diff options
Diffstat (limited to 'docs/articles/web_only')
19 files changed, 7987 insertions, 97 deletions
diff --git a/docs/articles/web_only/FOCUS_Z.html b/docs/articles/web_only/FOCUS_Z.html index e91942ce..26268f75 100644 --- a/docs/articles/web_only/FOCUS_Z.html +++ b/docs/articles/web_only/FOCUS_Z.html @@ -20,7 +20,7 @@ <a class="navbar-brand me-2" href="../../index.html">mkin</a> - <small class="nav-text text-default me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">1.2.9</small> + <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">1.2.10</small> <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation"> @@ -84,7 +84,7 @@ Ranke</h4> <h4 data-toc-skip class="date">Last change 16 January 2018 -(rebuilt 2025-02-13)</h4> +(rebuilt 2025-05-12)</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="d-none name"><code>FOCUS_Z.rmd</code></div> diff --git a/docs/articles/web_only/NAFTA_examples.html b/docs/articles/web_only/NAFTA_examples.html index 88551103..53e1db48 100644 --- a/docs/articles/web_only/NAFTA_examples.html +++ b/docs/articles/web_only/NAFTA_examples.html @@ -20,7 +20,7 @@ <a class="navbar-brand me-2" href="../../index.html">mkin</a> - <small class="nav-text text-default me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">1.2.9</small> + <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">1.2.10</small> <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation"> @@ -84,7 +84,7 @@ Ranke</h4> <h4 data-toc-skip class="date">26 February 2019 (rebuilt -2025-02-13)</h4> +2025-05-12)</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="d-none name"><code>NAFTA_examples.rmd</code></div> @@ -119,7 +119,7 @@ same.</p> <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/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> +<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> <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> @@ -170,7 +170,7 @@ same.</p> <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/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> +<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> <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> @@ -221,7 +221,7 @@ same.</p> <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/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> +<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> <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> @@ -272,7 +272,7 @@ same.</p> <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/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> +<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> <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> @@ -331,7 +331,7 @@ lower value for the rate constant is used here.</p> <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/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> +<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> <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> @@ -386,7 +386,7 @@ lower value for the rate constant is used here.</p> <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/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> +<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> <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> @@ -440,7 +440,7 @@ suggest a simple exponential decline.</p> <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="cb40"><pre class="downlit sourceCode r"> -<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> +<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> <p><img src="NAFTA_examples_files/figure-html/p9b-1.png" width="700"></p> <div class="sourceCode" id="cb41"><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> @@ -498,7 +498,7 @@ in PestDF and g in mkin. In mkin, it is restricted to the interval from <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="cb47"><pre class="downlit sourceCode r"> -<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> +<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> <p><img src="NAFTA_examples_files/figure-html/p10-1.png" width="700"></p> <div class="sourceCode" id="cb48"><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> @@ -558,7 +558,7 @@ difference in IORE model parameters between PestDF and mkin.</p> <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/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> +<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> <p><img src="NAFTA_examples_files/figure-html/p11-1.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">p11</span><span class="op">)</span></span></code></pre></div> @@ -624,7 +624,7 @@ overparameterisation.</p> <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="cb61"><pre class="downlit sourceCode r"> -<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> +<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> <p><img src="NAFTA_examples_files/figure-html/p12a-1.png" width="700"></p> <div class="sourceCode" id="cb62"><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> @@ -681,7 +681,7 @@ overparameterisation.</p> <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="cb72"><pre class="downlit sourceCode r"> -<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> +<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> <p><img src="NAFTA_examples_files/figure-html/p12b-1.png" width="700"></p> <div class="sourceCode" id="cb73"><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> @@ -732,7 +732,7 @@ overparameterisation.</p> <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="cb78"><pre class="downlit sourceCode r"> -<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> +<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> <p><img src="NAFTA_examples_files/figure-html/p13-1.png" width="700"></p> <div class="sourceCode" id="cb79"><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> @@ -787,7 +787,7 @@ overparameterisation.</p> <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/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> +<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> <p><img src="NAFTA_examples_files/figure-html/p14-1.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">p14</span><span class="op">)</span></span></code></pre></div> @@ -844,7 +844,7 @@ same results in mkin and PestDF.</p> <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="cb94"><pre class="downlit sourceCode r"> -<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> +<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> <p><img src="NAFTA_examples_files/figure-html/p15a-1.png" width="700"></p> <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/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> @@ -893,7 +893,7 @@ same results in mkin and PestDF.</p> <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/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> +<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> <p><img src="NAFTA_examples_files/figure-html/p15b-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">p15b</span><span class="op">)</span></span></code></pre></div> @@ -950,7 +950,7 @@ mkin and PestDF.</p> <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="cb109"><pre class="downlit sourceCode r"> -<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> +<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> <p><img src="NAFTA_examples_files/figure-html/p16-1.png" width="700"></p> <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/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> diff --git a/docs/articles/web_only/benchmarks.html b/docs/articles/web_only/benchmarks.html index 3566be42..8b16b8e1 100644 --- a/docs/articles/web_only/benchmarks.html +++ b/docs/articles/web_only/benchmarks.html @@ -20,7 +20,7 @@ <a class="navbar-brand me-2" href="../../index.html">mkin</a> - <small class="nav-text text-default me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">1.2.9</small> + <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">1.2.10</small> <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation"> @@ -43,7 +43,7 @@ <li><h6 class="dropdown-header" data-toc-skip>Example evaluations with hierarchical models (nonlinear mixed-effects models)</h6></li> <li><a class="dropdown-item" href="../../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a></li> <li><a class="dropdown-item" href="../../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a></li> - <li><a class="dropdown-item" href="../../articles/prebuilt/2023_mesotrione_parent.html">Testing covariate modelling in hierarchical parent degradation kinetics with residue data on mesotrione</a></li> + <li><a class="dropdown-item" href="../../articles/web_only/2023_mesotrione_parent.html">Testing covariate modelling in hierarchical parent degradation kinetics with residue data on mesotrione</a></li> <li><a class="dropdown-item" href="../../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a></li> <li><a class="dropdown-item" href="../../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a></li> <li><a class="dropdown-item" href="../../articles/web_only/multistart.html">Short demo of the multistart method</a></li> @@ -84,7 +84,7 @@ Ranke</h4> <h4 data-toc-skip class="date">Last change 17 February 2023 -(rebuilt 2025-02-13)</h4> +(rebuilt 2025-05-13)</h4> <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/benchmarks.rmd" class="external-link"><code>vignettes/web_only/benchmarks.rmd</code></a></small> <div class="d-none name"><code>benchmarks.rmd</code></div> @@ -422,6 +422,22 @@ models fitted to two datasets, i.e. eight fits for each test.</p> <td align="right">1.323</td> <td align="right">1.925</td> </tr> +<tr class="odd"> +<td align="left">Linux</td> +<td align="left">Ryzen 9 7950X</td> +<td align="left">4.4.2</td> +<td align="left">1.2.10</td> +<td align="right">1.407</td> +<td align="right">1.990</td> +</tr> +<tr class="even"> +<td align="left">Linux</td> +<td align="left">Ryzen 9 7950X</td> +<td align="left">4.5.0</td> +<td align="left">1.2.10</td> +<td align="right">1.355</td> +<td align="right">1.976</td> +</tr> </tbody> </table> </div> @@ -703,6 +719,24 @@ for each test.</p> <td align="right">2.153</td> <td align="right">1.139</td> </tr> +<tr class="odd"> +<td align="left">Linux</td> +<td align="left">Ryzen 9 7950X</td> +<td align="left">4.4.2</td> +<td align="left">1.2.10</td> +<td align="right">0.775</td> +<td align="right">2.199</td> +<td align="right">1.161</td> +</tr> +<tr class="even"> +<td align="left">Linux</td> +<td align="left">Ryzen 9 7950X</td> +<td align="left">4.5.0</td> +<td align="left">1.2.10</td> +<td align="right">0.774</td> +<td align="right">2.128</td> +<td align="right">1.095</td> +</tr> </tbody> </table> </div> @@ -1074,6 +1108,30 @@ dataset, i.e. one fit for each test.</p> <td align="right">0.735</td> <td align="right">0.981</td> </tr> +<tr class="odd"> +<td align="left">Linux</td> +<td align="left">Ryzen 9 7950X</td> +<td align="left">4.4.2</td> +<td align="left">1.2.10</td> +<td align="right">0.433</td> +<td align="right">0.541</td> +<td align="right">0.576</td> +<td align="right">1.307</td> +<td align="right">0.744</td> +<td align="right">0.988</td> +</tr> +<tr class="even"> +<td align="left">Linux</td> +<td align="left">Ryzen 9 7950X</td> +<td align="left">4.5.0</td> +<td align="left">1.2.10</td> +<td align="right">0.407</td> +<td align="right">0.519</td> +<td align="right">0.544</td> +<td align="right">1.266</td> +<td align="right">0.738</td> +<td align="right">0.977</td> +</tr> </tbody> </table> </div> diff --git a/docs/articles/web_only/compiled_models.html b/docs/articles/web_only/compiled_models.html index bbf6e897..5790a964 100644 --- a/docs/articles/web_only/compiled_models.html +++ b/docs/articles/web_only/compiled_models.html @@ -20,7 +20,7 @@ <a class="navbar-brand me-2" href="../../index.html">mkin</a> - <small class="nav-text text-default me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">1.2.9</small> + <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">1.2.10</small> <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation"> @@ -83,7 +83,7 @@ <h4 data-toc-skip class="author">Johannes Ranke</h4> - <h4 data-toc-skip class="date">2025-02-13</h4> + <h4 data-toc-skip class="date">2025-05-12</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="d-none name"><code>compiled_models.rmd</code></div> @@ -161,10 +161,10 @@ solution is also implemented, which is included in the tests below.</p> <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 0.105</span></span> -<span><span class="co">## 3 deSolve, compiled 1 1.333 0.140</span></span> -<span><span class="co">## 2 Eigenvalue based 1 1.667 0.175</span></span> -<span><span class="co">## 1 deSolve, not compiled 1 22.486 2.361</span></span></code></pre> +<span><span class="co">## 4 analytical 1 1.000 0.111</span></span> +<span><span class="co">## 3 deSolve, compiled 1 1.270 0.141</span></span> +<span><span class="co">## 2 Eigenvalue based 1 1.658 0.184</span></span> +<span><span class="co">## 1 deSolve, not compiled 1 21.973 2.439</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> @@ -195,12 +195,12 @@ compiled code is available.</p> <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 0.175</span></span> -<span><span class="co">## 1 deSolve, not compiled 1 23.937 4.189</span></span></code></pre> +<span><span class="co">## 2 deSolve, compiled 1 1.000 0.182</span></span> +<span><span class="co">## 1 deSolve, not compiled 1 23.808 4.333</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 1.2.9 on</p> -<pre><code><span><span class="co">## R version 4.4.2 (2024-10-31)</span></span> +<p>This vignette was built with mkin 1.2.10 on</p> +<pre><code><span><span class="co">## R version 4.5.0 (2025-04-11)</span></span> <span><span class="co">## Platform: x86_64-pc-linux-gnu</span></span> <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> diff --git a/docs/articles/web_only/dimethenamid_2018.html b/docs/articles/web_only/dimethenamid_2018.html index 5d39704d..bb2509ad 100644 --- a/docs/articles/web_only/dimethenamid_2018.html +++ b/docs/articles/web_only/dimethenamid_2018.html @@ -20,7 +20,7 @@ <a class="navbar-brand me-2" href="../../index.html">mkin</a> - <small class="nav-text text-default me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">1.2.9</small> + <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">1.2.10</small> <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation"> @@ -84,7 +84,7 @@ Ranke</h4> <h4 data-toc-skip class="date">Last change 1 July 2022, -built on 13 Feb 2025</h4> +built on 12 May 2025</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="d-none name"><code>dimethenamid_2018.rmd</code></div> @@ -170,12 +170,12 @@ 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/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> +<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> <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> <div class="sourceCode" id="cb4"><pre class="downlit sourceCode r"> -<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> +<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> <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 @@ -187,7 +187,7 @@ 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/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> +<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> <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 @@ -199,7 +199,7 @@ degradation model and the error model (see below).</p> 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/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> +<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> <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 @@ -289,7 +289,7 @@ 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/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> +<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> <p><img src="dimethenamid_2018_files/figure-html/plot_parent_nlme-1.png" width="700"></p> </div> <div class="section level4"> @@ -306,17 +306,8 @@ 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></code></pre></div> -<pre><code>Loading required package: npde</code></pre> -<pre><code>Package saemix, version 3.3, March 2024 - please direct bugs, questions and feedback to emmanuelle.comets@inserm.fr</code></pre> -<pre><code> -Attaching package: 'saemix'</code></pre> -<pre><code>The following objects are masked from 'package:npde': - - kurtosis, skewness</code></pre> -<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><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> +<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> <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_moreiter</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">1600</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> @@ -324,7 +315,7 @@ Attaching package: 'saemix'</code></pre> <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> -<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r"> +<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">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></span></code></pre></div> @@ -332,19 +323,19 @@ shown below.</p> <p>Obviously the selected number of iterations is sufficient to reach convergence. This can also be said for the SFO fit using the two-component error model.</p> -<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r"> +<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span><span class="va">f_parent_saemix_sfo_tc</span> <span class="op"><-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span> <span> control <span class="op">=</span> <span class="va">saemix_control</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span></span> <span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_parent_saemix_sfo_tc</span><span class="op">$</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> -<div class="sourceCode" id="cb22"><pre class="downlit sourceCode r"> +<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> <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_dfop_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_dfop_const-1.png" width="700"></p> -<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r"> +<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/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_const</span><span class="op">)</span></span></code></pre></div> <pre><code>Kinetic nonlinear mixed-effects model fit by SAEM Structural model: @@ -380,14 +371,14 @@ this model.</p> 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="cb25"><pre class="downlit sourceCode r"> +<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> <span><span class="va">f_parent_saemix_dfop_tc_moreiter</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_moreiter</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_dfop_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_dfop_tc-1.png" width="700"></p> -<div class="sourceCode" id="cb26"><pre class="downlit sourceCode r"> +<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/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc</span><span class="op">)</span></span></code></pre></div> <pre><code>Kinetic nonlinear mixed-effects model fit by SAEM Structural model: @@ -429,7 +420,7 @@ 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="cb28"><pre class="downlit sourceCode r"> +<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">$</span><span class="va">so</span>,</span> <span> <span class="va">f_parent_saemix_sfo_tc</span><span class="op">$</span><span class="va">so</span>,</span> @@ -437,7 +428,7 @@ comparison function of the saemix package:</p> <span> <span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span>,</span> <span> <span class="va">f_parent_saemix_dfop_tc_moreiter</span><span class="op">$</span><span class="va">so</span><span class="op">)</span></span></code></pre></div> <pre><code>Likelihoods calculated by importance sampling</code></pre> -<div class="sourceCode" id="cb30"><pre class="downlit sourceCode r"> +<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/colnames.html" class="external-link">rownames</a></span><span class="op">(</span><span class="va">AIC_parent_saemix</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> <span> <span class="st">"SFO const"</span>, <span class="st">"SFO tc"</span>, <span class="st">"DFOP const"</span>, <span class="st">"DFOP tc"</span>, <span class="st">"DFOP tc more iterations"</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">AIC_parent_saemix</span><span class="op">)</span></span></code></pre></div> @@ -451,7 +442,7 @@ DFOP tc more iterations 665.85 663.76</code></pre> 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="cb32"><pre class="downlit sourceCode r"> +<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> <span><span class="va">AIC_parent_saemix_methods</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> @@ -475,7 +466,7 @@ 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="cb34"><pre class="downlit sourceCode r"> +<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">$</span><span class="va">so</span> <span class="op"><-</span></span> <span> <span class="fu">saemix</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/llgq.saemix.html" class="external-link">llgq.saemix</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc_defaults</span><span class="op">$</span><span class="va">so</span><span class="op">)</span></span> @@ -495,7 +486,7 @@ using defaults for the fit.</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="cb36"><pre class="downlit sourceCode r"> +<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> <span> <span class="st">"Degradation model"</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">"SFO"</span>, <span class="st">"DFOP"</span>, <span class="st">"DFOP"</span><span class="op">)</span>,</span> @@ -506,7 +497,7 @@ iterations second phase, 15 chains).</p> <span> saemix_is <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="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">f_parent_saemix_sfo_const</span><span class="op">$</span><span class="va">so</span>, <span class="va">f_parent_saemix_sfo_tc</span><span class="op">$</span><span class="va">so</span>,</span> <span> <span class="va">f_parent_saemix_dfop_const</span><span class="op">$</span><span class="va">so</span>, <span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span><span class="op">)</span>, <span class="va">AIC</span>, method <span class="op">=</span> <span class="st">"is"</span><span class="op">)</span></span> <span><span class="op">)</span></span> -<span><span class="fu">kable</span><span class="op">(</span><span class="va">AIC_all</span><span class="op">)</span></span></code></pre></div> +<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">AIC_all</span><span class="op">)</span></span></code></pre></div> <table class="table"> <thead><tr class="header"> <th align="left">Degradation model</th> @@ -569,15 +560,15 @@ satisfactory precision.</p> <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="cb37"><pre class="downlit sourceCode r"> +<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 4.4.2 (2024-10-31) +<pre><code>R version 4.5.0 (2025-04-11) Platform: x86_64-pc-linux-gnu Running under: Debian GNU/Linux 12 (bookworm) Matrix products: default BLAS: /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.11.0 -LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.11.0 +LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.11.0 LAPACK version 3.11.0 locale: [1] LC_CTYPE=de_DE.UTF-8 LC_NUMERIC=C @@ -594,22 +585,21 @@ attached base packages: [1] stats graphics grDevices utils datasets methods base other attached packages: -[1] saemix_3.3 npde_3.5 nlme_3.1-166 mkin_1.2.9 knitr_1.49 +[1] saemix_3.3 npde_3.5 nlme_3.1-168 mkin_1.2.10 knitr_1.49 loaded via a namespace (and not attached): - [1] gtable_0.3.6 jsonlite_1.8.9 dplyr_1.1.4 compiler_4.4.2 - [5] tidyselect_1.2.1 parallel_4.4.2 gridExtra_2.3 jquerylib_0.1.4 - [9] systemfonts_1.1.0 scales_1.3.0 textshaping_0.4.1 yaml_2.3.10 -[13] fastmap_1.2.0 lattice_0.22-6 ggplot2_3.5.1 R6_2.5.1 -[17] generics_0.1.3 lmtest_0.9-40 MASS_7.3-61 htmlwidgets_1.6.4 -[21] tibble_3.2.1 desc_1.4.3 munsell_0.5.1 bslib_0.8.0 -[25] pillar_1.9.0 rlang_1.1.4 utf8_1.2.4 cachem_1.1.0 -[29] xfun_0.49 fs_1.6.5 sass_0.4.9 cli_3.6.3 -[33] pkgdown_2.1.1 magrittr_2.0.3 digest_0.6.37 grid_4.4.2 -[37] mclust_6.1.1 lifecycle_1.0.4 vctrs_0.6.5 evaluate_1.0.1 -[41] glue_1.8.0 codetools_0.2-20 ragg_1.3.3 zoo_1.8-12 -[45] fansi_1.0.6 colorspace_2.1-1 rmarkdown_2.29 pkgconfig_2.0.3 -[49] tools_4.4.2 htmltools_0.5.8.1</code></pre> + [1] gtable_0.3.6 jsonlite_1.9.0 dplyr_1.1.4 compiler_4.5.0 + [5] tidyselect_1.2.1 parallel_4.5.0 gridExtra_2.3 jquerylib_0.1.4 + [9] systemfonts_1.2.1 scales_1.3.0 textshaping_1.0.0 yaml_2.3.10 +[13] fastmap_1.2.0 lattice_0.22-6 ggplot2_3.5.1 R6_2.6.1 +[17] generics_0.1.3 lmtest_0.9-40 MASS_7.3-65 htmlwidgets_1.6.4 +[21] tibble_3.2.1 desc_1.4.3 munsell_0.5.1 bslib_0.9.0 +[25] pillar_1.10.1 rlang_1.1.5 cachem_1.1.0 xfun_0.51 +[29] fs_1.6.5 sass_0.4.9 cli_3.6.4 pkgdown_2.1.1 +[33] magrittr_2.0.3 digest_0.6.37 grid_4.5.0 mclust_6.1.1 +[37] lifecycle_1.0.4 vctrs_0.6.5 evaluate_1.0.3 glue_1.8.0 +[41] codetools_0.2-20 ragg_1.3.3 zoo_1.8-13 colorspace_2.1-1 +[45] rmarkdown_2.29 tools_4.5.0 pkgconfig_2.0.3 htmltools_0.5.8.1</code></pre> </div> <div class="section level2"> <h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a> diff --git a/docs/articles/web_only/mesotrione_parent_2023.html b/docs/articles/web_only/mesotrione_parent_2023.html new file mode 100644 index 00000000..13b62fe3 --- /dev/null +++ b/docs/articles/web_only/mesotrione_parent_2023.html @@ -0,0 +1,3886 @@ +<!DOCTYPE html> +<!