Fix and rebuild documentation, see NEWS

I had to fix the two pathway vignettes, as they did not work with
the released version any more. So they and the multistart vignette
which got some small fixes as well were rebuilt.

Complete rebuild of the online docs with the released version. The
documentation of the 'hierarchial_kinetics' format had to be fixed
as well.

1 files changed, 130 insertions, 46 deletions

diff --git a/docs/articles/web_only/FOCUS_Z.html b/docs/articles/web_only/FOCUS_Z.html
index ea20ecd9..9602adb5 100644
--- a/docs/articles/web_only/FOCUS_Z.html
+++ b/docs/articles/web_only/FOCUS_Z.html
@@ -33,14 +33,14 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../../index.html">mkin</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">1.2.0</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">1.2.3</span>
       </span>
     </div>
 
     <div id="navbar" class="navbar-collapse collapse">
       <ul class="nav navbar-nav">
 <li>
-  <a href="../../reference/index.html">Functions and data</a>
+  <a href="../../reference/index.html">Reference</a>
 </li>
 <li class="dropdown">
   <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false">
@@ -52,6 +52,9 @@
 <li>
       <a href="../../articles/mkin.html">Introduction to mkin</a>
     </li>
+    <li class="divider">
+    </li>
+<li class="dropdown-header">Example evaluations with (generalised) nonlinear least squares</li>
     <li>
       <a href="../../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a>
     </li>
@@ -59,22 +62,31 @@
       <a href="../../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a>
     </li>
     <li>
-      <a href="../../articles/web_only/dimethenamid_2018.html">Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models</a>
+      <a href="../../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a>
+    </li>
+    <li class="divider">
     </li>
+<li class="dropdown-header">Example evaluations with hierarchical models (nonlinear mixed-effects models)</li>
     <li>
-      <a href="../../articles/web_only/multistart.html">Short demo of the multistart method</a>
+      <a href="../../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a>
     </li>
     <li>
-      <a href="../../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a>
+      <a href="../../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a>
     </li>
     <li>
-      <a href="../../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a>
+      <a href="../../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a>
     </li>
     <li>
-      <a href="../../articles/twa.html">Calculation of time weighted average concentrations with mkin</a>
+      <a href="../../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a>
     </li>
     <li>
-      <a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
+      <a href="../../articles/web_only/multistart.html">Short demo of the multistart method</a>
+    </li>
+    <li class="divider">
+    </li>
+<li class="dropdown-header">Performance</li>
+    <li>
+      <a href="../../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a>
     </li>
     <li>
       <a href="../../articles/web_only/benchmarks.html">Benchmark timings for mkin</a>
@@ -82,6 +94,15 @@
     <li>
       <a href="../../articles/web_only/saem_benchmarks.html">Benchmark timings for saem.mmkin</a>
     </li>
+    <li class="divider">
+    </li>
+<li class="dropdown-header">Miscellaneous</li>
+    <li>
+      <a href="../../articles/twa.html">Calculation of time weighted average concentrations with mkin</a>
+    </li>
+    <li>
+      <a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
+    </li>
   </ul>
 </li>
 <li>
@@ -105,13 +126,15 @@
 
       
 
-      </header><script src="FOCUS_Z_files/accessible-code-block-0.0.1/empty-anchor.js"></script><div class="row">
+      </header><div class="row">
   <div class="col-md-9 contents">
     <div class="page-header toc-ignore">
       <h1 data-toc-skip>Example evaluation of FOCUS dataset Z</h1>
-                        <h4 data-toc-skip class="author">Johannes Ranke</h4>
+                        <h4 data-toc-skip class="author">Johannes
+Ranke</h4>
             
-            <h4 data-toc-skip class="date">Last change 16 January 2018 (rebuilt 2022-11-17)</h4>
+            <h4 data-toc-skip class="date">Last change 16 January 2018
+(rebuilt 2023-04-20)</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/FOCUS_Z.rmd" class="external-link"><code>vignettes/web_only/FOCUS_Z.rmd</code></a></small>
       <div class="hidden name"><code>FOCUS_Z.rmd</code></div>
@@ -120,11 +143,15 @@
 
