Create up to date pkgdown docs in development mode

author: Johannes Ranke <jranke@uni-bremen.de> 2020-05-27 06:06:08 +0200
committer: Johannes Ranke <jranke@uni-bremen.de> 2020-05-27 06:06:08 +0200
commit: a77a10ea6c607346778ba0700b3b66ac393101a2 (patch)
tree: e91f627fba0580ef237ecbc8f24d6294a59597d3 /docs/dev/articles/web_only
parent: 675a733fa2acc08daabb9b8b571c7d658f281f73 (diff)
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+      <h1 data-toc-skip>Example evaluation of FOCUS dataset Z</h1>
+                        <h4 class="author">Johannes Ranke</h4>
+            
+            <h4 class="date">2020-05-27</h4>
+      
+      <small class="dont-index">Source: <a href="http://github.com/jranke/mkin/blob/master/vignettes/web_only/FOCUS_Z.rmd"><code>vignettes/web_only/FOCUS_Z.rmd</code></a></small>
+      <div class="hidden name"><code>FOCUS_Z.rmd</code></div>
+
+    </div>
+
+    
+    
+<p><a href="http://www.jrwb.de">Wissenschaftlicher Berater, Kronacher Str. 12, 79639 Grenzach-Wyhlen, Germany</a><br><a href="http://chem.uft.uni-bremen.de/ranke">Privatdozent at the University of Bremen</a></p>
+<div id="the-data" class="section level1">
+<h1 class="hasAnchor">
+<a href="#the-data" class="anchor"></a>The data</h1>
+<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"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/library.html">library</a></span>(<span class="no">mkin</span>, <span class="kw">quietly</span> <span class="kw">=</span> <span class="fl">TRUE</span>)
+<span class="no">LOD</span> <span class="kw">=</span> <span class="fl">0.5</span>
+<span class="no">FOCUS_2006_Z</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html">data.frame</a></span>(
+  <span class="kw">t</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="fl">0</span>, <span class="fl">0.04</span>, <span class="fl">0.125</span>, <span class="fl">0.29</span>, <span class="fl">0.54</span>, <span class="fl">1</span>, <span class="fl">2</span>, <span class="fl">3</span>, <span class="fl">4</span>, <span class="fl">7</span>, <span class="fl">10</span>, <span class="fl">14</span>, <span class="fl">21</span>,
+        <span class="fl">42</span>, <span class="fl">61</span>, <span class="fl">96</span>, <span class="fl">124</span>),
+  <span class="kw">Z0</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="fl">100</span>, <span class="fl">81.7</span>, <span class="fl">70.4</span>, <span class="fl">51.1</span>, <span class="fl">41.2</span>, <span class="fl">6.6</span>, <span class="fl">4.6</span>, <span class="fl">3.9</span>, <span class="fl">4.6</span>, <span class="fl">4.3</span>, <span class="fl">6.8</span>,
+         <span class="fl">2.9</span>, <span class="fl">3.5</span>, <span class="fl">5.3</span>, <span class="fl">4.4</span>, <span class="fl">1.2</span>, <span class="fl">0.7</span>),
+  <span class="kw">Z1</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="fl">0</span>, <span class="fl">18.3</span>, <span class="fl">29.6</span>, <span class="fl">46.3</span>, <span class="fl">55.1</span>, <span class="fl">65.7</span>, <span class="fl">39.1</span>, <span class="fl">36</span>, <span class="fl">15.3</span>, <span class="fl">5.6</span>, <span class="fl">1.1</span>,
+         <span class="fl">1.6</span>, <span class="fl">0.6</span>, <span class="fl">0.5</span> * <span class="no">LOD</span>, <span class="fl">NA</span>, <span class="fl">NA</span>, <span class="fl">NA</span>),
+  <span class="kw">Z2</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="fl">0</span>, <span class="fl">NA</span>, <span class="fl">0.5</span> * <span class="no">LOD</span>, <span class="fl">2.6</span>, <span class="fl">3.8</span>, <span class="fl">15.3</span>, <span class="fl">37.2</span>, <span class="fl">31.7</span>, <span class="fl">35.6</span>, <span class="fl">14.5</span>,
+         <span class="fl">0.8</span>, <span class="fl">2.1</span>, <span class="fl">1.9</span>, <span class="fl">0.5</span> * <span class="no">LOD</span>, <span class="fl">NA</span>, <span class="fl">NA</span>, <span class="fl">NA</span>),
+  <span class="kw">Z3</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="fl">0</span>, <span class="fl">NA</span>, <span class="fl">NA</span>, <span class="fl">NA</span>, <span class="fl">NA</span>, <span class="fl">0.5</span> * <span class="no">LOD</span>, <span class="fl">9.2</span>, <span class="fl">13.1</span>, <span class="fl">22.3</span>, <span class="fl">28.4</span>, <span class="fl">32.5</span>,
+         <span class="fl">25.2</span>, <span class="fl">17.2</span>, <span class="fl">4.8</span>, <span class="fl">4.5</span>, <span class="fl">2.8</span>, <span class="fl">4.4</span>))
+
+<span class="no">FOCUS_2006_Z_mkin</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span>(<span class="no">FOCUS_2006_Z</span>)</pre></body></html></div>
+</div>
+<div id="parent-and-one-metabolite" class="section level1">
+<h1 class="hasAnchor">
+<a href="#parent-and-one-metabolite" class="anchor"></a>Parent and one metabolite</h1>
+<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"><html><body><pre class="r"><span class="no">Z.2a</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="kw">Z0</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z1"</span>),
+                <span class="kw">Z1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>))</pre></body></html></div>
+<pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