-- Generated by pkgdown: do not edit by hand --><html lang="en"> +<head> 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kinetics with residue data on mesotrione</a></li> + <li><a class="dropdown-item" href="../../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a></li> + <li><a class="dropdown-item" href="../../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a></li> + <li><a class="dropdown-item" href="../../articles/web_only/multistart.html">Short demo of the multistart method</a></li> + <li><hr class="dropdown-divider"></li> + <li><h6 class="dropdown-header" data-toc-skip>Performance</h6></li> + <li><a class="dropdown-item" href="../../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a></li> + <li><a class="dropdown-item" href="../../articles/web_only/benchmarks.html">Benchmark timings for mkin</a></li> + <li><a class="dropdown-item" href="../../articles/web_only/saem_benchmarks.html">Benchmark timings for saem.mmkin</a></li> + <li><hr class="dropdown-divider"></li> + <li><h6 class="dropdown-header" data-toc-skip>Miscellaneous</h6></li> + <li><a class="dropdown-item" href="../../articles/twa.html">Calculation of time weighted average concentrations with mkin</a></li> + <li><a class="dropdown-item" href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a></li> + </ul> +</li> +<li class="nav-item"><a class="nav-link" href="../../coverage/coverage.html">Test coverage</a></li> +<li class="nav-item"><a class="nav-link" href="../../news/index.html">News</a></li> + </ul> +<ul class="navbar-nav"> +<li class="nav-item"><form class="form-inline" role="search"> + <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../../search.json"> +</form></li> +<li class="nav-item"><a class="external-link nav-link" href="https://github.com/jranke/mkin/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li> + </ul> +</div> + + + </div> +</nav><div class="container template-article"> + + + + +<div class="row"> + <main id="main" class="col-md-9"><div class="page-header"> + + <h1>Testing covariate modelling in hierarchical parent degradation kinetics with residue data on mesotrione</h1> + <h4 data-toc-skip class="author">Johannes +Ranke</h4> + + <h4 data-toc-skip class="date">Last change 13 May 2025 +(rebuilt 2025-05-14)</h4> + + <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/mesotrione_parent_2023.rmd" class="external-link"><code>vignettes/web_only/mesotrione_parent_2023.rmd</code></a></small> + <div class="d-none name"><code>mesotrione_parent_2023.rmd</code></div> + </div> + + + +<div class="section level2"> +<h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#introduction"></a> +</h2> +<p>The purpose of this document is to test demonstrate how nonlinear +hierarchical models (NLHM) based on the parent degradation models SFO, +FOMC, DFOP and HS can be fitted with the mkin package, also considering +the influence of covariates like soil pH on different degradation +parameters. Because in some other case studies, the SFORB +parameterisation of biexponential decline has shown some advantages over +the DFOP parameterisation, SFORB was included in the list of tested +models as well.</p> +<p>The mkin package is used in version 1.2.10, which is contains the +functions that were used for the evaluations. The <code>saemix</code> +package is used as a backend for fitting the NLHM, but is also loaded to +make the convergence plot function available.</p> +<p>This document is processed with the <code>knitr</code> package, which +also provides the <code>kable</code> function that is used to improve +the display of tabular data in R markdown documents. For parallel +processing, the <code>parallel</code> package is used.</p> +<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://pkgdown.jrwb.de/mkin/">mkin</a></span><span class="op">)</span></span> +<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://yihui.org/knitr/" class="external-link">knitr</a></span><span class="op">)</span></span> +<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">saemix</span><span class="op">)</span></span> +<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">parallel</span><span class="op">)</span></span> +<span><span class="va">n_cores</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/detectCores.html" class="external-link">detectCores</a></span><span class="op">(</span><span class="op">)</span></span> +<span><span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/Sys.info.html" class="external-link">Sys.info</a></span><span class="op">(</span><span class="op">)</span><span class="op">[</span><span class="st">"sysname"</span><span class="op">]</span> <span class="op">==</span> <span class="st">"Windows"</span><span class="op">)</span> <span class="op">{</span></span> +<span> <span class="va">cl</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makePSOCKcluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> +<span><span class="op">}</span> <span class="kw">else</span> <span class="op">{</span></span> +<span> <span class="va">cl</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makeForkCluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> +<span><span class="op">}</span></span></code></pre></div> +<div class="section level3"> +<h3 id="test-data">Test data<a class="anchor" aria-label="anchor" href="#test-data"></a> +</h3> +<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">data_file</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.file.html" class="external-link">system.file</a></span><span class="op">(</span></span> +<span> <span class="st">"testdata"</span>, <span class="st">"mesotrione_soil_efsa_2016.xlsx"</span>, package <span class="op">=</span> <span class="st">"mkin"</span><span class="op">)</span></span> +<span><span class="va">meso_ds</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/read_spreadsheet.html">read_spreadsheet</a></span><span class="op">(</span><span class="va">data_file</span>, parent_only <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<p>The following tables show the covariate data and the 18 datasets that +were read in from the spreadsheet file.</p> +<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">pH</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/attr.html" class="external-link">attr</a></span><span class="op">(</span><span class="va">meso_ds</span>, <span class="st">"covariates"</span><span class="op">)</span></span> +<span><span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="va">pH</span>, caption <span class="op">=</span> <span class="st">"Covariate data"</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<caption>Covariate data</caption> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">pH</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">Richmond</td> +<td align="right">6.2</td> +</tr> +<tr class="even"> +<td align="left">Richmond 2</td> +<td align="right">6.2</td> +</tr> +<tr class="odd"> +<td align="left">ERTC</td> +<td align="right">6.4</td> +</tr> +<tr class="even"> +<td align="left">Toulouse</td> +<td align="right">7.7</td> +</tr> +<tr class="odd"> +<td align="left">Picket Piece</td> +<td align="right">7.1</td> +</tr> +<tr class="even"> +<td align="left">721</td> +<td align="right">5.6</td> +</tr> +<tr class="odd"> +<td align="left">722</td> +<td align="right">5.7</td> +</tr> +<tr class="even"> +<td align="left">723</td> +<td align="right">5.4</td> +</tr> +<tr class="odd"> +<td align="left">724</td> +<td align="right">4.8</td> +</tr> +<tr class="even"> +<td align="left">725</td> +<td align="right">5.8</td> +</tr> +<tr class="odd"> +<td align="left">727</td> +<td align="right">5.1</td> +</tr> +<tr class="even"> +<td align="left">728</td> +<td align="right">5.9</td> +</tr> +<tr class="odd"> +<td align="left">729</td> +<td align="right">5.6</td> +</tr> +<tr class="even"> +<td align="left">730</td> +<td align="right">5.3</td> +</tr> +<tr class="odd"> +<td align="left">731</td> +<td align="right">6.1</td> +</tr> +<tr class="even"> +<td align="left">732</td> +<td align="right">5.0</td> +</tr> +<tr class="odd"> +<td align="left">741</td> +<td align="right">5.7</td> +</tr> +<tr class="even"> +<td align="left">742</td> +<td align="right">7.2</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="kw">for</span> <span class="op">(</span><span class="va">ds_name</span> <span class="kw">in</span> <span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">meso_ds</span><span class="op">)</span><span class="op">)</span> <span class="op">{</span></span> +<span> <span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span></span> +<span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="fu"><a href="../../reference/mkin_long_to_wide.html">mkin_long_to_wide</a></span><span class="op">(</span><span class="va">meso_ds</span><span class="op">[[</span><span class="va">ds_name</span><span class="op">]</span><span class="op">]</span><span class="op">)</span>,</span> +<span> caption <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste</a></span><span class="op">(</span><span class="st">"Dataset"</span>, <span class="va">ds_name</span><span class="op">)</span>,</span> +<span> booktabs <span class="op">=</span> <span class="cn">TRUE</span>, row.names <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="op">}</span></span></code></pre></div> +<table class="table"> +<caption>Dataset Richmond</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">91.00</td> +</tr> +<tr class="even"> +<td align="right">1.179050</td> +<td align="right">86.70</td> +</tr> +<tr class="odd"> +<td align="right">3.537149</td> +<td align="right">73.60</td> +</tr> +<tr class="even"> +<td align="right">7.074299</td> +<td align="right">61.50</td> +</tr> +<tr class="odd"> +<td align="right">10.611448</td> +<td align="right">55.70</td> +</tr> +<tr class="even"> +<td align="right">15.327647</td> +<td align="right">47.70</td> +</tr> +<tr class="odd"> +<td align="right">17.685747</td> +<td align="right">39.50</td> +</tr> +<tr class="even"> +<td align="right">24.760046</td> +<td align="right">29.80</td> +</tr> +<tr class="odd"> +<td align="right">35.371494</td> +<td align="right">19.60</td> +</tr> +<tr class="even"> +<td align="right">68.384889</td> +<td align="right">5.67</td> +</tr> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">97.90</td> +</tr> +<tr class="even"> +<td align="right">1.179050</td> +<td align="right">96.40</td> +</tr> +<tr class="odd"> +<td align="right">3.537149</td> +<td align="right">89.10</td> +</tr> +<tr class="even"> +<td align="right">7.074299</td> +<td align="right">74.40</td> +</tr> +<tr class="odd"> +<td align="right">10.611448</td> +<td align="right">57.40</td> +</tr> +<tr class="even"> +<td align="right">15.327647</td> +<td align="right">46.30</td> +</tr> +<tr class="odd"> +<td align="right">18.864797</td> +<td align="right">35.50</td> +</tr> +<tr class="even"> +<td align="right">27.118146</td> +<td align="right">27.20</td> +</tr> +<tr class="odd"> +<td align="right">35.371494</td> +<td align="right">19.10</td> +</tr> +<tr class="even"> +<td align="right">74.280138</td> +<td align="right">6.50</td> +</tr> +<tr class="odd"> +<td align="right">108.472582</td> +<td align="right">3.40</td> +</tr> +<tr class="even"> +<td align="right">142.665027</td> +<td align="right">2.20</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset Richmond 2</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">96.0</td> +</tr> +<tr class="even"> +<td align="right">2.422004</td> +<td align="right">82.4</td> +</tr> +<tr class="odd"> +<td align="right">5.651343</td> +<td align="right">71.2</td> +</tr> +<tr class="even"> +<td align="right">8.073348</td> +<td align="right">53.1</td> +</tr> +<tr class="odd"> +<td align="right">11.302687</td> +<td align="right">48.5</td> +</tr> +<tr class="even"> +<td align="right">16.954030</td> +<td align="right">33.4</td> +</tr> +<tr class="odd"> +<td align="right">22.605373</td> +<td align="right">24.2</td> +</tr> +<tr class="even"> +<td align="right">45.210746</td> +<td align="right">11.9</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset ERTC</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">99.9</td> +</tr> +<tr class="even"> +<td align="right">2.755193</td> +<td align="right">80.0</td> +</tr> +<tr class="odd"> +<td align="right">6.428782</td> +<td align="right">42.1</td> +</tr> +<tr class="even"> +<td align="right">9.183975</td> +<td align="right">50.1</td> +</tr> +<tr class="odd"> +<td align="right">12.857565</td> +<td align="right">28.4</td> +</tr> +<tr class="even"> +<td align="right">19.286347</td> +<td align="right">39.8</td> +</tr> +<tr class="odd"> +<td align="right">25.715130</td> +<td align="right">29.9</td> +</tr> +<tr class="even"> +<td align="right">51.430259</td> +<td align="right">2.5</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset Toulouse</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">96.8</td> +</tr> +<tr class="even"> +<td align="right">2.897983</td> +<td align="right">63.3</td> +</tr> +<tr class="odd"> +<td align="right">6.761960</td> +<td align="right">22.3</td> +</tr> +<tr class="even"> +<td align="right">9.659942</td> +<td align="right">16.6</td> +</tr> +<tr class="odd"> +<td align="right">13.523919</td> +<td align="right">16.1</td> +</tr> +<tr class="even"> +<td align="right">20.285879</td> +<td align="right">17.2</td> +</tr> +<tr class="odd"> +<td align="right">27.047838</td> +<td align="right">1.8</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset Picket Piece</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">102.0</td> +</tr> +<tr class="even"> +<td align="right">2.841195</td> +<td align="right">73.7</td> +</tr> +<tr class="odd"> +<td align="right">6.629454</td> +<td align="right">35.5</td> +</tr> +<tr class="even"> +<td align="right">9.470649</td> +<td align="right">31.8</td> +</tr> +<tr class="odd"> +<td align="right">13.258909</td> +<td align="right">18.0</td> +</tr> +<tr class="even"> +<td align="right">19.888364</td> +<td align="right">3.7</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 721</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">86.4</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">61.4</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">49.8</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">41.0</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">35.1</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 722</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">90.3</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">52.1</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">37.4</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">21.2</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">14.3</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 723</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">89.3</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">70.8</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">51.1</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">42.7</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">26.7</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 724</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">89.4</td> +</tr> +<tr class="even"> +<td align="right">9.008208</td> +<td align="right">65.2</td> +</tr> +<tr class="odd"> +<td align="right">18.016415</td> +<td align="right">55.8</td> +</tr> +<tr class="even"> +<td align="right">27.024623</td> +<td align="right">46.0</td> +</tr> +<tr class="odd"> +<td align="right">36.032831</td> +<td align="right">41.7</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 725</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">89.0</td> +</tr> +<tr class="even"> +<td align="right">10.99058</td> +<td align="right">35.4</td> +</tr> +<tr class="odd"> +<td align="right">21.98116</td> +<td align="right">18.6</td> +</tr> +<tr class="even"> +<td align="right">32.97174</td> +<td align="right">11.6</td> +</tr> +<tr class="odd"> +<td align="right">43.96232</td> +<td align="right">7.6</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 727</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">91.3</td> +</tr> +<tr class="even"> +<td align="right">10.96104</td> +<td align="right">63.2</td> +</tr> +<tr class="odd"> +<td align="right">21.92209</td> +<td align="right">51.1</td> +</tr> +<tr class="even"> +<td align="right">32.88313</td> +<td align="right">42.0</td> +</tr> +<tr class="odd"> +<td align="right">43.84417</td> +<td align="right">40.8</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 728</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">91.8</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">43.6</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">22.0</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">15.9</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">8.8</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 729</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">91.6</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">60.5</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">43.5</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">28.4</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">20.5</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 730</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">92.7</td> +</tr> +<tr class="even"> +<td align="right">11.07446</td> +<td align="right">58.9</td> +</tr> +<tr class="odd"> +<td align="right">22.14893</td> +<td align="right">44.0</td> +</tr> +<tr class="even"> +<td align="right">33.22339</td> +<td align="right">46.0</td> +</tr> +<tr class="odd"> +<td align="right">44.29785</td> +<td align="right">29.3</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 731</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">92.1</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">64.4</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">45.3</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">33.6</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">23.5</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 732</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">90.3</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">58.2</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">40.1</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">33.1</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">25.8</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 741</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">90.3</td> +</tr> +<tr class="even"> +<td align="right">10.84712</td> +<td align="right">68.7</td> +</tr> +<tr class="odd"> +<td align="right">21.69424</td> +<td align="right">58.0</td> +</tr> +<tr class="even"> +<td align="right">32.54136</td> +<td align="right">52.2</td> +</tr> +<tr class="odd"> +<td align="right">43.38848</td> +<td align="right">48.0</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 742</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">92.0</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">60.9</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">36.2</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">18.3</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">8.7</td> +</tr> +</tbody> +</table> +</div> +</div> +<div class="section level2"> +<h2 id="separate-evaluations">Separate evaluations<a class="anchor" aria-label="anchor" href="#separate-evaluations"></a> +</h2> +<p>In order to obtain suitable starting parameters for the NLHM fits, +separate fits of the five models to the data for each soil are generated +using the <code>mmkin</code> function from the mkin package. In a first +step, constant variance is assumed. Convergence is checked with the +<code>status</code> function.</p> +<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">deg_mods</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>, <span class="st">"SFORB"</span>, <span class="st">"HS"</span><span class="op">)</span></span> +<span><span class="va">f_sep_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span></span> +<span> <span class="va">deg_mods</span>,</span> +<span> <span class="va">meso_ds</span>,</span> +<span> error_model <span class="op">=</span> <span class="st">"const"</span>,</span> +<span> cluster <span class="op">=</span> <span class="va">cl</span>,</span> +<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span>, <span class="fl">1</span><span class="op">:</span><span class="fl">5</span><span class="op">]</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">Richmond</th> +<th align="left">Richmond 2</th> +<th align="left">ERTC</th> +<th align="left">Toulouse</th> +<th align="left">Picket Piece</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span>, <span class="fl">6</span><span class="op">:</span><span class="fl">18</span><span class="op">]</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<colgroup> +<col width="10%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +</colgroup> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">721</th> +<th align="left">722</th> +<th align="left">723</th> +<th align="left">724</th> +<th align="left">725</th> +<th align="left">727</th> +<th align="left">728</th> +<th align="left">729</th> +<th align="left">730</th> +<th align="left">731</th> +<th align="left">732</th> +<th align="left">741</th> +<th align="left">742</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<p>In the tables above, OK indicates convergence and C indicates failure +to converge. Most separate fits with constant variance converged, with +the exception of two FOMC fits, one SFORB fit and one HS fit.</p> +<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">f_sep_tc</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_sep_const</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_tc</span><span class="op">[</span>, <span class="fl">1</span><span class="op">:</span><span class="fl">5</span><span class="op">]</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">Richmond</th> +<th align="left">Richmond 2</th> +<th align="left">ERTC</th> +<th align="left">Toulouse</th> +<th align="left">Picket Piece</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_tc</span><span class="op">[</span>, <span class="fl">6</span><span class="op">:</span><span class="fl">18</span><span class="op">]</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<colgroup> +<col width="10%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +</colgroup> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">721</th> +<th align="left">722</th> +<th align="left">723</th> +<th align="left">724</th> +<th align="left">725</th> +<th align="left">727</th> +<th align="left">728</th> +<th align="left">729</th> +<th align="left">730</th> +<th align="left">731</th> +<th align="left">732</th> +<th align="left">741</th> +<th align="left">742</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<p>With the two-component error model, the set of fits that did not +converge is larger, with convergence problems appearing for a number of +non-SFO fits.</p> +</div> +<div class="section level2"> +<h2 id="hierarchical-models-without-covariate">Hierarchical models without covariate<a class="anchor" aria-label="anchor" href="#hierarchical-models-without-covariate"></a> +</h2> +<p>The following code fits hierarchical kinetic models for the ten +combinations of the five different degradation models with the two +different error models in parallel.</p> +<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">f_saem_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mhmkin.html">mhmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">f_sep_const</span>, <span class="va">f_sep_tc</span><span class="op">)</span>, cluster <span class="op">=</span> <span class="va">cl</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<p>All fits terminate without errors (status OK).</p> +<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">npar</th> +<th align="right">AIC</th> +<th align="right">BIC</th> +<th align="right">Lik</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO const</td> +<td align="right">5</td> +<td align="right">800.0</td> +<td align="right">804.5</td> +<td align="right">-395.0</td> +</tr> +<tr class="even"> +<td align="left">SFO tc</td> +<td align="right">6</td> +<td align="right">801.9</td> +<td align="right">807.2</td> +<td align="right">-394.9</td> +</tr> +<tr class="odd"> +<td align="left">FOMC const</td> +<td align="right">7</td> +<td align="right">787.4</td> +<td align="right">793.6</td> +<td align="right">-386.7</td> +</tr> +<tr class="even"> +<td align="left">FOMC tc</td> +<td align="right">8</td> +<td align="right">788.9</td> +<td align="right">796.1</td> +<td align="right">-386.5</td> +</tr> +<tr class="odd"> +<td align="left">DFOP const</td> +<td align="right">9</td> +<td align="right">787.6</td> +<td align="right">795.6</td> +<td align="right">-384.8</td> +</tr> +<tr class="even"> +<td align="left">SFORB const</td> +<td align="right">9</td> +<td align="right">787.4</td> +<td align="right">795.4</td> +<td align="right">-384.7</td> +</tr> +<tr class="odd"> +<td align="left">HS const</td> +<td align="right">9</td> +<td align="right">781.9</td> +<td align="right">789.9</td> +<td align="right">-382.0</td> +</tr> +<tr class="even"> +<td align="left">DFOP tc</td> +<td align="right">10</td> +<td align="right">787.4</td> +<td align="right">796.3</td> +<td align="right">-383.7</td> +</tr> +<tr class="odd"> +<td align="left">SFORB tc</td> +<td align="right">10</td> +<td align="right">795.8</td> +<td align="right">804.7</td> +<td align="right">-387.9</td> +</tr> +<tr class="even"> +<td align="left">HS tc</td> +<td align="right">10</td> +<td align="right">783.7</td> +<td align="right">792.7</td> +<td align="right">-381.9</td> +</tr> +</tbody> +</table> +<p>The model comparisons show that the fits with constant variance are +consistently preferable to the corresponding fits with two-component +error for these data. This is confirmed by the fact that the parameter +<code>b.1</code> (the relative standard deviation in the fits obtained +with the saemix package), is ill-defined in all fits.</p> +<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<colgroup> +<col width="6%"> +<col width="44%"> +<col width="49%"> +</colgroup> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">sd(meso_0)</td> +<td align="left">sd(meso_0), b.1</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">sd(meso_0), sd(log_beta)</td> +<td align="left">sd(meso_0), sd(log_beta), b.1</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">sd(meso_0), sd(log_k1)</td> +<td align="left">sd(meso_0), sd(g_qlogis), b.1</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">sd(meso_free_0), sd(log_k_meso_free_bound)</td> +<td align="left">sd(meso_free_0), sd(log_k_meso_free_bound), b.1</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">sd(meso_0)</td> +<td align="left">sd(meso_0), b.1</td> +</tr> +</tbody> +</table> +<p>For obtaining fits with only well-defined random effects, we update +the set of fits, excluding random effects that were ill-defined +according to the <code>illparms</code> function.</p> +<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">f_saem_2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_saem_1</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<p>The updated fits terminate without errors.</p> +<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left"></td> +<td align="left">b.1</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left"></td> +<td align="left">b.1</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left"></td> +<td align="left">b.1</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left"></td> +<td align="left">b.1</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left"></td> +<td align="left">b.1</td> +</tr> +</tbody> +</table> +<p>No ill-defined errors remain in the fits with constant variance.