unity. Here, the covariance matrix +used for the calculation of confidence intervals is not returned as the +model is overparameterised.</p> +<p>A simplified model is obtained by removing the pathway to the sink. +</p> +<p>In the following, we use the parameterisation with formation +fractions in order to be able to compare with the results in the FOCUS +guidance, and as it makes it easier to use parameters obtained in a +previous fit when adding a further metabolite.</p> <div class="sourceCode" id="cb16"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">Z.3</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <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">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> <span> Z1 <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>, use_of_ff <span class="op">=</span> <span class="st">"max"</span><span class="op">)</span></span></code></pre></div> @@ -202,18 +247,24 @@ <code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.3</span><span class="op">)</span></span></code></pre></div> <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png" width="700"></p> <div class="sourceCode" id="cb21"><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">m.Z.3</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></code></pre></div> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.3</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></code></pre></div> <pre><code><span><span class="co">## Estimate se_notrans t value Pr(>t) Lower Upper</span></span> <span><span class="co">## Z0_0 97.01488 2.597342 37.352 2.0106e-24 91.67597 102.3538</span></span> <span><span class="co">## k_Z0 2.23601 0.146904 15.221 9.1477e-15 1.95354 2.5593</span></span> <span><span class="co">## k_Z1 0.48212 0.041727 11.554 4.8268e-12 0.40355 0.5760</span></span> <span><span class="co">## sigma 4.80411 0.620208 7.746 1.6110e-08 3.52925 6.0790</span></span></code></pre> -<p>As there is only one transformation product for Z0 and no pathway to sink, the formation fraction is internally fixed to unity.</p> +<p>As there is only one transformation product for Z0 and no pathway to +sink, the formation fraction is internally fixed to unity.</p> </div> <div class="section level2"> <h2 id="metabolites-z2-and-z3">Metabolites Z2 and Z3<a class="anchor" aria-label="anchor" href="#metabolites-z2-and-z3"></a> </h2> -<p>As suggested in the FOCUS report, the pathway to sink was removed for metabolite Z1 as well in the next step. While this step appears questionable on the basis of the above results, it is followed here for the purpose of comparison. Also, in the FOCUS report, it is assumed that there is additional empirical evidence that Z1 quickly and exclusively hydrolyses to Z2.</p> +<p>As suggested in the FOCUS report, the pathway to sink was removed for +metabolite Z1 as well in the next step. While this step appears +questionable on the basis of the above results, it is followed here for +the purpose of comparison. Also, in the FOCUS report, it is assumed that +there is additional empirical evidence that Z1 quickly and exclusively +hydrolyses to Z2.</p> <div class="sourceCode" id="cb23"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">Z.5</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <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">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> <span> Z1 <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">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> @@ -226,7 +277,9 @@ <div class="sourceCode" id="cb27"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.5</span><span class="op">)</span></span></code></pre></div> <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png" width="700"></p> -<p>Finally, metabolite Z3 is added to the model. We use the optimised differential equation parameter values from the previous fit in order to accelerate the optimization.</p> +<p>Finally, metabolite Z3 is added to the model. We use the optimised +differential equation parameter values from the previous fit in order to +accelerate the optimization.</p> <div class="sourceCode" id="cb28"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">Z.FOCUS</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <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">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> <span> Z1 <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">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> @@ -246,7 +299,7 @@ <code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.FOCUS</span><span class="op">)</span></span></code></pre></div> <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png" width="700"></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">m.Z.FOCUS</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></code></pre></div> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.FOCUS</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></code></pre></div> <pre><code><span><span class="co">## Estimate se_notrans t value Pr(>t) Lower Upper</span></span> <span><span class="co">## Z0_0 96.838822 1.994274 48.5584 4.0280e-42 92.826981 100.850664</span></span> <span><span class="co">## k_Z0 2.215393 0.118458 18.7019 1.0413e-23 1.989456 2.466989</span></span> @@ -267,13 +320,22 @@ <span><span class="co">## Z1 1.44917 4.8141</span></span> <span><span class="co">## Z2 1.53478 5.0984</span></span> <span><span class="co">## Z3 11.80986 39.2315</span></span></code></pre> -<p>This fit corresponds to the final result chosen in Appendix 7 of the FOCUS report. Confidence intervals returned by mkin are based on internally transformed parameters, however.</p> +<p>This fit corresponds to the final result chosen in Appendix 7 of the +FOCUS report. Confidence intervals returned by mkin are based on +internally transformed parameters, however.</p> </div> <div class="section level2"> <h2 id="using-the-sforb-model">Using the SFORB model<a class="anchor" aria-label="anchor" href="#using-the-sforb-model"></a> </h2> -<p>As the FOCUS report states, there is a certain tailing of the time course of metabolite Z3. Also, the time course of the parent compound is not fitted very well using the SFO model, as residues at a certain low level remain.</p> -<p>Therefore, an additional model is offered here, using the single first-order reversible binding (SFORB) model for metabolite Z3. As expected, the <span class="math inline">\(\chi^2\)</span> error level is lower for metabolite Z3 using this model and the graphical fit for Z3 is improved. However, the covariance matrix is not returned.</p> +<p>As the FOCUS report states, there is a certain tailing of the time +course of metabolite Z3. Also, the time course of the parent compound is +not fitted very well using the SFO model, as residues at a certain low +level remain.</p> +<p>Therefore, an additional model is offered here, using the single +first-order reversible binding (SFORB) model for metabolite Z3. As +expected, the <span class="math inline">\(\chi^2\)</span> error level is +lower for metabolite Z3 using this model and the graphical fit for Z3 is +improved. However, the covariance matrix is not returned.</p> <div class="sourceCode" id="cb38"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">Z.mkin.1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <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">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> <span> Z1 <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">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> @@ -282,15 +344,18 @@ <pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre> <div class="sourceCode" id="cb40"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">m.Z.mkin.1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.mkin.1</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Warning in mkinfit(Z.mkin.1, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with</span></span> -<span><span class="co">## value of zero were removed from the data</span></span></code></pre> +<pre><code><span><span class="co">## Warning in mkinfit(Z.mkin.1, FOCUS_2006_Z_mkin, quiet = TRUE): Observations</span></span> +<span><span class="co">## with value of zero were removed from the data</span></span></code></pre> <div class="sourceCode" id="cb42"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.1</span><span class="op">)</span></span></code></pre></div> <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png" width="700"></p> <div class="sourceCode" id="cb43"><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">m.Z.mkin.1</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">cov.unscaled</span></span></code></pre></div> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.mkin.1</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">cov.unscaled</span></span></code></pre></div> <pre><code><span><span class="co">## NULL</span></span></code></pre> -<p>Therefore, a further stepwise model building is performed starting from the stage of parent and two metabolites, starting from the assumption that the model fit for the parent compound can be improved by using the SFORB model.</p> +<p>Therefore, a further stepwise model building is performed starting +from the stage of parent and two metabolites, starting from the +assumption that the model fit for the parent compound can be improved by +using the SFORB model.</p> <div class="sourceCode" id="cb45"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">Z.mkin.3</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <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="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> <span> Z1 <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">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> @@ -298,13 +363,16 @@ <pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre> <div class="sourceCode" id="cb47"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">m.Z.mkin.3</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.mkin.3</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> -<pre><code><span><span class="co">## Warning in mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with</span></span> -<span><span class="co">## value of zero were removed from the data</span></span></code></pre> +<pre><code><span><span class="co">## Warning in mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE): Observations</span></span> +<span><span class="co">## with value of zero were removed from the data</span></span></code></pre> <div class="sourceCode" id="cb49"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.3</span><span class="op">)</span></span></code></pre></div> <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png" width="700"></p> -<p>This results in a much better representation of the behaviour of the parent compound Z0.</p> -<p>Finally, Z3 is added as well. These models appear overparameterised (no covariance matrix returned) if the sink for Z1 is left in the models.</p> +<p>This results in a much better representation of the behaviour of the +parent compound Z0.</p> +<p>Finally, Z3 is added as well. These models appear overparameterised +(no covariance matrix returned) if the sink for Z1 is left in the +models.</p> <div class="sourceCode" id="cb50"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">Z.mkin.4</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <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="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> <span> Z1 <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">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> @@ -321,7 +389,10 @@ <div class="sourceCode" id="cb54"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.4</span><span class="op">)</span></span></code></pre></div> <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png" width="700"></p> -<p>The error level of the fit, but especially of metabolite Z3, can be improved if the SFORB model is chosen for this metabolite, as this model is capable of representing the tailing of the metabolite decline phase.</p> +<p>The error level of the fit, but especially of metabolite Z3, can be +improved if the SFORB model is chosen for this metabolite, as this model +is capable of representing the tailing of the metabolite decline +phase.</p> <div class="sourceCode" id="cb55"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">Z.mkin.5</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <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="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> <span> Z1 <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">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span> @@ -338,7 +409,9 @@ <div class="sourceCode" id="cb59"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.5</span><span class="op">)</span></span></code></pre></div> <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png" width="700"></p> -<p>The summary view of the backtransformed parameters shows that we get no confidence intervals due to overparameterisation. As the optimized is excessively small, it seems reasonable to fix it to zero.</p> +<p>The summary view of the backtransformed parameters shows that we get +no confidence intervals due to overparameterisation. As the optimized is +excessively small, it seems reasonable to fix it to zero.</p> <div class="sourceCode" id="cb60"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">m.Z.mkin.5a</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.mkin.5</span>, <span class="va">FOCUS_2006_Z_mkin</span>,</span> <span> parms.ini <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="va">m.Z.mkin.5</span><span class="op">$</span><span class="va">bparms.ode</span><span class="op">[</span><span class="fl">1</span><span class="op">:</span><span class="fl">7</span><span class="op">]</span>,</span> @@ -351,8 +424,12 @@ <div class="sourceCode" id="cb62"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.5a</span><span class="op">)</span></span></code></pre></div> <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png" width="700"></p> -<p>As expected, the residual plots for Z0 and Z3 are more random than in the case of the all SFO model for which they were shown above. In conclusion, the model is proposed as the best-fit model for the dataset from Appendix 7 of the FOCUS report.</p> -<p>A graphical representation of the confidence intervals can finally be obtained.</p> +<p>As expected, the residual plots for Z0 and Z3 are more random than in +the case of the all SFO model for which they were shown above. In +conclusion, the model is proposed as the best-fit model for the dataset +from Appendix 7 of the FOCUS report.</p> +<p>A graphical representation of the confidence intervals can finally be +obtained.</p> <div class="sourceCode" id="cb63"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="fu"><a href="../../reference/mkinparplot.html">mkinparplot</a></span><span class="op">(</span><span class="va">m.Z.mkin.5a</span><span class="op">)</span></span></code></pre></div> <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png" width="700"></p> @@ -373,15 +450,22 @@ <span><span class="co">## Z1 1.5148 5.0320 NA NA NA NA NA</span></span> <span><span class="co">## Z2 1.6414 5.4526 NA NA NA NA NA</span></span> <span><span class="co">## Z3 NA NA NA NA NA 8.6636 Inf</span></span></code></pre> -<p>It is clear the degradation rate of Z3 towards the end of the experiment is very low as DT50_Z3_b2 (the second Eigenvalue of the system of two differential equations representing the SFORB system for Z3, corresponding to the slower rate constant of the DFOP model) is reported to be infinity. However, this appears to be a feature of the data.</p> +<p>It is clear the degradation rate of Z3 towards the end of the +experiment is very low as DT50_Z3_b2 (the second Eigenvalue of the +system of two differential equations representing the SFORB system for +Z3, corresponding to the slower rate constant of the DFOP model) is +reported to be infinity. However, this appears to be a feature of the +data.</p> </div> <div class="section level2"> <h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a> </h2> <!-- vim: set foldmethod=syntax: --> -<div id="refs" class="references hanging-indent"> -<div id="ref-FOCUSkinetics2014"> -<p>FOCUS Work Group on Degradation Kinetics. 2014. <em>Generic Guidance for Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in Eu Registration</em>. 1.1 ed. <a href="http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics" class="external-link">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>.</p> +<div id="refs" class="references csl-bib-body hanging-indent"> +<div id="ref-FOCUSkinetics2014" class="csl-entry"> +FOCUS Work Group on Degradation Kinetics. 2014. <em>Generic Guidance for +Estimating Persistence and Degradation Kinetics from Environmental Fate +Studies on Pesticides in EU Registration</em>. 