     
     
-<p><a href="http://www.jrwb.de" class="external-link">Wissenschaftlicher Berater, Kronacher Str. 12, 79639 Grenzach-Wyhlen, Germany</a><br><a href="http://chem.uft.uni-bremen.de/ranke" class="external-link">Privatdozent at the University of Bremen</a></p>
+<p><a href="http://www.jrwb.de" class="external-link">Wissenschaftlicher Berater, Kronacher
+Str. 12, 79639 Grenzach-Wyhlen, Germany</a><br><a href="http://chem.uft.uni-bremen.de/ranke" class="external-link">Privatdozent at the
+University of Bremen</a></p>
 <div class="section level2">
 <h2 id="the-data">The data<a class="anchor" aria-label="anchor" href="#the-data"></a>
 </h2>
-<p>The following code defines the example dataset from Appendix 7 to the FOCUS kinetics report <span class="citation">(FOCUS Work Group on Degradation Kinetics 2014, 354)</span>.</p>
+<p>The following code defines the example dataset from Appendix 7 to the
+FOCUS kinetics report <span class="citation">(FOCUS Work Group on
+Degradation Kinetics 2014, 354)</span>.</p>
 <div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://pkgdown.jrwb.de/mkin/">mkin</a></span>, quietly <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
 <span><span class="va">LOD</span> <span class="op">=</span> <span class="fl">0.5</span></span>
@@ -145,7 +172,11 @@
 <div class="section level2">
 <h2 id="parent-and-one-metabolite">Parent and one metabolite<a class="anchor" aria-label="anchor" href="#parent-and-one-metabolite"></a>
 </h2>
-<p>The next step is to set up the models used for the kinetic analysis. As the simultaneous fit of parent and the first metabolite is usually straightforward, Step 1 (SFO for parent only) is skipped here. We start with the model 2a, with formation and decline of metabolite Z1 and the pathway from parent directly to sink included (default in mkin).</p>
+<p>The next step is to set up the models used for the kinetic analysis.
+As the simultaneous fit of parent and the first metabolite is usually
+straightforward, Step 1 (SFO for parent only) is skipped here. We start
+with the model 2a, with formation and decline of metabolite Z1 and the
+pathway from parent directly to sink included (default in mkin).</p>
 <div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">Z.2a</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z1"</span><span class="op">)</span>,</span>
 <span>                Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
@@ -158,15 +189,21 @@
 <code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.2a</span><span class="op">)</span></span></code></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png" width="700"></p>
 <div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.2a</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></code></pre></div>
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.2a</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></code></pre></div>
 <pre><code><span><span class="co">##            Estimate se_notrans t value     Pr(&gt;t)    Lower    Upper</span></span>
 <span><span class="co">## Z0_0       97.01488   3.301084 29.3888 3.2971e-21 91.66556 102.3642</span></span>
 <span><span class="co">## k_Z0        2.23601   0.207078 10.7979 3.3309e-11  1.95303   2.5600</span></span>
 <span><span class="co">## k_Z1        0.48212   0.063265  7.6207 2.8154e-08  0.40341   0.5762</span></span>
 <span><span class="co">## f_Z0_to_Z1  1.00000   0.094764 10.5525 5.3560e-11  0.00000   1.0000</span></span>
 <span><span class="co">## sigma       4.80411   0.635638  7.5579 3.2592e-08  3.52677   6.0815</span></span></code></pre>
-<p>As obvious from the parameter summary (the  component of the summary), the kinetic rate constant from parent compound Z to sink is very small and the t-test for this parameter suggests that it is not significantly different from zero. This suggests, in agreement with the analysis in the FOCUS kinetics report, to simplify the model by removing the pathway to sink.</p>
-<p>A similar result can be obtained when formation fractions are used in the model formulation:</p>
+<p>As obvious from the parameter summary (the component of the summary),
+the kinetic rate constant from parent compound Z to sink is very small
+and the t-test for this parameter suggests that it is not significantly
+different from zero. This suggests, in agreement with the analysis in
+the FOCUS kinetics report, to simplify the model by removing the pathway
+to sink.</p>
+<p>A similar result can be obtained when formation fractions are used in
+the model formulation:</p>
 <div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">Z.2a.ff</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z1"</span><span class="op">)</span>,</span>