</p> +</div> +<div class="section level2"> +<h2 id="hierarchical-models-with-covariate">Hierarchical models with covariate<a class="anchor" aria-label="anchor" href="#hierarchical-models-with-covariate"></a> +</h2> +<p>In the following sections, hierarchical fits including a model for +the influence of pH on selected degradation parameters are shown for all +parent models. Constant variance is selected as the error model based on +the fits without covariate effects. Random effects that were ill-defined +in the fits without pH influence are excluded. A potential influence of +the soil pH is only included for parameters with a well-defined random +effect, because experience has shown that only for such parameters a +significant pH effect could be found.</p> +<div class="section level3"> +<h3 id="sfo">SFO<a class="anchor" aria-label="anchor" href="#sfo"></a> +</h3> +<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">sfo_pH</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="st">"meso_0"</span>, covariates <span class="op">=</span> <span class="va">pH</span>,</span> +<span> covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_k_meso</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">sfo_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_0</td> +<td align="right">91.35</td> +<td align="right">89.27</td> +<td align="right">93.43</td> +</tr> +<tr class="even"> +<td align="left">log_k_meso</td> +<td align="right">-6.66</td> +<td align="right">-7.97</td> +<td align="right">-5.35</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_k_meso)</td> +<td align="right">0.59</td> +<td align="right">0.37</td> +<td align="right">0.81</td> +</tr> +<tr class="even"> +<td align="left">a.1</td> +<td align="right">5.48</td> +<td align="right">4.71</td> +<td align="right">6.24</td> +</tr> +<tr class="odd"> +<td align="left">SD.log_k_meso</td> +<td align="right">0.35</td> +<td align="right">0.23</td> +<td align="right">0.47</td> +</tr> +</tbody> +</table> +<p>The parameter showing the pH influence in the above table is +<code>beta_pH(log_k_meso)</code>. Its confidence interval does not +include zero, indicating that the influence of soil pH on the log of the +degradation rate constant is significantly greater than zero.</p> +<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"SFO"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span>, <span class="va">sfo_pH</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets + + npar AIC BIC Lik Chisq Df Pr(>Chisq) +f_saem_2[["SFO", "const"]] 4 797.56 801.12 -394.78 +sfo_pH 5 783.09 787.54 -386.54 16.473 1 4.934e-05 *** +--- +Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre> +<p>The comparison with the SFO fit without covariate effect confirms +that considering the soil pH improves the model, both by comparison of +AIC and BIC and by the likelihood ratio test.</p> +<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">sfo_pH</span><span class="op">)</span></span></code></pre></div> +<p><img src="mesotrione_parent_2023_files/figure-html/unnamed-chunk-8-1.png" width="700" style="display: block; margin: auto;"></p> +<p>Endpoints for a model with covariates are by default calculated for +the median of the covariate values. This quantile can be adapted, or a +specific covariate value can be given as shown below.</p> +<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">sfo_pH</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +50% 5.75 + +$distimes + DT50 DT90 +meso 18.52069 61.52441</code></pre> +<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">sfo_pH</span>, covariate_quantile <span class="op">=</span> <span class="fl">0.9</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +90% 7.13 + +$distimes + DT50 DT90 +meso 8.237019 27.36278</code></pre> +<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">sfo_pH</span>, covariates <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>pH <span class="op">=</span> <span class="fl">7.0</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +User 7 + +$distimes + DT50 DT90 +meso 8.89035 29.5331</code></pre> +</div> +<div class="section level3"> +<h3 id="fomc">FOMC<a class="anchor" aria-label="anchor" href="#fomc"></a> +</h3> +<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">fomc_pH</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"FOMC"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="st">"meso_0"</span>, covariates <span class="op">=</span> <span class="va">pH</span>,</span> +<span> covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_alpha</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb28"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">fomc_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_0</td> +<td align="right">92.84</td> +<td align="right">90.75</td> +<td align="right">94.93</td> +</tr> +<tr class="even"> +<td align="left">log_alpha</td> +<td align="right">-2.21</td> +<td align="right">-3.49</td> +<td align="right">-0.92</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_alpha)</td> +<td align="right">0.58</td> +<td align="right">0.37</td> +<td align="right">0.79</td> +</tr> +<tr class="even"> +<td align="left">log_beta</td> +<td align="right">4.21</td> +<td align="right">3.44</td> +<td align="right">4.99</td> +</tr> +<tr class="odd"> +<td align="left">a.1</td> +<td align="right">5.03</td> +<td align="right">4.32</td> +<td align="right">5.73</td> +</tr> +<tr class="even"> +<td align="left">SD.log_alpha</td> +<td align="right">0.00</td> +<td align="right">-23.77</td> +<td align="right">23.78</td> +</tr> +<tr class="odd"> +<td align="left">SD.log_beta</td> +<td align="right">0.37</td> +<td align="right">0.01</td> +<td align="right">0.74</td> +</tr> +</tbody> +</table> +<p>As in the case of SFO, the confidence interval of the slope parameter +(here <code>beta_pH(log_alpha)</code>) quantifying the influence of soil +pH does not include zero, and the model comparison clearly indicates +that the model with covariate influence is preferable. However, the +random effect for <code>alpha</code> is not well-defined any more after +inclusion of the covariate effect (the confidence interval of +<code>SD.log_alpha</code> includes zero).</p> +<div class="sourceCode" id="cb29"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">fomc_pH</span><span class="op">)</span></span></code></pre></div> +<pre><code>[1] "sd(log_alpha)"</code></pre> +<p>Therefore, the model is updated without this random effect, and no +ill-defined parameters remain.</p> +<div class="sourceCode" id="cb31"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">fomc_pH_2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">fomc_pH</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_0"</span>, <span class="st">"log_alpha"</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">fomc_pH_2</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb32"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"FOMC"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span>, <span class="va">fomc_pH</span>, <span class="va">fomc_pH_2</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets + + npar AIC BIC Lik Chisq Df Pr(>Chisq) +f_saem_2[["FOMC", "const"]] 5 783.25 787.71 -386.63 +fomc_pH_2 6 767.49 772.83 -377.75 17.762 1 2.503e-05 *** +fomc_pH 7 770.07 776.30 -378.04 0.000 1 1 +--- +Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre> +<p>Model comparison indicates that including pH dependence significantly +improves the fit, and that the reduced model with covariate influence +results in the most preferable FOMC fit.</p> +<div class="sourceCode" id="cb34"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">fomc_pH_2</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_0</td> +<td align="right">93.05</td> +<td align="right">90.98</td> +<td align="right">95.13</td> +</tr> +<tr class="even"> +<td align="left">log_alpha</td> +<td align="right">-2.91</td> +<td align="right">-4.18</td> +<td align="right">-1.63</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_alpha)</td> +<td align="right">0.66</td> +<td align="right">0.44</td> +<td align="right">0.87</td> +</tr> +<tr class="even"> +<td align="left">log_beta</td> +<td align="right">3.95</td> +<td align="right">3.29</td> +<td align="right">4.62</td> +</tr> +<tr class="odd"> +<td align="left">a.1</td> +<td align="right">4.98</td> +<td align="right">4.28</td> +<td align="right">5.68</td> +</tr> +<tr class="even"> +<td align="left">SD.log_beta</td> +<td align="right">0.40</td> +<td align="right">0.26</td> +<td align="right">0.54</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb35"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">fomc_pH_2</span><span class="op">)</span></span></code></pre></div> +<p><img src="mesotrione_parent_2023_files/figure-html/unnamed-chunk-14-1.png" width="700" style="display: block; margin: auto;"></p> +<div class="sourceCode" id="cb36"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">fomc_pH_2</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +50% 5.75 + +$distimes + DT50 DT90 DT50back +meso 17.30248 82.91343 24.95943</code></pre> +<div class="sourceCode" id="cb38"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">fomc_pH_2</span>, covariates <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>pH <span class="op">=</span> <span class="fl">7</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +User 7 + +$distimes + DT50 DT90 DT50back +meso 6.986239 27.02927 8.136621</code></pre> +</div> +<div class="section level3"> +<h3 id="dfop">DFOP<a class="anchor" aria-label="anchor" href="#dfop"></a> +</h3> +<p>In the DFOP fits without covariate effects, random effects for two +degradation parameters (<code>k2</code> and <code>g</code>) were +identifiable.</p> +<div class="sourceCode" id="cb40"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_0</td> +<td align="right">93.61</td> +<td align="right">91.58</td> +<td align="right">95.63</td> +</tr> +<tr class="even"> +<td align="left">log_k1</td> +<td align="right">-1.53</td> +<td align="right">-2.27</td> +<td align="right">-0.79</td> +</tr> +<tr class="odd"> +<td align="left">log_k2</td> +<td align="right">-3.42</td> +<td align="right">-3.73</td> +<td align="right">-3.11</td> +</tr> +<tr class="even"> +<td align="left">g_qlogis</td> +<td align="right">-1.67</td> +<td align="right">-2.57</td> +<td align="right">-0.77</td> +</tr> +<tr class="odd"> +<td align="left">a.1</td> +<td align="right">4.74</td> +<td align="right">4.02</td> +<td align="right">5.45</td> +</tr> +<tr class="even"> +<td align="left">SD.log_k2</td> +<td align="right">0.60</td> +<td align="right">0.38</td> +<td align="right">0.81</td> +</tr> +<tr class="odd"> +<td align="left">SD.g_qlogis</td> +<td align="right">0.94</td> +<td align="right">0.33</td> +<td align="right">1.54</td> +</tr> +</tbody> +</table> +<p>A fit with pH dependent degradation parameters was obtained by +excluding the same random effects as in the refined DFOP fit without +covariate influence, and including covariate models for the two +identifiable parameters <code>k2</code> and <code>g</code>.</p> +<div class="sourceCode" id="cb41"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">dfop_pH</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_0"</span>, <span class="st">"log_k1"</span><span class="op">)</span>,</span> +<span> covariates <span class="op">=</span> <span class="va">pH</span>,</span> +<span> covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_k2</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">g_qlogis</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<p>The corresponding parameters for the influence of soil pH are +<code>beta_pH(log_k2)</code> for the influence of soil pH on +<code>k2</code>, and <code>beta_pH(g_qlogis)</code> for its influence on +<code>g</code>.</p> +<div class="sourceCode" id="cb42"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">dfop_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_0</td> +<td align="right">92.84</td> +<td align="right">90.85</td> +<td align="right">94.84</td> +</tr> +<tr class="even"> +<td align="left">log_k1</td> +<td align="right">-2.82</td> +<td align="right">-3.09</td> +<td align="right">-2.54</td> +</tr> +<tr class="odd"> +<td align="left">log_k2</td> +<td align="right">-11.48</td> +<td align="right">-15.32</td> +<td align="right">-7.64</td> +</tr> +<tr class="even"> +<td align="left">beta_pH(log_k2)</td> +<td align="right">1.31</td> +<td align="right">0.69</td> +<td align="right">1.92</td> +</tr> +<tr class="odd"> +<td align="left">g_qlogis</td> +<td align="right">3.13</td> +<td align="right">0.47</td> +<td align="right">5.80</td> +</tr> +<tr class="even"> +<td align="left">beta_pH(g_qlogis)</td> +<td align="right">-0.57</td> +<td align="right">-1.04</td> +<td align="right">-0.09</td> +</tr> +<tr class="odd"> +<td align="left">a.1</td> +<td align="right">4.96</td> +<td align="right">4.26</td> +<td align="right">5.65</td> +</tr> +<tr class="even"> +<td align="left">SD.log_k2</td> +<td align="right">0.76</td> +<td align="right">0.47</td> +<td align="right">1.05</td> +</tr> +<tr class="odd"> +<td align="left">SD.g_qlogis</td> +<td align="right">0.01</td> +<td align="right">-9.96</td> +<td align="right">9.97</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb43"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">dfop_pH</span><span class="op">)</span></span></code></pre></div> +<pre><code>[1] "sd(g_qlogis)"</code></pre> +<p>Confidence intervals for neither of them include zero, indicating a +significant difference from zero. However, the random effect for +<code>g</code> is now ill-defined. The fit is updated without this +ill-defined random effect.</p> +<div class="sourceCode" id="cb45"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">dfop_pH_2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">dfop_pH</span>,</span> +<span> no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_0"</span>, <span class="st">"log_k1"</span>, <span class="st">"g_qlogis"</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">dfop_pH_2</span><span class="op">)</span></span></code></pre></div> +<pre><code>[1] "beta_pH(g_qlogis)"</code></pre> +<p>Now, the slope parameter for the pH effect on <code>g</code> is +ill-defined. Therefore, another attempt is made without the +corresponding covariate model.</p> +<div class="sourceCode" id="cb47"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">dfop_pH_3</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_0"</span>, <span class="st">"log_k1"</span><span class="op">)</span>,</span> +<span> covariates <span class="op">=</span> <span class="va">pH</span>,</span> +<span> covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_k2</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">dfop_pH_3</span><span class="op">)</span></span></code></pre></div> +<pre><code>[1] "sd(g_qlogis)"</code></pre> +<p>As the random effect for <code>g</code> is again ill-defined, the fit +is repeated without it.</p> +<div class="sourceCode" id="cb49"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">dfop_pH_4</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">dfop_pH_3</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_0"</span>, <span class="st">"log_k1"</span>, <span class="st">"g_qlogis"</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">dfop_pH_4</span><span class="op">)</span></span></code></pre></div> +<p>While no ill-defined parameters remain, model comparison suggests +that the previous model <code>dfop_pH_2</code> with two pH dependent +parameters is preferable, based on information criteria as well as based +on the likelihood ratio test.</p> +<div class="sourceCode" id="cb50"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span>, <span class="va">dfop_pH</span>, <span class="va">dfop_pH_2</span>, <span class="va">dfop_pH_3</span>, <span class="va">dfop_pH_4</span><span class="op">)</span></span></code></pre></div> +<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets + + npar AIC BIC Lik +f_saem_2[["DFOP", "const"]] 7 782.94 789.18 -384.47 +dfop_pH_4 7 767.35 773.58 -376.68 +dfop_pH_2 8 765.14 772.26 -374.57 +dfop_pH_3 8 769.00 776.12 -376.50 +dfop_pH 9 769.10 777.11 -375.55</code></pre> +<div class="sourceCode" id="cb52"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">dfop_pH_2</span>, <span class="va">dfop_pH_4</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets + + npar AIC BIC Lik Chisq Df Pr(>Chisq) +dfop_pH_4 7 767.35 773.58 -376.68 +dfop_pH_2 8 765.14 772.26 -374.57 4.2153 1 0.04006 * +--- +Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre> +<p>When focussing on parameter identifiability using the test if the +confidence interval includes zero, <code>dfop_pH_4</code> would still be +the preferred model. However, it should be kept in mind that parameter +confidence intervals are constructed using a simple linearisation of the +likelihood. As the confidence interval of the random effect for +<code>g</code> only marginally includes zero, it is suggested that this +is acceptable, and that <code>dfop_pH_2</code> can be considered the +most preferable model.</p> +<div class="sourceCode" id="cb54"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">dfop_pH_2</span><span class="op">)</span></span></code></pre></div> +<p><img src="mesotrione_parent_2023_files/figure-html/unnamed-chunk-19-1.png" width="700" style="display: block; margin: auto;"></p> +<div class="sourceCode" id="cb55"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">dfop_pH_2</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +50% 5.75 + +$distimes + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 18.36876 73.51841 22.13125 4.191901 23.98672</code></pre> +<div class="sourceCode" id="cb57"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">dfop_pH_2</span>, covariates <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>pH <span class="op">=</span> <span class="fl">7</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +User 7 + +$distimes + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 8.346428 28.34437 8.532507 4.191901 8.753618</code></pre> +</div> +<div class="section level3"> +<h3 id="sforb">SFORB<a class="anchor" aria-label="anchor" href="#sforb"></a> +</h3> +<div class="sourceCode" id="cb59"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">sforb_pH</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"SFORB"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_free_0"</span>, <span class="st">"log_k_meso_free_bound"</span><span class="op">)</span>,</span> +<span> covariates <span class="op">=</span> <span class="va">pH</span>,</span> +<span> covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_k_meso_free</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">log_k_meso_bound_free</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb60"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">sforb_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_free_0</td> +<td align="right">93.42</td> +<td align="right">91.32</td> +<td align="right">95.52</td> +</tr> +<tr class="even"> +<td align="left">log_k_meso_free</td> +<td align="right">-5.37</td> +<td align="right">-6.94</td> +<td align="right">-3.81</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_k_meso_free)</td> +<td align="right">0.42</td> +<td align="right">0.18</td> +<td align="right">0.67</td> +</tr> +<tr class="even"> +<td align="left">log_k_meso_free_bound</td> +<td align="right">-3.49</td> +<td align="right">-4.92</td> +<td align="right">-2.05</td> +</tr> +<tr class="odd"> +<td align="left">log_k_meso_bound_free</td> +<td align="right">-9.98</td> +<td align="right">-19.22</td> +<td align="right">-0.74</td> +</tr> +<tr class="even"> +<td align="left">beta_pH(log_k_meso_bound_free)</td> +<td align="right">1.23</td> +<td align="right">-0.21</td> +<td align="right">2.67</td> +</tr> +<tr class="odd"> +<td align="left">a.1</td> +<td align="right">4.90</td> +<td align="right">4.18</td> +<td align="right">5.63</td> +</tr> +<tr class="even"> +<td align="left">SD.log_k_meso_free</td> +<td align="right">0.35</td> +<td align="right">0.23</td> +<td align="right">0.47</td> +</tr> +<tr class="odd"> +<td align="left">SD.log_k_meso_bound_free</td> +<td align="right">0.13</td> +<td align="right">-1.95</td> +<td align="right">2.20</td> +</tr> +</tbody> +</table> +<p>The confidence interval of +<code>beta_pH(log_k_meso_bound_free)</code> includes zero, indicating +that the influence of soil pH on <code>k_meso_bound_free</code> cannot +reliably be quantified. Also, the confidence interval for the random +effect on this parameter (<code>SD.log_k_meso_bound_free</code>) +includes zero.</p> +<p>Using the <code>illparms</code> function, these ill-defined +parameters can be found more conveniently.</p> +<div class="sourceCode" id="cb61"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">sforb_pH</span><span class="op">)</span></span></code></pre></div> +<pre><code>[1] "sd(log_k_meso_bound_free)" "beta_pH(log_k_meso_bound_free)"</code></pre> +<p>To remove the ill-defined parameters, a second variant of the SFORB +model with pH influence is fitted. No ill-defined parameters remain.</p> +<div class="sourceCode" id="cb63"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">sforb_pH_2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">sforb_pH</span>,</span> +<span> no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_free_0"</span>, <span class="st">"log_k_meso_free_bound"</span>, <span class="st">"log_k_meso_bound_free"</span><span class="op">)</span>,</span> +<span> covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_k_meso_free</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">sforb_pH_2</span><span class="op">)</span></span></code></pre></div> +<p>The model comparison of the SFORB fits includes the refined model +without covariate effect, and both versions of the SFORB fit with +covariate effect.</p> +<div class="sourceCode" id="cb64"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"SFORB"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span>, <span class="va">sforb_pH</span>, <span class="va">sforb_pH_2</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets + + npar AIC BIC Lik Chisq Df Pr(>Chisq) +f_saem_2[["SFORB", "const"]] 7 783.40 789.63 -384.70 +sforb_pH_2 7 770.94 777.17 -378.47 12.4616 0 +sforb_pH 9 768.81 776.83 -375.41 6.1258 2 0.04675 * +--- +Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre> +<p>The first model including pH influence is preferable based on +information criteria and the likelihood ratio test. However, as it is +not fully identifiable, the second model is selected.</p> +<div class="sourceCode" id="cb66"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">sforb_pH_2</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_free_0</td> +<td align="right">93.32</td> +<td align="right">91.16</td> +<td align="right">95.48</td> +</tr> +<tr class="even"> +<td align="left">log_k_meso_free</td> +<td align="right">-6.15</td> +<td align="right">-7.43</td> +<td align="right">-4.86</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_k_meso_free)</td> +<td align="right">0.54</td> +<td align="right">0.33</td> +<td align="right">0.75</td> +</tr> +<tr class="even"> +<td align="left">log_k_meso_free_bound</td> +<td align="right">-3.80</td> +<td align="right">-5.20</td> +<td align="right">-2.40</td> +</tr> +<tr class="odd"> +<td align="left">log_k_meso_bound_free</td> +<td align="right">-2.95</td> +<td align="right">-4.26</td> +<td align="right">-1.64</td> +</tr> +<tr class="even"> +<td align="left">a.1</td> +<td align="right">5.08</td> +<td align="right">4.38</td> +<td align="right">5.79</td> +</tr> +<tr class="odd"> +<td align="left">SD.log_k_meso_free</td> +<td align="right">0.33</td> +<td align="right">0.22</td> +<td align="right">0.45</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb67"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">sforb_pH_2</span><span class="op">)</span></span></code></pre></div> +<p><img src="mesotrione_parent_2023_files/figure-html/unnamed-chunk-25-1.png" width="700" style="display: block; margin: auto;"></p> +<div class="sourceCode" id="cb68"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">sforb_pH_2</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +50% 5.75 + +$ff +meso_free + 1 + +$SFORB + meso_b1 meso_b2 meso_g +0.09735824 0.02631699 0.31602120 + +$distimes + DT50 DT90 DT50back DT50_meso_b1 DT50_meso_b2 +meso 16.86549 73.15824 22.02282 7.119554 26.33839</code></pre> +<div class="sourceCode" id="cb70"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">sforb_pH_2</span>, covariates <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>pH <span class="op">=</span> <span class="fl">7</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +User 7 + +$ff +meso_free + 1 + +$SFORB + meso_b1 meso_b2 meso_g +0.13315233 0.03795988 0.61186191 + +$distimes + DT50 DT90 DT50back DT50_meso_b1 DT50_meso_b2 +meso 7.932495 36.93311 11.11797 5.205671 18.26</code></pre> +</div> +<div class="section level3"> +<h3 id="hs">HS<a class="anchor" aria-label="anchor" href="#hs"></a> +</h3> +<div class="sourceCode" id="cb72"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">hs_pH</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"HS"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_0"</span><span class="op">)</span>,</span> +<span> covariates <span class="op">=</span> <span class="va">pH</span>,</span> +<span> covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_k1</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">log_k2</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">log_tb</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb73"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">hs_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_0</td> +<td align="right">93.33</td> +<td align="right">91.47</td> +<td align="right">95.19</td> +</tr> +<tr class="even"> +<td align="left">log_k1</td> +<td align="right">-5.81</td> +<td align="right">-7.27</td> +<td align="right">-4.36</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_k1)</td> +<td align="right">0.47</td> +<td align="right">0.23</td> +<td align="right">0.72</td> +</tr> +<tr class="even"> +<td align="left">log_k2</td> +<td align="right">-6.80</td> +<td align="right">-8.76</td> +<td align="right">-4.83</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_k2)</td> +<td align="right">0.54</td> +<td align="right">0.21</td> +<td align="right">0.87</td> +</tr> +<tr class="even"> +<td align="left">log_tb</td> +<td align="right">3.25</td> +<td align="right">1.25</td> +<td align="right">5.25</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_tb)</td> +<td align="right">-0.10</td> +<td align="right">-0.43</td> +<td align="right">0.23</td> +</tr> +<tr class="even"> +<td align="left">a.1</td> +<td align="right">4.49</td> +<td align="right">3.78</td> +<td align="right">5.21</td> +</tr> +<tr class="odd"> +<td align="left">SD.log_k1</td> +<td align="right">0.37</td> +<td align="right">0.24</td> +<td align="right">0.51</td> +</tr> +<tr class="even"> +<td align="left">SD.log_k2</td> +<td align="right">0.29</td> +<td align="right">0.10</td> +<td align="right">0.48</td> +</tr> +<tr class="odd"> +<td align="left">SD.log_tb</td> +<td align="right">0.25</td> +<td align="right">-0.07</td> +<td align="right">0.57</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb74"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">hs_pH</span><span class="op">)</span></span></code></pre></div> +<pre><code>[1] "sd(log_tb)" "beta_pH(log_tb)"</code></pre> +<p>According to the output of the <code>illparms</code> function, the +random effect on the break time <code>tb</code> cannot reliably be +quantified, neither can the influence of soil pH on <code>tb</code>. The +fit is repeated without the corresponding covariate model, and no +ill-defined parameters remain.