1.1 ed. <a href="http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics" class="external-link">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>. </div> </div> </div> @@ -404,7 +488,7 @@ <div class="pkgdown"> <p></p> -<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p> +<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p> </div> </footer> diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png Binary files differindex be652d31..98bc135b 100644 --- a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png +++ b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png Binary 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</button> <span class="navbar-brand"> <a class="navbar-link" href="../../index.html">mkin</a> - <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">1.2.0</span> + <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">1.2.3</span> </span> </div> <div id="navbar" class="navbar-collapse collapse"> <ul class="nav navbar-nav"> <li> - <a href="../../reference/index.html">Functions and data</a> + <a href="../../reference/index.html">Reference</a> </li> <li class="dropdown"> <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false"> @@ -52,6 +52,9 @@ <li> <a href="../../articles/mkin.html">Introduction to mkin</a> </li> + <li class="divider"> + </li> +<li class="dropdown-header">Example evaluations with (generalised) nonlinear least squares</li> <li> <a href="../../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a> </li> @@ -59,22 +62,31 @@ <a href="../../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a> </li> <li> - <a href="../../articles/web_only/dimethenamid_2018.html">Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models</a> + <a href="../../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> + </li> + <li class="divider"> </li> +<li class="dropdown-header">Example evaluations with hierarchical models (nonlinear mixed-effects models)</li> <li> - <a href="../../articles/web_only/multistart.html">Short demo of the multistart method</a> + <a href="../../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a> </li> <li> - <a href="../../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> + <a href="../../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a> </li> <li> - <a href="../../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> + <a href="../../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a> </li> <li> - <a href="../../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> + <a href="../../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a> </li> <li> - <a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> + <a href="../../articles/web_only/multistart.html">Short demo of the multistart method</a> + </li> + <li class="divider"> + </li> +<li class="dropdown-header">Performance</li> + <li> + <a href="../../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> </li> <li> <a href="../../articles/web_only/benchmarks.html">Benchmark timings for mkin</a> @@ -82,6 +94,15 @@ <li> <a href="../../articles/web_only/saem_benchmarks.html">Benchmark timings for saem.mmkin</a> </li> + <li class="divider"> + </li> +<li class="dropdown-header">Miscellaneous</li> + <li> + <a href="../../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> + </li> + <li> + <a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> + </li> </ul> </li> <li> @@ -105,13 +126,16 @@ - </header><script src="NAFTA_examples_files/accessible-code-block-0.0.1/empty-anchor.js"></script><div class="row"> + </header><div class="row"> <div class="col-md-9 contents"> <div class="page-header toc-ignore"> - <h1 data-toc-skip>Evaluation of example datasets from Attachment 1 to the US EPA SOP for the NAFTA guidance</h1> - <h4 data-toc-skip class="author">Johannes Ranke</h4> + <h1 data-toc-skip>Evaluation of example datasets from Attachment 1 +to the US EPA SOP for the NAFTA guidance</h1> + <h4 data-toc-skip class="author">Johannes +Ranke</h4> - <h4 data-toc-skip class="date">26 February 2019 (rebuilt 2022-11-17)</h4> + <h4 data-toc-skip class="date">26 February 2019 (rebuilt +2023-04-20)</h4> <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/NAFTA_examples.rmd" class="external-link"><code>vignettes/web_only/NAFTA_examples.rmd</code></a></small> <div class="hidden name"><code>NAFTA_examples.rmd</code></div> @@ -123,13 +147,22 @@ <div class="section level2"> <h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#introduction"></a> </h2> -<p>In this document, the example evaluations provided in Attachment 1 to the SOP of US EPA for using the NAFTA guidance <span class="citation">(US EPA 2015)</span> are repeated using mkin. The original evaluations reported in the attachment were performed using PestDF in version 0.8.4. Note that PestDF 0.8.13 is the version distributed at the US EPA website today (2019-02-26).</p> +<p>In this document, the example evaluations provided in Attachment 1 to +the SOP of US EPA for using the NAFTA guidance <span class="citation">(US EPA 2015)</span> are repeated using mkin. The +original evaluations reported in the attachment were performed using +PestDF in version 0.8.4. Note that PestDF 0.8.13 is the version +distributed at the US EPA website today (2019-02-26).</p> <p>The datasets are now distributed with the mkin package.</p> </div> <div class="section level2"> <h2 id="examples-where-dfop-did-not-converge-with-pestdf-0-8-4">Examples where DFOP did not converge with PestDF 0.8.4<a class="anchor" aria-label="anchor" href="#examples-where-dfop-did-not-converge-with-pestdf-0-8-4"></a> </h2> -<p>In attachment 1, it is reported that the DFOP model does not converge for these datasets when PestDF 0.8.4 was used. For all four datasets, the DFOP model can be fitted with mkin (see below). The negative half-life given by PestDF 0.8.4 for these fits appears to be the result of a bug. The results for the other two models (SFO and IORE) are the same.</p> +<p>In attachment 1, it is reported that the DFOP model does not converge +for these datasets when PestDF 0.8.4 was used. For all four datasets, +the DFOP model can be fitted with mkin (see below). The negative +half-life given by PestDF 0.8.4 for these fits appears to be the result +of a bug. The results for the other two models (SFO and IORE) are the +same.</p> <div class="section level3"> <h3 id="example-on-page-5-upper-panel">Example on page 5, upper panel<a class="anchor" aria-label="anchor" href="#example-on-page-5-upper-panel"></a> </h3> @@ -138,7 +171,7 @@ <pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre> <pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre> <div class="sourceCode" id="cb4"><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">p5a</span><span class="op">)</span></span></code></pre></div> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p5a</span><span class="op">)</span></span></code></pre></div> <p><img src="NAFTA_examples_files/figure-html/p5a-1.png" width="700"></p> <div class="sourceCode" id="cb5"><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">p5a</span><span class="op">)</span></span></code></pre></div> @@ -189,7 +222,7 @@ <pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre> <pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre> <div class="sourceCode" id="cb10"><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">p5b</span><span class="op">)</span></span></code></pre></div> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p5b</span><span class="op">)</span></span></code></pre></div> <p><img src="NAFTA_examples_files/figure-html/p5b-1.png" width="700"></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/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p5b</span><span class="op">)</span></span></code></pre></div> @@ -240,7 +273,7 @@ <pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre> <pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre> <div class="sourceCode" id="cb16"><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">p6</span><span class="op">)</span></span></code></pre></div> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p6</span><span class="op">)</span></span></code></pre></div> <p><img src="NAFTA_examples_files/figure-html/p6-1.png" width="700"></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/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p6</span><span class="op">)</span></span></code></pre></div> @@ -291,7 +324,7 @@ <pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre> <pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre> <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">p7</span><span class="op">)</span></span></code></pre></div> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p7</span><span class="op">)</span></span></code></pre></div> <p><img src="NAFTA_examples_files/figure-html/p7-1.png" width="700"></p> <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/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p7</span><span class="op">)</span></span></code></pre></div> @@ -336,18 +369,21 @@ </div> </div> <div class="section level2"> -<h2 id="examples-where-the-representative-half-life-deviates-from-the-observed-dt50">Examples where the representative half-life deviates from the observed DT50<a class="anchor" aria-label="anchor" href="#examples-where-the-representative-half-life-deviates-from-the-observed-dt50"></a> +<h2 id="examples-where-the-representative-half-life-deviates-from-the-observed-dt50">Examples where the representative half-life deviates from the +observed DT50<a class="anchor" aria-label="anchor" href="#examples-where-the-representative-half-life-deviates-from-the-observed-dt50"></a> </h2> <div class="section level3"> <h3 id="example-on-page-8">Example on page 8<a class="anchor" aria-label="anchor" href="#example-on-page-8"></a> </h3> -<p>For this dataset, the IORE fit does not converge when the default starting values used by mkin for the IORE model are used. Therefore, a lower value for the rate constant is used here.</p> +<p>For this dataset, the IORE fit does not converge when the default +starting values used by mkin for the IORE model are used. Therefore, a +lower value for the rate constant is used here.</p> <div class="sourceCode" id="cb25"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">p8</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p8"</span><span class="op">]</span><span class="op">]</span>, parms.ini <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>k__iore_parent <span class="op">=</span> <span class="fl">1e-3</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> <pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre> <pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre> <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">p8</span><span class="op">)</span></span></code></pre></div> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p8</span><span class="op">)</span></span></code></pre></div> <p><img src="NAFTA_examples_files/figure-html/p8-1.png" width="700"></p> <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/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p8</span><span class="op">)</span></span></code></pre></div> @@ -402,7 +438,7 @@ <pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre> <pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre> <div class="sourceCode" id="cb34"><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">p9a</span><span class="op">)</span></span></code></pre></div> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p9a</span><span class="op">)</span></span></code></pre></div> <p><img src="NAFTA_examples_files/figure-html/p9a-1.png" width="700"></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/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p9a</span><span class="op">)</span></span></code></pre></div> @@ -444,7 +480,9 @@ <span><span class="co">## </span></span> <span><span class="co">## Representative half-life:</span></span> <span><span class="co">## [1] 101.43</span></span></code></pre> -<p>In this example, the residuals of the SFO indicate a lack of fit of this model, so even if it was an abiotic experiment, the data do not suggest a simple exponential decline.</p> +<p>In this example, the residuals of the SFO indicate a lack of fit of +this model, so even if it was an abiotic experiment, the data do not +suggest a simple exponential decline.</p> </div> <div class="section level3"> <h3 id="example-on-page-9-lower-panel">Example on page 9, lower panel<a class="anchor" aria-label="anchor" href="#example-on-page-9-lower-panel"></a> @@ -454,12 +492,12 @@ <pre><code><span><span class="co">## Warning in sqrt(diag(covar)): NaNs produced</span></span></code></pre> <pre><code><span><span class="co">## Warning in sqrt(diag(covar_notrans)): NaNs produced</span></span></code></pre> <pre><code><span><span class="co">## Warning in sqrt(1/diag(V)): NaNs produced</span></span></code></pre> -<pre><code><span><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is</span></span> -<span><span class="co">## doubtful</span></span></code></pre> +<pre><code><span><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result</span></span> +<span><span class="co">## is doubtful</span></span></code></pre> <pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre> <pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre> <div class="sourceCode" id="cb44"><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">p9b</span><span class="op">)</span></span></code></pre></div> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p9b</span><span class="op">)</span></span></code></pre></div> <p><img src="NAFTA_examples_files/figure-html/p9b-1.png" width="700"></p> <div class="sourceCode" id="cb45"><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">p9b</span><span class="op">)</span></span></code></pre></div> @@ -501,7 +539,12 @@ <span><span class="co">## </span></span> <span><span class="co">## Representative half-life:</span></span> <span><span class="co">## [1] 14.8</span></span></code></pre> -<p>Here, mkin gives a longer slow DT50 for the DFOP model (17.8 days) than PestDF (13.5 days). Presumably, this is related to the fact that PestDF gives a negative value for the proportion of the fast degradation which should be between 0 and 1, inclusive. This parameter is called f in PestDF and g in mkin. In mkin, it is restricted to the interval from 0 to 1.</p> +<p>Here, mkin gives a longer slow DT50 for the DFOP model (17.8 days) +than PestDF (13.5 days). Presumably, this is related to the fact that +PestDF gives a negative value for the proportion of the fast degradation +which should be between 0 and 1, inclusive. This parameter is called f +in PestDF and g in mkin. In mkin, it is restricted to the interval from +0 to 1.</p> </div> <div class="section level3"> <h3 id="example-on-page-10">Example on page 10<a class="anchor" aria-label="anchor" href="#example-on-page-10"></a> @@ -510,12 +553,12 @@ <code class="sourceCode R"><span><span class="va">p10</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p10"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> <pre><code><span><span class="co">## Warning in sqrt(diag(covar)): NaNs produced</span></span></code></pre> <pre><code><span><span class="co">## Warning in sqrt(1/diag(V)): NaNs produced</span></span></code></pre> -<pre><code><span><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is</span></span> -<span><span class="co">## doubtful</span></span></code></pre> +<pre><code><span><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result</span></span> +<span><span class="co">## is doubtful</span></span></code></pre> <pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre> <pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre> <div class="sourceCode" id="cb53"><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">p10</span><span class="op">)</span></span></code></pre></div> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p10</span><span class="op">)</span></span></code></pre></div> <p><img src="NAFTA_examples_files/figure-html/p10-1.png" width="700"></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/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p10</span><span class="op">)</span></span></code></pre></div> @@ -557,7 +600,11 @@ <span><span class="co">## </span></span> <span><span class="co">## Representative half-life:</span></span> <span><span class="co">## [1] 8.86</span></span></code></pre> -<p>Here, a value below N is given for the IORE model, because the data suggests a faster decline towards the end of the experiment, which appears physically rather unlikely in the case of a photolysis study. It seems PestDF does not constrain N to values above zero, thus the slight difference in IORE model parameters between PestDF and mkin.</p> +<p>Here, a value below N is given for the IORE model, because the data +suggests a faster decline towards the end of the experiment, which +appears physically rather unlikely in the case of a photolysis study. It +seems PestDF does not constrain N to values above zero, thus the slight +difference in IORE model parameters between PestDF and mkin.</p> </div> </div> <div class="section level2"> @@ -571,7 +618,7 @@ <pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre> <pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre> <div class="sourceCode" id="cb59"><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">p11</span><span class="op">)</span></span></code></pre></div> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p11</span><span class="op">)</span></span></code></pre></div> <p><img src="NAFTA_examples_files/figure-html/p11-1.png" width="700"></p> <div class="sourceCode" id="cb60"><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">p11</span><span class="op">)</span></span></code></pre></div> @@ -613,13 +660,19 @@ <span><span class="co">## </span></span> <span><span class="co">## Representative half-life:</span></span> <span><span class="co">## [1] 41148170</span></span></code></pre> -<p>In this case, the DFOP fit reported for PestDF resulted in a negative value for the slower rate constant, which is not possible in mkin. The other results are in agreement.</p> +<p>In this case, the DFOP fit reported for PestDF resulted in a negative +value for the slower rate constant, which is not possible in mkin. The +other results are in agreement.</p> </div> </div> <div class="section level2"> -<h2 id="n-is-less-than-1-and-the-dfop-rate-constants-are-like-the-sfo-rate-constant">N is less than 1 and the DFOP rate constants are like the SFO rate constant<a class="anchor" aria-label="anchor" href="#n-is-less-than-1-and-the-dfop-rate-constants-are-like-the-sfo-rate-constant"></a> +<h2 id="n-is-less-than-1-and-the-dfop-rate-constants-are-like-the-sfo-rate-constant">N is less than 1 and the DFOP rate constants are like the SFO rate +constant<a class="anchor" aria-label="anchor" href="#n-is-less-than-1-and-the-dfop-rate-constants-are-like-the-sfo-rate-constant"></a> </h2> -<p>In the following three examples, the same results are obtained with mkin as reported for PestDF. As in the case on page 10, the N values below 1 are deemed unrealistic and appear to be the result of an overparameterisation.</p> +<p>In the following three examples, the same results are obtained with +mkin as reported for PestDF. As in the case on page 10, the N values +below 1 are deemed unrealistic and appear to be the result of an +overparameterisation.