 <span>                   Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span>
@@ -180,16 +217,24 @@
 <code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.2a.ff</span><span class="op">)</span></span></code></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png" width="700"></p>
 <div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.2a.ff</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></code></pre></div>
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.2a.ff</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></code></pre></div>
 <pre><code><span><span class="co">##            Estimate se_notrans t value     Pr(&gt;t)    Lower    Upper</span></span>
 <span><span class="co">## Z0_0       97.01488   3.301084 29.3888 3.2971e-21 91.66556 102.3642</span></span>
 <span><span class="co">## k_Z0        2.23601   0.207078 10.7979 3.3309e-11  1.95303   2.5600</span></span>
 <span><span class="co">## k_Z1        0.48212   0.063265  7.6207 2.8154e-08  0.40341   0.5762</span></span>
 <span><span class="co">## f_Z0_to_Z1  1.00000   0.094764 10.5525 5.3560e-11  0.00000   1.0000</span></span>
 <span><span class="co">## sigma       4.80411   0.635638  7.5579 3.2592e-08  3.52677   6.0815</span></span></code></pre>
-<p>Here, the ilr transformed formation fraction fitted in the model takes a very large value, and the backtransformed formation fraction from parent Z to Z1 is practically unity. Here, the covariance matrix used for the calculation of confidence intervals is not returned as the model is overparameterised.</p>
-<p>A simplified model is obtained by removing the pathway to the sink. </p>
-<p>In the following, we use the parameterisation with formation fractions in order to be able to compare with the results in the FOCUS guidance, and as it makes it easier to use parameters obtained in a previous fit when adding a further metabolite.</p>
+<p>Here, the ilr transformed formation fraction fitted in the model
+takes a very large value, and the backtransformed formation fraction
+from parent Z to Z1 is practically unity. Here, the covariance matrix
+used for the calculation of confidence intervals is not returned as the
+model is overparameterised.</p>
+<p>A simplified model is obtained by removing the pathway to the sink.
+</p>
+<p>In the following, we use the parameterisation with formation
+fractions in order to be able to compare with the results in the FOCUS
+guidance, and as it makes it easier to use parameters obtained in a
+previous fit when adding a further metabolite.</p>
 <div class="sourceCode" id="cb16"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">Z.3</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
 <span>               Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>, use_of_ff <span class="op">=</span> <span class="st">"max"</span><span class="op">)</span></span></code></pre></div>
@@ -202,18 +247,24 @@
 <code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.3</span><span class="op">)</span></span></code></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png" width="700"></p>
 <div class="sourceCode" id="cb21"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.3</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></code></pre></div>
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.3</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></code></pre></div>
 <pre><code><span><span class="co">##       Estimate se_notrans t value     Pr(&gt;t)    Lower    Upper</span></span>
 <span><span class="co">## Z0_0  97.01488   2.597342  37.352 2.0106e-24 91.67597 102.3538</span></span>
 <span><span class="co">## k_Z0   2.23601   0.146904  15.221 9.1477e-15  1.95354   2.5593</span></span>
 <span><span class="co">## k_Z1   0.48212   0.041727  11.554 4.8268e-12  0.40355   0.5760</span></span>
 <span><span class="co">## sigma  4.80411   0.620208   7.746 1.6110e-08  3.52925   6.0790</span></span></code></pre>
-<p>As there is only one transformation product for Z0 and no pathway to sink, the formation fraction is internally fixed to unity.</p>
+<p>As there is only one transformation product for Z0 and no pathway to
+sink, the formation fraction is internally fixed to unity.</p>
 </div>
 <div class="section level2">
 <h2 id="metabolites-z2-and-z3">Metabolites Z2 and Z3<a class="anchor" aria-label="anchor" href="#metabolites-z2-and-z3"></a>
 </h2>
-<p>As suggested in the FOCUS report, the pathway to sink was removed for metabolite Z1 as well in the next step. While this step appears questionable on the basis of the above results, it is followed here for the purpose of comparison. Also, in the FOCUS report, it is assumed that there is additional empirical evidence that Z1 quickly and exclusively hydrolyses to Z2.</p>