</p> +<div class="sourceCode" id="cb76"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">hs_pH_2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">hs_pH</span>, covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_k1</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">log_k2</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">hs_pH_2</span><span class="op">)</span></span></code></pre></div> +<p>Model comparison confirms that this model is preferable to the fit +without covariate influence, and also to the first version with +covariate influence.</p> +<div class="sourceCode" id="cb77"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"HS"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span>, <span class="va">hs_pH</span>, <span class="va">hs_pH_2</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets + + npar AIC BIC Lik Chisq Df Pr(>Chisq) +f_saem_2[["HS", "const"]] 8 780.08 787.20 -382.04 +hs_pH_2 10 766.47 775.37 -373.23 17.606 2 0.0001503 *** +hs_pH 11 769.80 779.59 -373.90 0.000 1 1.0000000 +--- +Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre> +<div class="sourceCode" id="cb79"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">hs_pH_2</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_0</td> +<td align="right">93.33</td> +<td align="right">91.50</td> +<td align="right">95.15</td> +</tr> +<tr class="even"> +<td align="left">log_k1</td> +<td align="right">-5.68</td> +<td align="right">-7.09</td> +<td align="right">-4.27</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_k1)</td> +<td align="right">0.46</td> +<td align="right">0.22</td> +<td align="right">0.69</td> +</tr> +<tr class="even"> +<td align="left">log_k2</td> +<td align="right">-6.61</td> +<td align="right">-8.34</td> +<td align="right">-4.88</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_k2)</td> +<td align="right">0.50</td> +<td align="right">0.21</td> +<td align="right">0.79</td> +</tr> +<tr class="even"> +<td align="left">log_tb</td> +<td align="right">2.70</td> +<td align="right">2.33</td> +<td align="right">3.08</td> +</tr> +<tr class="odd"> +<td align="left">a.1</td> +<td align="right">4.45</td> +<td align="right">3.74</td> +<td align="right">5.16</td> +</tr> +<tr class="even"> +<td align="left">SD.log_k1</td> +<td align="right">0.36</td> +<td align="right">0.22</td> +<td align="right">0.49</td> +</tr> +<tr class="odd"> +<td align="left">SD.log_k2</td> +<td align="right">0.23</td> +<td align="right">0.02</td> +<td align="right">0.43</td> +</tr> +<tr class="even"> +<td align="left">SD.log_tb</td> +<td align="right">0.55</td> +<td align="right">0.25</td> +<td align="right">0.85</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb80"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">hs_pH_2</span><span class="op">)</span></span></code></pre></div> +<p><img src="mesotrione_parent_2023_files/figure-html/unnamed-chunk-30-1.png" width="700" style="display: block; margin: auto;"></p> +<div class="sourceCode" id="cb81"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">hs_pH_2</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +50% 5.75 + +$distimes + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 14.68725 82.45287 24.82079 14.68725 29.29299</code></pre> +<div class="sourceCode" id="cb83"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">hs_pH_2</span>, covariates <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>pH <span class="op">=</span> <span class="fl">7</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +User 7 + +$distimes + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 8.298536 38.85371 11.69613 8.298536 15.71561</code></pre> +</div> +<div class="section level3"> +<h3 id="comparison-across-parent-models">Comparison across parent models<a class="anchor" aria-label="anchor" href="#comparison-across-parent-models"></a> +</h3> +<p>After model reduction for all models with pH influence, they are +compared with each other.</p> +<div class="sourceCode" id="cb85"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">sfo_pH</span>, <span class="va">fomc_pH_2</span>, <span class="va">dfop_pH_2</span>, <span class="va">dfop_pH_4</span>, <span class="va">sforb_pH_2</span>, <span class="va">hs_pH_2</span><span class="op">)</span></span></code></pre></div> +<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets + + npar AIC BIC Lik +sfo_pH 5 783.09 787.54 -386.54 +fomc_pH_2 6 767.49 772.83 -377.75 +dfop_pH_4 7 767.35 773.58 -376.68 +sforb_pH_2 7 770.94 777.17 -378.47 +dfop_pH_2 8 765.14 772.26 -374.57 +hs_pH_2 10 766.47 775.37 -373.23</code></pre> +<p>The DFOP model with pH influence on <code>k2</code> and +<code>g</code> and a random effect only on <code>k2</code> is finally +selected as the best fit.</p> +<p>The endpoints resulting from this model are listed below. Please +refer to the Appendix for a detailed listing.</p> +<div class="sourceCode" id="cb87"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">dfop_pH_2</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +50% 5.75 + +$distimes + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 18.36876 73.51841 22.13125 4.191901 23.98672</code></pre> +<div class="sourceCode" id="cb89"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">dfop_pH_2</span>, covariates <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>pH <span class="op">=</span> <span class="fl">7</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +User 7 + +$distimes + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 8.346428 28.34437 8.532507 4.191901 8.753618</code></pre> +</div> +</div> +<div class="section level2"> +<h2 id="conclusions">Conclusions<a class="anchor" aria-label="anchor" href="#conclusions"></a> +</h2> +<p>These evaluations demonstrate that covariate effects can be included +for all types of parent degradation models. These models can then be +further refined to make them fully identifiable.</p> +</div> +<div class="section level2"> +<h2 id="appendix">Appendix<a class="anchor" aria-label="anchor" href="#appendix"></a> +</h2> +<div class="section level3"> +<h3 id="hierarchical-fit-listings">Hierarchical fit listings<a class="anchor" aria-label="anchor" href="#hierarchical-fit-listings"></a> +</h3> +<div class="section level4"> +<h4 id="fits-without-covariate-effects">Fits without covariate effects<a class="anchor" aria-label="anchor" href="#fits-without-covariate-effects"></a> +</h4> +<caption> +Hierarchical SFO fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Wed May 14 05:12:46 2025 +Date of summary: Wed May 14 05:13:35 2025 + +Equations: +d_meso/dt = - k_meso * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 0.71 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_k_meso + 90.832 -3.192 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k_meso +meso_0 6.752 0.0000 +log_k_meso 0.000 0.9155 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 800 804.5 -395 + +Optimised parameters: + est. lower upper +meso_0 92.0705 89.9917 94.1493 +log_k_meso -3.1641 -3.4286 -2.8996 +a.1 5.4628 4.6421 6.2835 +SD.meso_0 0.0611 -98.3545 98.4767 +SD.log_k_meso 0.5616 0.3734 0.7499 + +Correlation: + meso_0 +log_k_meso 0.1132 + +Random effects: + est. lower upper +SD.meso_0 0.0611 -98.3545 98.4767 +SD.log_k_meso 0.5616 0.3734 0.7499 + +Variance model: + est. lower upper +a.1 5.463 4.642 6.284 + +Backtransformed parameters: + est. lower upper +meso_0 92.07053 89.99172 94.14933 +k_meso 0.04225 0.03243 0.05505 + +Estimated disappearance times: + DT50 DT90 +meso 16.41 54.5 + +</code></pre> +<p></p> +<caption> +Hierarchical FOMC fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Wed May 14 05:12:46 2025 +Date of summary: Wed May 14 05:13:35 2025 + +Equations: +d_meso/dt = - (alpha/beta) * 1/((time/beta) + 1) * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 0.842 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_alpha log_beta + 93.0520 0.6008 3.4176 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_alpha log_beta +meso_0 6.287 0.00 0.000 +log_alpha 0.000 1.53 0.000 +log_beta 0.000 0.00 1.724 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 787.4 793.6 -386.7 + +Optimised parameters: + est. lower upper +meso_0 93.5648 91.42864 95.7009 +log_alpha 0.7645 0.28068 1.2484 +log_beta 3.6597 3.05999 4.2594 +a.1 5.0708 4.29823 5.8435 +SD.meso_0 0.1691 -34.01517 34.3535 +SD.log_alpha 0.3764 0.05834 0.6945 +SD.log_beta 0.3903 -0.06074 0.8414 + +Correlation: + meso_0 log_lph +log_alpha -0.2839 +log_beta -0.3443 0.8855 + +Random effects: + est. lower upper +SD.meso_0 0.1691 -34.01517 34.3535 +SD.log_alpha 0.3764 0.05834 0.6945 +SD.log_beta 0.3903 -0.06074 0.8414 + +Variance model: + est. lower upper +a.1 5.071 4.298 5.843 + +Backtransformed parameters: + est. lower upper +meso_0 93.565 91.429 95.701 +alpha 2.148 1.324 3.485 +beta 38.850 21.327 70.770 + +Estimated disappearance times: + DT50 DT90 DT50back +meso 14.8 74.64 22.47 + +</code></pre> +<p></p> +<caption> +Hierarchical DFOP fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Wed May 14 05:12:47 2025 +Date of summary: Wed May 14 05:13:35 2025 + +Equations: +d_meso/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * + time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) + * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 1.168 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_k1 log_k2 g_qlogis +93.14689 -2.05241 -3.53079 -0.09522 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k1 log_k2 g_qlogis +meso_0 6.418 0.000 0.000 0.00 +log_k1 0.000 1.018 0.000 0.00 +log_k2 0.000 0.000 1.694 0.00 +g_qlogis 0.000 0.000 0.000 2.37 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 787.6 795.6 -384.8 + +Optimised parameters: + est. lower upper +meso_0 93.6684 91.63599 95.7008 +log_k1 -1.7354 -2.61433 -0.8565 +log_k2 -3.4015 -3.73323 -3.0697 +g_qlogis -1.6341 -2.66133 -0.6069 +a.1 4.7803 4.01269 5.5479 +SD.meso_0 0.1661 -30.97086 31.3031 +SD.log_k1 0.1127 -2.59680 2.8223 +SD.log_k2 0.6394 0.41499 0.8638 +SD.g_qlogis 0.8166 0.09785 1.5353 + +Correlation: + meso_0 log_k1 log_k2 +log_k1 0.1757 +log_k2 0.0199 0.2990 +g_qlogis 0.0813 -0.7431 -0.3826 + +Random effects: + est. lower upper +SD.meso_0 0.1661 -30.97086 31.3031 +SD.log_k1 0.1127 -2.59680 2.8223 +SD.log_k2 0.6394 0.41499 0.8638 +SD.g_qlogis 0.8166 0.09785 1.5353 + +Variance model: + est. lower upper +a.1 4.78 4.013 5.548 + +Backtransformed parameters: + est. lower upper +meso_0 93.66841 91.63599 95.70082 +k1 0.17633 0.07322 0.42466 +k2 0.03332 0.02392 0.04643 +g 0.16327 0.06529 0.35277 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 16.04 63.75 19.19 3.931 20.8 + +</code></pre> +<p></p> +<caption> +Hierarchical SFORB fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Wed May 14 05:12:47 2025 +Date of summary: Wed May 14 05:13:35 2025 + +Equations: +d_meso_free/dt = - k_meso_free * meso_free - k_meso_free_bound * + meso_free + k_meso_bound_free * meso_bound +d_meso_bound/dt = + k_meso_free_bound * meso_free - k_meso_bound_free * + meso_bound + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 1.256 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_free_0 log_k_meso_free log_k_meso_free_bound + 93.147 -2.305 -4.230 +log_k_meso_bound_free + -3.761 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_free_0 log_k_meso_free log_k_meso_free_bound +meso_free_0 6.418 0.0000 0.000 +log_k_meso_free 0.000 0.9276 0.000 +log_k_meso_free_bound 0.000 0.0000 2.272 +log_k_meso_bound_free 0.000 0.0000 0.000 + log_k_meso_bound_free +meso_free_0 0.000 +log_k_meso_free 0.000 +log_k_meso_free_bound 0.000 +log_k_meso_bound_free 1.447 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 787.4 795.4 -384.7 + +Optimised parameters: + est. lower upper +meso_free_0 93.6285 91.6262 95.631 +log_k_meso_free -2.8314 -3.1375 -2.525 +log_k_meso_free_bound -3.2213 -4.4695 -1.973 +log_k_meso_bound_free -2.4246 -3.5668 -1.282 +a.1 4.7372 3.9542 5.520 +SD.meso_free_0 0.1634 -32.7769 33.104 +SD.log_k_meso_free 0.4885 0.3080 0.669 +SD.log_k_meso_free_bound 0.2876 -1.7955 2.371 +SD.log_k_meso_bound_free 0.9942 0.2181 1.770 + +Correlation: + ms_fr_0 lg_k_m_ lg_k_ms_f_ +log_k_meso_free 0.2332 +log_k_meso_free_bound 0.1100 0.5964 +log_k_meso_bound_free -0.0413 0.3697 0.8025 + +Random effects: + est. lower upper +SD.meso_free_0 0.1634 -32.7769 33.104 +SD.log_k_meso_free 0.4885 0.3080 0.669 +SD.log_k_meso_free_bound 0.2876 -1.7955 2.371 +SD.log_k_meso_bound_free 0.9942 0.2181 1.770 + +Variance model: + est. lower upper +a.1 4.737 3.954 5.52 + +Backtransformed parameters: + est. lower upper +meso_free_0 93.62849 91.62622 95.63075 +k_meso_free 0.05893 0.04339 0.08004 +k_meso_free_bound 0.03990 0.01145 0.13903 +k_meso_bound_free 0.08851 0.02825 0.27736 + +Estimated Eigenvalues of SFORB model(s): +meso_b1 meso_b2 meso_g +0.15333 0.03402 0.20881 + +Resulting formation fractions: + ff +meso_free 1 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_meso_b1 DT50_meso_b2 +meso 14.79 60.81 18.3 4.521 20.37 + +</code></pre> +<p></p> +<caption> +Hierarchical HS fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Wed May 14 05:12:48 2025 +Date of summary: Wed May 14 05:13:35 2025 + +Equations: +d_meso/dt = - ifelse(time <= tb, k1, k2) * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 1.653 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: +meso_0 log_k1 log_k2 log_tb +92.920 -2.409 -3.295 2.471 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k1 log_k2 log_tb +meso_0 6.477 0.0000 0.0000 0.00 +log_k1 0.000 0.8675 0.0000 0.00 +log_k2 0.000 0.0000 0.4035 0.00 +log_tb 0.000 0.0000 0.0000 1.16 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 781.9 789.9 -382 + +Optimised parameters: + est. lower upper +meso_0 93.34242 91.4730 95.2118 +log_k1 -2.77312 -3.0826 -2.4637 +log_k2 -3.61854 -3.8430 -3.3941 +log_tb 2.00266 1.3357 2.6696 +a.1 4.47693 3.7059 5.2479 +SD.meso_0 0.07963 -63.1661 63.3253 +SD.log_k1 0.47817 0.2467 0.7097 +SD.log_k2 0.39216 0.2137 0.5706 +SD.log_tb 0.94683 0.4208 1.4728 + +Correlation: + meso_0 log_k1 log_k2 +log_k1 0.1627 +log_k2 0.0063 -0.0301 +log_tb 0.0083 -0.3931 -0.1225 + +Random effects: + est. lower upper +SD.meso_0 0.07963 -63.1661 63.3253 +SD.log_k1 0.47817 0.2467 0.7097 +SD.log_k2 0.39216 0.2137 0.5706 +SD.log_tb 0.94683 0.4208 1.4728 + +Variance model: + est. lower upper +a.1 4.477 3.706 5.248 + +Backtransformed parameters: + est. lower upper +meso_0 93.34242 91.47303 95.21181 +k1 0.06247 0.04584 0.08512 +k2 0.02682 0.02143 0.03357 +tb 7.40872 3.80282 14.43376 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 16 76 22.88 11.1 25.84 + +</code></pre> +<p></p> +</div> +<div class="section level4"> +<h4 id="fits-with-covariate-effects">Fits with covariate effects<a class="anchor" aria-label="anchor" href="#fits-with-covariate-effects"></a> +</h4> +<caption> +Hierarchichal SFO fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Wed May 14 05:13:00 2025 +Date of summary: Wed May 14 05:13:35 2025 + +Equations: +d_meso/dt = - k_meso * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 1.343 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_k_meso + 90.832 -3.192 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k_meso +meso_0 6.752 0.0000 +log_k_meso 0.000 0.9155 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 783.1 787.5 -386.5 + +Optimised parameters: + est. lower upper +meso_0 91.3481 89.2688 93.4275 +log_k_meso -6.6614 -7.9715 -5.3514 +beta_pH(log_k_meso) 0.5871 0.3684 0.8059 +a.1 5.4750 4.7085 6.2415 +SD.log_k_meso 0.3471 0.2258 0.4684 + +Correlation: + meso_0 lg_k_ms +log_k_meso 0.0414 +beta_pH(log_k_meso) -0.0183 -0.9917 + +Random effects: + est. lower upper +SD.log_k_meso 0.3471 0.2258 0.4684 + +Variance model: + est. lower upper +a.1 5.475 4.709 6.242 + +Backtransformed parameters: + est. lower upper +meso_0 91.348139 8.927e+01 93.427476 +k_meso 0.001279 3.452e-04 0.004741 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated disappearance times: + DT50 DT90 +meso 18.52 61.52 + +</code></pre> +<p></p> +<caption> +Hierarchichal FOMC fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Wed May 14 05:13:03 2025 +Date of summary: Wed May 14 05:13:35 2025 + +Equations: +d_meso/dt = - (alpha/beta) * 1/((time/beta) + 1) * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 1.897 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_alpha log_beta + 93.0520 0.6008 3.4176 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_alpha log_beta +meso_0 6.287 0.00 0.000 +log_alpha 0.000 1.53 0.000 +log_beta 0.000 0.00 1.724 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 770.1 776.3 -378 + +Optimised parameters: + est. lower upper +meso_0 92.840646 90.750461 94.9308 +log_alpha -2.206602 -3.494546 -0.9187 +beta_pH(log_alpha) 0.577505 0.369805 0.7852 +log_beta 4.214099 3.438851 4.9893 +a.1 5.027768 4.322028 5.7335 +SD.log_alpha 0.004034 -23.766993 23.7751 +SD.log_beta 0.374640 0.009252 0.7400 + +Correlation: + meso_0 log_lph bt_H(_) +log_alpha -0.0865 +beta_pH(log_alpha) -0.0789 -0.8704 +log_beta -0.3544 0.3302 0.1628 + +Random effects: + est. lower upper +SD.log_alpha 0.004034 -23.766993 23.78 +SD.log_beta 0.374640 0.009252 0.74 + +Variance model: + est. lower upper +a.1 5.028 4.322 5.734 + +Backtransformed parameters: + est. lower upper +meso_0 92.8406 90.75046 94.9308 +alpha 0.1101 0.03036 0.3991 +beta 67.6332 31.15113 146.8404 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated disappearance times: + DT50 DT90 DT50back +meso 17.28 76.37 22.99 + +</code></pre> +<p></p> +<caption> +Refined hierarchichal FOMC fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Wed May 14 05:13:08 2025 +Date of summary: Wed May 14 05:13:35 2025 + +Equations: +d_meso/dt = - (alpha/beta) * 1/((time/beta) + 1) * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 4.184 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_alpha log_beta + 93.0520 0.6008 3.4176 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_alpha log_beta +meso_0 6.287 0.00 0.000 +log_alpha 0.000 1.53 0.000 +log_beta 0.000 0.00 1.724 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 767.5 772.8 -377.7 + +Optimised parameters: + est. lower upper +meso_0 93.0536 90.9771 95.1300 +log_alpha -2.9054 -4.1803 -1.6304 +beta_pH(log_alpha) 0.6590 0.4437 0.8744 +log_beta 3.9549 3.2860 4.6239 +a.1 4.9784 4.2815 5.6754 +SD.log_beta 0.4019 0.2632 0.5406 + +Correlation: + meso_0 log_lph bt_H(_) +log_alpha -0.0397 +beta_pH(log_alpha) -0.0899 -0.9146 +log_beta -0.3473 0.2038 0.1919 + +Random effects: + est. lower upper +SD.log_beta 0.4019 0.2632 0.5406 + +Variance model: + est. lower upper +a.1 4.978 4.281 5.675 + +Backtransformed parameters: + est. lower upper +meso_0 93.05359 90.97713 95.1300 +alpha 0.05473 0.01529 0.1958 +beta 52.19251 26.73597 101.8874 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated disappearance times: + DT50 DT90 DT50back +meso 17.3 82.91 24.96 + +</code></pre> +<p></p> +<caption> +Hierarchichal DFOP fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Wed May 14 05:13:11 2025 +Date of summary: Wed May 14 05:13:35 2025 + +Equations: +d_meso/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * + time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) + * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 2.18 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_k1 log_k2 g_qlogis +93.14689 -2.05241 -3.53079 -0.09522 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k1 log_k2 g_qlogis +meso_0 6.418 0.000 0.000 0.00 +log_k1 0.000 1.018 0.000 0.00 +log_k2 0.000 0.000 1.694 0.00 +g_qlogis 0.000 0.000 0.000 2.37 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 769.1 777.1 -375.5 + +Optimised parameters: + est. lower upper +meso_0 92.843344 90.8464 94.84028 +log_k1 -2.815685 -3.0888 -2.54261 +log_k2 -11.479779 -15.3203 -7.63923 +beta_pH(log_k2) 1.308417 0.6948 1.92203 +g_qlogis 3.133036 0.4657 5.80035 +beta_pH(g_qlogis) -0.565988 -1.0394 -0.09262 +a.1 4.955518 4.2597 5.65135 +SD.log_k2 0.758963 0.4685 1.04943 +SD.g_qlogis 0.005215 -9.9561 9.96656 + +Correlation: + meso_0 log_k1 log_k2 b_H(_2) g_qlogs +log_k1 0.2706 +log_k2 -0.0571 0.1096 +beta_pH(log_k2) 0.0554 -0.1291 -0.9937 +g_qlogis -0.1125 -0.5062 -0.1305 0.1294 +beta_pH(g_qlogis) 0.1267 0.4226 0.0419 -0.0438 -0.9864 + +Random effects: + est. lower upper +SD.log_k2 0.758963 0.4685 1.049 +SD.g_qlogis 0.005215 -9.9561 9.967 + +Variance model: + est. lower upper +a.1 4.956 4.26 5.651 + +Backtransformed parameters: + est. lower upper +meso_0 9.284e+01 9.085e+01 9.484e+01 +k1 5.986e-02 4.556e-02 7.866e-02 +k2 1.034e-05 2.221e-07 4.812e-04 +g 9.582e-01 6.144e-01 9.970e-01 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 20.23 88.45 26.62 11.58 36.23 + +</code></pre> +<p></p> +<caption> +Refined hierarchical DFOP fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Wed May 14 05:13:14 2025 +Date of summary: Wed May 14 05:13:35 2025 + +Equations: +d_meso/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * + time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) + * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 2.424 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_k1 log_k2 g_qlogis +93.14689 -2.05241 -3.53079 -0.09522 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k1 log_k2 g_qlogis +meso_0 6.418 0.000 0.000 0.00 +log_k1 0.000 1.018 0.000 0.00 +log_k2 0.000 0.000 1.694 0.00 +g_qlogis 0.000 0.000 0.000 2.37 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 765.1 772.3 -374.6 + +Optimised parameters: + est. lower upper +meso_0 93.3333 91.2427 95.42394 +log_k1 -1.7997 -2.9124 -0.68698 +log_k2 -8.1810 -10.1819 -6.18008 +beta_pH(log_k2) 0.8064 0.4903 1.12257 +g_qlogis 3.3513 -1.1792 7.88182 +beta_pH(g_qlogis) -0.8672 -1.7661 0.03177 +a.1 4.9158 4.2277 5.60390 +SD.log_k2 0.3946 0.2565 0.53281 + +Correlation: + meso_0 log_k1 log_k2 b_H(_2) g_qlogs +log_k1 0.1730 +log_k2 0.0442 0.5370 +beta_pH(log_k2) -0.0392 -0.4880 -0.9923 +g_qlogis -0.1536 0.1431 -0.1129 0.1432 +beta_pH(g_qlogis) 0.1504 -0.3151 -0.0196 -0.0212 -0.9798 + +Random effects: + est. lower upper +SD.log_k2 0.3946 0.2565 0.5328 + +Variance model: + est. lower upper +a.1 4.916 4.228 5.604 + +Backtransformed parameters: + est. lower upper +meso_0 9.333e+01 9.124e+01 95.42394 +k1 1.654e-01 5.435e-02 0.50309 +k2 2.799e-04 3.785e-05 0.00207 +g 9.661e-01 2.352e-01 0.99962 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 18.37 73.52 22.13 4.192 23.99 + +</code></pre> +<p></p> +<caption> +Further refined hierarchical DFOP fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Wed May 14 05:13:23 2025 +Date of summary: Wed May 14 05:13:35 2025 + +Equations: +d_meso/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * + time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) + * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 3.211 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_k1 log_k2 g_qlogis +93.14689 -2.05241 -3.53079 -0.09522 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k1 log_k2 g_qlogis +meso_0 6.418 0.000 0.000 0.00 +log_k1 0.000 1.018 0.000 0.00 +log_k2 0.000 0.000 1.694 0.00 +g_qlogis 0.000 0.000 0.000 2.37 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 767.4 773.6 -376.7 + +Optimised parameters: + est. lower upper +meso_0 93.3011 91.1905 95.4118 +log_k1 -2.1487 -2.7607 -1.5367 +log_k2 -8.1039 -10.4225 -5.7853 +beta_pH(log_k2) 0.7821 0.4126 1.1517 +g_qlogis -1.0373 -1.9337 -0.1409 +a.1 5.0095 4.3082 5.7108 +SD.log_k2 0.4622 0.3009 0.6235 + +Correlation: + meso_0 log_k1 log_k2 b_H(_2) +log_k1 0.2179 +log_k2 0.0337 0.5791 +beta_pH(log_k2) -0.0326 -0.5546 -0.9932 +g_qlogis 0.0237 -0.8479 -0.6571 0.6123 + +Random effects: + est. lower upper +SD.log_k2 0.4622 0.3009 0.6235 + +Variance model: + est. lower upper +a.1 5.009 4.308 5.711 + +Backtransformed parameters: + est. lower upper +meso_0 9.330e+01 9.119e+01 95.411751 +k1 1.166e-01 6.325e-02 0.215084 +k2 3.024e-04 2.975e-05 0.003072 +g 2.617e-01 1.263e-01 0.464832 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 17.09 73.67 22.18 5.943 25.54 + +</code></pre> +<p></p> +<caption> +Hierarchichal SFORB fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Wed May 14 05:13:26 2025 +Date of summary: Wed May 14 05:13:35 2025 + +Equations: +d_meso_free/dt = - k_meso_free * meso_free - k_meso_free_bound * + meso_free + k_meso_bound_free * meso_bound +d_meso_bound/dt = + k_meso_free_bound * meso_free - k_meso_bound_free * + meso_bound + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 2.649 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_free_0 log_k_meso_free log_k_meso_free_bound + 93.147 -2.305 -4.230 +log_k_meso_bound_free + -3.761 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_free_0 log_k_meso_free log_k_meso_free_bound +meso_free_0 6.418 0.0000 0.000 +log_k_meso_free 0.000 0.9276 0.000 +log_k_meso_free_bound 0.000 0.0000 2.272 +log_k_meso_bound_free 0.000 0.0000 0.000 + log_k_meso_bound_free +meso_free_0 0.000 +log_k_meso_free 0.000 +log_k_meso_free_bound 0.000 +log_k_meso_bound_free 1.447 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 768.8 776.8 -375.4 + +Optimised parameters: + est. lower upper +meso_free_0 93.4204 91.3213 95.5195 +log_k_meso_free -5.3742 -6.9366 -3.8117 +beta_pH(log_k_meso_free) 0.4232 0.1769 0.6695 +log_k_meso_free_bound -3.4889 -4.9243 -2.0535 +log_k_meso_bound_free -9.9797 -19.2232 -0.7362 +beta_pH(log_k_meso_bound_free) 1.2290 -0.2107 2.6687 +a.1 4.9031 4.1795 5.6268 +SD.log_k_meso_free 0.3454 0.2252 0.4656 +SD.log_k_meso_bound_free 0.1277 -1.9459 2.2012 + +Correlation: + ms_fr_0 lg_k_m_ b_H(___) lg_k_ms_f_ lg_k_ms_b_ +log_k_meso_free 0.1493 +beta_pH(log_k_meso_free) -0.0930 -0.9854 +log_k_meso_free_bound 0.2439 0.4621 -0.3492 +log_k_meso_bound_free 0.2188 0.1292 -0.0339 0.7287 +beta_pH(log_k_meso_bound_free) -0.2216 -0.0797 -0.0111 -0.6566 -0.9934 + +Random effects: + est. lower upper +SD.log_k_meso_free 0.3454 0.2252 0.4656 +SD.log_k_meso_bound_free 0.1277 -1.9459 2.2012 + +Variance model: + est. lower upper +a.1 4.903 4.18 5.627 + +Backtransformed parameters: + est. lower upper +meso_free_0 9.342e+01 9.132e+01 95.51946 +k_meso_free 4.635e-03 9.716e-04 0.02211 +k_meso_free_bound 3.054e-02 7.268e-03 0.12829 +k_meso_bound_free 4.633e-05 4.482e-09 0.47894 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated Eigenvalues of SFORB model(s): +meso_b1 meso_b2 meso_g + 0.1121 0.0256 0.3148 + +Resulting formation fractions: + ff +meso_free 1 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_meso_b1 DT50_meso_b2 +meso 16.42 75.2 22.64 6.185 27.08 + +</code></pre> +<p> </p> +<caption> +Refined hierarchichal SFORB fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Wed May 14 05:13:30 2025 +Date of summary: Wed May 14 05:13:35 2025 + +Equations: +d_meso_free/dt = - k_meso_free * meso_free - k_meso_free_bound * + meso_free + k_meso_bound_free * meso_bound +d_meso_bound/dt = + k_meso_free_bound * meso_free - k_meso_bound_free * + meso_bound + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 3.186 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_free_0 log_k_meso_free log_k_meso_free_bound + 93.147 -2.305 -4.230 +log_k_meso_bound_free + -3.761 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_free_0 log_k_meso_free log_k_meso_free_bound +meso_free_0 6.418 0.0000 0.000 +log_k_meso_free 0.000 0.9276 0.000 +log_k_meso_free_bound 0.000 0.0000 2.272 +log_k_meso_bound_free 0.000 0.0000 0.000 + log_k_meso_bound_free +meso_free_0 0.000 +log_k_meso_free 0.000 +log_k_meso_free_bound 0.000 +log_k_meso_bound_free 1.447 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 770.9 777.2 -378.5 + +Optimised parameters: + est. lower upper +meso_free_0 93.3196 91.1633 95.4760 +log_k_meso_free -6.1460 -7.4306 -4.8614 +beta_pH(log_k_meso_free) 0.5435 0.3329 0.7542 +log_k_meso_free_bound -3.8001 -5.2027 -2.3975 +log_k_meso_bound_free -2.9462 -4.2565 -1.6359 +a.1 5.0825 4.3793 5.7856 +SD.log_k_meso_free 0.3338 0.2175 0.4502 + +Correlation: + ms_fr_0 lg_k_m_ b_H(___ lg_k_ms_f_ +log_k_meso_free 0.1086 +beta_pH(log_k_meso_free) -0.0426 -0.9821 +log_k_meso_free_bound 0.2513 0.1717 -0.0409 +log_k_meso_bound_free 0.1297 0.1171 -0.0139 0.9224 + +Random effects: + est. lower upper +SD.log_k_meso_free 0.3338 0.2175 0.4502 + +Variance model: + est. lower upper +a.1 5.082 4.379 5.786 + +Backtransformed parameters: + est. lower upper +meso_free_0 93.319649 9.116e+01 95.47601 +k_meso_free 0.002142 5.928e-04 0.00774 +k_meso_free_bound 0.022369 5.502e-03 0.09095 +k_meso_bound_free 0.052539 1.417e-02 0.19478 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated Eigenvalues of SFORB model(s): +meso_b1 meso_b2 meso_g +0.09736 0.02632 0.31602 + +Resulting formation fractions: + ff +meso_free 1 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_meso_b1 DT50_meso_b2 +meso 16.87 73.16 22.02 7.12 26.34 + +</code></pre> +<p> </p> +<caption> +Hierarchichal HS fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Wed May 14 05:13:32 2025 +Date of summary: Wed May 14 05:13:35 2025 + +Equations: +d_meso/dt = - ifelse(time <= tb, k1, k2) * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 1.833 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: +meso_0 log_k1 log_k2 log_tb +92.920 -2.409 -3.295 2.471 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k1 log_k2 log_tb +meso_0 6.477 0.0000 0.0000 0.00 +log_k1 0.000 0.8675 0.0000 0.00 +log_k2 0.000 0.0000 0.4035 0.00 +log_tb 0.000 0.0000 0.0000 1.16 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 769.8 779.6 -373.9 + +Optimised parameters: + est. lower upper +meso_0 93.32599 91.4658 95.1862 +log_k1 -5.81463 -7.2710 -4.3583 +beta_pH(log_k1) 0.47472 0.2334 0.7160 +log_k2 -6.79633 -8.7605 -4.8322 +beta_pH(log_k2) 0.54151 0.2124 0.8706 +log_tb 3.24674 1.2470 5.2465 +beta_pH(log_tb) -0.09889 -0.4258 0.2280 +a.1 4.49487 3.7766 5.2132 +SD.log_k1 0.37191 0.2370 0.5068 +SD.log_k2 0.29210 0.0994 0.4848 +SD.log_tb 0.25353 -0.0664 0.5735 + +Correlation: + meso_0 log_k1 b_H(_1) log_k2 b_H(_2) log_tb +log_k1 0.0744 +beta_pH(log_k1) -0.0452 -0.9915 +log_k2 0.0066 -0.0363 0.0376 +beta_pH(log_k2) -0.0071 0.0372 -0.0391 -0.9939 +log_tb -0.0238 -0.1483 0.1362 -0.3836 0.3696 +beta_pH(log_tb) 0.0097 0.1359 -0.1265 0.3736 -0.3653 -0.9905 + +Random effects: + est. lower upper +SD.log_k1 0.3719 0.2370 0.5068 +SD.log_k2 0.2921 0.0994 0.4848 +SD.log_tb 0.2535 -0.0664 0.5735 + +Variance model: + est. lower upper +a.1 4.495 3.777 5.213 + +Backtransformed parameters: + est. lower upper +meso_0 93.325994 9.147e+01 9.519e+01 +k1 0.002984 6.954e-04 1.280e-02 +k2 0.001118 1.568e-04 7.969e-03 +tb 25.706437 3.480e+00 1.899e+02 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 15.65 79.63 23.97 15.16 27.55 + +</code></pre> +<p> </p> +<caption> +Refined hierarchichal HS fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Wed May 14 05:13:35 2025 +Date of summary: Wed May 14 05:13:35 2025 + +Equations: +d_meso/dt = - ifelse(time <= tb, k1, k2) * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 1.852 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: +meso_0 log_k1 log_k2 log_tb +92.920 -2.409 -3.295 2.471 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k1 log_k2 log_tb +meso_0 6.477 0.0000 0.0000 0.00 +log_k1 0.000 0.8675 0.0000 0.00 +log_k2 0.000 0.0000 0.4035 0.00 +log_tb 0.000 0.0000 0.0000 1.16 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 766.5 775.4 -373.2 + +Optimised parameters: + est. lower upper +meso_0 93.3251 91.49823 95.1520 +log_k1 -5.6796 -7.08789 -4.2714 +beta_pH(log_k1) 0.4567 0.22400 0.6894 +log_k2 -6.6083 -8.33839 -4.8781 +beta_pH(log_k2) 0.4982 0.20644 0.7899 +log_tb 2.7040 2.33033 3.0777 +a.1 4.4452 3.73537 5.1551 +SD.log_k1 0.3570 0.22104 0.4930 +SD.log_k2 0.2252 0.01864 0.4318 +SD.log_tb 0.5488 0.24560 0.8521 + +Correlation: + meso_0 log_k1 b_H(_1) log_k2 b_H(_2) +log_k1 0.0740 +beta_pH(log_k1) -0.0453 -0.9912 +log_k2 0.0115 -0.0650 0.0661 +beta_pH(log_k2) -0.0116 0.0649 -0.0667 -0.9936 +log_tb -0.0658 -0.1135 0.0913 -0.1500 0.1210 + +Random effects: + est. lower upper +SD.log_k1 0.3570 0.22104 0.4930 +SD.log_k2 0.2252 0.01864 0.4318 +SD.log_tb 0.5488 0.24560 0.8521 + +Variance model: + est. lower upper +a.1 4.445 3.735 5.155 + +Backtransformed parameters: + est. lower upper +meso_0 93.325134 9.150e+01 95.152036 +k1 0.003415 8.352e-04 0.013962 +k2 0.001349 2.392e-04 0.007611 +tb 14.939247 1.028e+01 21.707445 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 14.69 82.45 24.82 14.69 29.29 + +</code></pre> +<p></p> +</div> +</div> +<div class="section level3"> +<h3 id="session-info">Session info<a class="anchor" aria-label="anchor" href="#session-info"></a> +</h3> +<pre><code>R version 4.5.0 (2025-04-11) +Platform: x86_64-pc-linux-gnu +Running under: Debian GNU/Linux 12 (bookworm) + +Matrix products: default +BLAS: /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.11.0 +LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.11.0 LAPACK version 3.11.0 + +locale: + [1] LC_CTYPE=de_DE.UTF-8 LC_NUMERIC=C + [3] LC_TIME=de_DE.UTF-8 LC_COLLATE=de_DE.UTF-8 + [5] LC_MONETARY=de_DE.UTF-8 LC_MESSAGES=de_DE.UTF-8 + [7] LC_PAPER=de_DE.UTF-8 LC_NAME=C + [9] LC_ADDRESS=C LC_TELEPHONE=C +[11] LC_MEASUREMENT=de_DE.UTF-8 LC_IDENTIFICATION=C + +time zone: Europe/Berlin +tzcode source: system (glibc) + +attached base packages: +[1] parallel stats graphics grDevices utils datasets methods +[8] base + +other attached packages: +[1] rmarkdown_2.29 nvimcom_0.9-167 saemix_3.3 npde_3.5 +[5] knitr_1.49 mkin_1.2.10 + +loaded via a namespace (and not attached): + [1] gtable_0.3.6 jsonlite_1.9.0 dplyr_1.1.4 compiler_4.5.0 + [5] tidyselect_1.2.1 gridExtra_2.3 jquerylib_0.1.4 systemfonts_1.2.1 + [9] scales_1.3.0 textshaping_1.0.0 readxl_1.4.4 yaml_2.3.10 +[13] fastmap_1.2.0 lattice_0.22-6 ggplot2_3.5.1 R6_2.6.1 +[17] generics_0.1.3 lmtest_0.9-40 MASS_7.3-65 htmlwidgets_1.6.4 +[21] tibble_3.2.1 desc_1.4.3 munsell_0.5.1 bslib_0.9.0 +[25] pillar_1.10.1 rlang_1.1.5 cachem_1.1.0 xfun_0.51 +[29] fs_1.6.5 sass_0.4.9 cli_3.6.4 pkgdown_2.1.1 +[33] magrittr_2.0.3 digest_0.6.37 grid_4.5.0 mclust_6.1.1 +[37] lifecycle_1.0.4 nlme_3.1-168 vctrs_0.6.5 evaluate_1.0.3 +[41] glue_1.8.0 cellranger_1.1.0 codetools_0.2-20 ragg_1.3.3 +[45] zoo_1.8-13 colorspace_2.1-1 tools_4.5.0 pkgconfig_2.0.3 +[49] htmltools_0.5.8.1</code></pre> +</div> +<div class="section level3"> +<h3 id="hardware-info">Hardware info<a class="anchor" aria-label="anchor" href="#hardware-info"></a> +</h3> +<pre><code>CPU model: AMD Ryzen 9 7950X 16-Core Processor</code></pre> +<pre><code>MemTotal: 64927780 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<h1>Testing covariate modelling in hierarchical parent degradation kinetics with residue data on mesotrione</h1> + <h4 data-toc-skip class="author">Johannes +Ranke</h4> + + <h4 data-toc-skip class="date">Last change 13 May 2025 +(rebuilt 2025-05-13)</h4> + + <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/mesotrione_parent_2023_prebuilt.rmd" class="external-link"><code>vignettes/web_only/mesotrione_parent_2023_prebuilt.rmd</code></a></small> + <div class="d-none name"><code>mesotrione_parent_2023_prebuilt.rmd</code></div> + </div> + + + +<div class="section level2"> +<h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#introduction"></a> +</h2> +<p>The purpose of this document is to test demonstrate how nonlinear +hierarchical models (NLHM) based on the parent degradation models SFO, +FOMC, DFOP and HS can be fitted with the mkin package, also considering +the influence of covariates like soil pH on different degradation +parameters. Because in some other case studies, the SFORB +parameterisation of biexponential decline has shown some advantages over +the DFOP parameterisation, SFORB was included in the list of tested +models as well.</p> +<p>The mkin package is used in version 1.2.10, which is contains the +functions that were used for the evaluations. The <code>saemix</code> +package is used as a backend for fitting the NLHM, but is also loaded to +make the convergence plot function available.</p> +<p>This document is processed with the <code>knitr</code> package, which +also provides the <code>kable</code> function that is used to improve +the display of tabular data in R markdown documents. For parallel +processing, the <code>parallel</code> package is used.</p> +<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://pkgdown.jrwb.de/mkin/">mkin</a></span><span class="op">)</span></span> +<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://yihui.org/knitr/" class="external-link">knitr</a></span><span class="op">)</span></span> +<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">saemix</span><span class="op">)</span></span> +<span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">parallel</span><span class="op">)</span></span> +<span><span class="va">n_cores</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/detectCores.html" class="external-link">detectCores</a></span><span class="op">(</span><span class="op">)</span></span> +<span><span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/Sys.info.html" class="external-link">Sys.info</a></span><span class="op">(</span><span class="op">)</span><span class="op">[</span><span class="st">"sysname"</span><span class="op">]</span> <span class="op">==</span> <span class="st">"Windows"</span><span class="op">)</span> <span class="op">{</span></span> +<span> <span class="va">cl</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makePSOCKcluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> +<span><span class="op">}</span> <span class="kw">else</span> <span class="op">{</span></span> +<span> <span class="va">cl</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/parallel/makeCluster.html" class="external-link">makeForkCluster</a></span><span class="op">(</span><span class="va">n_cores</span><span class="op">)</span></span> +<span><span class="op">}</span></span></code></pre></div> +<div class="section level3"> +<h3 id="test-data">Test data<a class="anchor" aria-label="anchor" href="#test-data"></a> +</h3> +<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">data_file</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.file.html" class="external-link">system.file</a></span><span class="op">(</span></span> +<span> <span class="st">"testdata"</span>, <span class="st">"mesotrione_soil_efsa_2016.xlsx"</span>, package <span class="op">=</span> <span class="st">"mkin"</span><span class="op">)</span></span> +<span><span class="va">meso_ds</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/read_spreadsheet.html">read_spreadsheet</a></span><span class="op">(</span><span class="va">data_file</span>, parent_only <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<p>The following tables show the covariate data and the 18 datasets that +were read in from the spreadsheet file.</p> +<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">pH</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/attr.html" class="external-link">attr</a></span><span class="op">(</span><span class="va">meso_ds</span>, <span class="st">"covariates"</span><span class="op">)</span></span> +<span><span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="va">pH</span>, caption <span class="op">=</span> <span class="st">"Covariate data"</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<caption>Covariate data</caption> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">pH</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">Richmond</td> +<td align="right">6.2</td> +</tr> +<tr class="even"> +<td align="left">Richmond 2</td> +<td align="right">6.2</td> +</tr> +<tr class="odd"> +<td align="left">ERTC</td> +<td align="right">6.4</td> +</tr> +<tr class="even"> +<td align="left">Toulouse</td> +<td align="right">7.7</td> +</tr> +<tr class="odd"> +<td align="left">Picket Piece</td> +<td align="right">7.1</td> +</tr> +<tr class="even"> +<td align="left">721</td> +<td align="right">5.6</td> +</tr> +<tr class="odd"> +<td align="left">722</td> +<td align="right">5.7</td> +</tr> +<tr class="even"> +<td align="left">723</td> +<td align="right">5.4</td> +</tr> +<tr class="odd"> +<td align="left">724</td> +<td align="right">4.8</td> +</tr> +<tr class="even"> +<td align="left">725</td> +<td align="right">5.8</td> +</tr> +<tr class="odd"> +<td align="left">727</td> +<td align="right">5.1</td> +</tr> +<tr class="even"> +<td align="left">728</td> +<td align="right">5.9</td> +</tr> +<tr class="odd"> +<td align="left">729</td> +<td align="right">5.6</td> +</tr> +<tr class="even"> +<td align="left">730</td> +<td align="right">5.3</td> +</tr> +<tr class="odd"> +<td align="left">731</td> +<td align="right">6.1</td> +</tr> +<tr class="even"> +<td align="left">732</td> +<td align="right">5.0</td> +</tr> +<tr class="odd"> +<td align="left">741</td> +<td align="right">5.7</td> +</tr> +<tr class="even"> +<td align="left">742</td> +<td align="right">7.2</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="kw">for</span> <span class="op">(</span><span class="va">ds_name</span> <span class="kw">in</span> <span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">meso_ds</span><span class="op">)</span><span class="op">)</span> <span class="op">{</span></span> +<span> <span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span></span> +<span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="fu"><a href="../../reference/mkin_long_to_wide.html">mkin_long_to_wide</a></span><span class="op">(</span><span class="va">meso_ds</span><span class="op">[[</span><span class="va">ds_name</span><span class="op">]</span><span class="op">]</span><span class="op">)</span>,</span> +<span> caption <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste</a></span><span class="op">(</span><span class="st">"Dataset"</span>, <span class="va">ds_name</span><span class="op">)</span>,</span> +<span> booktabs <span class="op">=</span> <span class="cn">TRUE</span>, row.names <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="op">}</span></span></code></pre></div> +<table class="table"> +<caption>Dataset Richmond</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">91.00</td> +</tr> +<tr class="even"> +<td align="right">1.179050</td> +<td align="right">86.70</td> +</tr> +<tr class="odd"> +<td align="right">3.537149</td> +<td align="right">73.60</td> +</tr> +<tr class="even"> +<td align="right">7.074299</td> +<td align="right">61.50</td> +</tr> +<tr class="odd"> +<td align="right">10.611448</td> +<td align="right">55.70</td> +</tr> +<tr class="even"> +<td align="right">15.327647</td> +<td align="right">47.70</td> +</tr> +<tr class="odd"> +<td align="right">17.685747</td> +<td align="right">39.50</td> +</tr> +<tr class="even"> +<td align="right">24.760046</td> +<td align="right">29.80</td> +</tr> +<tr class="odd"> +<td align="right">35.371494</td> +<td align="right">19.60</td> +</tr> +<tr class="even"> +<td align="right">68.384889</td> +<td align="right">5.67</td> +</tr> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">97.90</td> +</tr> +<tr class="even"> +<td align="right">1.179050</td> +<td align="right">96.40</td> +</tr> +<tr class="odd"> +<td align="right">3.537149</td> +<td align="right">89.10</td> +</tr> +<tr class="even"> +<td align="right">7.074299</td> +<td align="right">74.40</td> +</tr> +<tr class="odd"> +<td align="right">10.611448</td> +<td align="right">57.40</td> +</tr> +<tr class="even"> +<td align="right">15.327647</td> +<td align="right">46.30</td> +</tr> +<tr class="odd"> +<td align="right">18.864797</td> +<td align="right">35.50</td> +</tr> +<tr class="even"> +<td align="right">27.118146</td> +<td align="right">27.20</td> +</tr> +<tr class="odd"> +<td align="right">35.371494</td> +<td align="right">19.10</td> +</tr> +<tr class="even"> +<td align="right">74.280138</td> +<td align="right">6.50</td> +</tr> +<tr class="odd"> +<td align="right">108.472582</td> +<td align="right">3.40</td> +</tr> +<tr class="even"> +<td align="right">142.665027</td> +<td align="right">2.20</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset Richmond 2</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">96.0</td> +</tr> +<tr class="even"> +<td align="right">2.422004</td> +<td align="right">82.4</td> +</tr> +<tr class="odd"> +<td align="right">5.651343</td> +<td align="right">71.2</td> +</tr> +<tr class="even"> +<td align="right">8.073348</td> +<td align="right">53.1</td> +</tr> +<tr class="odd"> +<td align="right">11.302687</td> +<td align="right">48.5</td> +</tr> +<tr class="even"> +<td align="right">16.954030</td> +<td align="right">33.4</td> +</tr> +<tr class="odd"> +<td align="right">22.605373</td> +<td align="right">24.2</td> +</tr> +<tr class="even"> +<td align="right">45.210746</td> +<td align="right">11.9</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset ERTC</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">99.9</td> +</tr> +<tr class="even"> +<td align="right">2.755193</td> +<td align="right">80.0</td> +</tr> +<tr class="odd"> +<td align="right">6.428782</td> +<td align="right">42.1</td> +</tr> +<tr class="even"> +<td align="right">9.183975</td> +<td align="right">50.1</td> +</tr> +<tr class="odd"> +<td align="right">12.857565</td> +<td align="right">28.4</td> +</tr> +<tr class="even"> +<td align="right">19.286347</td> +<td align="right">39.8</td> +</tr> +<tr class="odd"> +<td align="right">25.715130</td> +<td align="right">29.9</td> +</tr> +<tr class="even"> +<td align="right">51.430259</td> +<td align="right">2.5</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset Toulouse</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">96.8</td> +</tr> +<tr class="even"> +<td align="right">2.897983</td> +<td align="right">63.3</td> +</tr> +<tr class="odd"> +<td align="right">6.761960</td> +<td align="right">22.3</td> +</tr> +<tr class="even"> +<td align="right">9.659942</td> +<td align="right">16.6</td> +</tr> +<tr class="odd"> +<td align="right">13.523919</td> +<td align="right">16.1</td> +</tr> +<tr class="even"> +<td align="right">20.285879</td> +<td align="right">17.2</td> +</tr> +<tr class="odd"> +<td align="right">27.047838</td> +<td align="right">1.8</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset Picket Piece</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">102.0</td> +</tr> +<tr class="even"> +<td align="right">2.841195</td> +<td align="right">73.7</td> +</tr> +<tr class="odd"> +<td align="right">6.629454</td> +<td align="right">35.5</td> +</tr> +<tr class="even"> +<td align="right">9.470649</td> +<td align="right">31.8</td> +</tr> +<tr class="odd"> +<td align="right">13.258909</td> +<td align="right">18.0</td> +</tr> +<tr class="even"> +<td align="right">19.888364</td> +<td align="right">3.7</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 721</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">86.4</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">61.4</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">49.8</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">41.0</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">35.1</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 722</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">90.3</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">52.1</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">37.4</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">21.2</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">14.3</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 723</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">89.3</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">70.8</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">51.1</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">42.7</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">26.7</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 724</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.000000</td> +<td align="right">89.4</td> +</tr> +<tr class="even"> +<td align="right">9.008208</td> +<td align="right">65.2</td> +</tr> +<tr class="odd"> +<td align="right">18.016415</td> +<td align="right">55.8</td> +</tr> +<tr class="even"> +<td align="right">27.024623</td> +<td align="right">46.0</td> +</tr> +<tr class="odd"> +<td align="right">36.032831</td> +<td align="right">41.7</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 725</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">89.0</td> +</tr> +<tr class="even"> +<td align="right">10.99058</td> +<td align="right">35.4</td> +</tr> +<tr class="odd"> +<td align="right">21.98116</td> +<td align="right">18.6</td> +</tr> +<tr class="even"> +<td align="right">32.97174</td> +<td align="right">11.6</td> +</tr> +<tr class="odd"> +<td align="right">43.96232</td> +<td align="right">7.6</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 727</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">91.3</td> +</tr> +<tr class="even"> +<td align="right">10.96104</td> +<td align="right">63.2</td> +</tr> +<tr class="odd"> +<td align="right">21.92209</td> +<td align="right">51.1</td> +</tr> +<tr class="even"> +<td align="right">32.88313</td> +<td align="right">42.0</td> +</tr> +<tr class="odd"> +<td align="right">43.84417</td> +<td align="right">40.8</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 728</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">91.8</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">43.6</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">22.0</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">15.9</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">8.8</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 729</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">91.6</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">60.5</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">43.5</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">28.4</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">20.5</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 730</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">92.7</td> +</tr> +<tr class="even"> +<td align="right">11.07446</td> +<td align="right">58.9</td> +</tr> +<tr class="odd"> +<td align="right">22.14893</td> +<td align="right">44.0</td> +</tr> +<tr class="even"> +<td align="right">33.22339</td> +<td align="right">46.0</td> +</tr> +<tr class="odd"> +<td align="right">44.29785</td> +<td align="right">29.3</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 731</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">92.1</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">64.4</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">45.3</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">33.6</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">23.5</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 732</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">90.3</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">58.2</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">40.1</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">33.1</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">25.8</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 741</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">90.3</td> +</tr> +<tr class="even"> +<td align="right">10.84712</td> +<td align="right">68.7</td> +</tr> +<tr class="odd"> +<td align="right">21.69424</td> +<td align="right">58.0</td> +</tr> +<tr class="even"> +<td align="right">32.54136</td> +<td align="right">52.2</td> +</tr> +<tr class="odd"> +<td align="right">43.38848</td> +<td align="right">48.0</td> +</tr> +</tbody> +</table> +<table class="table"> +<caption>Dataset 742</caption> +<thead><tr class="header"> +<th align="right">time</th> +<th align="right">meso</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="right">0.00000</td> +<td align="right">92.0</td> +</tr> +<tr class="even"> +<td align="right">11.24366</td> +<td align="right">60.9</td> +</tr> +<tr class="odd"> +<td align="right">22.48733</td> +<td align="right">36.2</td> +</tr> +<tr class="even"> +<td align="right">33.73099</td> +<td align="right">18.3</td> +</tr> +<tr class="odd"> +<td align="right">44.97466</td> +<td align="right">8.7</td> +</tr> +</tbody> +</table> +</div> +</div> +<div class="section level2"> +<h2 id="separate-evaluations">Separate evaluations<a class="anchor" aria-label="anchor" href="#separate-evaluations"></a> +</h2> +<p>In order to obtain suitable starting parameters for the NLHM fits, +separate fits of the five models to the data for each soil are generated +using the <code>mmkin</code> function from the mkin package. In a first +step, constant variance is assumed. Convergence is checked with the +<code>status</code> function.