</p> <div class="section level3"> <h3 id="example-on-page-12-upper-panel">Example on page 12, upper panel<a class="anchor" aria-label="anchor" href="#example-on-page-12-upper-panel"></a> </h3> @@ -630,12 +683,12 @@ <pre><code><span><span class="co">## Warning in sqrt(diag(covar)): NaNs produced</span></span></code></pre> <pre><code><span><span class="co">## Warning in sqrt(diag(covar_notrans)): NaNs produced</span></span></code></pre> <pre><code><span><span class="co">## Warning in sqrt(1/diag(V)): NaNs produced</span></span></code></pre> -<pre><code><span><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is</span></span> -<span><span class="co">## doubtful</span></span></code></pre> +<pre><code><span><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result</span></span> +<span><span class="co">## is doubtful</span></span></code></pre> <pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre> <pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre> <div class="sourceCode" id="cb70"><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">p12a</span><span class="op">)</span></span></code></pre></div> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p12a</span><span class="op">)</span></span></code></pre></div> <p><img src="NAFTA_examples_files/figure-html/p12a-1.png" width="700"></p> <div class="sourceCode" id="cb71"><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">p12a</span><span class="op">)</span></span></code></pre></div> @@ -690,7 +743,7 @@ <pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre> <pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre> <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">p12b</span><span class="op">)</span></span></code></pre></div> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p12b</span><span class="op">)</span></span></code></pre></div> <p><img src="NAFTA_examples_files/figure-html/p12b-1.png" width="700"></p> <div class="sourceCode" id="cb81"><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">p12b</span><span class="op">)</span></span></code></pre></div> @@ -741,7 +794,7 @@ <pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre> <pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre> <div class="sourceCode" id="cb86"><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">p13</span><span class="op">)</span></span></code></pre></div> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p13</span><span class="op">)</span></span></code></pre></div> <p><img src="NAFTA_examples_files/figure-html/p13-1.png" width="700"></p> <div class="sourceCode" id="cb87"><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">p13</span><span class="op">)</span></span></code></pre></div> @@ -792,12 +845,12 @@ <code class="sourceCode R"><span><span class="va">p14</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p14"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> <pre><code><span><span class="co">## Warning in sqrt(diag(covar)): NaNs produced</span></span></code></pre> <pre><code><span><span class="co">## Warning in sqrt(1/diag(V)): NaNs produced</span></span></code></pre> -<pre><code><span><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is</span></span> -<span><span class="co">## doubtful</span></span></code></pre> +<pre><code><span><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result</span></span> +<span><span class="co">## is doubtful</span></span></code></pre> <pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre> <pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre> <div class="sourceCode" id="cb95"><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">p14</span><span class="op">)</span></span></code></pre></div> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p14</span><span class="op">)</span></span></code></pre></div> <p><img src="NAFTA_examples_files/figure-html/p14-1.png" width="700"></p> <div class="sourceCode" id="cb96"><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">p14</span><span class="op">)</span></span></code></pre></div> @@ -839,7 +892,9 @@ <span><span class="co">## </span></span> <span><span class="co">## Representative half-life:</span></span> <span><span class="co">## [1] 6697.44</span></span></code></pre> -<p>The slower rate constant reported by PestDF is negative, which is not physically realistic, and not possible in mkin. The other fits give the same results in mkin and PestDF.</p> +<p>The slower rate constant reported by PestDF is negative, which is not +physically realistic, and not possible in mkin. The other fits give the +same results in mkin and PestDF.</p> </div> <div class="section level2"> <h2 id="n-is-less-than-1-and-dfop-fraction-parameter-is-below-zero">N is less than 1 and DFOP fraction parameter is below zero<a class="anchor" aria-label="anchor" href="#n-is-less-than-1-and-dfop-fraction-parameter-is-below-zero"></a> @@ -849,7 +904,7 @@ <pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre> <pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre> <div class="sourceCode" id="cb101"><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">p15a</span><span class="op">)</span></span></code></pre></div> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p15a</span><span class="op">)</span></span></code></pre></div> <p><img src="NAFTA_examples_files/figure-html/p15a-1.png" width="700"></p> <div class="sourceCode" id="cb102"><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">p15a</span><span class="op">)</span></span></code></pre></div> @@ -895,12 +950,12 @@ <code class="sourceCode R"><span><span class="va">p15b</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p15b"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div> <pre><code><span><span class="co">## Warning in sqrt(diag(covar)): NaNs produced</span></span></code></pre> <pre><code><span><span class="co">## Warning in sqrt(1/diag(V)): NaNs produced</span></span></code></pre> -<pre><code><span><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is</span></span> -<span><span class="co">## doubtful</span></span></code></pre> +<pre><code><span><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result</span></span> +<span><span class="co">## is doubtful</span></span></code></pre> <pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre> <pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre> <div class="sourceCode" id="cb110"><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">p15b</span><span class="op">)</span></span></code></pre></div> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p15b</span><span class="op">)</span></span></code></pre></div> <p><img src="NAFTA_examples_files/figure-html/p15b-1.png" width="700"></p> <div class="sourceCode" id="cb111"><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">p15b</span><span class="op">)</span></span></code></pre></div> @@ -942,7 +997,10 @@ <span><span class="co">## </span></span> <span><span class="co">## Representative half-life:</span></span> <span><span class="co">## [1] 71.18</span></span></code></pre> -<p>In mkin, only the IORE fit is affected (deemed unrealistic), as the fraction parameter of the DFOP model is restricted to the interval between 0 and 1 in mkin. The SFO fits give the same results for both mkin and PestDF.</p> +<p>In mkin, only the IORE fit is affected (deemed unrealistic), as the +fraction parameter of the DFOP model is restricted to the interval +between 0 and 1 in mkin. The SFO fits give the same results for both +mkin and PestDF.</p> </div> <div class="section level2"> <h2 id="the-dfop-fraction-parameter-is-greater-than-1">The DFOP fraction parameter is greater than 1<a class="anchor" aria-label="anchor" href="#the-dfop-fraction-parameter-is-greater-than-1"></a> @@ -954,7 +1012,7 @@ <pre><code><span><span class="co">## to the terminal degradation rate found with the DFOP model.</span></span></code></pre> <pre><code><span><span class="co">## The representative half-life obtained from the DFOP model may be used</span></span></code></pre> <div class="sourceCode" id="cb118"><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">p16</span><span class="op">)</span></span></code></pre></div> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p16</span><span class="op">)</span></span></code></pre></div> <p><img src="NAFTA_examples_files/figure-html/p16-1.png" width="700"></p> <div class="sourceCode" id="cb119"><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">p16</span><span class="op">)</span></span></code></pre></div> @@ -996,20 +1054,32 @@ <span><span class="co">## </span></span> <span><span class="co">## Representative half-life:</span></span> <span><span class="co">## [1] 8.93</span></span></code></pre> -<p>In PestDF, the DFOP fit seems to have stuck in a local minimum, as mkin finds a solution with a much lower <span class="math inline">\(\chi^2\)</span> error level. As the half-life from the slower rate constant of the DFOP model is larger than the IORE derived half-life, the NAFTA recommendation obtained with mkin is to use the DFOP representative half-life of 8.9 days.</p> +<p>In PestDF, the DFOP fit seems to have stuck in a local minimum, as +mkin finds a solution with a much lower <span class="math inline">\(\chi^2\)</span> error level. As the half-life from +the slower rate constant of the DFOP model is larger than the IORE +derived half-life, the NAFTA recommendation obtained with mkin is to use +the DFOP representative half-life of 8.9 days.</p> </div> <div class="section level2"> <h2 id="conclusions">Conclusions<a class="anchor" aria-label="anchor" href="#conclusions"></a> </h2> -<p>The results obtained with mkin deviate from the results obtained with PestDF either in cases where one of the interpretive rules would apply, i.e. the IORE parameter N is less than one or the DFOP k values obtained with PestDF are equal to the SFO k values, or in cases where the DFOP model did not converge, which often lead to negative rate constants returned by PestDF.</p> -<p>Therefore, mkin appears to suitable for kinetic evaluations according to the NAFTA guidance.</p> +<p>The results obtained with mkin deviate from the results obtained with +PestDF either in cases where one of the interpretive rules would apply, +i.e. the IORE parameter N is less than one or the DFOP k values obtained +with PestDF are equal to the SFO k values, or in cases where the DFOP +model did not converge, which often lead to negative rate constants +returned by PestDF.</p> +<p>Therefore, mkin appears to suitable for kinetic evaluations according +to the NAFTA guidance.</p> </div> <div class="section level2"> <h2 class="unnumbered" id="references">References<a class="anchor" aria-label="anchor" href="#references"></a> </h2> -<div id="refs" class="references hanging-indent"> -<div id="ref-usepa2015"> -<p>US EPA. 2015. “Standard Operating Procedure for Using the NAFTA Guidance to Calculate Representative Half-Life Values and Characterizing Pesticide Degradation.”</p> +<div id="refs" class="references csl-bib-body hanging-indent"> +<div id="ref-usepa2015" class="csl-entry"> +US EPA. 2015. <span>“Standard Operating Procedure for Using the NAFTA +Guidance to Calculate Representative Half-Life Values and Characterizing +Pesticide Degradation.”</span> <a href="https://www.epa.gov/pesticide-science-and-assessing-pesticide-risks/standard-operating-procedure-using-nafta-guidance" class="external-link">https://www.epa.gov/pesticide-science-and-assessing-pesticide-risks/standard-operating-procedure-using-nafta-guidance</a>. </div> </div> </div> @@ -1032,7 +1102,7 @@ <div class="pkgdown"> <p></p> -<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p> +<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p> </div> </footer> diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p10-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p10-1.png Binary files differindex 75611a70..566625ea 100644 --- a/docs/articles/web_only/NAFTA_examples_files/figure-html/p10-1.png +++ b/docs/articles/web_only/NAFTA_examples_files/figure-html/p10-1.png diff --git 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navbar-nav"> <li> - <a href="../../reference/index.html">Functions and data</a> + <a href="../../reference/index.html">Reference</a> </li> <li class="dropdown"> <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false"> @@ -52,6 +52,9 @@ <li> <a href="../../articles/mkin.html">Introduction to mkin</a> </li> + <li class="divider"> + </li> +<li class="dropdown-header">Example evaluations with (generalised) nonlinear least squares</li> <li> <a href="../../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a> </li> @@ -59,22 +62,31 @@ <a href="../../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a> </li> <li> - <a href="../../articles/web_only/dimethenamid_2018.html">Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models</a> + <a href="../../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> + </li> + <li class="divider"> </li> +<li class="dropdown-header">Example evaluations with hierarchical models (nonlinear mixed-effects models)</li> <li> - <a href="../../articles/web_only/multistart.html">Short demo of the multistart method</a> + <a href="../../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a> </li> <li> - <a href="../../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> + <a href="../../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a> </li> <li> - <a href="../../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> + <a href="../../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a> </li> <li> - <a href="../../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> + <a href="../../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a> </li> <li> - <a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> + <a href="../../articles/web_only/multistart.html">Short demo of the multistart method</a> + </li> + <li class="divider"> + </li> +<li class="dropdown-header">Performance</li> + <li> + <a href="../../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> </li> <li> <a href="../../articles/web_only/benchmarks.html">Benchmark timings for mkin</a> @@ -82,6 +94,15 @@ <li> <a href="../../articles/web_only/saem_benchmarks.html">Benchmark timings for saem.mmkin</a> </li> + <li class="divider"> + </li> +<li class="dropdown-header">Miscellaneous</li> + <li> + <a href="../../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> + </li> + <li> + <a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> + </li> </ul> </li> <li> @@ -105,13 +126,15 @@ - </header><script src="benchmarks_files/accessible-code-block-0.0.1/empty-anchor.js"></script><div class="row"> + </header><div class="row"> <div class="col-md-9 contents"> <div class="page-header toc-ignore"> <h1 data-toc-skip>Benchmark timings for mkin</h1> - <h4 data-toc-skip class="author">Johannes Ranke</h4> + <h4 data-toc-skip class="author">Johannes +Ranke</h4> - <h4 data-toc-skip class="date">Last change 14 July 2022 (rebuilt 2022-11-17)</h4> + <h4 data-toc-skip class="date">Last change 17 February 2023 +(rebuilt 2023-04-20)</h4> <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/benchmarks.rmd" class="external-link"><code>vignettes/web_only/benchmarks.rmd</code></a></small> <div class="hidden name"><code>benchmarks.rmd</code></div> @@ -120,9 +143,15 @@ -<p>Each system is characterized by the operating system type, the CPU type, the mkin version, and, as in June 2022 the current R version lead to worse performance, the R version. A compiler was available, so if no analytical solution was available, compiled ODE models are used.</p> -<p>Every fit is only performed once, so the accuracy of the benchmarks is limited.</p> -<p>The following wrapper function for <code>mmkin</code> is used because the way the error model is specified was changed in mkin version 0.9.49.1.</p> +<p>Each system is characterized by the operating system type, the CPU +type, the mkin version, and, as in June 2022 the current R version lead +to worse performance, the R version. A compiler was available, so if no +analytical solution was available, compiled ODE models are used.</p> +<p>Every fit is only performed once, so the accuracy of the benchmarks +is limited.</p> +<p>The following wrapper function for <code>mmkin</code> is used because +the way the error model is specified was changed in mkin version +0.9.49.1.</p> <div class="sourceCode" id="cb1"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/utils/packageDescription.html" class="external-link">packageVersion</a></span><span class="op">(</span><span class="st">"mkin"</span><span class="op">)</span> <span class="op">></span> <span class="st">"0.9.48.1"</span><span class="op">)</span> <span class="op">{</span></span> <span> <span class="va">mmkin_bench</span> <span class="op"><-</span> <span class="kw">function</span><span class="op">(</span><span class="va">models</span>, <span class="va">datasets</span>, <span class="va">error_model</span> <span class="op">=</span> <span class="st">"const"</span><span class="op">)</span> <span class="op">{</span></span> @@ -194,11 +223,14 @@ <div class="section level2"> <h2 id="results">Results<a class="anchor" aria-label="anchor" href="#results"></a> </h2> -<p>Benchmarks for all available error models are shown. They are intended for improving mkin, not for comparing CPUs or operating systems. All trademarks belong to their respective owners.</p> +<p>Benchmarks for all available error models are shown. They are +intended for improving mkin, not for comparing CPUs or operating +systems. All trademarks belong to their respective owners.</p> <div class="section level3"> <h3 id="parent-only">Parent only<a class="anchor" aria-label="anchor" href="#parent-only"></a> </h3> -<p>Constant variance (t1) and two-component error model (t2) for four models fitted to two datasets, i.e. eight fits for each test.</p> +<p>Constant variance (t1) and two-component error model (t2) for four +models fitted to two datasets, i.e. eight fits for each test.</p> <table class="table"> <thead><tr class="header"> <th align="left">OS</th> @@ -353,13 +385,55 @@ <td align="right">2.140</td> <td align="right">3.774</td> </tr> +<tr class="odd"> +<td align="left">Linux</td> +<td align="left">Ryzen 7 1700</td> +<td align="left">4.2.2</td> +<td align="left">1.2.2</td> +<td align="right">2.187</td> +<td align="right">3.851</td> +</tr> +<tr class="even"> +<td align="left">Linux</td> +<td align="left">Ryzen 9 7950X</td> +<td align="left">4.2.2</td> +<td align="left">1.2.0</td> +<td align="right">1.288</td> +<td align="right">1.794</td> +</tr> +<tr class="odd"> +<td align="left">Linux</td> +<td align="left">Ryzen 9 7950X</td> +<td align="left">4.2.2</td> +<td align="left">1.2.2</td> +<td align="right">1.276</td> +<td align="right">1.804</td> +</tr> +<tr class="even"> +<td align="left">Linux</td> +<td align="left">Ryzen 9 7950X</td> +<td align="left">4.2.2</td> +<td align="left">1.2.3</td> +<td align="right">1.370</td> +<td align="right">1.883</td> +</tr> +<tr class="odd"> +<td align="left">Linux</td> +<td align="left">Ryzen 9 7950X</td> +<td align="left">4.2.3</td> +<td align="left">1.2.3</td> +<td align="right">1.406</td> +<td align="right">1.948</td> +</tr> </tbody> </table> </div> <div class="section level3"> <h3 id="one-metabolite">One metabolite<a class="anchor" aria-label="anchor" href="#one-metabolite"></a> </h3> -<p>Constant variance (t3), two-component error model (t4), and variance by variable (t5) for three models fitted to one dataset, i.e. three fits for each test.</p> +<p>Constant variance (t3), two-component error model (t4), and variance +by variable (t5) for three models fitted to one dataset, i.e. three fits +for each test.</p> <table class="table"> <thead><tr class="header"> <th align="left">OS</th> @@ -533,14 +607,73 @@ <td align="right">6.193</td> <td align="right">2.843</td> </tr> +<tr class="odd"> +<td align="left">Linux</td> +<td align="left">Ryzen 7 1700</td> +<td align="left">4.2.2</td> +<td align="left">1.2.2</td> +<td align="right">1.585</td> +<td align="right">6.335</td> +<td align="right">3.003</td> +</tr> +<tr class="even"> +<td align="left">Linux</td> +<td align="left">Ryzen 9 7950X</td> +<td align="left">4.2.2</td> +<td align="left">1.2.0</td> +<td align="right">0.792</td> +<td align="right">2.378</td> +<td align="right">1.245</td> +</tr> +<tr class="odd"> +<td align="left">Linux</td> +<td align="left">Ryzen 9 7950X</td> +<td align="left">4.2.2</td> +<td align="left">1.2.2</td> +<td align="right">0.784</td> +<td align="right">2.355</td> +<td align="right">1.233</td> +</tr> +<tr class="even"> +<td align="left">Linux</td> +<td align="left">Ryzen 9 7950X</td> +<td align="left">4.2.2</td> +<td align="left">1.2.3</td> +<td align="right">0.770</td> +<td align="right">2.011</td> +<td align="right">1.123</td> +</tr> +<tr class="odd"> +<td align="left">Linux</td> +<td align="left">Ryzen 9 7950X</td> +<td align="left">4.2.3</td> +<td align="left">1.2.3</td> +<td align="right">0.793</td> +<td align="right">2.109</td> +<td align="right">1.178</td> +</tr> </tbody> </table> </div> <div class="section level3"> <h3 id="two-metabolites">Two metabolites<a class="anchor" aria-label="anchor" href="#two-metabolites"></a> </h3> -<p>Constant variance (t6 and t7), two-component error model (t8 and t9), and variance by variable (t10 and t11) for one model fitted to one dataset, i.e. one fit for each test.