+<p>As suggested in the FOCUS report, the pathway to sink was removed for
+metabolite Z1 as well in the next step. While this step appears
+questionable on the basis of the above results, it is followed here for
+the purpose of comparison. Also, in the FOCUS report, it is assumed that
+there is additional empirical evidence that Z1 quickly and exclusively
+hydrolyses to Z2.</p>
 <div class="sourceCode" id="cb23"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">Z.5</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
 <span>               Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
@@ -226,7 +277,9 @@
 <div class="sourceCode" id="cb27"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.5</span><span class="op">)</span></span></code></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png" width="700"></p>
-<p>Finally, metabolite Z3 is added to the model. We use the optimised differential equation parameter values from the previous fit in order to accelerate the optimization.</p>
+<p>Finally, metabolite Z3 is added to the model. We use the optimised
+differential equation parameter values from the previous fit in order to
+accelerate the optimization.</p>
 <div class="sourceCode" id="cb28"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">Z.FOCUS</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
 <span>                   Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
@@ -246,7 +299,7 @@
 <code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.FOCUS</span><span class="op">)</span></span></code></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png" width="700"></p>
 <div class="sourceCode" id="cb34"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.FOCUS</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></code></pre></div>
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.FOCUS</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></span></code></pre></div>
 <pre><code><span><span class="co">##             Estimate se_notrans t value     Pr(&gt;t)     Lower      Upper</span></span>
 <span><span class="co">## Z0_0       96.838822   1.994274 48.5584 4.0280e-42 92.826981 100.850664</span></span>
 <span><span class="co">## k_Z0        2.215393   0.118458 18.7019 1.0413e-23  1.989456   2.466989</span></span>
@@ -267,13 +320,22 @@
 <span><span class="co">## Z1  1.44917  4.8141</span></span>
 <span><span class="co">## Z2  1.53478  5.0984</span></span>
 <span><span class="co">## Z3 11.80986 39.2315</span></span></code></pre>
-<p>This fit corresponds to the final result chosen in Appendix 7 of the FOCUS report. Confidence intervals returned by mkin are based on internally transformed parameters, however.</p>
+<p>This fit corresponds to the final result chosen in Appendix 7 of the
+FOCUS report. Confidence intervals returned by mkin are based on
+internally transformed parameters, however.</p>
 </div>
 <div class="section level2">
 <h2 id="using-the-sforb-model">Using the SFORB model<a class="anchor" aria-label="anchor" href="#using-the-sforb-model"></a>
 </h2>
-<p>As the FOCUS report states, there is a certain tailing of the time course of metabolite Z3. Also, the time course of the parent compound is not fitted very well using the SFO model, as residues at a certain low level remain.</p>
-<p>Therefore, an additional model is offered here, using the single first-order reversible binding (SFORB) model for metabolite Z3. As expected, the <span class="math inline">\(\chi^2\)</span> error level is lower for metabolite Z3 using this model and the graphical fit for Z3 is improved. However, the covariance matrix is not returned.</p>
+<p>As the FOCUS report states, there is a certain tailing of the time
+course of metabolite Z3. Also, the time course of the parent compound is
+not fitted very well using the SFO model, as residues at a certain low
+level remain.</p>
+<p>Therefore, an additional model is offered here, using the single
+first-order reversible binding (SFORB) model for metabolite Z3. As
+expected, the <span class="math inline">\(\chi^2\)</span> error level is
+lower for metabolite Z3 using this model and the graphical fit for Z3 is
+improved. However, the covariance matrix is not returned.</p>
 <div class="sourceCode" id="cb38"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">Z.mkin.1</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
 <span>                    Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
@@ -282,15 +344,18 @@
 <pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre>
 <div class="sourceCode" id="cb40"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">m.Z.mkin.1</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.mkin.1</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