</p> +<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">deg_mods</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>, <span class="st">"SFORB"</span>, <span class="st">"HS"</span><span class="op">)</span></span> +<span><span class="va">f_sep_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span></span> +<span> <span class="va">deg_mods</span>,</span> +<span> <span class="va">meso_ds</span>,</span> +<span> error_model <span class="op">=</span> <span class="st">"const"</span>,</span> +<span> cluster <span class="op">=</span> <span class="va">cl</span>,</span> +<span> quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span>, <span class="fl">1</span><span class="op">:</span><span class="fl">5</span><span class="op">]</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">Richmond</th> +<th align="left">Richmond 2</th> +<th align="left">ERTC</th> +<th align="left">Toulouse</th> +<th align="left">Picket Piece</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span>, <span class="fl">6</span><span class="op">:</span><span class="fl">18</span><span class="op">]</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<colgroup> +<col width="10%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +</colgroup> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">721</th> +<th align="left">722</th> +<th align="left">723</th> +<th align="left">724</th> +<th align="left">725</th> +<th align="left">727</th> +<th align="left">728</th> +<th align="left">729</th> +<th align="left">730</th> +<th align="left">731</th> +<th align="left">732</th> +<th align="left">741</th> +<th align="left">742</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<p>In the tables above, OK indicates convergence and C indicates failure +to converge. Most separate fits with constant variance converged, with +the exception of two FOMC fits, one SFORB fit and one HS fit.</p> +<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">f_sep_tc</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_sep_const</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_tc</span><span class="op">[</span>, <span class="fl">1</span><span class="op">:</span><span class="fl">5</span><span class="op">]</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">Richmond</th> +<th align="left">Richmond 2</th> +<th align="left">ERTC</th> +<th align="left">Toulouse</th> +<th align="left">Picket Piece</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_sep_tc</span><span class="op">[</span>, <span class="fl">6</span><span class="op">:</span><span class="fl">18</span><span class="op">]</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<colgroup> +<col width="10%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +<col width="6%"> +</colgroup> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">721</th> +<th align="left">722</th> +<th align="left">723</th> +<th align="left">724</th> +<th align="left">725</th> +<th align="left">727</th> +<th align="left">728</th> +<th align="left">729</th> +<th align="left">730</th> +<th align="left">731</th> +<th align="left">732</th> +<th align="left">741</th> +<th align="left">742</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">C</td> +<td align="left">OK</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<p>With the two-component error model, the set of fits that did not +converge is larger, with convergence problems appearing for a number of +non-SFO fits.</p> +</div> +<div class="section level2"> +<h2 id="hierarchical-models-without-covariate">Hierarchical models without covariate<a class="anchor" aria-label="anchor" href="#hierarchical-models-without-covariate"></a> +</h2> +<p>The following code fits hierarchical kinetic models for the ten +combinations of the five different degradation models with the two +different error models in parallel.</p> +<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">f_saem_1</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mhmkin.html">mhmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">f_sep_const</span>, <span class="va">f_sep_tc</span><span class="op">)</span>, cluster <span class="op">=</span> <span class="va">cl</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<p>All fits terminate without errors (status OK).</p> +<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">npar</th> +<th align="right">AIC</th> +<th align="right">BIC</th> +<th align="right">Lik</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO const</td> +<td align="right">5</td> +<td align="right">800.0</td> +<td align="right">804.5</td> +<td align="right">-395.0</td> +</tr> +<tr class="even"> +<td align="left">SFO tc</td> +<td align="right">6</td> +<td align="right">801.9</td> +<td align="right">807.2</td> +<td align="right">-394.9</td> +</tr> +<tr class="odd"> +<td align="left">FOMC const</td> +<td align="right">7</td> +<td align="right">787.4</td> +<td align="right">793.6</td> +<td align="right">-386.7</td> +</tr> +<tr class="even"> +<td align="left">FOMC tc</td> +<td align="right">8</td> +<td align="right">788.9</td> +<td align="right">796.1</td> +<td align="right">-386.5</td> +</tr> +<tr class="odd"> +<td align="left">DFOP const</td> +<td align="right">9</td> +<td align="right">787.6</td> +<td align="right">795.6</td> +<td align="right">-384.8</td> +</tr> +<tr class="even"> +<td align="left">SFORB const</td> +<td align="right">9</td> +<td align="right">787.4</td> +<td align="right">795.4</td> +<td align="right">-384.7</td> +</tr> +<tr class="odd"> +<td align="left">HS const</td> +<td align="right">9</td> +<td align="right">781.9</td> +<td align="right">789.9</td> +<td align="right">-382.0</td> +</tr> +<tr class="even"> +<td align="left">DFOP tc</td> +<td align="right">10</td> +<td align="right">787.4</td> +<td align="right">796.3</td> +<td align="right">-383.7</td> +</tr> +<tr class="odd"> +<td align="left">SFORB tc</td> +<td align="right">10</td> +<td align="right">795.8</td> +<td align="right">804.7</td> +<td align="right">-387.9</td> +</tr> +<tr class="even"> +<td align="left">HS tc</td> +<td align="right">10</td> +<td align="right">783.7</td> +<td align="right">792.7</td> +<td align="right">-381.9</td> +</tr> +</tbody> +</table> +<p>The model comparisons show that the fits with constant variance are +consistently preferable to the corresponding fits with two-component +error for these data. This is confirmed by the fact that the parameter +<code>b.1</code> (the relative standard deviation in the fits obtained +with the saemix package), is ill-defined in all fits.</p> +<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<colgroup> +<col width="6%"> +<col width="44%"> +<col width="49%"> +</colgroup> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">sd(meso_0)</td> +<td align="left">sd(meso_0), b.1</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">sd(meso_0), sd(log_beta)</td> +<td align="left">sd(meso_0), sd(log_beta), b.1</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">sd(meso_0), sd(log_k1)</td> +<td align="left">sd(meso_0), sd(g_qlogis), b.1</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">sd(meso_free_0), sd(log_k_meso_free_bound)</td> +<td align="left">sd(meso_free_0), sd(log_k_meso_free_bound), b.1</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">sd(meso_0)</td> +<td align="left">sd(meso_0), b.1</td> +</tr> +</tbody> +</table> +<p>For obtaining fits with only well-defined random effects, we update +the set of fits, excluding random effects that were ill-defined +according to the <code>illparms</code> function.</p> +<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">f_saem_2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_saem_1</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/status.html">status</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left">OK</td> +<td align="left">OK</td> +</tr> +</tbody> +</table> +<p>The updated fits terminate without errors.</p> +<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="left">const</th> +<th align="left">tc</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">SFO</td> +<td align="left"></td> +<td align="left">b.1</td> +</tr> +<tr class="even"> +<td align="left">FOMC</td> +<td align="left"></td> +<td align="left">b.1</td> +</tr> +<tr class="odd"> +<td align="left">DFOP</td> +<td align="left"></td> +<td align="left">b.1</td> +</tr> +<tr class="even"> +<td align="left">SFORB</td> +<td align="left"></td> +<td align="left">b.1</td> +</tr> +<tr class="odd"> +<td align="left">HS</td> +<td align="left"></td> +<td align="left">b.1</td> +</tr> +</tbody> +</table> +<p>No ill-defined errors remain in the fits with constant variance.</p> +</div> +<div class="section level2"> +<h2 id="hierarchical-models-with-covariate">Hierarchical models with covariate<a class="anchor" aria-label="anchor" href="#hierarchical-models-with-covariate"></a> +</h2> +<p>In the following sections, hierarchical fits including a model for +the influence of pH on selected degradation parameters are shown for all +parent models. Constant variance is selected as the error model based on +the fits without covariate effects. Random effects that were ill-defined +in the fits without pH influence are excluded. A potential influence of +the soil pH is only included for parameters with a well-defined random +effect, because experience has shown that only for such parameters a +significant pH effect could be found.</p> +<div class="section level3"> +<h3 id="sfo">SFO<a class="anchor" aria-label="anchor" href="#sfo"></a> +</h3> +<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">sfo_pH</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="st">"meso_0"</span>, covariates <span class="op">=</span> <span class="va">pH</span>,</span> +<span> covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_k_meso</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">sfo_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_0</td> +<td align="right">91.35</td> +<td align="right">89.27</td> +<td align="right">93.43</td> +</tr> +<tr class="even"> +<td align="left">log_k_meso</td> +<td align="right">-6.66</td> +<td align="right">-7.97</td> +<td align="right">-5.35</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_k_meso)</td> +<td align="right">0.59</td> +<td align="right">0.37</td> +<td align="right">0.81</td> +</tr> +<tr class="even"> +<td align="left">a.1</td> +<td align="right">5.48</td> +<td align="right">4.71</td> +<td align="right">6.24</td> +</tr> +<tr class="odd"> +<td align="left">SD.log_k_meso</td> +<td align="right">0.35</td> +<td align="right">0.23</td> +<td align="right">0.47</td> +</tr> +</tbody> +</table> +<p>The parameter showing the pH influence in the above table is +<code>beta_pH(log_k_meso)</code>. Its confidence interval does not +include zero, indicating that the influence of soil pH on the log of the +degradation rate constant is significantly greater than zero.</p> +<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"SFO"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span>, <span class="va">sfo_pH</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets + + npar AIC BIC Lik Chisq Df Pr(>Chisq) +f_saem_2[["SFO", "const"]] 4 797.56 801.12 -394.78 +sfo_pH 5 783.09 787.54 -386.54 16.473 1 4.934e-05 *** +--- +Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre> +<p>The comparison with the SFO fit without covariate effect confirms +that considering the soil pH improves the model, both by comparison of +AIC and BIC and by the likelihood ratio test.</p> +<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">sfo_pH</span><span class="op">)</span></span></code></pre></div> +<p><img src="mesotrione_parent_2023_prebuilt_files/figure-html/unnamed-chunk-8-1.png" width="700" style="display: block; margin: auto;"></p> +<p>Endpoints for a model with covariates are by default calculated for +the median of the covariate values. This quantile can be adapted, or a +specific covariate value can be given as shown below.</p> +<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">sfo_pH</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +50% 5.75 + +$distimes + DT50 DT90 +meso 18.52069 61.52441</code></pre> +<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">sfo_pH</span>, covariate_quantile <span class="op">=</span> <span class="fl">0.9</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +90% 7.13 + +$distimes + DT50 DT90 +meso 8.237019 27.36278</code></pre> +<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">sfo_pH</span>, covariates <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>pH <span class="op">=</span> <span class="fl">7.0</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +User 7 + +$distimes + DT50 DT90 +meso 8.89035 29.5331</code></pre> +</div> +<div class="section level3"> +<h3 id="fomc">FOMC<a class="anchor" aria-label="anchor" href="#fomc"></a> +</h3> +<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">fomc_pH</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"FOMC"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="st">"meso_0"</span>, covariates <span class="op">=</span> <span class="va">pH</span>,</span> +<span> covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_alpha</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb28"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">fomc_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_0</td> +<td align="right">92.84</td> +<td align="right">90.75</td> +<td align="right">94.93</td> +</tr> +<tr class="even"> +<td align="left">log_alpha</td> +<td align="right">-2.21</td> +<td align="right">-3.49</td> +<td align="right">-0.92</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_alpha)</td> +<td align="right">0.58</td> +<td align="right">0.37</td> +<td align="right">0.79</td> +</tr> +<tr class="even"> +<td align="left">log_beta</td> +<td align="right">4.21</td> +<td align="right">3.44</td> +<td align="right">4.99</td> +</tr> +<tr class="odd"> +<td align="left">a.1</td> +<td align="right">5.03</td> +<td align="right">4.32</td> +<td align="right">5.73</td> +</tr> +<tr class="even"> +<td align="left">SD.log_alpha</td> +<td align="right">0.00</td> +<td align="right">-23.77</td> +<td align="right">23.78</td> +</tr> +<tr class="odd"> +<td align="left">SD.log_beta</td> +<td align="right">0.37</td> +<td align="right">0.01</td> +<td align="right">0.74</td> +</tr> +</tbody> +</table> +<p>As in the case of SFO, the confidence interval of the slope parameter +(here <code>beta_pH(log_alpha)</code>) quantifying the influence of soil +pH does not include zero, and the model comparison clearly indicates +that the model with covariate influence is preferable. However, the +random effect for <code>alpha</code> is not well-defined any more after +inclusion of the covariate effect (the confidence interval of +<code>SD.log_alpha</code> includes zero).</p> +<div class="sourceCode" id="cb29"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">fomc_pH</span><span class="op">)</span></span></code></pre></div> +<pre><code>[1] "sd(log_alpha)"</code></pre> +<p>Therefore, the model is updated without this random effect, and no +ill-defined parameters remain.</p> +<div class="sourceCode" id="cb31"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">fomc_pH_2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">fomc_pH</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_0"</span>, <span class="st">"log_alpha"</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">fomc_pH_2</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb32"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"FOMC"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span>, <span class="va">fomc_pH</span>, <span class="va">fomc_pH_2</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets + + npar AIC BIC Lik Chisq Df Pr(>Chisq) +f_saem_2[["FOMC", "const"]] 5 783.25 787.71 -386.63 +fomc_pH_2 6 767.49 772.83 -377.75 17.762 1 2.503e-05 *** +fomc_pH 7 770.07 776.30 -378.04 0.000 1 1 +--- +Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre> +<p>Model comparison indicates that including pH dependence significantly +improves the fit, and that the reduced model with covariate influence +results in the most preferable FOMC fit.</p> +<div class="sourceCode" id="cb34"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">fomc_pH_2</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_0</td> +<td align="right">93.05</td> +<td align="right">90.98</td> +<td align="right">95.13</td> +</tr> +<tr class="even"> +<td align="left">log_alpha</td> +<td align="right">-2.91</td> +<td align="right">-4.18</td> +<td align="right">-1.63</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_alpha)</td> +<td align="right">0.66</td> +<td align="right">0.44</td> +<td align="right">0.87</td> +</tr> +<tr class="even"> +<td align="left">log_beta</td> +<td align="right">3.95</td> +<td align="right">3.29</td> +<td align="right">4.62</td> +</tr> +<tr class="odd"> +<td align="left">a.1</td> +<td align="right">4.98</td> +<td align="right">4.28</td> +<td align="right">5.68</td> +</tr> +<tr class="even"> +<td align="left">SD.log_beta</td> +<td align="right">0.40</td> +<td align="right">0.26</td> +<td align="right">0.54</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb35"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">fomc_pH_2</span><span class="op">)</span></span></code></pre></div> +<p><img src="mesotrione_parent_2023_prebuilt_files/figure-html/unnamed-chunk-14-1.png" width="700" style="display: block; margin: auto;"></p> +<div class="sourceCode" id="cb36"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">fomc_pH_2</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +50% 5.75 + +$distimes + DT50 DT90 DT50back +meso 17.30248 82.91343 24.95943</code></pre> +<div class="sourceCode" id="cb38"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">fomc_pH_2</span>, covariates <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>pH <span class="op">=</span> <span class="fl">7</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +User 7 + +$distimes + DT50 DT90 DT50back +meso 6.986239 27.02927 8.136621</code></pre> +</div> +<div class="section level3"> +<h3 id="dfop">DFOP<a class="anchor" aria-label="anchor" href="#dfop"></a> +</h3> +<p>In the DFOP fits without covariate effects, random effects for two +degradation parameters (<code>k2</code> and <code>g</code>) were +identifiable.</p> +<div class="sourceCode" id="cb40"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_0</td> +<td align="right">93.61</td> +<td align="right">91.58</td> +<td align="right">95.63</td> +</tr> +<tr class="even"> +<td align="left">log_k1</td> +<td align="right">-1.53</td> +<td align="right">-2.27</td> +<td align="right">-0.79</td> +</tr> +<tr class="odd"> +<td align="left">log_k2</td> +<td align="right">-3.42</td> +<td align="right">-3.73</td> +<td align="right">-3.11</td> +</tr> +<tr class="even"> +<td align="left">g_qlogis</td> +<td align="right">-1.67</td> +<td align="right">-2.57</td> +<td align="right">-0.77</td> +</tr> +<tr class="odd"> +<td align="left">a.1</td> +<td align="right">4.74</td> +<td align="right">4.02</td> +<td align="right">5.45</td> +</tr> +<tr class="even"> +<td align="left">SD.log_k2</td> +<td align="right">0.60</td> +<td align="right">0.38</td> +<td align="right">0.81</td> +</tr> +<tr class="odd"> +<td align="left">SD.g_qlogis</td> +<td align="right">0.94</td> +<td align="right">0.33</td> +<td align="right">1.54</td> +</tr> +</tbody> +</table> +<p>A fit with pH dependent degradation parameters was obtained by +excluding the same random effects as in the refined DFOP fit without +covariate influence, and including covariate models for the two +identifiable parameters <code>k2</code> and <code>g</code>.</p> +<div class="sourceCode" id="cb41"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">dfop_pH</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_0"</span>, <span class="st">"log_k1"</span><span class="op">)</span>,</span> +<span> covariates <span class="op">=</span> <span class="va">pH</span>,</span> +<span> covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_k2</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">g_qlogis</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<p>The corresponding parameters for the influence of soil pH are +<code>beta_pH(log_k2)</code> for the influence of soil pH on +<code>k2</code>, and <code>beta_pH(g_qlogis)</code> for its influence on +<code>g</code>.</p> +<div class="sourceCode" id="cb42"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">dfop_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_0</td> +<td align="right">92.84</td> +<td align="right">90.85</td> +<td align="right">94.84</td> +</tr> +<tr class="even"> +<td align="left">log_k1</td> +<td align="right">-2.82</td> +<td align="right">-3.09</td> +<td align="right">-2.54</td> +</tr> +<tr class="odd"> +<td align="left">log_k2</td> +<td align="right">-11.48</td> +<td align="right">-15.32</td> +<td align="right">-7.64</td> +</tr> +<tr class="even"> +<td align="left">beta_pH(log_k2)</td> +<td align="right">1.31</td> +<td align="right">0.69</td> +<td align="right">1.92</td> +</tr> +<tr class="odd"> +<td align="left">g_qlogis</td> +<td align="right">3.13</td> +<td align="right">0.47</td> +<td align="right">5.80</td> +</tr> +<tr class="even"> +<td align="left">beta_pH(g_qlogis)</td> +<td align="right">-0.57</td> +<td align="right">-1.04</td> +<td align="right">-0.09</td> +</tr> +<tr class="odd"> +<td align="left">a.1</td> +<td align="right">4.96</td> +<td align="right">4.26</td> +<td align="right">5.65</td> +</tr> +<tr class="even"> +<td align="left">SD.log_k2</td> +<td align="right">0.76</td> +<td align="right">0.47</td> +<td align="right">1.05</td> +</tr> +<tr class="odd"> +<td align="left">SD.g_qlogis</td> +<td align="right">0.01</td> +<td align="right">-9.96</td> +<td align="right">9.97</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb43"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">dfop_pH</span><span class="op">)</span></span></code></pre></div> +<pre><code>[1] "sd(g_qlogis)"</code></pre> +<p>Confidence intervals for neither of them include zero, indicating a +significant difference from zero. However, the random effect for +<code>g</code> is now ill-defined. The fit is updated without this +ill-defined random effect.</p> +<div class="sourceCode" id="cb45"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">dfop_pH_2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">dfop_pH</span>,</span> +<span> no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_0"</span>, <span class="st">"log_k1"</span>, <span class="st">"g_qlogis"</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">dfop_pH_2</span><span class="op">)</span></span></code></pre></div> +<pre><code>[1] "beta_pH(g_qlogis)"</code></pre> +<p>Now, the slope parameter for the pH effect on <code>g</code> is +ill-defined. Therefore, another attempt is made without the +corresponding covariate model.</p> +<div class="sourceCode" id="cb47"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">dfop_pH_3</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_0"</span>, <span class="st">"log_k1"</span><span class="op">)</span>,</span> +<span> covariates <span class="op">=</span> <span class="va">pH</span>,</span> +<span> covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_k2</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">dfop_pH_3</span><span class="op">)</span></span></code></pre></div> +<pre><code>[1] "sd(g_qlogis)"</code></pre> +<p>As the random effect for <code>g</code> is again ill-defined, the fit +is repeated without it.</p> +<div class="sourceCode" id="cb49"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">dfop_pH_4</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">dfop_pH_3</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_0"</span>, <span class="st">"log_k1"</span>, <span class="st">"g_qlogis"</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">dfop_pH_4</span><span class="op">)</span></span></code></pre></div> +<p>While no ill-defined parameters remain, model comparison suggests +that the previous model <code>dfop_pH_2</code> with two pH dependent +parameters is preferable, based on information criteria as well as based +on the likelihood ratio test.</p> +<div class="sourceCode" id="cb50"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span>, <span class="va">dfop_pH</span>, <span class="va">dfop_pH_2</span>, <span class="va">dfop_pH_3</span>, <span class="va">dfop_pH_4</span><span class="op">)</span></span></code></pre></div> +<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets + + npar AIC BIC Lik +f_saem_2[["DFOP", "const"]] 7 782.94 789.18 -384.47 +dfop_pH_4 7 767.35 773.58 -376.68 +dfop_pH_2 8 765.14 772.26 -374.57 +dfop_pH_3 8 769.00 776.12 -376.50 +dfop_pH 9 769.10 777.11 -375.55</code></pre> +<div class="sourceCode" id="cb52"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">dfop_pH_2</span>, <span class="va">dfop_pH_4</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets + + npar AIC BIC Lik Chisq Df Pr(>Chisq) +dfop_pH_4 7 767.35 773.58 -376.68 +dfop_pH_2 8 765.14 772.26 -374.57 4.2153 1 0.04006 * +--- +Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre> +<p>When focussing on parameter identifiability using the test if the +confidence interval includes zero, <code>dfop_pH_4</code> would still be +the preferred model. However, it should be kept in mind that parameter +confidence intervals are constructed using a simple linearisation of the +likelihood. As the confidence interval of the random effect for +<code>g</code> only marginally includes zero, it is suggested that this +is acceptable, and that <code>dfop_pH_2</code> can be considered the +most preferable model.