</p> +<p>Constant variance (t6 and t7), two-component error model (t8 and t9), +and variance by variable (t10 and t11) for one model fitted to one +dataset, i.e. one fit for each test.</p> <table class="table"> +<colgroup> +<col width="8%"> +<col width="19%"> +<col width="8%"> +<col width="12%"> +<col width="8%"> +<col width="8%"> +<col width="8%"> +<col width="9%"> +<col width="8%"> +<col width="9%"> +</colgroup> <thead><tr class="header"> <th align="left">OS</th> <th align="left">CPU</th> @@ -770,6 +903,66 @@ <td align="right">1.987</td> <td align="right">2.802</td> </tr> +<tr class="odd"> +<td align="left">Linux</td> +<td align="left">Ryzen 7 1700</td> +<td align="left">4.2.2</td> +<td align="left">1.2.2</td> +<td align="right">0.935</td> +<td align="right">1.381</td> +<td align="right">1.551</td> +<td align="right">3.209</td> +<td align="right">1.976</td> +<td align="right">3.013</td> +</tr> +<tr class="even"> +<td align="left">Linux</td> +<td align="left">Ryzen 9 7950X</td> +<td align="left">4.2.2</td> +<td align="left">1.2.0</td> +<td align="right">0.445</td> +<td align="right">0.591</td> +<td align="right">0.660</td> +<td align="right">1.190</td> +<td align="right">0.814</td> +<td align="right">1.100</td> +</tr> +<tr class="odd"> +<td align="left">Linux</td> +<td align="left">Ryzen 9 7950X</td> +<td align="left">4.2.2</td> +<td align="left">1.2.2</td> +<td align="right">0.443</td> +<td align="right">0.586</td> +<td align="right">0.661</td> +<td align="right">1.176</td> +<td align="right">0.803</td> +<td align="right">1.097</td> +</tr> +<tr class="even"> +<td align="left">Linux</td> +<td align="left">Ryzen 9 7950X</td> +<td align="left">4.2.2</td> +<td align="left">1.2.3</td> +<td align="right">0.418</td> +<td align="right">0.530</td> +<td align="right">0.591</td> +<td align="right">1.006</td> +<td align="right">0.716</td> +<td align="right">0.949</td> +</tr> +<tr class="odd"> +<td align="left">Linux</td> +<td align="left">Ryzen 9 7950X</td> +<td align="left">4.2.3</td> +<td align="left">1.2.3</td> +<td align="right">0.432</td> +<td align="right">0.549</td> +<td align="right">0.609</td> +<td align="right">1.052</td> +<td align="right">0.743</td> +<td align="right">0.989</td> +</tr> </tbody> </table> </div> @@ -793,7 +986,7 @@ <div class="pkgdown"> <p></p> -<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p> +<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p> </div> </footer> diff --git a/docs/articles/web_only/compiled_models.html b/docs/articles/web_only/compiled_models.html index d17d7aeb..a411dad1 100644 --- a/docs/articles/web_only/compiled_models.html +++ b/docs/articles/web_only/compiled_models.html @@ -33,14 +33,14 @@ </button> <span class="navbar-brand"> <a class="navbar-link" href="../../index.html">mkin</a> - <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">1.2.0</span> + <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">1.2.3</span> </span> </div> <div id="navbar" class="navbar-collapse collapse"> <ul class="nav navbar-nav"> <li> - <a href="../../reference/index.html">Functions and data</a> + <a href="../../reference/index.html">Reference</a> </li> <li class="dropdown"> <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false"> @@ -52,6 +52,9 @@ <li> <a href="../../articles/mkin.html">Introduction to mkin</a> </li> + <li class="divider"> + </li> +<li class="dropdown-header">Example evaluations with (generalised) nonlinear least squares</li> <li> <a href="../../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a> </li> @@ -59,22 +62,31 @@ <a href="../../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a> </li> <li> - <a href="../../articles/web_only/dimethenamid_2018.html">Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models</a> + <a href="../../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> + </li> + <li class="divider"> </li> +<li class="dropdown-header">Example evaluations with hierarchical models (nonlinear mixed-effects models)</li> <li> - <a href="../../articles/web_only/multistart.html">Short demo of the multistart method</a> + <a href="../../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a> </li> <li> - <a href="../../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> + <a href="../../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a> </li> <li> - <a href="../../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> + <a href="../../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a> </li> <li> - <a href="../../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> + <a href="../../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a> </li> <li> - <a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> + <a href="../../articles/web_only/multistart.html">Short demo of the multistart method</a> + </li> + <li class="divider"> + </li> +<li class="dropdown-header">Performance</li> + <li> + <a href="../../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> </li> <li> <a href="../../articles/web_only/benchmarks.html">Benchmark timings for mkin</a> @@ -82,6 +94,15 @@ <li> <a href="../../articles/web_only/saem_benchmarks.html">Benchmark timings for saem.mmkin</a> </li> + <li class="divider"> + </li> +<li class="dropdown-header">Miscellaneous</li> + <li> + <a href="../../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> + </li> + <li> + <a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> + </li> </ul> </li> <li> @@ -105,13 +126,15 @@ - </header><script src="compiled_models_files/accessible-code-block-0.0.1/empty-anchor.js"></script><div class="row"> + </header><div class="row"> <div class="col-md-9 contents"> <div class="page-header toc-ignore"> - <h1 data-toc-skip>Performance benefit by using compiled model definitions in mkin</h1> - <h4 data-toc-skip class="author">Johannes Ranke</h4> + <h1 data-toc-skip>Performance benefit by using compiled model +definitions in mkin</h1> + <h4 data-toc-skip class="author">Johannes +Ranke</h4> - <h4 data-toc-skip class="date">2022-11-17</h4> + <h4 data-toc-skip class="date">2023-04-20</h4> <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/compiled_models.rmd" class="external-link"><code>vignettes/web_only/compiled_models.rmd</code></a></small> <div class="hidden name"><code>compiled_models.rmd</code></div> @@ -123,23 +146,39 @@ <div class="section level2"> <h2 id="how-to-benefit-from-compiled-models">How to benefit from compiled models<a class="anchor" aria-label="anchor" href="#how-to-benefit-from-compiled-models"></a> </h2> -<p>When using an mkin version equal to or greater than 0.9-36 and a C compiler is available, you will see a message that the model is being compiled from autogenerated C code when defining a model using mkinmod. Starting from version 0.9.49.9, the <code><a href="../../reference/mkinmod.html">mkinmod()</a></code> function checks for presence of a compiler using</p> +<p>When using an mkin version equal to or greater than 0.9-36 and a C +compiler is available, you will see a message that the model is being +compiled from autogenerated C code when defining a model using mkinmod. +Starting from version 0.9.49.9, the <code><a href="../../reference/mkinmod.html">mkinmod()</a></code> function +checks for presence of a compiler using</p> <div class="sourceCode" id="cb1"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu">pkgbuild</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/pkgbuild/man/has_compiler.html" class="external-link">has_compiler</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<p>In previous versions, it used <code>Sys.which("gcc")</code> for this check.</p> -<p>On Linux, you need to have the essential build tools like make and gcc or clang installed. On Debian based linux distributions, these will be pulled in by installing the build-essential package.</p> -<p>On MacOS, which I do not use personally, I have had reports that a compiler is available by default.</p> -<p>On Windows, you need to install Rtools and have the path to its bin directory in your PATH variable. You do not need to modify the PATH variable when installing Rtools. Instead, I would recommend to put the line</p> +<code class="sourceCode R"><span><span class="fu">pkgbuild</span><span class="fu">::</span><span class="fu"><a href="https://r-lib.github.io/pkgbuild/reference/has_compiler.html" class="external-link">has_compiler</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<p>In previous versions, it used <code>Sys.which("gcc")</code> for this +check.</p> +<p>On Linux, you need to have the essential build tools like make and +gcc or clang installed. On Debian based linux distributions, these will +be pulled in by installing the build-essential package.</p> +<p>On MacOS, which I do not use personally, I have had reports that a +compiler is available by default.</p> +<p>On Windows, you need to install Rtools and have the path to its bin +directory in your PATH variable. You do not need to modify the PATH +variable when installing Rtools. Instead, I would recommend to put the +line</p> <div class="sourceCode" id="cb2"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/Sys.setenv.html" class="external-link">Sys.setenv</a></span><span class="op">(</span>PATH <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">"C:/Rtools/bin"</span>, <span class="fu"><a href="https://rdrr.io/r/base/Sys.getenv.html" class="external-link">Sys.getenv</a></span><span class="op">(</span><span class="st">"PATH"</span><span class="op">)</span>, sep<span class="op">=</span><span class="st">";"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> -<p>into your .Rprofile startup file. This is just a text file with some R code that is executed when your R session starts. It has to be named .Rprofile and has to be located in your home directory, which will generally be your Documents folder. You can check the location of the home directory used by R by issuing</p> +<p>into your .Rprofile startup file. This is just a text file with some +R code that is executed when your R session starts. It has to be named +.Rprofile and has to be located in your home directory, which will +generally be your Documents folder. You can check the location of the +home directory used by R by issuing</p> <div class="sourceCode" id="cb3"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/Sys.getenv.html" class="external-link">Sys.getenv</a></span><span class="op">(</span><span class="st">"HOME"</span><span class="op">)</span></span></code></pre></div> </div> <div class="section level2"> <h2 id="comparison-with-other-solution-methods">Comparison with other solution methods<a class="anchor" aria-label="anchor" href="#comparison-with-other-solution-methods"></a> </h2> -<p>First, we build a simple degradation model for a parent compound with one metabolite, and we remove zero values from the dataset.</p> +<p>First, we build a simple degradation model for a parent compound with +one metabolite, and we remove zero values from the dataset.</p> <div class="sourceCode" id="cb4"><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="st"><a href="https://pkgdown.jrwb.de/mkin/">"mkin"</a></span>, quietly <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> <span><span class="va">SFO_SFO</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> @@ -148,7 +187,12 @@ <pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre> <div class="sourceCode" id="cb6"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">FOCUS_D</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">FOCUS_2006_D</span>, <span class="va">value</span> <span class="op">!=</span> <span class="fl">0</span><span class="op">)</span></span></code></pre></div> -<p>We can compare the performance of the Eigenvalue based solution against the compiled version and the R implementation of the differential equations using the benchmark package. In the output of below code, the warnings about zero being removed from the FOCUS D dataset are suppressed. Since mkin version 0.9.49.11, an analytical solution is also implemented, which is included in the tests below.</p> +<p>We can compare the performance of the Eigenvalue based solution +against the compiled version and the R implementation of the +differential equations using the benchmark package. In the output of +below code, the warnings about zero being removed from the FOCUS D +dataset are suppressed. Since mkin version 0.9.49.11, an analytical +solution is also implemented, which is included in the tests below.</p> <div class="sourceCode" id="cb7"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="kw">if</span> <span class="op">(</span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">require</a></span><span class="op">(</span><span class="va"><a href="http://rbenchmark.googlecode.com" class="external-link">rbenchmark</a></span><span class="op">)</span><span class="op">)</span> <span class="op">{</span></span> <span> <span class="va">b.1</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/rbenchmark/man/benchmark.html" class="external-link">benchmark</a></span><span class="op">(</span></span> @@ -169,16 +213,20 @@ <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="st">"R package rbenchmark is not available"</span><span class="op">)</span></span> <span><span class="op">}</span></span></code></pre></div> <pre><code><span><span class="co">## test replications relative elapsed</span></span> -<span><span class="co">## 4 analytical 1 1.000 0.218</span></span> -<span><span class="co">## 3 deSolve, compiled 1 1.550 0.338</span></span> -<span><span class="co">## 2 Eigenvalue based 1 1.950 0.425</span></span> -<span><span class="co">## 1 deSolve, not compiled 1 33.041 7.203</span></span></code></pre> -<p>We see that using the compiled model is by more than a factor of 10 faster than using deSolve without compiled code.</p> +<span><span class="co">## 4 analytical 1 1.000 0.103</span></span> +<span><span class="co">## 3 deSolve, compiled 1 1.291 0.133</span></span> +<span><span class="co">## 2 Eigenvalue based 1 1.718 0.177</span></span> +<span><span class="co">## 1 deSolve, not compiled 1 22.136 2.280</span></span></code></pre> +<p>We see that using the compiled model is by more than a factor of 10 +faster than using deSolve without compiled code.</p> </div> <div class="section level2"> <h2 id="model-without-analytical-solution">Model without analytical solution<a class="anchor" aria-label="anchor" href="#model-without-analytical-solution"></a> </h2> -<p>This evaluation is also taken from the example section of mkinfit. No analytical solution is available for this system, and now Eigenvalue based solution is possible, so only deSolve using with or without compiled code is available.</p> +<p>This evaluation is also taken from the example section of mkinfit. No +analytical solution is available for this system, and now Eigenvalue +based solution is possible, so only deSolve using with or without +compiled code is available.</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="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">require</a></span><span class="op">(</span><span class="va"><a href="http://rbenchmark.googlecode.com" class="external-link">rbenchmark</a></span><span class="op">)</span><span class="op">)</span> <span class="op">{</span></span> <span> <span class="va">FOMC_SFO</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> @@ -199,14 +247,15 @@ <span><span class="op">}</span></span></code></pre></div> <pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre> <pre><code><span><span class="co">## test replications relative elapsed</span></span> -<span><span class="co">## 2 deSolve, compiled 1 1.000 0.510</span></span> -<span><span class="co">## 1 deSolve, not compiled 1 26.247 13.386</span></span></code></pre> -<p>Here we get a performance benefit of a factor of 26 using the version of the differential equation model compiled from C code!</p> -<p>This vignette was built with mkin 1.2.0 on</p> -<pre><code><span><span class="co">## R version 4.2.2 (2022-10-31)</span></span> +<span><span class="co">## 2 deSolve, compiled 1 1.000 0.171</span></span> +<span><span class="co">## 1 deSolve, not compiled 1 24.199 4.138</span></span></code></pre> +<p>Here we get a performance benefit of a factor of 24 using the version +of the differential equation model compiled from C code!