-<pre><code><span><span class="co">## Warning in mkinfit(Z.mkin.1, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with</span></span>
-<span><span class="co">## value of zero were removed from the data</span></span></code></pre>
+<pre><code><span><span class="co">## Warning in mkinfit(Z.mkin.1, FOCUS_2006_Z_mkin, quiet = TRUE): Observations</span></span>
+<span><span class="co">## with value of zero were removed from the data</span></span></code></pre>
 <div class="sourceCode" id="cb42"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.1</span><span class="op">)</span></span></code></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png" width="700"></p>
 <div class="sourceCode" id="cb43"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.mkin.1</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">cov.unscaled</span></span></code></pre></div>
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.Z.mkin.1</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">cov.unscaled</span></span></code></pre></div>
 <pre><code><span><span class="co">## NULL</span></span></code></pre>
-<p>Therefore, a further stepwise model building is performed starting from the stage of parent and two metabolites, starting from the assumption that the model fit for the parent compound can be improved by using the SFORB model.</p>
+<p>Therefore, a further stepwise model building is performed starting
+from the stage of parent and two metabolites, starting from the
+assumption that the model fit for the parent compound can be improved by
+using the SFORB model.</p>
 <div class="sourceCode" id="cb45"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">Z.mkin.3</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span>, <span class="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
 <span>                    Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
@@ -298,13 +363,16 @@
 <pre><code><span><span class="co">## Temporary DLL for differentials generated and loaded</span></span></code></pre>
 <div class="sourceCode" id="cb47"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">m.Z.mkin.3</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.mkin.3</span>, <span class="va">FOCUS_2006_Z_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
-<pre><code><span><span class="co">## Warning in mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with</span></span>
-<span><span class="co">## value of zero were removed from the data</span></span></code></pre>
+<pre><code><span><span class="co">## Warning in mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE): Observations</span></span>
+<span><span class="co">## with value of zero were removed from the data</span></span></code></pre>
 <div class="sourceCode" id="cb49"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.3</span><span class="op">)</span></span></code></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png" width="700"></p>
-<p>This results in a much better representation of the behaviour of the parent compound Z0.</p>
-<p>Finally, Z3 is added as well. These models appear overparameterised (no covariance matrix returned) if the sink for Z1 is left in the models.</p>
+<p>This results in a much better representation of the behaviour of the
+parent compound Z0.</p>
+<p>Finally, Z3 is added as well. These models appear overparameterised
+(no covariance matrix returned) if the sink for Z1 is left in the
+models.</p>
 <div class="sourceCode" id="cb50"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">Z.mkin.4</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span>, <span class="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
 <span>                    Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
@@ -321,7 +389,10 @@
 <div class="sourceCode" id="cb54"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.4</span><span class="op">)</span></span></code></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png" width="700"></p>
-<p>The error level of the fit, but especially of metabolite Z3, can be improved if the SFORB model is chosen for this metabolite, as this model is capable of representing the tailing of the metabolite decline phase.</p>
+<p>The error level of the fit, but especially of metabolite Z3, can be
+improved if the SFORB model is chosen for this metabolite, as this model
+is capable of representing the tailing of the metabolite decline
+phase.</p>
 <div class="sourceCode" id="cb55"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">Z.mkin.5</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>Z0 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span>, <span class="st">"Z1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