</p> +<div class="sourceCode" id="cb54"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">dfop_pH_2</span><span class="op">)</span></span></code></pre></div> +<p><img src="mesotrione_parent_2023_prebuilt_files/figure-html/unnamed-chunk-19-1.png" width="700" style="display: block; margin: auto;"></p> +<div class="sourceCode" id="cb55"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">dfop_pH_2</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +50% 5.75 + +$distimes + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 18.36876 73.51841 22.13125 4.191901 23.98672</code></pre> +<div class="sourceCode" id="cb57"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">dfop_pH_2</span>, covariates <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>pH <span class="op">=</span> <span class="fl">7</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +User 7 + +$distimes + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 8.346428 28.34437 8.532507 4.191901 8.753618</code></pre> +</div> +<div class="section level3"> +<h3 id="sforb">SFORB<a class="anchor" aria-label="anchor" href="#sforb"></a> +</h3> +<div class="sourceCode" id="cb59"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">sforb_pH</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"SFORB"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_free_0"</span>, <span class="st">"log_k_meso_free_bound"</span><span class="op">)</span>,</span> +<span> covariates <span class="op">=</span> <span class="va">pH</span>,</span> +<span> covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_k_meso_free</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">log_k_meso_bound_free</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb60"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">sforb_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_free_0</td> +<td align="right">93.42</td> +<td align="right">91.32</td> +<td align="right">95.52</td> +</tr> +<tr class="even"> +<td align="left">log_k_meso_free</td> +<td align="right">-5.37</td> +<td align="right">-6.94</td> +<td align="right">-3.81</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_k_meso_free)</td> +<td align="right">0.42</td> +<td align="right">0.18</td> +<td align="right">0.67</td> +</tr> +<tr class="even"> +<td align="left">log_k_meso_free_bound</td> +<td align="right">-3.49</td> +<td align="right">-4.92</td> +<td align="right">-2.05</td> +</tr> +<tr class="odd"> +<td align="left">log_k_meso_bound_free</td> +<td align="right">-9.98</td> +<td align="right">-19.22</td> +<td align="right">-0.74</td> +</tr> +<tr class="even"> +<td align="left">beta_pH(log_k_meso_bound_free)</td> +<td align="right">1.23</td> +<td align="right">-0.21</td> +<td align="right">2.67</td> +</tr> +<tr class="odd"> +<td align="left">a.1</td> +<td align="right">4.90</td> +<td align="right">4.18</td> +<td align="right">5.63</td> +</tr> +<tr class="even"> +<td align="left">SD.log_k_meso_free</td> +<td align="right">0.35</td> +<td align="right">0.23</td> +<td align="right">0.47</td> +</tr> +<tr class="odd"> +<td align="left">SD.log_k_meso_bound_free</td> +<td align="right">0.13</td> +<td align="right">-1.95</td> +<td align="right">2.20</td> +</tr> +</tbody> +</table> +<p>The confidence interval of +<code>beta_pH(log_k_meso_bound_free)</code> includes zero, indicating +that the influence of soil pH on <code>k_meso_bound_free</code> cannot +reliably be quantified. Also, the confidence interval for the random +effect on this parameter (<code>SD.log_k_meso_bound_free</code>) +includes zero.</p> +<p>Using the <code>illparms</code> function, these ill-defined +parameters can be found more conveniently.</p> +<div class="sourceCode" id="cb61"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">sforb_pH</span><span class="op">)</span></span></code></pre></div> +<pre><code>[1] "sd(log_k_meso_bound_free)" "beta_pH(log_k_meso_bound_free)"</code></pre> +<p>To remove the ill-defined parameters, a second variant of the SFORB +model with pH influence is fitted. No ill-defined parameters remain.</p> +<div class="sourceCode" id="cb63"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">sforb_pH_2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">sforb_pH</span>,</span> +<span> no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_free_0"</span>, <span class="st">"log_k_meso_free_bound"</span>, <span class="st">"log_k_meso_bound_free"</span><span class="op">)</span>,</span> +<span> covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_k_meso_free</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">sforb_pH_2</span><span class="op">)</span></span></code></pre></div> +<p>The model comparison of the SFORB fits includes the refined model +without covariate effect, and both versions of the SFORB fit with +covariate effect.</p> +<div class="sourceCode" id="cb64"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"SFORB"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span>, <span class="va">sforb_pH</span>, <span class="va">sforb_pH_2</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets + + npar AIC BIC Lik Chisq Df Pr(>Chisq) +f_saem_2[["SFORB", "const"]] 7 783.40 789.63 -384.70 +sforb_pH_2 7 770.94 777.17 -378.47 12.4616 0 +sforb_pH 9 768.81 776.83 -375.41 6.1258 2 0.04675 * +--- +Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre> +<p>The first model including pH influence is preferable based on +information criteria and the likelihood ratio test. However, as it is +not fully identifiable, the second model is selected.</p> +<div class="sourceCode" id="cb66"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">sforb_pH_2</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_free_0</td> +<td align="right">93.32</td> +<td align="right">91.16</td> +<td align="right">95.48</td> +</tr> +<tr class="even"> +<td align="left">log_k_meso_free</td> +<td align="right">-6.15</td> +<td align="right">-7.43</td> +<td align="right">-4.86</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_k_meso_free)</td> +<td align="right">0.54</td> +<td align="right">0.33</td> +<td align="right">0.75</td> +</tr> +<tr class="even"> +<td align="left">log_k_meso_free_bound</td> +<td align="right">-3.80</td> +<td align="right">-5.20</td> +<td align="right">-2.40</td> +</tr> +<tr class="odd"> +<td align="left">log_k_meso_bound_free</td> +<td align="right">-2.95</td> +<td align="right">-4.26</td> +<td align="right">-1.64</td> +</tr> +<tr class="even"> +<td align="left">a.1</td> +<td align="right">5.08</td> +<td align="right">4.38</td> +<td align="right">5.79</td> +</tr> +<tr class="odd"> +<td align="left">SD.log_k_meso_free</td> +<td align="right">0.33</td> +<td align="right">0.22</td> +<td align="right">0.45</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb67"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">sforb_pH_2</span><span class="op">)</span></span></code></pre></div> +<p><img src="mesotrione_parent_2023_prebuilt_files/figure-html/unnamed-chunk-25-1.png" width="700" style="display: block; margin: auto;"></p> +<div class="sourceCode" id="cb68"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">sforb_pH_2</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +50% 5.75 + +$ff +meso_free + 1 + +$SFORB + meso_b1 meso_b2 meso_g +0.09735824 0.02631699 0.31602120 + +$distimes + DT50 DT90 DT50back DT50_meso_b1 DT50_meso_b2 +meso 16.86549 73.15824 22.02282 7.119554 26.33839</code></pre> +<div class="sourceCode" id="cb70"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">sforb_pH_2</span>, covariates <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>pH <span class="op">=</span> <span class="fl">7</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +User 7 + +$ff +meso_free + 1 + +$SFORB + meso_b1 meso_b2 meso_g +0.13315233 0.03795988 0.61186191 + +$distimes + DT50 DT90 DT50back DT50_meso_b1 DT50_meso_b2 +meso 7.932495 36.93311 11.11797 5.205671 18.26</code></pre> +</div> +<div class="section level3"> +<h3 id="hs">HS<a class="anchor" aria-label="anchor" href="#hs"></a> +</h3> +<div class="sourceCode" id="cb72"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">hs_pH</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_sep_const</span><span class="op">[</span><span class="st">"HS"</span>, <span class="op">]</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"meso_0"</span><span class="op">)</span>,</span> +<span> covariates <span class="op">=</span> <span class="va">pH</span>,</span> +<span> covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_k1</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">log_k2</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">log_tb</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<div class="sourceCode" id="cb73"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">hs_pH</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_0</td> +<td align="right">93.33</td> +<td align="right">91.47</td> +<td align="right">95.19</td> +</tr> +<tr class="even"> +<td align="left">log_k1</td> +<td align="right">-5.81</td> +<td align="right">-7.27</td> +<td align="right">-4.36</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_k1)</td> +<td align="right">0.47</td> +<td align="right">0.23</td> +<td align="right">0.72</td> +</tr> +<tr class="even"> +<td align="left">log_k2</td> +<td align="right">-6.80</td> +<td align="right">-8.76</td> +<td align="right">-4.83</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_k2)</td> +<td align="right">0.54</td> +<td align="right">0.21</td> +<td align="right">0.87</td> +</tr> +<tr class="even"> +<td align="left">log_tb</td> +<td align="right">3.25</td> +<td align="right">1.25</td> +<td align="right">5.25</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_tb)</td> +<td align="right">-0.10</td> +<td align="right">-0.43</td> +<td align="right">0.23</td> +</tr> +<tr class="even"> +<td align="left">a.1</td> +<td align="right">4.49</td> +<td align="right">3.78</td> +<td align="right">5.21</td> +</tr> +<tr class="odd"> +<td align="left">SD.log_k1</td> +<td align="right">0.37</td> +<td align="right">0.24</td> +<td align="right">0.51</td> +</tr> +<tr class="even"> +<td align="left">SD.log_k2</td> +<td align="right">0.29</td> +<td align="right">0.10</td> +<td align="right">0.48</td> +</tr> +<tr class="odd"> +<td align="left">SD.log_tb</td> +<td align="right">0.25</td> +<td align="right">-0.07</td> +<td align="right">0.57</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb74"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">hs_pH</span><span class="op">)</span></span></code></pre></div> +<pre><code>[1] "sd(log_tb)" "beta_pH(log_tb)"</code></pre> +<p>According to the output of the <code>illparms</code> function, the +random effect on the break time <code>tb</code> cannot reliably be +quantified, neither can the influence of soil pH on <code>tb</code>. The +fit is repeated without the corresponding covariate model, and no +ill-defined parameters remain.</p> +<div class="sourceCode" id="cb76"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="va">hs_pH_2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">hs_pH</span>, covariate_models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="va">log_k1</span> <span class="op">~</span> <span class="va">pH</span>, <span class="va">log_k2</span> <span class="op">~</span> <span class="va">pH</span><span class="op">)</span><span class="op">)</span></span> +<span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">hs_pH_2</span><span class="op">)</span></span></code></pre></div> +<p>Model comparison confirms that this model is preferable to the fit +without covariate influence, and also to the first version with +covariate influence.</p> +<div class="sourceCode" id="cb77"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"HS"</span>, <span class="st">"const"</span><span class="op">]</span><span class="op">]</span>, <span class="va">hs_pH</span>, <span class="va">hs_pH_2</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div> +<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets + + npar AIC BIC Lik Chisq Df Pr(>Chisq) +f_saem_2[["HS", "const"]] 8 780.08 787.20 -382.04 +hs_pH_2 10 766.47 775.37 -373.23 17.606 2 0.0001503 *** +hs_pH 11 769.80 779.59 -373.90 0.000 1 1.0000000 +--- +Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre> +<div class="sourceCode" id="cb79"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">hs_pH_2</span><span class="op">)</span><span class="op">$</span><span class="va">confint_trans</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></code></pre></div> +<table class="table"> +<thead><tr class="header"> +<th align="left"></th> +<th align="right">est.</th> +<th align="right">lower</th> +<th align="right">upper</th> +</tr></thead> +<tbody> +<tr class="odd"> +<td align="left">meso_0</td> +<td align="right">93.33</td> +<td align="right">91.50</td> +<td align="right">95.15</td> +</tr> +<tr class="even"> +<td align="left">log_k1</td> +<td align="right">-5.68</td> +<td align="right">-7.09</td> +<td align="right">-4.27</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_k1)</td> +<td align="right">0.46</td> +<td align="right">0.22</td> +<td align="right">0.69</td> +</tr> +<tr class="even"> +<td align="left">log_k2</td> +<td align="right">-6.61</td> +<td align="right">-8.34</td> +<td align="right">-4.88</td> +</tr> +<tr class="odd"> +<td align="left">beta_pH(log_k2)</td> +<td align="right">0.50</td> +<td align="right">0.21</td> +<td align="right">0.79</td> +</tr> +<tr class="even"> +<td align="left">log_tb</td> +<td align="right">2.70</td> +<td align="right">2.33</td> +<td align="right">3.08</td> +</tr> +<tr class="odd"> +<td align="left">a.1</td> +<td align="right">4.45</td> +<td align="right">3.74</td> +<td align="right">5.16</td> +</tr> +<tr class="even"> +<td align="left">SD.log_k1</td> +<td align="right">0.36</td> +<td align="right">0.22</td> +<td align="right">0.49</td> +</tr> +<tr class="odd"> +<td align="left">SD.log_k2</td> +<td align="right">0.23</td> +<td align="right">0.02</td> +<td align="right">0.43</td> +</tr> +<tr class="even"> +<td align="left">SD.log_tb</td> +<td align="right">0.55</td> +<td align="right">0.25</td> +<td align="right">0.85</td> +</tr> +</tbody> +</table> +<div class="sourceCode" id="cb80"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">hs_pH_2</span><span class="op">)</span></span></code></pre></div> +<p><img src="mesotrione_parent_2023_prebuilt_files/figure-html/unnamed-chunk-30-1.png" width="700" style="display: block; margin: auto;"></p> +<div class="sourceCode" id="cb81"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">hs_pH_2</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +50% 5.75 + +$distimes + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 14.68725 82.45287 24.82079 14.68725 29.29299</code></pre> +<div class="sourceCode" id="cb83"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">hs_pH_2</span>, covariates <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>pH <span class="op">=</span> <span class="fl">7</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +User 7 + +$distimes + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 8.298536 38.85371 11.69613 8.298536 15.71561</code></pre> +</div> +<div class="section level3"> +<h3 id="comparison-across-parent-models">Comparison across parent models<a class="anchor" aria-label="anchor" href="#comparison-across-parent-models"></a> +</h3> +<p>After model reduction for all models with pH influence, they are +compared with each other.</p> +<div class="sourceCode" id="cb85"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">sfo_pH</span>, <span class="va">fomc_pH_2</span>, <span class="va">dfop_pH_2</span>, <span class="va">dfop_pH_4</span>, <span class="va">sforb_pH_2</span>, <span class="va">hs_pH_2</span><span class="op">)</span></span></code></pre></div> +<pre><code>Data: 116 observations of 1 variable(s) grouped in 18 datasets + + npar AIC BIC Lik +sfo_pH 5 783.09 787.54 -386.54 +fomc_pH_2 6 767.49 772.83 -377.75 +dfop_pH_4 7 767.35 773.58 -376.68 +sforb_pH_2 7 770.94 777.17 -378.47 +dfop_pH_2 8 765.14 772.26 -374.57 +hs_pH_2 10 766.47 775.37 -373.23</code></pre> +<p>The DFOP model with pH influence on <code>k2</code> and +<code>g</code> and a random effect only on <code>k2</code> is finally +selected as the best fit.</p> +<p>The endpoints resulting from this model are listed below. Please +refer to the Appendix for a detailed listing.</p> +<div class="sourceCode" id="cb87"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">dfop_pH_2</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +50% 5.75 + +$distimes + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 18.36876 73.51841 22.13125 4.191901 23.98672</code></pre> +<div class="sourceCode" id="cb89"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">dfop_pH_2</span>, covariates <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>pH <span class="op">=</span> <span class="fl">7</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<pre><code>$covariates + pH +User 7 + +$distimes + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 8.346428 28.34437 8.532507 4.191901 8.753618</code></pre> +</div> +</div> +<div class="section level2"> +<h2 id="conclusions">Conclusions<a class="anchor" aria-label="anchor" href="#conclusions"></a> +</h2> +<p>These evaluations demonstrate that covariate effects can be included +for all types of parent degradation models. These models can then be +further refined to make them fully identifiable.</p> +</div> +<div class="section level2"> +<h2 id="appendix">Appendix<a class="anchor" aria-label="anchor" href="#appendix"></a> +</h2> +<div class="section level3"> +<h3 id="hierarchical-fit-listings">Hierarchical fit listings<a class="anchor" aria-label="anchor" href="#hierarchical-fit-listings"></a> +</h3> +<div class="section level4"> +<h4 id="fits-without-covariate-effects">Fits without covariate effects<a class="anchor" aria-label="anchor" href="#fits-without-covariate-effects"></a> +</h4> +<caption> +Hierarchical SFO fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Tue May 13 19:59:35 2025 +Date of summary: Tue May 13 20:00:23 2025 + +Equations: +d_meso/dt = - k_meso * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 0.682 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_k_meso + 90.832 -3.192 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k_meso +meso_0 6.752 0.0000 +log_k_meso 0.000 0.9155 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 800 804.5 -395 + +Optimised parameters: + est. lower upper +meso_0 92.0705 89.9917 94.1493 +log_k_meso -3.1641 -3.4286 -2.8996 +a.1 5.4628 4.6421 6.2835 +SD.meso_0 0.0611 -98.3545 98.4767 +SD.log_k_meso 0.5616 0.3734 0.7499 + +Correlation: + meso_0 +log_k_meso 0.1132 + +Random effects: + est. lower upper +SD.meso_0 0.0611 -98.3545 98.4767 +SD.log_k_meso 0.5616 0.3734 0.7499 + +Variance model: + est. lower upper +a.1 5.463 4.642 6.284 + +Backtransformed parameters: + est. lower upper +meso_0 92.07053 89.99172 94.14933 +k_meso 0.04225 0.03243 0.05505 + +Estimated disappearance times: + DT50 DT90 +meso 16.41 54.5 + +</code></pre> +<p></p> +<caption> +Hierarchical FOMC fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Tue May 13 19:59:35 2025 +Date of summary: Tue May 13 20:00:23 2025 + +Equations: +d_meso/dt = - (alpha/beta) * 1/((time/beta) + 1) * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 0.817 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_alpha log_beta + 93.0520 0.6008 3.4176 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_alpha log_beta +meso_0 6.287 0.00 0.000 +log_alpha 0.000 1.53 0.000 +log_beta 0.000 0.00 1.724 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 787.4 793.6 -386.7 + +Optimised parameters: + est. lower upper +meso_0 93.5648 91.42864 95.7009 +log_alpha 0.7645 0.28068 1.2484 +log_beta 3.6597 3.05999 4.2594 +a.1 5.0708 4.29823 5.8435 +SD.meso_0 0.1691 -34.01517 34.3535 +SD.log_alpha 0.3764 0.05834 0.6945 +SD.log_beta 0.3903 -0.06074 0.8414 + +Correlation: + meso_0 log_lph +log_alpha -0.2839 +log_beta -0.3443 0.8855 + +Random effects: + est. lower upper +SD.meso_0 0.1691 -34.01517 34.3535 +SD.log_alpha 0.3764 0.05834 0.6945 +SD.log_beta 0.3903 -0.06074 0.8414 + +Variance model: + est. lower upper +a.1 5.071 4.298 5.843 + +Backtransformed parameters: + est. lower upper +meso_0 93.565 91.429 95.701 +alpha 2.148 1.324 3.485 +beta 38.850 21.327 70.770 + +Estimated disappearance times: + DT50 DT90 DT50back +meso 14.8 74.64 22.47 + +</code></pre> +<p></p> +<caption> +Hierarchical DFOP fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Tue May 13 19:59:35 2025 +Date of summary: Tue May 13 20:00:23 2025 + +Equations: +d_meso/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * + time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) + * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 1.188 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_k1 log_k2 g_qlogis +93.14689 -2.05241 -3.53079 -0.09522 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k1 log_k2 g_qlogis +meso_0 6.418 0.000 0.000 0.00 +log_k1 0.000 1.018 0.000 0.00 +log_k2 0.000 0.000 1.694 0.00 +g_qlogis 0.000 0.000 0.000 2.37 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 787.6 795.6 -384.8 + +Optimised parameters: + est. lower upper +meso_0 93.6684 91.63599 95.7008 +log_k1 -1.7354 -2.61433 -0.8565 +log_k2 -3.4015 -3.73323 -3.0697 +g_qlogis -1.6341 -2.66133 -0.6069 +a.1 4.7803 4.01269 5.5479 +SD.meso_0 0.1661 -30.97086 31.3031 +SD.log_k1 0.1127 -2.59680 2.8223 +SD.log_k2 0.6394 0.41499 0.8638 +SD.g_qlogis 0.8166 0.09785 1.5353 + +Correlation: + meso_0 log_k1 log_k2 +log_k1 0.1757 +log_k2 0.0199 0.2990 +g_qlogis 0.0813 -0.7431 -0.3826 + +Random effects: + est. lower upper +SD.meso_0 0.1661 -30.97086 31.3031 +SD.log_k1 0.1127 -2.59680 2.8223 +SD.log_k2 0.6394 0.41499 0.8638 +SD.g_qlogis 0.8166 0.09785 1.5353 + +Variance model: + est. lower upper +a.1 4.78 4.013 5.548 + +Backtransformed parameters: + est. lower upper +meso_0 93.66841 91.63599 95.70082 +k1 0.17633 0.07322 0.42466 +k2 0.03332 0.02392 0.04643 +g 0.16327 0.06529 0.35277 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 16.04 63.75 19.19 3.931 20.8 + +</code></pre> +<p></p> +<caption> +Hierarchical SFORB fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Tue May 13 19:59:35 2025 +Date of summary: Tue May 13 20:00:23 2025 + +Equations: +d_meso_free/dt = - k_meso_free * meso_free - k_meso_free_bound * + meso_free + k_meso_bound_free * meso_bound +d_meso_bound/dt = + k_meso_free_bound * meso_free - k_meso_bound_free * + meso_bound + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 1.223 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_free_0 log_k_meso_free log_k_meso_free_bound + 93.147 -2.305 -4.230 +log_k_meso_bound_free + -3.761 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_free_0 log_k_meso_free log_k_meso_free_bound +meso_free_0 6.418 0.0000 0.000 +log_k_meso_free 0.000 0.9276 0.000 +log_k_meso_free_bound 0.000 0.0000 2.272 +log_k_meso_bound_free 0.000 0.0000 0.000 + log_k_meso_bound_free +meso_free_0 0.000 +log_k_meso_free 0.000 +log_k_meso_free_bound 0.000 +log_k_meso_bound_free 1.447 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 787.4 795.4 -384.7 + +Optimised parameters: + est. lower upper +meso_free_0 93.6285 91.6262 95.631 +log_k_meso_free -2.8314 -3.1375 -2.525 +log_k_meso_free_bound -3.2213 -4.4695 -1.973 +log_k_meso_bound_free -2.4246 -3.5668 -1.282 +a.1 4.7372 3.9542 5.520 +SD.meso_free_0 0.1634 -32.7769 33.104 +SD.log_k_meso_free 0.4885 0.3080 0.669 +SD.log_k_meso_free_bound 0.2876 -1.7955 2.371 +SD.log_k_meso_bound_free 0.9942 0.2181 1.770 + +Correlation: + ms_fr_0 lg_k_m_ lg_k_ms_f_ +log_k_meso_free 0.2332 +log_k_meso_free_bound 0.1100 0.5964 +log_k_meso_bound_free -0.0413 0.3697 0.8025 + +Random effects: + est. lower upper +SD.meso_free_0 0.1634 -32.7769 33.104 +SD.log_k_meso_free 0.4885 0.3080 0.669 +SD.log_k_meso_free_bound 0.2876 -1.7955 2.371 +SD.log_k_meso_bound_free 0.9942 0.2181 1.770 + +Variance model: + est. lower upper +a.1 4.737 3.954 5.52 + +Backtransformed parameters: + est. lower upper +meso_free_0 93.62849 91.62622 95.63075 +k_meso_free 0.05893 0.04339 0.08004 +k_meso_free_bound 0.03990 0.01145 0.13903 +k_meso_bound_free 0.08851 0.02825 0.27736 + +Estimated Eigenvalues of SFORB model(s): +meso_b1 meso_b2 meso_g +0.15333 0.03402 0.20881 + +Resulting formation fractions: + ff +meso_free 1 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_meso_b1 DT50_meso_b2 +meso 14.79 60.81 18.3 4.521 20.37 + +</code></pre> +<p></p> +<caption> +Hierarchical HS fit with constant variance +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Tue May 13 19:59:36 2025 +Date of summary: Tue May 13 20:00:23 2025 + +Equations: +d_meso/dt = - ifelse(time <= tb, k1, k2) * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 1.307 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: +meso_0 log_k1 log_k2 log_tb +92.920 -2.409 -3.295 2.471 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k1 log_k2 log_tb +meso_0 6.477 0.0000 0.0000 0.00 +log_k1 0.000 0.8675 0.0000 0.00 +log_k2 0.000 0.0000 0.4035 0.00 +log_tb 0.000 0.0000 0.0000 1.16 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 781.9 789.9 -382 + +Optimised parameters: + est. lower upper +meso_0 93.34242 91.4730 95.2118 +log_k1 -2.77312 -3.0826 -2.4637 +log_k2 -3.61854 -3.8430 -3.3941 +log_tb 2.00266 1.3357 2.6696 +a.1 4.47693 3.7059 5.2479 +SD.meso_0 0.07963 -63.1661 63.3253 +SD.log_k1 0.47817 0.2467 0.7097 +SD.log_k2 0.39216 0.2137 0.5706 +SD.log_tb 0.94683 0.4208 1.4728 + +Correlation: + meso_0 log_k1 log_k2 +log_k1 0.1627 +log_k2 0.0063 -0.0301 +log_tb 0.0083 -0.3931 -0.1225 + +Random effects: + est. lower upper +SD.meso_0 0.07963 -63.1661 63.3253 +SD.log_k1 0.47817 0.2467 0.7097 +SD.log_k2 0.39216 0.2137 0.5706 +SD.log_tb 0.94683 0.4208 1.4728 + +Variance model: + est. lower upper +a.1 4.477 3.706 5.248 + +Backtransformed parameters: + est. lower upper +meso_0 93.34242 91.47303 95.21181 +k1 0.06247 0.04584 0.08512 +k2 0.02682 0.02143 0.03357 +tb 7.40872 3.80282 14.43376 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 16 76 22.88 11.1 25.84 + +</code></pre> +<p></p> +</div> +<div class="section level4"> +<h4 id="fits-with-covariate-effects">Fits with covariate effects<a class="anchor" aria-label="anchor" href="#fits-with-covariate-effects"></a> +</h4> +<caption> +Hierarchichal SFO fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Tue May 13 19:59:49 2025 +Date of summary: Tue May 13 20:00:23 2025 + +Equations: +d_meso/dt = - k_meso * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 1.739 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_k_meso + 90.832 -3.192 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k_meso +meso_0 6.752 0.0000 +log_k_meso 0.000 0.9155 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 783.1 787.5 -386.5 + +Optimised parameters: + est. lower upper +meso_0 91.3481 89.2688 93.4275 +log_k_meso -6.6614 -7.9715 -5.3514 +beta_pH(log_k_meso) 0.5871 0.3684 0.8059 +a.1 5.4750 4.7085 6.2415 +SD.log_k_meso 0.3471 0.2258 0.4684 + +Correlation: + meso_0 lg_k_ms +log_k_meso 0.0414 +beta_pH(log_k_meso) -0.0183 -0.9917 + +Random effects: + est. lower upper +SD.log_k_meso 0.3471 0.2258 0.4684 + +Variance