</p> +<p>This vignette was built with mkin 1.2.3 on</p> +<pre><code><span><span class="co">## R version 4.2.3 (2023-03-15)</span></span> <span><span class="co">## Platform: x86_64-pc-linux-gnu (64-bit)</span></span> -<span><span class="co">## Running under: Debian GNU/Linux 11 (bullseye)</span></span></code></pre> -<pre><code><span><span class="co">## CPU model: AMD Ryzen 7 1700 Eight-Core Processor</span></span></code></pre> +<span><span class="co">## Running under: Debian GNU/Linux 12 (bookworm)</span></span></code></pre> +<pre><code><span><span class="co">## CPU model: AMD Ryzen 9 7950X 16-Core Processor</span></span></code></pre> </div> </div> @@ -227,7 +276,7 @@ <div class="pkgdown"> <p></p> -<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p> +<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p> </div> </footer> diff --git a/docs/articles/web_only/dimethenamid_2018.html b/docs/articles/web_only/dimethenamid_2018.html index 8c37edd6..4575067b 100644 --- a/docs/articles/web_only/dimethenamid_2018.html +++ b/docs/articles/web_only/dimethenamid_2018.html @@ -33,14 +33,14 @@ </button> <span class="navbar-brand"> <a class="navbar-link" href="../../index.html">mkin</a> - <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">1.2.0</span> + <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">1.2.3</span> </span> </div> <div id="navbar" class="navbar-collapse collapse"> <ul class="nav navbar-nav"> <li> - <a href="../../reference/index.html">Functions and data</a> + <a href="../../reference/index.html">Reference</a> </li> <li class="dropdown"> <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false"> @@ -52,6 +52,9 @@ <li> <a href="../../articles/mkin.html">Introduction to mkin</a> </li> + <li class="divider"> + </li> +<li class="dropdown-header">Example evaluations with (generalised) nonlinear least squares</li> <li> <a href="../../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a> </li> @@ -59,22 +62,31 @@ <a href="../../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a> </li> <li> - <a href="../../articles/web_only/dimethenamid_2018.html">Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models</a> + <a href="../../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> + </li> + <li class="divider"> </li> +<li class="dropdown-header">Example evaluations with hierarchical models (nonlinear mixed-effects models)</li> <li> - <a href="../../articles/web_only/multistart.html">Short demo of the multistart method</a> + <a href="../../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a> </li> <li> - <a href="../../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> + <a href="../../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a> </li> <li> - <a href="../../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> + <a href="../../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a> </li> <li> - <a href="../../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> + <a href="../../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a> </li> <li> - <a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> + <a href="../../articles/web_only/multistart.html">Short demo of the multistart method</a> + </li> + <li class="divider"> + </li> +<li class="dropdown-header">Performance</li> + <li> + <a href="../../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> </li> <li> <a href="../../articles/web_only/benchmarks.html">Benchmark timings for mkin</a> @@ -82,6 +94,15 @@ <li> <a href="../../articles/web_only/saem_benchmarks.html">Benchmark timings for saem.mmkin</a> </li> + <li class="divider"> + </li> +<li class="dropdown-header">Miscellaneous</li> + <li> + <a href="../../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> + </li> + <li> + <a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> + </li> </ul> </li> <li> @@ -105,13 +126,16 @@ - </header><script src="dimethenamid_2018_files/accessible-code-block-0.0.1/empty-anchor.js"></script><div class="row"> + </header><div class="row"> <div class="col-md-9 contents"> <div class="page-header toc-ignore"> - <h1 data-toc-skip>Example evaluations of the dimethenamid data from 2018</h1> - <h4 data-toc-skip class="author">Johannes Ranke</h4> + <h1 data-toc-skip>Example evaluations of the dimethenamid data +from 2018</h1> + <h4 data-toc-skip class="author">Johannes +Ranke</h4> - <h4 data-toc-skip class="date">Last change 1 July 2022, built on 17 Nov 2022</h4> + <h4 data-toc-skip class="date">Last change 1 July 2022, +built on 20 Apr 2023</h4> <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/dimethenamid_2018.rmd" class="external-link"><code>vignettes/web_only/dimethenamid_2018.rmd</code></a></small> <div class="hidden name"><code>dimethenamid_2018.rmd</code></div> @@ -120,19 +144,48 @@ -<p><a href="http://www.jrwb.de" class="external-link">Wissenschaftlicher Berater, Kronacher Str. 12, 79639 Grenzach-Wyhlen, Germany</a></p> +<p><a href="http://www.jrwb.de" class="external-link">Wissenschaftlicher Berater, Kronacher +Str. 12, 79639 Grenzach-Wyhlen, Germany</a></p> <div class="section level2"> <h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#introduction"></a> </h2> -<p>A first analysis of the data analysed here was presented in a recent journal article on nonlinear mixed-effects models in degradation kinetics <span class="citation">(Ranke et al. 2021)</span>. That analysis was based on the <code>nlme</code> package and a development version of the <code>saemix</code> package that was unpublished at the time. Meanwhile, version 3.0 of the <code>saemix</code> package is available from the CRAN repository. Also, it turned out that there was an error in the handling of the Borstel data in the mkin package at the time, leading to the duplication of a few data points from that soil. The dataset in the mkin package has been corrected, and the interface to <code>saemix</code> in the mkin package has been updated to use the released version.</p> -<p>This vignette is intended to present an up to date analysis of the data, using the corrected dataset and released versions of <code>mkin</code> and <code>saemix</code>.</p> +<p>A first analysis of the data analysed here was presented in a recent +journal article on nonlinear mixed-effects models in degradation +kinetics <span class="citation">(Ranke et al. 2021)</span>. That +analysis was based on the <code>nlme</code> package and a development +version of the <code>saemix</code> package that was unpublished at the +time. Meanwhile, version 3.0 of the <code>saemix</code> package is +available from the CRAN repository. Also, it turned out that there was +an error in the handling of the Borstel data in the mkin package at the +time, leading to the duplication of a few data points from that soil. +The dataset in the mkin package has been corrected, and the interface to +<code>saemix</code> in the mkin package has been updated to use the +released version.</p> +<p>This vignette is intended to present an up to date analysis of the +data, using the corrected dataset and released versions of +<code>mkin</code> and <code>saemix</code>.</p> </div> <div class="section level2"> <h2 id="data">Data<a class="anchor" aria-label="anchor" href="#data"></a> </h2> -<p>Residue data forming the basis for the endpoints derived in the conclusion on the peer review of the pesticide risk assessment of dimethenamid-P published by the European Food Safety Authority (EFSA) in 2018 <span class="citation">(EFSA 2018)</span> were transcribed from the risk assessment report <span class="citation">(Rapporteur Member State Germany, Co-Rapporteur Member State Bulgaria 2018)</span> which can be downloaded from the Open EFSA repository <a href="https://open.efsa.europa.eu" class="external-link">https://open.efsa.europa.eu/study-inventory/EFSA-Q-2014-00716</a>.</p> -<p>The data are <a href="https://pkgdown.jrwb.de/mkin/reference/dimethenamid_2018.html">available in the mkin package</a>. The following code (hidden by default, please use the button to the right to show it) treats the data available for the racemic mixture dimethenamid (DMTA) and its enantiomer dimethenamid-P (DMTAP) in the same way, as no difference between their degradation behaviour was identified in the EU risk assessment. 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.</p> -<p>Also, datasets observed in the same soil are merged, resulting in dimethenamid (DMTA) data from six soils.</p> +<p>Residue data forming the basis for the endpoints derived in the +conclusion on the peer review of the pesticide risk assessment of +dimethenamid-P published by the European Food Safety Authority (EFSA) in +2018 <span class="citation">(EFSA 2018)</span> were transcribed from the +risk assessment report <span class="citation">(Rapporteur Member State +Germany, Co-Rapporteur Member State Bulgaria 2018)</span> which can be +downloaded from the Open EFSA repository <a href="https://open.efsa.europa.eu" class="external-link">https://open.efsa.europa.eu/study-inventory/EFSA-Q-2014-00716</a>.</p> +<p>The data are <a href="https://pkgdown.jrwb.de/mkin/reference/dimethenamid_2018.html">available +in the mkin package</a>. The following code (hidden by default, please +use the button to the right to show it) treats the data available for +the racemic mixture dimethenamid (DMTA) and its enantiomer +dimethenamid-P (DMTAP) in the same way, as no difference between their +degradation behaviour was identified in the EU risk assessment. 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.</p> +<p>Also, datasets observed in the same soil are merged, resulting in +dimethenamid (DMTA) data from six soils.</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>, quietly <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</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> @@ -149,34 +202,60 @@ <div class="section level2"> <h2 id="parent-degradation">Parent degradation<a class="anchor" aria-label="anchor" href="#parent-degradation"></a> </h2> -<p>We evaluate the observed degradation of the parent compound using simple exponential decline (SFO) and biexponential decline (DFOP), using constant variance (const) and a two-component variance (tc) as error models.</p> +<p>We evaluate the observed degradation of the parent compound using +simple exponential decline (SFO) and biexponential decline (DFOP), using +constant variance (const) and a two-component variance (tc) as error +models.</p> <div class="section level3"> <h3 id="separate-evaluations">Separate evaluations<a class="anchor" aria-label="anchor" href="#separate-evaluations"></a> </h3> -<p>As a first step, to get a visual impression of the fit of the different models, we do separate evaluations for each soil using the mmkin function from the mkin package:</p> +<p>As a first step, to get a visual impression of the fit of the +different models, we do separate evaluations for each soil using the +mmkin function from the mkin package:</p> <div class="sourceCode" id="cb2"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">f_parent_mkin_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">"DFOP"</span><span class="op">)</span>, <span class="va">dmta_ds</span>,</span> <span> error_model <span class="op">=</span> <span class="st">"const"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> <span><span class="va">f_parent_mkin_tc</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">"DFOP"</span><span class="op">)</span>, <span class="va">dmta_ds</span>,</span> <span> error_model <span class="op">=</span> <span class="st">"tc"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> -<p>The plot of the individual SFO fits shown below suggests that at least in some datasets the degradation slows down towards later time points, and that the scatter of the residuals error is smaller for smaller values (panel to the right):</p> +<p>The plot of the individual SFO fits shown below suggests that at +least in some datasets the degradation slows down towards later time +points, and that the scatter of the residuals error is smaller for +smaller values (panel to the right):</p> <div class="sourceCode" id="cb3"><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="fu"><a href="../../reference/mixed.html">mixed</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="fu"><a href="../../reference/mixed.html">mixed</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> <p><img src="dimethenamid_2018_files/figure-html/f_parent_mkin_sfo_const-1.png" width="700"></p> -<p>Using biexponential decline (DFOP) results in a slightly more random scatter of the residuals:</p> +<p>Using biexponential decline (DFOP) results in a slightly more random +scatter of the residuals:</p> <div class="sourceCode" id="cb4"><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="fu"><a href="../../reference/mixed.html">mixed</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="fu"><a href="../../reference/mixed.html">mixed</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> <p><img src="dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const-1.png" width="700"></p> -<p>The population curve (bold line) in the above plot results from taking the mean of the individual transformed parameters, i.e. of log k1 and log k2, as well as of the logit of the g parameter of the DFOP model). Here, this procedure does not result in parameters that represent the degradation well, because in some datasets the fitted value for k2 is extremely close to zero, leading to a log k2 value that dominates the average. This is alleviated if only rate constants that pass the t-test for significant difference from zero (on the untransformed scale) are considered in the averaging:</p> +<p>The population curve (bold line) in the above plot results from +taking the mean of the individual transformed parameters, i.e. of log k1 +and log k2, as well as of the logit of the g parameter of the DFOP +model). Here, this procedure does not result in parameters that +represent the degradation well, because in some datasets the fitted +value for k2 is extremely close to zero, leading to a log k2 value that +dominates the average. This is alleviated if only rate constants that +pass the t-test for significant difference from zero (on the +untransformed scale) are considered in the averaging:</p> <div class="sourceCode" id="cb5"><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="fu"><a href="../../reference/mixed.html">mixed</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span><span class="op">)</span>, test_log_parms <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="fu"><a href="../../reference/mixed.html">mixed</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span><span class="op">)</span>, test_log_parms <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> <p><img src="dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const_test-1.png" width="700"></p> -<p>While this is visually much more satisfactory, such an average procedure could introduce a bias, as not all results from the individual fits enter the population curve with the same weight. This is where nonlinear mixed-effects models can help out by treating all datasets with equally by fitting a parameter distribution model together with the degradation model and the error model (see below).</p> -<p>The remaining trend of the residuals to be higher for higher predicted residues is reduced by using the two-component error model:</p> +<p>While this is visually much more satisfactory, such an average +procedure could introduce a bias, as not all results from the individual +fits enter the population curve with the same weight. This is where +nonlinear mixed-effects models can help out by treating all datasets +with equally by fitting a parameter distribution model together with the +degradation model and the error model (see below).</p> +<p>The remaining trend of the residuals to be higher for higher +predicted residues is reduced by using the two-component error +model:</p> <div class="sourceCode" id="cb6"><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="fu"><a href="../../reference/mixed.html">mixed</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span><span class="op">)</span>, test_log_parms <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="fu"><a href="../../reference/mixed.html">mixed</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span><span class="op">)</span>, test_log_parms <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> <p><img src="dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_tc_test-1.png" width="700"></p> -<p>However, note that in the case of using this error model, the fits to the Flaach and BBA 2.3 datasets appear to be ill-defined, indicated by the fact that they did not converge:</p> +<p>However, note that in the case of using this error model, the fits to +the Flaach and BBA 2.3 datasets appear to be ill-defined, indicated by +the fact that they did not converge:</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/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span><span class="op">)</span></span></code></pre></div> <pre><code><mmkin> object @@ -186,26 +265,53 @@ Status of individual fits: model Calke Borstel Flaach BBA 2.2 BBA 2.3 Elliot DFOP OK OK C OK C OK -OK: No warnings C: Optimisation did not converge: -iteration limit reached without convergence (10)</code></pre> +iteration limit reached without convergence (10) +OK: No warnings</code></pre> </div> <div class="section level3"> <h3 id="nonlinear-mixed-effects-models">Nonlinear mixed-effects models<a class="anchor" aria-label="anchor" href="#nonlinear-mixed-effects-models"></a> </h3> -<p>Instead of taking a model selection decision for each of the individual fits, we fit nonlinear mixed-effects models (using different fitting algorithms as implemented in different packages) and do model selection using all available data at the same time. In order to make sure that these decisions are not unduly influenced by the type of algorithm used, by implementation details or by the use of wrong control parameters, we compare the model selection results obtained with different R packages, with different algorithms and checking control parameters.</p> +<p>Instead of taking a model selection decision for each of the +individual fits, we fit nonlinear mixed-effects models (using different +fitting algorithms as implemented in different packages) and do model +selection using all available data at the same time. In order to make +sure that these decisions are not unduly influenced by the type of +algorithm used, by implementation details or by the use of wrong control +parameters, we compare the model selection results obtained with +different R packages, with different algorithms and checking control +parameters.</p> <div class="section level4"> <h4 id="nlme">nlme<a class="anchor" aria-label="anchor" href="#nlme"></a> </h4> -<p>The nlme package was the first R extension providing facilities to fit nonlinear mixed-effects models. We would like to do model selection from all four combinations of degradation models and error models based on the AIC. However, fitting the DFOP model with constant variance and using default control parameters results in an error, signalling that the maximum number of 50 iterations was reached, potentially indicating overparameterisation. Nevertheless, the algorithm converges when the two-component error model is used in combination with the DFOP model. This can be explained by the fact that the smaller residues observed at later sampling times get more weight when using the two-component error model which will counteract the tendency of the algorithm to try parameter combinations unsuitable for fitting these data.</p> +<p>The nlme package was the first R extension providing facilities to +fit nonlinear mixed-effects models. We would like to do model selection +from all four combinations of degradation models and error models based +on the AIC. However, fitting the DFOP model with constant variance and +using default control parameters results in an error, signalling that +the maximum number of 50 iterations was reached, potentially indicating +overparameterisation. Nevertheless, the algorithm converges when the +two-component error model is used in combination with the DFOP model. +This can be explained by the fact that the smaller residues observed at +later sampling times get more weight when using the two-component error +model which will counteract the tendency of the algorithm to try +parameter combinations unsuitable for fitting these data.</p> <div class="sourceCode" id="cb9"><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://svn.r-project.org/R-packages/trunk/nlme/" class="external-link">nlme</a></span><span class="op">)</span></span> <span><span class="va">f_parent_nlme_sfo_const</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlme/man/nlme.html" class="external-link">nlme</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span><span class="op">)</span></span> <span><span class="co"># f_parent_nlme_dfop_const <- nlme(f_parent_mkin_const["DFOP", ])</span></span> <span><span class="va">f_parent_nlme_sfo_tc</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlme/man/nlme.html" class="external-link">nlme</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span><span class="op">)</span></span> <span><span class="va">f_parent_nlme_dfop_tc</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlme/man/nlme.html" class="external-link">nlme</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span><span class="op">)</span></span></code></pre></div> -<p>Note that a certain degree of overparameterisation is also indicated by a warning obtained when fitting DFOP with the two-component error model (‘false convergence’ in the ‘LME step’ in iteration 3). However, as this warning does not occur in later iterations, and specifically not in the last of the 6 iterations, we can ignore this warning.