 <span>                    Z1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"Z2"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span>
@@ -338,7 +409,9 @@
 <div class="sourceCode" id="cb59"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.5</span><span class="op">)</span></span></code></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png" width="700"></p>
-<p>The summary view of the backtransformed parameters shows that we get no confidence intervals due to overparameterisation. As the optimized  is excessively small, it seems reasonable to fix it to zero.</p>
+<p>The summary view of the backtransformed parameters shows that we get
+no confidence intervals due to overparameterisation. As the optimized is
+excessively small, it seems reasonable to fix it to zero.</p>
 <div class="sourceCode" id="cb60"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">m.Z.mkin.5a</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">Z.mkin.5</span>, <span class="va">FOCUS_2006_Z_mkin</span>,</span>
 <span>                       parms.ini <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="va">m.Z.mkin.5</span><span class="op">$</span><span class="va">bparms.ode</span><span class="op">[</span><span class="fl">1</span><span class="op">:</span><span class="fl">7</span><span class="op">]</span>,</span>
@@ -351,8 +424,12 @@
 <div class="sourceCode" id="cb62"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">m.Z.mkin.5a</span><span class="op">)</span></span></code></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png" width="700"></p>
-<p>As expected, the residual plots for Z0 and Z3 are more random than in the case of the all SFO model for which they were shown above. In conclusion, the model  is proposed as the best-fit model for the dataset from Appendix 7 of the FOCUS report.</p>
-<p>A graphical representation of the confidence intervals can finally be obtained.</p>
+<p>As expected, the residual plots for Z0 and Z3 are more random than in
+the case of the all SFO model for which they were shown above. In
+conclusion, the model is proposed as the best-fit model for the dataset
+from Appendix 7 of the FOCUS report.</p>
+<p>A graphical representation of the confidence intervals can finally be
+obtained.</p>
 <div class="sourceCode" id="cb63"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../../reference/mkinparplot.html">mkinparplot</a></span><span class="op">(</span><span class="va">m.Z.mkin.5a</span><span class="op">)</span></span></code></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png" width="700"></p>
@@ -373,15 +450,22 @@
 <span><span class="co">## Z1 1.5148 5.0320       NA         NA         NA         NA         NA</span></span>
 <span><span class="co">## Z2 1.6414 5.4526       NA         NA         NA         NA         NA</span></span>
 <span><span class="co">## Z3     NA     NA       NA         NA         NA     8.6636        Inf</span></span></code></pre>
-<p>It is clear the degradation rate of Z3 towards the end of the experiment is very low as DT50_Z3_b2 (the second Eigenvalue of the system of two differential equations representing the SFORB system for Z3, corresponding to the slower rate constant of the DFOP model) is reported to be infinity. However, this appears to be a feature of the data.</p>
+<p>It is clear the degradation rate of Z3 towards the end of the
+experiment is very low as DT50_Z3_b2 (the second Eigenvalue of the
+system of two differential equations representing the SFORB system for
+Z3, corresponding to the slower rate constant of the DFOP model) is
+reported to be infinity. However, this appears to be a feature of the
+data.</p>
 </div>
 <div class="section level2">
 <h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a>
 </h2>
 <!-- vim: set foldmethod=syntax: -->
-<div id="refs" class="references hanging-indent">
-<div id="ref-FOCUSkinetics2014">
-<p>FOCUS Work Group on Degradation Kinetics. 2014. <em>Generic Guidance for Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in Eu Registration</em>. 1.1 ed. <a href="http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics" class="external-link">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>.</p>
+<div id="refs" class="references csl-bib-body hanging-indent">
+<div id="ref-FOCUSkinetics2014" class="csl-entry">
+FOCUS Work Group on Degradation Kinetics. 2014. <em>Generic Guidance for
+Estimating Persistence and Degradation Kinetics from Environmental Fate
+Studies on Pesticides in EU Registration</em>. 1.1 ed. <a href="http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics" class="external-link">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>.
 </div>
 </div>
 </div>
@@ -404,7 +488,7 @@
 
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