model: + est. lower upper +a.1 5.475 4.709 6.242 + +Backtransformed parameters: + est. lower upper +meso_0 91.348139 8.927e+01 93.427476 +k_meso 0.001279 3.452e-04 0.004741 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated disappearance times: + DT50 DT90 +meso 18.52 61.52 + +</code></pre> +<p></p> +<caption> +Hierarchichal FOMC fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Tue May 13 19:59:51 2025 +Date of summary: Tue May 13 20:00:23 2025 + +Equations: +d_meso/dt = - (alpha/beta) * 1/((time/beta) + 1) * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 1.076 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_alpha log_beta + 93.0520 0.6008 3.4176 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_alpha log_beta +meso_0 6.287 0.00 0.000 +log_alpha 0.000 1.53 0.000 +log_beta 0.000 0.00 1.724 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 770.1 776.3 -378 + +Optimised parameters: + est. lower upper +meso_0 92.840646 90.750461 94.9308 +log_alpha -2.206602 -3.494546 -0.9187 +beta_pH(log_alpha) 0.577505 0.369805 0.7852 +log_beta 4.214099 3.438851 4.9893 +a.1 5.027768 4.322028 5.7335 +SD.log_alpha 0.004034 -23.766993 23.7751 +SD.log_beta 0.374640 0.009252 0.7400 + +Correlation: + meso_0 log_lph bt_H(_) +log_alpha -0.0865 +beta_pH(log_alpha) -0.0789 -0.8704 +log_beta -0.3544 0.3302 0.1628 + +Random effects: + est. lower upper +SD.log_alpha 0.004034 -23.766993 23.78 +SD.log_beta 0.374640 0.009252 0.74 + +Variance model: + est. lower upper +a.1 5.028 4.322 5.734 + +Backtransformed parameters: + est. lower upper +meso_0 92.8406 90.75046 94.9308 +alpha 0.1101 0.03036 0.3991 +beta 67.6332 31.15113 146.8404 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated disappearance times: + DT50 DT90 DT50back +meso 17.28 76.37 22.99 + +</code></pre> +<p></p> +<caption> +Refined hierarchichal FOMC fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Tue May 13 19:59:55 2025 +Date of summary: Tue May 13 20:00:23 2025 + +Equations: +d_meso/dt = - (alpha/beta) * 1/((time/beta) + 1) * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 3.361 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_alpha log_beta + 93.0520 0.6008 3.4176 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_alpha log_beta +meso_0 6.287 0.00 0.000 +log_alpha 0.000 1.53 0.000 +log_beta 0.000 0.00 1.724 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 767.5 772.8 -377.7 + +Optimised parameters: + est. lower upper +meso_0 93.0536 90.9771 95.1300 +log_alpha -2.9054 -4.1803 -1.6304 +beta_pH(log_alpha) 0.6590 0.4437 0.8744 +log_beta 3.9549 3.2860 4.6239 +a.1 4.9784 4.2815 5.6754 +SD.log_beta 0.4019 0.2632 0.5406 + +Correlation: + meso_0 log_lph bt_H(_) +log_alpha -0.0397 +beta_pH(log_alpha) -0.0899 -0.9146 +log_beta -0.3473 0.2038 0.1919 + +Random effects: + est. lower upper +SD.log_beta 0.4019 0.2632 0.5406 + +Variance model: + est. lower upper +a.1 4.978 4.281 5.675 + +Backtransformed parameters: + est. lower upper +meso_0 93.05359 90.97713 95.1300 +alpha 0.05473 0.01529 0.1958 +beta 52.19251 26.73597 101.8874 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated disappearance times: + DT50 DT90 DT50back +meso 17.3 82.91 24.96 + +</code></pre> +<p></p> +<caption> +Hierarchichal DFOP fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Tue May 13 19:59:58 2025 +Date of summary: Tue May 13 20:00:23 2025 + +Equations: +d_meso/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * + time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) + * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 1.758 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_k1 log_k2 g_qlogis +93.14689 -2.05241 -3.53079 -0.09522 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k1 log_k2 g_qlogis +meso_0 6.418 0.000 0.000 0.00 +log_k1 0.000 1.018 0.000 0.00 +log_k2 0.000 0.000 1.694 0.00 +g_qlogis 0.000 0.000 0.000 2.37 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 769.1 777.1 -375.5 + +Optimised parameters: + est. lower upper +meso_0 92.843344 90.8464 94.84028 +log_k1 -2.815685 -3.0888 -2.54261 +log_k2 -11.479779 -15.3203 -7.63923 +beta_pH(log_k2) 1.308417 0.6948 1.92203 +g_qlogis 3.133036 0.4657 5.80035 +beta_pH(g_qlogis) -0.565988 -1.0394 -0.09262 +a.1 4.955518 4.2597 5.65135 +SD.log_k2 0.758963 0.4685 1.04943 +SD.g_qlogis 0.005215 -9.9561 9.96656 + +Correlation: + meso_0 log_k1 log_k2 b_H(_2) g_qlogs +log_k1 0.2706 +log_k2 -0.0571 0.1096 +beta_pH(log_k2) 0.0554 -0.1291 -0.9937 +g_qlogis -0.1125 -0.5062 -0.1305 0.1294 +beta_pH(g_qlogis) 0.1267 0.4226 0.0419 -0.0438 -0.9864 + +Random effects: + est. lower upper +SD.log_k2 0.758963 0.4685 1.049 +SD.g_qlogis 0.005215 -9.9561 9.967 + +Variance model: + est. lower upper +a.1 4.956 4.26 5.651 + +Backtransformed parameters: + est. lower upper +meso_0 9.284e+01 9.085e+01 9.484e+01 +k1 5.986e-02 4.556e-02 7.866e-02 +k2 1.034e-05 2.221e-07 4.812e-04 +g 9.582e-01 6.144e-01 9.970e-01 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 20.23 88.45 26.62 11.58 36.23 + +</code></pre> +<p></p> +<caption> +Refined hierarchical DFOP fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Tue May 13 20:00:03 2025 +Date of summary: Tue May 13 20:00:23 2025 + +Equations: +d_meso/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * + time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) + * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 4.465 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_k1 log_k2 g_qlogis +93.14689 -2.05241 -3.53079 -0.09522 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k1 log_k2 g_qlogis +meso_0 6.418 0.000 0.000 0.00 +log_k1 0.000 1.018 0.000 0.00 +log_k2 0.000 0.000 1.694 0.00 +g_qlogis 0.000 0.000 0.000 2.37 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 765.1 772.3 -374.6 + +Optimised parameters: + est. lower upper +meso_0 93.3333 91.2427 95.42394 +log_k1 -1.7997 -2.9124 -0.68698 +log_k2 -8.1810 -10.1819 -6.18008 +beta_pH(log_k2) 0.8064 0.4903 1.12257 +g_qlogis 3.3513 -1.1792 7.88182 +beta_pH(g_qlogis) -0.8672 -1.7661 0.03177 +a.1 4.9158 4.2277 5.60390 +SD.log_k2 0.3946 0.2565 0.53281 + +Correlation: + meso_0 log_k1 log_k2 b_H(_2) g_qlogs +log_k1 0.1730 +log_k2 0.0442 0.5370 +beta_pH(log_k2) -0.0392 -0.4880 -0.9923 +g_qlogis -0.1536 0.1431 -0.1129 0.1432 +beta_pH(g_qlogis) 0.1504 -0.3151 -0.0196 -0.0212 -0.9798 + +Random effects: + est. lower upper +SD.log_k2 0.3946 0.2565 0.5328 + +Variance model: + est. lower upper +a.1 4.916 4.228 5.604 + +Backtransformed parameters: + est. lower upper +meso_0 9.333e+01 9.124e+01 95.42394 +k1 1.654e-01 5.435e-02 0.50309 +k2 2.799e-04 3.785e-05 0.00207 +g 9.661e-01 2.352e-01 0.99962 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 18.37 73.52 22.13 4.192 23.99 + +</code></pre> +<p></p> +<caption> +Further refined hierarchical DFOP fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Tue May 13 20:00:10 2025 +Date of summary: Tue May 13 20:00:23 2025 + +Equations: +d_meso/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * + time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) + * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 2.781 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_0 log_k1 log_k2 g_qlogis +93.14689 -2.05241 -3.53079 -0.09522 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k1 log_k2 g_qlogis +meso_0 6.418 0.000 0.000 0.00 +log_k1 0.000 1.018 0.000 0.00 +log_k2 0.000 0.000 1.694 0.00 +g_qlogis 0.000 0.000 0.000 2.37 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 767.4 773.6 -376.7 + +Optimised parameters: + est. lower upper +meso_0 93.3011 91.1905 95.4118 +log_k1 -2.1487 -2.7607 -1.5367 +log_k2 -8.1039 -10.4225 -5.7853 +beta_pH(log_k2) 0.7821 0.4126 1.1517 +g_qlogis -1.0373 -1.9337 -0.1409 +a.1 5.0095 4.3082 5.7108 +SD.log_k2 0.4622 0.3009 0.6235 + +Correlation: + meso_0 log_k1 log_k2 b_H(_2) +log_k1 0.2179 +log_k2 0.0337 0.5791 +beta_pH(log_k2) -0.0326 -0.5546 -0.9932 +g_qlogis 0.0237 -0.8479 -0.6571 0.6123 + +Random effects: + est. lower upper +SD.log_k2 0.4622 0.3009 0.6235 + +Variance model: + est. lower upper +a.1 5.009 4.308 5.711 + +Backtransformed parameters: + est. lower upper +meso_0 9.330e+01 9.119e+01 95.411751 +k1 1.166e-01 6.325e-02 0.215084 +k2 3.024e-04 2.975e-05 0.003072 +g 2.617e-01 1.263e-01 0.464832 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 17.09 73.67 22.18 5.943 25.54 + +</code></pre> +<p></p> +<caption> +Hierarchichal SFORB fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Tue May 13 20:00:14 2025 +Date of summary: Tue May 13 20:00:23 2025 + +Equations: +d_meso_free/dt = - k_meso_free * meso_free - k_meso_free_bound * + meso_free + k_meso_bound_free * meso_bound +d_meso_bound/dt = + k_meso_free_bound * meso_free - k_meso_bound_free * + meso_bound + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 3.54 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_free_0 log_k_meso_free log_k_meso_free_bound + 93.147 -2.305 -4.230 +log_k_meso_bound_free + -3.761 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_free_0 log_k_meso_free log_k_meso_free_bound +meso_free_0 6.418 0.0000 0.000 +log_k_meso_free 0.000 0.9276 0.000 +log_k_meso_free_bound 0.000 0.0000 2.272 +log_k_meso_bound_free 0.000 0.0000 0.000 + log_k_meso_bound_free +meso_free_0 0.000 +log_k_meso_free 0.000 +log_k_meso_free_bound 0.000 +log_k_meso_bound_free 1.447 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 768.8 776.8 -375.4 + +Optimised parameters: + est. lower upper +meso_free_0 93.4204 91.3213 95.5195 +log_k_meso_free -5.3742 -6.9366 -3.8117 +beta_pH(log_k_meso_free) 0.4232 0.1769 0.6695 +log_k_meso_free_bound -3.4889 -4.9243 -2.0535 +log_k_meso_bound_free -9.9797 -19.2232 -0.7362 +beta_pH(log_k_meso_bound_free) 1.2290 -0.2107 2.6687 +a.1 4.9031 4.1795 5.6268 +SD.log_k_meso_free 0.3454 0.2252 0.4656 +SD.log_k_meso_bound_free 0.1277 -1.9459 2.2012 + +Correlation: + ms_fr_0 lg_k_m_ b_H(___) lg_k_ms_f_ lg_k_ms_b_ +log_k_meso_free 0.1493 +beta_pH(log_k_meso_free) -0.0930 -0.9854 +log_k_meso_free_bound 0.2439 0.4621 -0.3492 +log_k_meso_bound_free 0.2188 0.1292 -0.0339 0.7287 +beta_pH(log_k_meso_bound_free) -0.2216 -0.0797 -0.0111 -0.6566 -0.9934 + +Random effects: + est. lower upper +SD.log_k_meso_free 0.3454 0.2252 0.4656 +SD.log_k_meso_bound_free 0.1277 -1.9459 2.2012 + +Variance model: + est. lower upper +a.1 4.903 4.18 5.627 + +Backtransformed parameters: + est. lower upper +meso_free_0 9.342e+01 9.132e+01 95.51946 +k_meso_free 4.635e-03 9.716e-04 0.02211 +k_meso_free_bound 3.054e-02 7.268e-03 0.12829 +k_meso_bound_free 4.633e-05 4.482e-09 0.47894 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated Eigenvalues of SFORB model(s): +meso_b1 meso_b2 meso_g + 0.1121 0.0256 0.3148 + +Resulting formation fractions: + ff +meso_free 1 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_meso_b1 DT50_meso_b2 +meso 16.42 75.2 22.64 6.185 27.08 + +</code></pre> +<p> </p> +<caption> +Refined hierarchichal SFORB fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Tue May 13 20:00:18 2025 +Date of summary: Tue May 13 20:00:23 2025 + +Equations: +d_meso_free/dt = - k_meso_free * meso_free - k_meso_free_bound * + meso_free + k_meso_bound_free * meso_bound +d_meso_bound/dt = + k_meso_free_bound * meso_free - k_meso_bound_free * + meso_bound + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 2.815 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: + meso_free_0 log_k_meso_free log_k_meso_free_bound + 93.147 -2.305 -4.230 +log_k_meso_bound_free + -3.761 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_free_0 log_k_meso_free log_k_meso_free_bound +meso_free_0 6.418 0.0000 0.000 +log_k_meso_free 0.000 0.9276 0.000 +log_k_meso_free_bound 0.000 0.0000 2.272 +log_k_meso_bound_free 0.000 0.0000 0.000 + log_k_meso_bound_free +meso_free_0 0.000 +log_k_meso_free 0.000 +log_k_meso_free_bound 0.000 +log_k_meso_bound_free 1.447 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 770.9 777.2 -378.5 + +Optimised parameters: + est. lower upper +meso_free_0 93.3196 91.1633 95.4760 +log_k_meso_free -6.1460 -7.4306 -4.8614 +beta_pH(log_k_meso_free) 0.5435 0.3329 0.7542 +log_k_meso_free_bound -3.8001 -5.2027 -2.3975 +log_k_meso_bound_free -2.9462 -4.2565 -1.6359 +a.1 5.0825 4.3793 5.7856 +SD.log_k_meso_free 0.3338 0.2175 0.4502 + +Correlation: + ms_fr_0 lg_k_m_ b_H(___ lg_k_ms_f_ +log_k_meso_free 0.1086 +beta_pH(log_k_meso_free) -0.0426 -0.9821 +log_k_meso_free_bound 0.2513 0.1717 -0.0409 +log_k_meso_bound_free 0.1297 0.1171 -0.0139 0.9224 + +Random effects: + est. lower upper +SD.log_k_meso_free 0.3338 0.2175 0.4502 + +Variance model: + est. lower upper +a.1 5.082 4.379 5.786 + +Backtransformed parameters: + est. lower upper +meso_free_0 93.319649 9.116e+01 95.47601 +k_meso_free 0.002142 5.928e-04 0.00774 +k_meso_free_bound 0.022369 5.502e-03 0.09095 +k_meso_bound_free 0.052539 1.417e-02 0.19478 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated Eigenvalues of SFORB model(s): +meso_b1 meso_b2 meso_g +0.09736 0.02632 0.31602 + +Resulting formation fractions: + ff +meso_free 1 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_meso_b1 DT50_meso_b2 +meso 16.87 73.16 22.02 7.12 26.34 + +</code></pre> +<p> </p> +<caption> +Hierarchichal HS fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Tue May 13 20:00:20 2025 +Date of summary: Tue May 13 20:00:23 2025 + +Equations: +d_meso/dt = - ifelse(time <= tb, k1, k2) * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 1.849 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: +meso_0 log_k1 log_k2 log_tb +92.920 -2.409 -3.295 2.471 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k1 log_k2 log_tb +meso_0 6.477 0.0000 0.0000 0.00 +log_k1 0.000 0.8675 0.0000 0.00 +log_k2 0.000 0.0000 0.4035 0.00 +log_tb 0.000 0.0000 0.0000 1.16 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 769.8 779.6 -373.9 + +Optimised parameters: + est. lower upper +meso_0 93.32599 91.4658 95.1862 +log_k1 -5.81463 -7.2710 -4.3583 +beta_pH(log_k1) 0.47472 0.2334 0.7160 +log_k2 -6.79633 -8.7605 -4.8322 +beta_pH(log_k2) 0.54151 0.2124 0.8706 +log_tb 3.24674 1.2470 5.2465 +beta_pH(log_tb) -0.09889 -0.4258 0.2280 +a.1 4.49487 3.7766 5.2132 +SD.log_k1 0.37191 0.2370 0.5068 +SD.log_k2 0.29210 0.0994 0.4848 +SD.log_tb 0.25353 -0.0664 0.5735 + +Correlation: + meso_0 log_k1 b_H(_1) log_k2 b_H(_2) log_tb +log_k1 0.0744 +beta_pH(log_k1) -0.0452 -0.9915 +log_k2 0.0066 -0.0363 0.0376 +beta_pH(log_k2) -0.0071 0.0372 -0.0391 -0.9939 +log_tb -0.0238 -0.1483 0.1362 -0.3836 0.3696 +beta_pH(log_tb) 0.0097 0.1359 -0.1265 0.3736 -0.3653 -0.9905 + +Random effects: + est. lower upper +SD.log_k1 0.3719 0.2370 0.5068 +SD.log_k2 0.2921 0.0994 0.4848 +SD.log_tb 0.2535 -0.0664 0.5735 + +Variance model: + est. lower upper +a.1 4.495 3.777 5.213 + +Backtransformed parameters: + est. lower upper +meso_0 93.325994 9.147e+01 9.519e+01 +k1 0.002984 6.954e-04 1.280e-02 +k2 0.001118 1.568e-04 7.969e-03 +tb 25.706437 3.480e+00 1.899e+02 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 15.65 79.63 23.97 15.16 27.55 + +</code></pre> +<p> </p> +<caption> +Refined hierarchichal HS fit with pH influence +</caption> +<pre><code> +saemix version used for fitting: 3.3 +mkin version used for pre-fitting: 1.2.10 +R version used for fitting: 4.5.0 +Date of fit: Tue May 13 20:00:22 2025 +Date of summary: Tue May 13 20:00:23 2025 + +Equations: +d_meso/dt = - ifelse(time <= tb, k1, k2) * meso + +Data: +116 observations of 1 variable(s) grouped in 18 datasets + +Model predictions using solution type analytical + +Fitted in 1.439 s +Using 300, 100 iterations and 3 chains + +Variance model: Constant variance + +Starting values for degradation parameters: +meso_0 log_k1 log_k2 log_tb +92.920 -2.409 -3.295 2.471 + +Fixed degradation parameter values: +None + +Starting values for random effects (square root of initial entries in omega): + meso_0 log_k1 log_k2 log_tb +meso_0 6.477 0.0000 0.0000 0.00 +log_k1 0.000 0.8675 0.0000 0.00 +log_k2 0.000 0.0000 0.4035 0.00 +log_tb 0.000 0.0000 0.0000 1.16 + +Starting values for error model parameters: +a.1 + 1 + +Results: + +Likelihood computed by importance sampling + AIC BIC logLik + 766.5 775.4 -373.2 + +Optimised parameters: + est. lower upper +meso_0 93.3251 91.49823 95.1520 +log_k1 -5.6796 -7.08789 -4.2714 +beta_pH(log_k1) 0.4567 0.22400 0.6894 +log_k2 -6.6083 -8.33839 -4.8781 +beta_pH(log_k2) 0.4982 0.20644 0.7899 +log_tb 2.7040 2.33033 3.0777 +a.1 4.4452 3.73537 5.1551 +SD.log_k1 0.3570 0.22104 0.4930 +SD.log_k2 0.2252 0.01864 0.4318 +SD.log_tb 0.5488 0.24560 0.8521 + +Correlation: + meso_0 log_k1 b_H(_1) log_k2 b_H(_2) +log_k1 0.0740 +beta_pH(log_k1) -0.0453 -0.9912 +log_k2 0.0115 -0.0650 0.0661 +beta_pH(log_k2) -0.0116 0.0649 -0.0667 -0.9936 +log_tb -0.0658 -0.1135 0.0913 -0.1500 0.1210 + +Random effects: + est. lower upper +SD.log_k1 0.3570 0.22104 0.4930 +SD.log_k2 0.2252 0.01864 0.4318 +SD.log_tb 0.5488 0.24560 0.8521 + +Variance model: + est. lower upper +a.1 4.445 3.735 5.155 + +Backtransformed parameters: + est. lower upper +meso_0 93.325134 9.150e+01 95.152036 +k1 0.003415 8.352e-04 0.013962 +k2 0.001349 2.392e-04 0.007611 +tb 14.939247 1.028e+01 21.707445 + +Covariates used for endpoints below: + pH +50% 5.75 + +Estimated disappearance times: + DT50 DT90 DT50back DT50_k1 DT50_k2 +meso 14.69 82.45 24.82 14.69 29.29 + +</code></pre> +<p></p> +</div> +</div> +<div class="section level3"> +<h3 id="session-info">Session info<a class="anchor" aria-label="anchor" href="#session-info"></a> +</h3> +<pre><code>R version 4.5.0 (2025-04-11) +Platform: x86_64-pc-linux-gnu +Running under: Debian GNU/Linux 12 (bookworm) + +Matrix products: default +BLAS: /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.11.0 +LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.11.0 LAPACK version 3.11.0 + +locale: + [1] LC_CTYPE=de_DE.UTF-8 LC_NUMERIC=C + [3] LC_TIME=de_DE.UTF-8 LC_COLLATE=de_DE.UTF-8 + [5] LC_MONETARY=de_DE.UTF-8 LC_MESSAGES=de_DE.UTF-8 + [7] LC_PAPER=de_DE.UTF-8 LC_NAME=C + [9] LC_ADDRESS=C LC_TELEPHONE=C +[11] LC_MEASUREMENT=de_DE.UTF-8 LC_IDENTIFICATION=C + +time zone: Europe/Berlin +tzcode source: system (glibc) + +attached base packages: +[1] parallel stats graphics grDevices utils datasets methods +[8] base + +other attached packages: +[1] rmarkdown_2.29 nvimcom_0.9-167 saemix_3.3 npde_3.5 +[5] knitr_1.49 mkin_1.2.10 + +loaded via a namespace (and not attached): + [1] gtable_0.3.6 jsonlite_1.9.0 dplyr_1.1.4 compiler_4.5.0 + [5] tidyselect_1.2.1 gridExtra_2.3 jquerylib_0.1.4 systemfonts_1.2.1 + [9] scales_1.3.0 textshaping_1.0.0 readxl_1.4.4 yaml_2.3.10 +[13] fastmap_1.2.0 lattice_0.22-6 ggplot2_3.5.1 R6_2.6.1 +[17] generics_0.1.3 lmtest_0.9-40 MASS_7.3-65 htmlwidgets_1.6.4 +[21] tibble_3.2.1 desc_1.4.3 munsell_0.5.1 bslib_0.9.0 +[25] pillar_1.10.1 rlang_1.1.5 cachem_1.1.0 xfun_0.51 +[29] fs_1.6.5 sass_0.4.9 cli_3.6.4 pkgdown_2.1.1 +[33] magrittr_2.0.3 digest_0.6.37 grid_4.5.0 mclust_6.1.1 +[37] lifecycle_1.0.4 nlme_3.1-168 vctrs_0.6.5 evaluate_1.0.3 +[41] glue_1.8.0 cellranger_1.1.0 codetools_0.2-20 ragg_1.3.3 +[45] zoo_1.8-13 colorspace_2.1-1 tools_4.5.0 pkgconfig_2.0.3 +[49] htmltools_0.5.8.1</code></pre> +</div> +<div class="section level3"> +<h3 id="hardware-info">Hardware info<a class="anchor" aria-label="anchor" href="#hardware-info"></a> +</h3> +<pre><code>CPU model: AMD Ryzen 9 7950X 16-Core Processor</code></pre> +<pre><code>MemTotal: 64927780 kB</code></pre> +</div> +</div> + </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2> + </nav></aside> +</div> + + + + <footer><div class="pkgdown-footer-left"> + <p>Developed by Johannes Ranke.</p> +</div> + +<div class="pkgdown-footer-right"> + <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p> +</div> + + </footer> +</div> + + + + + + </body> +</html> diff --git a/docs/articles/web_only/mesotrione_parent_2023_prebuilt_files/figure-html/unnamed-chunk-14-1.png b/docs/articles/web_only/mesotrione_parent_2023_prebuilt_files/figure-html/unnamed-chunk-14-1.png Binary files differnew file mode 100644 index 00000000..67fa91dc --- /dev/null +++ b/docs/articles/web_only/mesotrione_parent_2023_prebuilt_files/figure-html/unnamed-chunk-14-1.png diff --git a/docs/articles/web_only/mesotrione_parent_2023_prebuilt_files/figure-html/unnamed-chunk-19-1.png 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b/docs/articles/web_only/mesotrione_parent_2023_prebuilt_files/figure-html/unnamed-chunk-30-1.png diff --git a/docs/articles/web_only/mesotrione_parent_2023_prebuilt_files/figure-html/unnamed-chunk-8-1.png b/docs/articles/web_only/mesotrione_parent_2023_prebuilt_files/figure-html/unnamed-chunk-8-1.png Binary files differnew file mode 100644 index 00000000..2379b895 --- /dev/null +++ b/docs/articles/web_only/mesotrione_parent_2023_prebuilt_files/figure-html/unnamed-chunk-8-1.png diff --git a/docs/articles/web_only/multistart.html b/docs/articles/web_only/multistart.html index f6ab46de..a2e452bc 100644 --- a/docs/articles/web_only/multistart.html +++ b/docs/articles/web_only/multistart.html @@ -20,7 +20,7 @@ <a class="navbar-brand me-2" href="../../index.html">mkin</a> - <small class="nav-text text-default me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">1.2.9</small> + <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">1.2.10</small> <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation"> @@ -84,7 +84,7 @@ Ranke</h4> <h4 data-toc-skip class="date">Last change 20 April 2023 -(rebuilt 2025-02-13)</h4> +(rebuilt 2025-05-12)</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="d-none name"><code>multistart.rmd</code></div> diff --git a/docs/articles/web_only/saem_benchmarks.html b/docs/articles/web_only/saem_benchmarks.html index 3116d0e6..1a49f6cd 100644 --- a/docs/articles/web_only/saem_benchmarks.html +++ b/docs/articles/web_only/saem_benchmarks.html @@ -20,7 +20,7 @@ <a class="navbar-brand me-2" href="../../index.html">mkin</a> - <small class="nav-text text-default me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">1.2.9</small> + <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">1.2.10</small> <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation"> @@ -84,7 +84,7 @@ Ranke</h4> <h4 data-toc-skip class="date">Last change 17 February 2023 -(rebuilt 2025-02-13)</h4> +(rebuilt 2025-05-12)</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="d-none name"><code>saem_benchmarks.rmd</code></div> @@ -139,7 +139,7 @@ explanation of the following preprocessing.</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/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> @@ -279,11 +279,11 @@ systems. All trademarks belong to their respective owners.</p> <h3 id="parent-only-1">Parent only<a class="anchor" aria-label="anchor" href="#parent-only-1"></a> </h3> <p>Constant variance for SFO, DFOP, SFORB and HS.</p> -<table style="width:100%;" class="table"> +<table class="table"> <colgroup> <col width="48%"> <col width="7%"> -<col width="7%"> +<col width="8%"> <col width="8%"> <col width="7%"> <col width="7%"> @@ -401,14 +401,34 @@ systems. All trademarks belong to their respective owners.</p> <td align="right">1.949</td> <td align="right">2.411</td> </tr> +<tr class="odd"> +<td align="left">Ryzen 9 7950X</td> +<td align="left">Linux</td> +<td align="left">1.2.10</td> +<td align="left">3.3</td> +<td align="right">1.115</td> +<td align="right">2.263</td> +<td align="right">1.991</td> +<td align="right">2.193</td> +</tr> +<tr class="even"> +<td align="left">Ryzen 9 7950X</td> +<td align="left">Linux</td> +<td align="left">1.2.10</td> +<td align="left">3.3</td> +<td align="right">1.876</td> +<td align="right">1.922</td> +<td align="right">2.423</td> +<td align="right">1.849</td> +</tr> </tbody> </table> <p>Two-component error fits for SFO, DFOP, SFORB and HS.</p> -<table style="width:100%;" class="table"> +<table class="table"> <colgroup> <col width="48%"> <col width="7%"> -<col width="7%"> +<col width="8%"> <col width="8%"> <col width="7%"> <col width="7%"> @@ -526,6 +546,26 @@ systems. All trademarks belong to their respective owners.</p> <td align="right">3.256</td> <td align="right">3.322</td> </tr> +<tr class="odd"> +<td align="left">Ryzen 9 7950X</td> +<td align="left">Linux</td> +<td align="left">1.2.10</td> +<td align="left">3.3</td> +<td align="right">2.380</td> +<td align="right">3.147</td> +<td align="right">3.131</td> +<td align="right">3.331</td> +</tr> +<tr class="even"> +<td align="left">Ryzen 9 7950X</td> +<td align="left">Linux</td> +<td align="left">1.2.10</td> +<td align="left">3.3</td> +<td align="right">2.397</td> +<td align="right">3.443</td> +<td align="right">3.414</td> +<td align="right">3.311</td> +</tr> </tbody> </table> </div> @@ -533,11 +573,11 @@ systems. All trademarks belong to their respective owners.</p> <h3 id="one-metabolite-1">One metabolite<a class="anchor" aria-label="anchor" href="#one-metabolite-1"></a> </h3> <p>Two-component error for DFOP-SFO and SFORB-SFO.</p> -<table class="table"> +<table style="width:100%;" class="table"> <colgroup> -<col width="54%"> -<col width="8%"> -<col width="8%"> +<col width="53%"> +<col width="7%"> +<col width="9%"> <col width="9%"> <col width="9%"> <col width="10%"> @@ -631,6 +671,22 @@ systems. All trademarks belong to their respective owners.</p> <td align="right">12.420</td> <td align="right">289.338</td> </tr> +<tr class="odd"> +<td align="left">Ryzen 9 7950X</td> +<td align="left">Linux</td> +<td align="left">1.2.10</td> +<td align="left">3.3</td> +<td align="right">11.581</td> +<td align="right">296.184</td> +</tr> +<tr class="even"> +<td align="left">Ryzen 9 7950X</td> +<td align="left">Linux</td> +<td align="left">1.2.10</td> +<td align="left">3.3</td> +<td align="right">12.067</td> +<td align="right">278.742</td> +</tr> </tbody> </table> </div> @@ -638,13 +694,13 @@ systems. All trademarks belong to their respective owners.</p> <h3 id="three-metabolites-1">Three metabolites<a class="anchor" aria-label="anchor" href="#three-metabolites-1"></a> </h3> <p>Two-component error for SFORB-SFO3-plus</p> -<table style="width:100%;" class="table"> +<table class="table"> <colgroup> -<col width="59%"> -<col width="8%"> +<col width="58%"> <col width="8%"> <col width="10%"> -<col width="13%"> +<col width="10%"> +<col width="12%"> </colgroup> <thead><tr class="header"> <th align="left">CPU</th> @@ -724,6 +780,20 @@ systems. All trademarks belong to their respective owners.</p> <td align="left">3.3</td> <td align="right">485.836</td> </tr> +<tr class="odd"> +<td align="left">Ryzen 9 7950X</td> +<td align="left">Linux</td> +<td align="left">1.2.10</td> +<td align="left">3.3</td> +<td align="right">486.856</td> +</tr> +<tr class="even"> +<td align="left">Ryzen 9 7950X</td> +<td align="left">Linux</td> +<td align="left">1.2.10</td> +<td align="left">3.3</td> +<td align="right">474.550</td> +</tr> </tbody> </table> </div> |