</p> -<p>The model comparison function of the nlme package can directly be applied to these fits showing a much lower AIC for the DFOP model fitted with the two-component error model. Also, the likelihood ratio test indicates that this difference is significant as the p-value is below 0.0001.</p> +<p>Note that a certain degree of overparameterisation is also indicated +by a warning obtained when fitting DFOP with the two-component error +model (‘false convergence’ in the ‘LME step’ in iteration 3). However, +as this warning does not occur in later iterations, and specifically not +in the last of the 5 iterations, we can ignore this warning.</p> +<p>The model comparison function of the nlme package can directly be +applied to these fits showing a much lower AIC for the DFOP model fitted +with the two-component error model. Also, the likelihood ratio test +indicates that this difference is significant as the p-value is below +0.0001.</p> <div class="sourceCode" id="cb10"><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> <span> <span class="va">f_parent_nlme_sfo_const</span>, <span class="va">f_parent_nlme_sfo_tc</span>, <span class="va">f_parent_nlme_dfop_tc</span></span> @@ -214,7 +320,10 @@ iteration limit reached without convergence (10)</code></pre> f_parent_nlme_sfo_const 1 5 796.60 811.82 -393.30 f_parent_nlme_sfo_tc 2 6 798.60 816.86 -393.30 1 vs 2 0.00 0.998 f_parent_nlme_dfop_tc 3 10 671.91 702.34 -325.96 2 vs 3 134.69 <.0001</code></pre> -<p>In addition to these fits, attempts were also made to include correlations between random effects by using the log Cholesky parameterisation of the matrix specifying them. The code used for these attempts can be made visible below.</p> +<p>In addition to these fits, attempts were also made to include +correlations between random effects by using the log Cholesky +parameterisation of the matrix specifying them. The code used for these +attempts can be made visible below.</p> <div class="sourceCode" id="cb12"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">f_parent_nlme_sfo_const_logchol</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlme/man/nlme.html" class="external-link">nlme</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span>,</span> <span> random <span class="op">=</span> <span class="fu">nlme</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/nlme/man/pdLogChol.html" class="external-link">pdLogChol</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">DMTA_0</span> <span class="op">~</span> <span class="fl">1</span>, <span class="va">log_k_DMTA</span> <span class="op">~</span> <span class="fl">1</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span> @@ -225,17 +334,29 @@ f_parent_nlme_dfop_tc 3 10 671.91 702.34 -325.96 2 vs 3 134.69 <.0001 <span><span class="va">f_parent_nlme_dfop_tc_logchol</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlme/man/nlme.html" class="external-link">nlme</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>,</span> <span> random <span class="op">=</span> <span class="fu">nlme</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/nlme/man/pdLogChol.html" class="external-link">pdLogChol</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">DMTA_0</span> <span class="op">~</span> <span class="fl">1</span>, <span class="va">log_k1</span> <span class="op">~</span> <span class="fl">1</span>, <span class="va">log_k2</span> <span class="op">~</span> <span class="fl">1</span>, <span class="va">g_qlogis</span> <span class="op">~</span> <span class="fl">1</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span> <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_parent_nlme_dfop_tc</span>, <span class="va">f_parent_nlme_dfop_tc_logchol</span><span class="op">)</span></span></code></pre></div> -<p>While the SFO variants converge fast, the additional parameters introduced by this lead to convergence warnings for the DFOP model. The model comparison clearly show that adding correlations between random effects does not improve the fits.</p> -<p>The selected model (DFOP with two-component error) fitted to the data assuming no correlations between random effects is shown below.</p> +<p>While the SFO variants converge fast, the additional parameters +introduced by this lead to convergence warnings for the DFOP model. The +model comparison clearly show that adding correlations between random +effects does not improve the fits.</p> +<p>The selected model (DFOP with two-component error) fitted to the data +assuming no correlations between random effects is shown below.</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_parent_nlme_dfop_tc</span><span class="op">)</span></span></code></pre></div> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_parent_nlme_dfop_tc</span><span class="op">)</span></span></code></pre></div> <p><img src="dimethenamid_2018_files/figure-html/plot_parent_nlme-1.png" width="700"></p> </div> <div class="section level4"> <h4 id="saemix">saemix<a class="anchor" aria-label="anchor" href="#saemix"></a> </h4> -<p>The saemix package provided the first Open Source implementation of the Stochastic Approximation to the Expectation Maximisation (SAEM) algorithm. SAEM fits of degradation models can be conveniently performed using an interface to the saemix package available in current development versions of the mkin package.</p> -<p>The corresponding SAEM fits of the four combinations of degradation and error models are fitted below. As there is no convergence criterion implemented in the saemix package, the convergence plots need to be manually checked for every fit. We define control settings that work well for all the parent data fits shown in this vignette.</p> +<p>The saemix package provided the first Open Source implementation of +the Stochastic Approximation to the Expectation Maximisation (SAEM) +algorithm. SAEM fits of degradation models can be conveniently performed +using an interface to the saemix package available in current +development versions of the mkin package.</p> +<p>The corresponding SAEM fits of the four combinations of degradation +and error models are fitted below. As there is no convergence criterion +implemented in the saemix package, the convergence plots need to be +manually checked for every fit. We define control settings that work +well for all the parent data fits shown in this vignette.</p> <div class="sourceCode" id="cb14"><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">saemix</span><span class="op">)</span></span> <span><span class="va">saemix_control</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/saemix/man/saemixControl.html" class="external-link">saemixControl</a></span><span class="op">(</span>nbiter.saemix <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">800</span>, <span class="fl">300</span><span class="op">)</span>, nb.chains <span class="op">=</span> <span class="fl">15</span>,</span> @@ -244,19 +365,23 @@ f_parent_nlme_dfop_tc 3 10 671.91 702.34 -325.96 2 vs 3 134.69 <.0001 <span> print <span class="op">=</span> <span class="cn">FALSE</span>, save <span class="op">=</span> <span class="cn">FALSE</span>, save.graphs <span class="op">=</span> <span class="cn">FALSE</span>, displayProgress <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span> <span><span class="va">saemix_control_10k</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/saemix/man/saemixControl.html" class="external-link">saemixControl</a></span><span class="op">(</span>nbiter.saemix <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">10000</span>, <span class="fl">300</span><span class="op">)</span>, nb.chains <span class="op">=</span> <span class="fl">15</span>,</span> <span> print <span class="op">=</span> <span class="cn">FALSE</span>, save <span class="op">=</span> <span class="cn">FALSE</span>, save.graphs <span class="op">=</span> <span class="cn">FALSE</span>, displayProgress <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div> -<p>The convergence plot for the SFO model using constant variance is shown below.</p> +<p>The convergence plot for the SFO model using constant variance is +shown below.</p> <div class="sourceCode" id="cb15"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">f_parent_saemix_sfo_const</span> <span class="op"><-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</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> control <span class="op">=</span> <span class="va">saemix_control</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span></span> <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_parent_saemix_sfo_const</span><span class="op">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></span></code></pre></div> <p><img src="dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_const-1.png" width="700"></p> -<p>Obviously the selected number of iterations is sufficient to reach convergence. This can also be said for the SFO fit using the two-component error model.</p> +<p>Obviously the selected number of iterations is sufficient to reach +convergence. This can also be said for the SFO fit using the +two-component error model.</p> <div class="sourceCode" id="cb16"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">f_parent_saemix_sfo_tc</span> <span class="op"><-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span> <span> control <span class="op">=</span> <span class="va">saemix_control</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span></span> <span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_parent_saemix_sfo_tc</span><span class="op">$</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="dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_tc-1.png" width="700"></p> -<p>When fitting the DFOP model with constant variance (see below), parameter convergence is not as unambiguous.</p> +<p>When fitting the DFOP model with constant variance (see below), +parameter convergence is not as unambiguous.</p> <div class="sourceCode" id="cb17"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">f_parent_saemix_dfop_const</span> <span class="op"><-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span> <span> control <span class="op">=</span> <span class="va">saemix_control</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span></span> @@ -283,13 +408,21 @@ DMTA_0 97.99583 96.50079 99.4909 k1 0.06377 0.03432 0.0932 k2 0.00848 0.00444 0.0125 g 0.95701 0.91313 1.0009 -a.1 1.82141 1.65974 1.9831 -SD.DMTA_0 1.64787 0.45779 2.8379 +a.1 1.82141 1.65122 1.9916 +SD.DMTA_0 1.64787 0.45772 2.8380 SD.k1 0.57439 0.24731 0.9015 -SD.k2 0.03296 -2.50143 2.5673 -SD.g 1.10266 0.32371 1.8816</code></pre> -<p>While the other parameters converge to credible values, the variance of k2 (<code>omega2.k2</code>) converges to a very small value. The printout of the <code>saem.mmkin</code> model shows that the estimated standard deviation of k2 across the population of soils (<code>SD.k2</code>) is ill-defined, indicating overparameterisation of this model.</p> -<p>When the DFOP model is fitted with the two-component error model, we also observe that the estimated variance of k2 becomes very small, while being ill-defined, as illustrated by the excessive confidence interval of <code>SD.k2</code>.</p> +SD.k2 0.03296 -2.50195 2.5679 +SD.g 1.10266 0.32369 1.8816</code></pre> +<p>While the other parameters converge to credible values, the variance +of k2 (<code>omega2.k2</code>) converges to a very small value. The +printout of the <code>saem.mmkin</code> model shows that the estimated +standard deviation of k2 across the population of soils +(<code>SD.k2</code>) is ill-defined, indicating overparameterisation of +this model.</p> +<p>When the DFOP model is fitted with the two-component error model, we +also observe that the estimated variance of k2 becomes very small, while +being ill-defined, as illustrated by the excessive confidence interval +of <code>SD.k2</code>.</p> <div class="sourceCode" id="cb20"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">f_parent_saemix_dfop_tc</span> <span class="op"><-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span> <span> control <span class="op">=</span> <span class="va">saemix_control</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span></span> @@ -324,9 +457,21 @@ SD.DMTA_0 2.06075 0.4187 3.7028 SD.k1 0.59357 0.2561 0.9310 SD.k2 0.00292 -10.2960 10.3019 SD.g 1.05725 0.3808 1.7337</code></pre> -<p>Doubling the number of iterations in the first phase of the algorithm leads to a slightly lower likelihood, and therefore to slightly higher AIC and BIC values. With even more iterations, the algorithm stops with an error message. This is related to the variance of k2 approximating zero and has been submitted as a <a href="https://github.com/saemixdevelopment/saemixextension/issues/29" class="external-link">bug to the saemix package</a>, as the algorithm does not converge in this case.</p> -<p>An alternative way to fit DFOP in combination with the two-component error model is to use the model formulation with transformed parameters as used per default in mkin. When using this option, convergence is slower, but eventually the algorithm stops as well with the same error message.</p> -<p>The four combinations (SFO/const, SFO/tc, DFOP/const and DFOP/tc) and the version with increased iterations can be compared using the model comparison function of the saemix package:</p> +<p>Doubling the number of iterations in the first phase of the algorithm +leads to a slightly lower likelihood, and therefore to slightly higher +AIC and BIC values. With even more iterations, the algorithm stops with +an error message. This is related to the variance of k2 approximating +zero and has been submitted as a <a href="https://github.com/saemixdevelopment/saemixextension/issues/29" class="external-link">bug +to the saemix package</a>, as the algorithm does not converge in this +case.</p> +<p>An alternative way to fit DFOP in combination with the two-component +error model is to use the model formulation with transformed parameters +as used per default in mkin. When using this option, convergence is +slower, but eventually the algorithm stops as well with the same error +message.</p> +<p>The four combinations (SFO/const, SFO/tc, DFOP/const and DFOP/tc) and +the version with increased iterations can be compared using the model +comparison function of the saemix package:</p> <div class="sourceCode" id="cb23"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">AIC_parent_saemix</span> <span class="op"><-</span> <span class="fu">saemix</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/compare.saemix.html" class="external-link">compare.saemix</a></span><span class="op">(</span></span> <span> <span class="va">f_parent_saemix_sfo_const</span><span class="op">$</span><span class="va">so</span>,</span> @@ -345,7 +490,10 @@ SFO tc 798.38 797.13 DFOP const 705.75 703.88 DFOP tc 665.65 663.57 DFOP tc more iterations 665.88 663.80</code></pre> -<p>In order to check the influence of the likelihood calculation algorithms implemented in saemix, the likelihood from Gaussian quadrature is added to the best fit, and the AIC values obtained from the three methods are compared.</p> +<p>In order to check the influence of the likelihood calculation +algorithms implemented in saemix, the likelihood from Gaussian +quadrature is added to the best fit, and the AIC values obtained from +the three methods are compared.</p> <div class="sourceCode" id="cb27"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span> <span class="op"><-</span></span> <span> <span class="fu">saemix</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/llgq.saemix.html" class="external-link">llgq.saemix</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span><span class="op">)</span></span> @@ -357,9 +505,19 @@ DFOP tc more iterations 665.88 663.80</code></pre> <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">AIC_parent_saemix_methods</span><span class="op">)</span></span></code></pre></div> <pre><code> is gq lin 665.65 665.68 665.11 </code></pre> -<p>The AIC values based on importance sampling and Gaussian quadrature are very similar. Using linearisation is known to be less accurate, but still gives a similar value.</p> -<p>In order to illustrate that the comparison of the three method depends on the degree of convergence obtained in the fit, the same comparison is shown below for the fit using the defaults for the number of iterations and the number of MCMC chains.</p> -<p>When using OpenBlas for linear algebra, there is a large difference in the values obtained with Gaussian quadrature, so the larger number of iterations makes a lot of difference. When using the LAPACK version coming with Debian Bullseye, the AIC based on Gaussian quadrature is almost the same as the one obtained with the other methods, also when using defaults for the fit.</p> +<p>The AIC values based on importance sampling and Gaussian quadrature +are very similar. Using linearisation is known to be less accurate, but +still gives a similar value.</p> +<p>In order to illustrate that the comparison of the three method +depends on the degree of convergence obtained in the fit, the same +comparison is shown below for the fit using the defaults for the number +of iterations and the number of MCMC chains.</p> +<p>When using OpenBlas for linear algebra, there is a large difference +in the values obtained with Gaussian quadrature, so the larger number of +iterations makes a lot of difference. When using the LAPACK version +coming with Debian Bullseye, the AIC based on Gaussian quadrature is +almost the same as the one obtained with the other methods, also when +using defaults for the fit.</p> <div class="sourceCode" id="cb29"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">f_parent_saemix_dfop_tc_defaults</span> <span class="op"><-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span><span class="op">)</span></span> <span><span class="va">f_parent_saemix_dfop_tc_defaults</span><span class="op">$</span><span class="va">so</span> <span class="op"><-</span></span> @@ -377,7 +535,9 @@ DFOP tc more iterations 665.88 663.80</code></pre> <div class="section level3"> <h3 id="comparison">Comparison<a class="anchor" aria-label="anchor" href="#comparison"></a> </h3> -<p>The following table gives the AIC values obtained with both backend packages using the same control parameters (800 iterations burn-in, 300 iterations second phase, 15 chains).</p> +<p>The following table gives the AIC values obtained with both backend +packages using the same control parameters (800 iterations burn-in, 300 +iterations second phase, 15 chains).</p> <div class="sourceCode" id="cb31"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">AIC_all</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span></span> <span> check.names <span class="op">=</span> <span class="cn">FALSE</span>,</span> @@ -417,7 +577,7 @@ DFOP tc more iterations 665.88 663.80</code></pre> <td align="left">DFOP</td> <td align="left">const</td> <td align="right">NA</td> -<td align="right">671.98</td> +<td align="right">709.26</td> <td align="right">705.75</td> </tr> <tr class="even"> @@ -434,21 +594,33 @@ DFOP tc more iterations 665.88 663.80</code></pre> <div class="section level2"> <h2 id="conclusion">Conclusion<a class="anchor" aria-label="anchor" href="#conclusion"></a> </h2> -<p>A more detailed analysis of the dimethenamid dataset confirmed that the DFOP model provides the most appropriate description of the decline of the parent compound in these data. On the other hand, closer inspection of the results revealed that the variability of the k2 parameter across the population of soils is ill-defined. This coincides with the observation that this parameter cannot robustly be quantified for some of the soils.</p> -<p>Regarding the regulatory use of these data, it is claimed that an improved characterisation of the mean parameter values across the population is obtained using the nonlinear mixed-effects models presented here. However, attempts to quantify the variability of the slower rate constant of the biphasic decline of dimethenamid indicate that the data are not sufficient to characterise this variability to a satisfactory precision.</p> +<p>A more detailed analysis of the dimethenamid dataset confirmed that +the DFOP model provides the most appropriate description of the decline +of the parent compound in these data. On the other hand, closer +inspection of the results revealed that the variability of the k2 +parameter across the population of soils is ill-defined. This coincides +with the observation that this parameter cannot robustly be quantified +for some of the soils.</p> +<p>Regarding the regulatory use of these data, it is claimed that an +improved characterisation of the mean parameter values across the +population is obtained using the nonlinear mixed-effects models +presented here. However, attempts to quantify the variability of the +slower rate constant of the biphasic decline of dimethenamid indicate +that the data are not sufficient to characterise this variability to a +satisfactory precision.</p> </div> <div class="section level2"> <h2 id="session-info">Session Info<a class="anchor" aria-label="anchor" href="#session-info"></a> </h2> <div class="sourceCode" id="cb32"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/utils/sessionInfo.html" class="external-link">sessionInfo</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> -<pre><code>R version 4.2.2 (2022-10-31) +<pre><code>R version 4.2.3 (2023-03-15) Platform: x86_64-pc-linux-gnu (64-bit) -Running under: Debian GNU/Linux 11 (bullseye) +Running under: Debian GNU/Linux 12 (bookworm) Matrix products: default BLAS: /usr/lib/x86_64-linux-gnu/openblas-serial/libblas.so.3 -LAPACK: /usr/lib/x86_64-linux-gnu/openblas-serial/libopenblas-r0.3.13.so +LAPACK: /usr/lib/x86_64-linux-gnu/openblas-serial/libopenblas-r0.3.21.so locale: [1] LC_CTYPE=de_DE.UTF-8 LC_NUMERIC=C @@ -462,38 +634,44 @@ attached base packages: [1] stats graphics grDevices utils datasets methods base other attached packages: -[1] nlme_3.1-160 mkin_1.2.0 knitr_1.40 +[1] saemix_3.2 npde_3.3 nlme_3.1-162 mkin_1.2.3 knitr_1.42 loaded via a namespace (and not attached): - [1] deSolve_1.34 zoo_1.8-11 tidyselect_1.2.0 xfun_0.33 - [5] bslib_0.4.0 purrr_0.3.5 lattice_0.20-45 colorspace_2.0-3 - [9] vctrs_0.5.0 generics_0.1.3 htmltools_0.5.3 yaml_2.3.6 -[13] utf8_1.2.2 rlang_1.0.6 pkgdown_2.0.6 saemix_3.2 -[17] jquerylib_0.1.4 pillar_1.8.1 glue_1.6.2 DBI_1.1.3 -[21] lifecycle_1.0.3 stringr_1.4.1 munsell_0.5.0 gtable_0.3.1 -[25] ragg_1.2.2 memoise_2.0.1 evaluate_0.18 npde_3.2 -[29] fastmap_1.1.0 lmtest_0.9-40 parallel_4.2.2 fansi_1.0.3 -[33] highr_0.9 scales_1.2.1 cachem_1.0.6 desc_1.4.2 -[37] jsonlite_1.8.3 systemfonts_1.0.4 fs_1.5.2 textshaping_0.3.6 -[41] gridExtra_2.3 ggplot2_3.4.0 digest_0.6.30 stringi_1.7.8 -[45] dplyr_1.0.10 grid_4.2.2 rprojroot_2.0.3 cli_3.4.1 -[49] tools_4.2.2 magrittr_2.0.3 sass_0.4.2 tibble_3.1.8 -[53] pkgconfig_2.0.3 assertthat_0.2.1 rmarkdown_2.16 R6_2.5.1 -[57] mclust_6.0.0 compiler_4.2.2 </code></pre> + [1] highr_0.10 pillar_1.9.0 bslib_0.4.2 compiler_4.2.3 + [5] jquerylib_0.1.4 tools_4.2.3 mclust_6.0.0 digest_0.6.31 + [9] tibble_3.2.1 jsonlite_1.8.4 evaluate_0.20 memoise_2.0.1 +[13] lifecycle_1.0.3 gtable_0.3.3 lattice_0.21-8 pkgconfig_2.0.3 +[17] rlang_1.1.0 DBI_1.1.3 cli_3.6.1 yaml_2.3.7 +[21] parallel_4.2.3 pkgdown_2.0.7 xfun_0.38 fastmap_1.1.1 +[25] gridExtra_2.3 dplyr_1.1.1 stringr_1.5.0 generics_0.1.3 +[29] desc_1.4.2 fs_1.6.1 vctrs_0.6.1 sass_0.4.5 +[33] systemfonts_1.0.4 tidyselect_1.2.0 rprojroot_2.0.3 lmtest_0.9-40 +[37] grid_4.2.3 glue_1.6.2 R6_2.5.1 textshaping_0.3.6 +[41] fansi_1.0.4 rmarkdown_2.21 purrr_1.0.1 ggplot2_3.4.2 +[45] magrittr_2.0.3 codetools_0.2-19 scales_1.2.1 htmltools_0.5.5 +[49] colorspace_2.1-0 ragg_1.2.5 utf8_1.2.3 stringi_1.7.12 +[53] munsell_0.5.0 cachem_1.0.7 zoo_1.8-12 </code></pre> </div> <div class="section level2"> <h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a> </h2> <!-- vim: set foldmethod=syntax: --> -<div id="refs" class="references hanging-indent"> -<div id="ref-efsa_2018_dimethenamid"> -<p>EFSA. 2018. “Peer Review of the Pesticide Risk Assessment of the Active Substance Dimethenamid-P.” <em>EFSA Journal</em> 16 (4): 5211.</p> +<div id="refs" class="references csl-bib-body hanging-indent"> +<div id="ref-efsa_2018_dimethenamid" class="csl-entry"> +EFSA. 2018. <span>“Peer Review of the Pesticide Risk Assessment of the +Active Substance Dimethenamid-p.”</span> <em>EFSA Journal</em> 16: 5211. </div> -<div id="ref-ranke2021"> -<p>Ranke, Johannes, Janina Wöltjen, Jana Schmidt, and Emmanuelle Comets. 2021. “Taking Kinetic Evaluations of Degradation Data to the Next Level with Nonlinear Mixed-Effects Models.” <em>Environments</em> 8 (8). <a href="https://doi.org/10.3390/environments8080071" class="external-link">https://doi.org/10.3390/environments8080071</a>.</p> +<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 id="ref-dimethenamid_rar_2018_b8"> -<p>Rapporteur Member State Germany, Co-Rapporteur Member State Bulgaria. 2018. “Renewal Assessment Report Dimethenamid-P Volume 3 - B.8 Environmental fate and behaviour, Rev. 2 - November 2017.” <a href="https://open.efsa.europa.eu/study-inventory/EFSA-Q-2014-00716" class="external-link">https://open.efsa.europa.eu/study-inventory/EFSA-Q-2014-00716</a>.</p> +<div id="ref-dimethenamid_rar_2018_b8" class="csl-entry"> +Rapporteur Member State Germany, Co-Rapporteur Member State Bulgaria. +2018. <span>“<span class="nocase">Renewal Assessment Report +Dimethenamid-P Volume 3 - B.8 Environmental fate and behaviour, Rev. 2 - +November 2017</span>.”</span> <a href="https://open.efsa.europa.eu/study-inventory/EFSA-Q-2014-00716" class="external-link">https://open.efsa.europa.eu/study-inventory/EFSA-Q-2014-00716</a>. </div> </div> </div> @@ -516,7 +694,7 @@ loaded via a namespace (and not attached): <div class="pkgdown"> <p></p> -<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p> +<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p> </div> </footer> diff --git a/docs/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const-1.png b/docs/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const-1.png Binary files differindex 4999e72c..505072ce 100644 --- a/docs/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const-1.png +++ b/docs/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const-1.png diff --git a/docs/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const_test-1.png b/docs/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const_test-1.png Binary files differindex b59764b1..505072ce 100644 --- a/docs/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const_test-1.png +++ b/docs/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const_test-1.png diff --git a/docs/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_tc_test-1.png b/docs/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_tc_test-1.png Binary files differindex da7ceeb6..0dd4da39 100644 --- a/docs/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_tc_test-1.png +++ b/docs/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_tc_test-1.png diff --git a/docs/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_sfo_const-1.png b/docs/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_sfo_const-1.png Binary files differindex 467c3c1a..0ed7448d 100644 --- a/docs/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_sfo_const-1.png +++ b/docs/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_sfo_const-1.png diff --git a/docs/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_tc-1.png b/docs/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_tc-1.png Binary files differindex 800c320b..d941f3e6 100644 --- a/docs/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_tc-1.png +++ b/docs/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_tc-1.png diff --git a/docs/articles/web_only/dimethenamid_2018_files/figure-html/plot_parent_nlme-1.png b/docs/articles/web_only/dimethenamid_2018_files/figure-html/plot_parent_nlme-1.png Binary files differindex 4d2dc94e..a799b14c 100644 --- a/docs/articles/web_only/dimethenamid_2018_files/figure-html/plot_parent_nlme-1.png +++ b/docs/articles/web_only/dimethenamid_2018_files/figure-html/plot_parent_nlme-1.png diff --git a/docs/articles/web_only/multistart.html b/docs/articles/web_only/multistart.html index 720c6742..04093e82 100644 --- a/docs/articles/web_only/multistart.html +++ b/docs/articles/web_only/multistart.html @@ -33,14 +33,14 @@ </button> <span class="navbar-brand"> <a class="navbar-link" href="../../index.html">mkin</a> - <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">1.2.0</span> + <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">1.2.3</span> </span> </div> <div id="navbar" class="navbar-collapse collapse"> <ul class="nav navbar-nav"> <li> - <a href="../../reference/index.html">Functions and data</a> + <a href="../../reference/index.html">Reference</a> </li> <li class="dropdown"> <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false"> @@ -52,6 +52,9 @@ <li> <a href="../../articles/mkin.html">Introduction to mkin</a> </li> + <li class="divider"> + </li> +<li class="dropdown-header">Example evaluations with (generalised) nonlinear least squares</li> <li> <a href="../../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a> </li> @@ -59,22 +62,31 @@ <a href="../../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a> </li> <li> - <a href="../../articles/web_only/dimethenamid_2018.html">Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models</a> + <a href="../../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> + </li> + <li class="divider"> </li> +<li class="dropdown-header">Example evaluations with hierarchical models (nonlinear mixed-effects models)</li> <li> - <a href="../../articles/web_only/multistart.html">Short demo of the multistart method</a> + <a href="../../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a> </li> <li> - <a href="../../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> + <a href="../../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a> </li> <li> - <a href="../../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> + <a href="../../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a> </li> <li> - <a href="../../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> + <a href="../../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a> </li> <li> - <a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> + <a href="../../articles/web_only/multistart.html">Short demo of the multistart method</a> + </li> + <li class="divider"> + </li> +<li class="dropdown-header">Performance</li> + <li> + <a href="../../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> </li> <li> <a href="../../articles/web_only/benchmarks.html">Benchmark timings for mkin</a> @@ -82,6 +94,15 @@ <li> <a href="../../articles/web_only/saem_benchmarks.html">Benchmark timings for saem.mmkin</a> </li> + <li class="divider"> + </li> +<li class="dropdown-header">Miscellaneous</li> + <li> + <a href="../../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> + </li> + <li> + <a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> + </li> </ul> </li> <li> @@ -105,13 +126,15 @@ - </header><script src="multistart_files/accessible-code-block-0.0.1/empty-anchor.js"></script><div class="row"> + </header><div class="row"> <div class="col-md-9 contents"> <div class="page-header toc-ignore"> <h1 data-toc-skip>Short demo of the multistart method</h1> - <h4 data-toc-skip class="author">Johannes Ranke</h4> + <h4 data-toc-skip class="author">Johannes +Ranke</h4> - <h4 data-toc-skip class="date">Last change 26 September 2022 (rebuilt 2022-11-17)</h4> + <h4 data-toc-skip class="date">Last change 20 April 2023 +(rebuilt 2023-04-20)</h4> <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/multistart.rmd" class="external-link"><code>vignettes/web_only/multistart.rmd</code></a></small> <div class="hidden name"><code>multistart.rmd</code></div> @@ -120,7 +143,8 @@ -<p>The dimethenamid data from 2018 from seven soils is used as example data in this vignette.</p> +<p>The dimethenamid data from 2018 from seven soils is used as example +data in this vignette.</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="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> @@ -132,42 +156,52 @@ <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 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> <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="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>First, we check the DFOP model with the two-component error model and random effects for all degradation parameters.</p> +<p>First, we check the DFOP model with the two-component error model and +random effects for all degradation parameters.</p> <div class="sourceCode" id="cb2"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">f_mmkin</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span><span class="st">"DFOP"</span>, <span class="va">dmta_ds</span>, error_model <span class="op">=</span> <span class="st">"tc"</span>, cores <span class="op">=</span> <span class="fl">7</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> <span><span class="va">f_saem_full</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_mmkin</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">f_saem_full</span><span class="op">)</span></span></code></pre></div> <pre><code><span><span class="co">## [1] "sd(log_k2)"</span></span></code></pre> -<p>We see that not all variability parameters are identifiable. The <code>illparms</code> function tells us that the confidence interval for the standard deviation of ‘log_k2’ includes zero. We check this assessment using multiple runs with different starting values.</p> +<p>We see that not all variability parameters are identifiable. The +<code>illparms</code> function tells us that the confidence interval for +the standard deviation of ‘log_k2’ includes zero. We check this +assessment using multiple runs with different starting values.</p> <div class="sourceCode" id="cb4"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">f_saem_full_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_full</span>, n <span class="op">=</span> <span class="fl">16</span>, cores <span class="op">=</span> <span class="fl">16</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_full_multi</span><span class="op">)</span></span></code></pre></div> +<span><span class="fu"><a href="../../reference/parplot.html">parplot</a></span><span class="op">(</span><span class="va">f_saem_full_multi</span>, lpos <span class="op">=</span> <span class="st">"topleft"</span><span class="op">)</span></span></code></pre></div> <p><img src="multistart_files/figure-html/unnamed-chunk-3-1.png" width="700"></p> -<p>This confirms that the variance of k2 is the most problematic parameter, so we reduce the parameter distribution model by removing the intersoil variability for k2.</p> +<p>This confirms that the variance of k2 is the most problematic +parameter, so we reduce the parameter distribution model by removing the +intersoil variability for k2.</p> <div class="sourceCode" id="cb5"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">f_saem_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">f_saem_full</span>, no_random_effect <span class="op">=</span> <span class="st">"log_k2"</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">f_saem_reduced</span><span class="op">)</span></span> <span><span class="va">f_saem_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">f_saem_reduced</span>, n <span class="op">=</span> <span class="fl">16</span>, cores <span class="op">=</span> <span class="fl">16</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_reduced_multi</span>, lpos <span class="op">=</span> <span class="st">"topright"</span><span class="op">)</span></span></code></pre></div> +<span><span class="fu"><a href="../../reference/parplot.html">parplot</a></span><span class="op">(</span><span class="va">f_saem_reduced_multi</span>, lpos <span class="op">=</span> <span class="st">"topright"</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><span class="op">)</span></span></code></pre></div> <p><img src="multistart_files/figure-html/unnamed-chunk-4-1.png" width="700"></p> -<p>The results confirm that all remaining parameters can be determined with sufficient certainty.</p> -<p>We can also analyse the log-likelihoods obtained in the multiple runs:</p> +<p>The results confirm that all remaining parameters can be determined +with sufficient certainty.</p> +<p>We can also analyse the log-likelihoods obtained in the multiple +runs:</p> <div class="sourceCode" id="cb6"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="fu"><a href="../../reference/llhist.html">llhist</a></span><span class="op">(</span><span class="va">f_saem_reduced_multi</span><span class="op">)</span></span></code></pre></div> <p><img src="multistart_files/figure-html/unnamed-chunk-5-1.png" width="700"></p> -<p>The parameter histograms can be further improved by excluding the result with the low likelihood.</p> +<p>We can use the <code>anova</code> method to compare the models.</p> <div class="sourceCode" id="cb7"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><span><span class="fu"><a href="../../reference/parplot.html">parplot</a></span><span class="op">(</span><span class="va">f_saem_reduced_multi</span>, lpos <span class="op">=</span> <span class="st">"topright"</span>, llmin <span class="op">=</span> <span class="op">-</span><span class="fl">326</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><span class="op">)</span></span></code></pre></div> -<p><img src="multistart_files/figure-html/unnamed-chunk-6-1.png" width="700"></p> -<p>We can use the <code>anova</code> method to compare the models, including a likelihood ratio test if the models are nested.</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_full</span>, <span class="fu"><a href="../../reference/multistart.html">best</a></span><span class="op">(</span><span class="va">f_saem_reduced_multi</span><span class="op">)</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<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_full</span>, <span class="fu"><a href="../../reference/multistart.html">best</a></span><span class="op">(</span><span class="va">f_saem_full_multi</span><span class="op">)</span>,</span> +<span> <span class="va">f_saem_reduced</span>, <span class="fu"><a href="../../reference/multistart.html">best</a></span><span class="op">(</span><span class="va">f_saem_reduced_multi</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> <pre><code><span><span class="co">## Data: 155 observations of 1 variable(s) grouped in 6 datasets</span></span> <span><span class="co">## </span></span> -<span><span class="co">## npar AIC BIC Lik Chisq Df Pr(>Chisq)</span></span> -<span><span class="co">## best(f_saem_reduced_multi) 9 663.69 661.82 -322.85 </span></span> -<span><span class="co">## f_saem_full 10 669.77 667.69 -324.89 0 1 1</span></span></code></pre> -<p>While AIC and BIC are lower for the reduced model, the likelihood ratio test does not indicate a significant difference between the fits.</p> +<span><span class="co">## npar AIC BIC Lik</span></span> +<span><span class="co">## f_saem_reduced 9 663.73 661.86 -322.86</span></span> +<span><span class="co">## best(f_saem_reduced_multi) 9 663.69 661.82 -322.85</span></span> +<span><span class="co">## f_saem_full 10 669.77 667.69 -324.89</span></span> +<span><span class="co">## best(f_saem_full_multi) 10 665.56 663.48 -322.78</span></span></code></pre> +<p>The reduced model gives the lowest information criteria and similar +likelihoods as the best variant of the full model. The multistart method +leads to a much lower improvement of the likelihood for the reduced +model, indicating that it converges faster.</p> </div> <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar"> @@ -185,7 +219,7 @@ <div class="pkgdown"> <p></p> -<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p> +<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p> </div> </footer> diff --git a/docs/articles/web_only/multistart_files/figure-html/unnamed-chunk-3-1.png b/docs/articles/web_only/multistart_files/figure-html/unnamed-chunk-3-1.png Binary files differindex 28991ae8..1ef2ba24 100644 --- a/docs/articles/web_only/multistart_files/figure-html/unnamed-chunk-3-1.png +++ b/docs/articles/web_only/multistart_files/figure-html/unnamed-chunk-3-1.png diff --git a/docs/articles/web_only/multistart_files/figure-html/unnamed-chunk-4-1.png b/docs/articles/web_only/multistart_files/figure-html/unnamed-chunk-4-1.png Binary files differindex 56147ae2..b1582557 100644 --- a/docs/articles/web_only/multistart_files/figure-html/unnamed-chunk-4-1.png +++ b/docs/articles/web_only/multistart_files/figure-html/unnamed-chunk-4-1.png diff --git a/docs/articles/web_only/multistart_files/figure-html/unnamed-chunk-5-1.png b/docs/articles/web_only/multistart_files/figure-html/unnamed-chunk-5-1.png Binary files differindex 7ce108a2..f0270537 100644 --- a/docs/articles/web_only/multistart_files/figure-html/unnamed-chunk-5-1.png +++ b/docs/articles/web_only/multistart_files/figure-html/unnamed-chunk-5-1.png diff --git a/docs/articles/web_only/multistart_files/figure-html/unnamed-chunk-6-1.png b/docs/articles/web_only/multistart_files/figure-html/unnamed-chunk-6-1.png Binary files differindex 00ccbaa8..b1582557 100644 --- a/docs/articles/web_only/multistart_files/figure-html/unnamed-chunk-6-1.png +++ b/docs/articles/web_only/multistart_files/figure-html/unnamed-chunk-6-1.png diff --git a/docs/articles/web_only/saem_benchmarks.html b/docs/articles/web_only/saem_benchmarks.html index 523d028c..587ee4a2 100644 --- a/docs/articles/web_only/saem_benchmarks.html +++ b/docs/articles/web_only/saem_benchmarks.html @@ -33,14 +33,14 @@ </button> <span class="navbar-brand"> <a class="navbar-link" href="../../index.html">mkin</a> - <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">1.2.0</span> + <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">1.2.3</span> </span> </div> <div id="navbar" class="navbar-collapse collapse"> <ul class="nav navbar-nav"> <li> - <a href="../../reference/index.html">Functions and data</a> + <a href="../../reference/index.html">Reference</a> </li> <li class="dropdown"> <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false"> @@ -52,6 +52,9 @@ <li> <a href="../../articles/mkin.html">Introduction to mkin</a> </li> + <li class="divider"> + </li> +<li class="dropdown-header">Example evaluations with (generalised) nonlinear least squares</li> <li> <a href="../../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a> </li> @@ -59,22 +62,31 @@ <a href="../../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a> </li> <li> - <a href="../../articles/web_only/dimethenamid_2018.html">Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models</a> + <a href="../../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> </li> + <li class="divider"> + </li> +<li class="dropdown-header">Example evaluations with hierarchical models (nonlinear mixed-effects models)</li> <li> - <a href="../../articles/web_only/multistart.html">Short demo of the multistart method</a> + <a href="../../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a> </li> <li> - <a href="../../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> + <a href="../../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a> </li> <li> - <a href="../../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> + <a href="../../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a> </li> <li> - <a href="../../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> + <a href="../../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a> </li> <li> - <a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> + <a href="../../articles/web_only/multistart.html">Short demo of the multistart method</a> + </li> + <li class="divider"> + </li> +<li class="dropdown-header">Performance</li> + <li> + <a href="../../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> </li> <li> <a href="../../articles/web_only/benchmarks.html">Benchmark timings for mkin</a> @@ -82,6 +94,15 @@ <li> <a href="../../articles/web_only/saem_benchmarks.html">Benchmark timings for saem.mmkin</a> </li> + <li class="divider"> + </li> +<li class="dropdown-header">Miscellaneous</li> + <li> + <a href="../../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> + </li> + <li> + <a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> + </li> </ul> </li> <li> @@ -105,13 +126,15 @@ - </header><script src="saem_benchmarks_files/accessible-code-block-0.0.1/empty-anchor.js"></script><div class="row"> + </header><div class="row"> <div class="col-md-9 contents"> <div class="page-header toc-ignore"> <h1 data-toc-skip>Benchmark timings for saem.mmkin</h1> - <h4 data-toc-skip class="author">Johannes Ranke</h4> + <h4 data-toc-skip class="author">Johannes +Ranke</h4> - <h4 data-toc-skip class="date">Last change 14 November 2022 (rebuilt 2022-11-17)</h4> + <h4 data-toc-skip class="date">Last change 17 February 2023 +(rebuilt 2023-04-20)</h4> <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/saem_benchmarks.rmd" class="external-link"><code>vignettes/web_only/saem_benchmarks.rmd</code></a></small> <div class="hidden name"><code>saem_benchmarks.rmd</code></div> @@ -120,15 +143,19 @@ -<p>Each system is characterized by operating system type, CPU type, mkin version, saemix version and R version. A compiler was available, so if no analytical solution was available, compiled ODE models are used.</p> -<p>Every fit is only performed once, so the accuracy of the benchmarks is limited.</p> +<p>Each system is characterized by operating system type, CPU type, mkin +version, saemix version and R version. A compiler was available, so if +no analytical solution was available, compiled ODE models are used.</p> +<p>Every fit is only performed once, so the accuracy of the benchmarks +is limited.</p> <p>For the initial mmkin fits, we use all available cores.</p> <div class="sourceCode" id="cb1"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">n_cores</span> <span class="op"><-</span> <span class="fu">parallel</span><span class="fu">::</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></code></pre></div> <div class="section level2"> <h2 id="test-data">Test data<a class="anchor" aria-label="anchor" href="#test-data"></a> </h2> -<p>Please refer to the vignette <code>dimethenamid_2018</code> for an explanation of the following preprocessing.</p> +<p>Please refer to the vignette <code>dimethenamid_2018</code> for an +explanation of the following preprocessing.</p> <div class="sourceCode" id="cb2"><pre class="downlit sourceCode r"> <code class="sourceCode R"><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> @@ -163,7 +190,7 @@ <div class="sourceCode" id="cb4"><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> <span> <span class="va">sfo_const</span>, <span class="va">dfop_const</span>, <span class="va">sforb_const</span>, <span class="va">hs_const</span>,</span> -<span> <span class="va">sfo_tc</span>, <span class="va">dfop_tc</span>, <span class="va">sforb_tc</span>, <span class="va">hs_tc</span><span class="op">)</span> <span class="op">|></span> <span class="fu">kable</span><span class="op">(</span>, digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> +<span> <span class="va">sfo_tc</span>, <span class="va">dfop_tc</span>, <span class="va">sforb_tc</span>, <span class="va">hs_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>, 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> @@ -231,19 +258,24 @@ </tr> </tbody> </table> -<p>The above model comparison suggests to use the SFORB model with two-component error. For comparison, we keep the DFOP model with two-component error, as it competes with SFORB for biphasic curves.</p> +<p>The above model comparison suggests to use the SFORB model with +two-component error. For comparison, we keep the DFOP model with +two-component error, as it competes with SFORB for biphasic curves.</p> <div class="sourceCode" id="cb5"><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_tc</span><span class="op">)</span></span></code></pre></div> <pre><code><span><span class="co">## [1] "sd(log_k2)"</span></span></code></pre> <div class="sourceCode" id="cb7"><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_tc</span><span class="op">)</span></span></code></pre></div> <pre><code><span><span class="co">## [1] "sd(log_k_DMTA_bound_free)"</span></span></code></pre> -<p>For these two models, random effects for the transformed parameters <code>k2</code> and <code>k_DMTA_bound_free</code> could not be quantified.</p> +<p>For these two models, random effects for the transformed parameters +<code>k2</code> and <code>k_DMTA_bound_free</code> could not be +quantified.</p> </div> <div class="section level3"> <h3 id="one-metabolite">One metabolite<a class="anchor" aria-label="anchor" href="#one-metabolite"></a> </h3> -<p>We remove parameters that were found to be ill-defined in the parent only fits.</p> +<p>We remove parameters that were found to be ill-defined in the parent +only fits.</p> <div class="sourceCode" id="cb9"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">one_met_mods</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> DFOP_SFO <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span> @@ -266,7 +298,11 @@ <div class="section level3"> <h3 id="three-metabolites">Three metabolites<a class="anchor" aria-label="anchor" href="#three-metabolites"></a> </h3> -<p>For the case of three metabolites, we only keep the SFORB model in order to limit the time for compiling this vignette, and as fitting in parallel may disturb the benchmark. Again, we do not include random effects that were ill-defined in previous fits of subsets of the degradation model.</p> +<p>For the case of three metabolites, we only keep the SFORB model in +order to limit the time for compiling this vignette, and as fitting in +parallel may disturb the benchmark. Again, we do not include random +effects that were ill-defined in previous fits of subsets of the +degradation model.</p> <div class="sourceCode" id="cb10"><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_sfo_tc</span><span class="op">)</span></span></code></pre></div> <div class="sourceCode" id="cb11"><pre class="downlit sourceCode r"> @@ -287,7 +323,9 @@ <div class="section level2"> <h2 id="results">Results<a class="anchor" aria-label="anchor" href="#results"></a> </h2> -<p>Benchmarks for all available error models are shown. They are intended for improving mkin, not for comparing CPUs or operating systems. All trademarks belong to their respective owners.</p> +<p>Benchmarks for all available error models are shown. They are +intended for improving mkin, not for comparing CPUs or operating +systems. All trademarks belong to their respective owners.</p> <div class="section level3"> <h3 id="parent-only-1">Parent only<a class="anchor" aria-label="anchor" href="#parent-only-1"></a> </h3> @@ -303,16 +341,68 @@ <th align="right">t3</th> <th align="right">t4</th> </tr></thead> -<tbody><tr class="odd"> +<tbody> +<tr class="odd"> <td align="left">Ryzen 7 1700</td> <td align="left">Linux</td> <td align="left">1.2.0</td> <td align="left">3.2</td> -<td align="right">2.14</td> +<td align="right">2.140</td> <td align="right">4.626</td> <td align="right">4.328</td> <td align="right">4.998</td> -</tr></tbody> +</tr> +<tr class="even"> +<td align="left">Ryzen 7 1700</td> +<td align="left">Linux</td> +<td align="left">1.2.2</td> +<td align="left">3.2</td> +<td align="right">2.427</td> +<td align="right">4.550</td> +<td align="right">4.217</td> +<td align="right">4.851</td> +</tr> +<tr class="odd"> +<td align="left">Ryzen 9 7950X</td> +<td align="left">Linux</td> +<td align="left">1.2.1</td> +<td align="left">3.2</td> +<td align="right">1.352</td> +<td align="right">2.813</td> +<td align="right">2.401</td> +<td align="right">2.074</td> +</tr> +<tr class="even"> +<td align="left">Ryzen 9 7950X</td> +<td align="left">Linux</td> +<td align="left">1.2.2</td> +<td align="left">3.2</td> +<td align="right">1.328</td> +<td align="right">2.738</td> +<td align="right">2.336</td> +<td align="right">2.023</td> +</tr> +<tr class="odd"> +<td align="left">Ryzen 9 7950X</td> +<td align="left">Linux</td> +<td align="left">1.2.3</td> +<td align="left">3.2</td> +<td align="right">1.118</td> +<td align="right">2.036</td> +<td align="right">2.010</td> +<td align="right">2.088</td> +</tr> +<tr class="even"> +<td align="left">Ryzen 9 7950X</td> +<td align="left">Linux</td> +<td align="left">1.2.3</td> +<td align="left">3.2</td> +<td align="right">1.419</td> +<td align="right">2.374</td> +<td align="right">1.926</td> +<td align="right">2.398</td> +</tr> +</tbody> </table> <p>Two-component error fits for SFO, DFOP, SFORB and HS.</p> <table class="table"> @@ -326,16 +416,68 @@ <th align="right">t7</th> <th align="right">t8</th> </tr></thead> -<tbody><tr class="odd"> +<tbody> +<tr class="odd"> <td align="left">Ryzen 7 1700</td> <td align="left">Linux</td> <td align="left">1.2.0</td> <td align="left">3.2</td> <td align="right">5.678</td> <td align="right">7.441</td> -<td align="right">8</td> -<td align="right">7.98</td> -</tr></tbody> +<td align="right">8.000</td> +<td align="right">7.980</td> +</tr> +<tr class="even"> +<td align="left">Ryzen 7 1700</td> +<td align="left">Linux</td> +<td align="left">1.2.2</td> +<td align="left">3.2</td> +<td align="right">5.352</td> +<td align="right">7.201</td> +<td align="right">8.174</td> +<td align="right">8.401</td> +</tr> +<tr class="odd"> +<td align="left">Ryzen 9 7950X</td> +<td align="left">Linux</td> +<td align="left">1.2.1</td> +<td align="left">3.2</td> +<td align="right">2.388</td> +<td align="right">3.033</td> +<td align="right">3.532</td> +<td align="right">3.310</td> +</tr> +<tr class="even"> +<td align="left">Ryzen 9 7950X</td> +<td align="left">Linux</td> +<td align="left">1.2.2</td> +<td align="left">3.2</td> +<td align="right">2.341</td> +<td align="right">2.968</td> +<td align="right">3.465</td> +<td align="right">3.341</td> +</tr> +<tr class="odd"> +<td align="left">Ryzen 9 7950X</td> +<td align="left">Linux</td> +<td align="left">1.2.3</td> +<td align="left">3.2</td> +<td align="right">2.159</td> +<td align="right">3.584</td> +<td align="right">3.307</td> +<td align="right">3.460</td> +</tr> +<tr class="even"> +<td align="left">Ryzen 9 7950X</td> +<td align="left">Linux</td> +<td align="left">1.2.3</td> +<td align="left">3.2</td> +<td align="right">2.348</td> +<td align="right">3.134</td> +<td align="right">3.253</td> +<td align="right">3.530</td> +</tr> +</tbody> </table> </div> <div class="section level3"> @@ -351,14 +493,56 @@ <th align="right">t9</th> <th align="right">t10</th> </tr></thead> -<tbody><tr class="odd"> +<tbody> +<tr class="odd"> <td align="left">Ryzen 7 1700</td> <td align="left">Linux</td> <td align="left">1.2.0</td> <td align="left">3.2</td> <td align="right">24.465</td> <td align="right">800.266</td> -</tr></tbody> +</tr> +<tr class="even"> +<td align="left">Ryzen 7 1700</td> +<td align="left">Linux</td> +<td align="left">1.2.2</td> +<td align="left">3.2</td> +<td align="right">25.193</td> +<td align="right">798.580</td> +</tr> +<tr class="odd"> +<td align="left">Ryzen 9 7950X</td> +<td align="left">Linux</td> +<td align="left">1.2.1</td> +<td align="left">3.2</td> +<td align="right">11.247</td> +<td align="right">285.216</td> +</tr> +<tr class="even"> +<td align="left">Ryzen 9 7950X</td> +<td align="left">Linux</td> +<td align="left">1.2.2</td> +<td align="left">3.2</td> +<td align="right">11.242</td> +<td align="right">284.258</td> +</tr> +<tr class="odd"> +<td align="left">Ryzen 9 7950X</td> +<td align="left">Linux</td> +<td align="left">1.2.3</td> +<td align="left">3.2</td> +<td align="right">11.796</td> +<td align="right">216.012</td> +</tr> +<tr class="even"> +<td align="left">Ryzen 9 7950X</td> +<td align="left">Linux</td> +<td align="left">1.2.3</td> +<td align="left">3.2</td> +<td align="right">12.841</td> +<td align="right">292.688</td> +</tr> +</tbody> </table> </div> <div class="section level3"> @@ -373,13 +557,50 @@ <th align="left">saemix</th> <th align="right">t11</th> </tr></thead> -<tbody><tr class="odd"> +<tbody> +<tr class="odd"> <td align="left">Ryzen 7 1700</td> <td align="left">Linux</td> <td align="left">1.2.0</td> <td align="left">3.2</td> <td align="right">1289.198</td> -</tr></tbody> +</tr> +<tr class="even"> +<td align="left">Ryzen 7 1700</td> +<td align="left">Linux</td> +<td align="left">1.2.2</td> +<td align="left">3.2</td> +<td align="right">1312.445</td> +</tr> +<tr class="odd"> +<td align="left">Ryzen 9 7950X</td> +<td align="left">Linux</td> +<td align="left">1.2.1</td> +<td align="left">3.2</td> +<td align="right">489.939</td> +</tr> +<tr class="even"> +<td align="left">Ryzen 9 7950X</td> +<td align="left">Linux</td> +<td align="left">1.2.2</td> +<td align="left">3.2</td> +<td align="right">482.970</td> +</tr> +<tr class="odd"> +<td align="left">Ryzen 9 7950X</td> +<td align="left">Linux</td> +<td align="left">1.2.3</td> +<td align="left">3.2</td> +<td align="right">392.364</td> +</tr> +<tr class="even"> +<td align="left">Ryzen 9 7950X</td> +<td align="left">Linux</td> +<td align="left">1.2.3</td> +<td align="left">3.2</td> +<td align="right">483.027</td> +</tr> +</tbody> </table> </div> </div> @@ -402,7 +623,7 @@ <div class="pkgdown"> <p></p> -<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p> +<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p> </div> </footer> |