+<div class="sourceCode" id="cb4"><html><body><pre class="r"><span class="no">m.Z.2a</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">Z.2a</span>, <span class="no">FOCUS_2006_Z_mkin</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)</pre></body></html></div>
+<pre><code>## Warning in mkinfit(Z.2a, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with
+## value of zero were removed from the data</code></pre>
+<div class="sourceCode" id="cb6"><html><body><pre class="r"><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(<span class="no">m.Z.2a</span>)</pre></body></html></div>
+<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png" width="700"></p>
+<div class="sourceCode" id="cb7"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">m.Z.2a</span>, <span class="kw">data</span> <span class="kw">=</span> <span class="fl">FALSE</span>)$<span class="no">bpar</span></pre></body></html></div>
+<pre><code>##            Estimate se_notrans t value     Pr(&gt;t)    Lower    Upper
+## Z0_0       97.01488   3.301084 29.3888 3.2971e-21 91.66556 102.3642
+## k_Z0        2.23601   0.207078 10.7979 3.3309e-11  1.95303   2.5600
+## k_Z1        0.48212   0.063265  7.6207 2.8154e-08  0.40341   0.5762
+## f_Z0_to_Z1  1.00000   0.094764 10.5525 5.3560e-11  0.00000   1.0000
+## sigma       4.80411   0.635638  7.5579 3.2592e-08  3.52677   6.0815</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>
+<div class="sourceCode" id="cb9"><html><body><pre class="r"><span class="no">Z.2a.ff</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="kw">Z0</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z1"</span>),
+                   <span class="kw">Z1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>),
+                   <span class="kw">use_of_ff</span> <span class="kw">=</span> <span class="st">"max"</span>)</pre></body></html></div>
+<pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
+<div class="sourceCode" id="cb11"><html><body><pre class="r"><span class="no">m.Z.2a.ff</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">Z.2a.ff</span>, <span class="no">FOCUS_2006_Z_mkin</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)</pre></body></html></div>
+<pre><code>## Warning in mkinfit(Z.2a.ff, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with
+## value of zero were removed from the data</code></pre>
+<div class="sourceCode" id="cb13"><html><body><pre class="r"><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(<span class="no">m.Z.2a.ff</span>)</pre></body></html></div>
+<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png" width="700"></p>
+<div class="sourceCode" id="cb14"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">m.Z.2a.ff</span>, <span class="kw">data</span> <span class="kw">=</span> <span class="fl">FALSE</span>)$<span class="no">bpar</span></pre></body></html></div>
+<pre><code>##            Estimate se_notrans t value     Pr(&gt;t)    Lower    Upper
+## Z0_0       97.01488   3.301084 29.3888 3.2971e-21 91.66556 102.3642
+## k_Z0        2.23601   0.207078 10.7979 3.3309e-11  1.95303   2.5600
+## k_Z1        0.48212   0.063265  7.6207 2.8154e-08  0.40341   0.5762
+## f_Z0_to_Z1  1.00000   0.094764 10.5525 5.3560e-11  0.00000   1.0000
+## sigma       4.80411   0.635638  7.5579 3.2592e-08  3.52677   6.0815</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>
+<div class="sourceCode" id="cb16"><html><body><pre class="r"><span class="no">Z.3</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="kw">Z0</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z1"</span>, <span class="kw">sink</span> <span class="kw">=</span> <span class="fl">FALSE</span>),
+               <span class="kw">Z1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>), <span class="kw">use_of_ff</span> <span class="kw">=</span> <span class="st">"max"</span>)</pre></body></html></div>
+<pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
+<div class="sourceCode" id="cb18"><html><body><pre class="r"><span class="no">m.Z.3</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">Z.3</span>, <span class="no">FOCUS_2006_Z_mkin</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)</pre></body></html></div>
+<pre><code>## Warning in mkinfit(Z.3, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with
+## value of zero were removed from the data</code></pre>
+<div class="sourceCode" id="cb20"><html><body><pre class="r"><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(<span class="no">m.Z.3</span>)</pre></body></html></div>
+<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png" width="700"></p>
+<div class="sourceCode" id="cb21"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">m.Z.3</span>, <span class="kw">data</span> <span class="kw">=</span> <span class="fl">FALSE</span>)$<span class="no">bpar</span></pre></body></html></div>
+<pre><code>##       Estimate se_notrans t value     Pr(&gt;t)    Lower    Upper
+## Z0_0  97.01488   2.597342  37.352 2.0106e-24 91.67597 102.3538
+## k_Z0   2.23601   0.146904  15.221 9.1477e-15  1.95354   2.5593
+## k_Z1   0.48212   0.041727  11.554 4.8268e-12  0.40355   0.5760
+## sigma  4.80411   0.620208   7.746 1.6110e-08  3.52925   6.0790</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>
+</div>
+<div id="metabolites-z2-and-z3" class="section level1">
+<h1 class="hasAnchor">
+<a href="#metabolites-z2-and-z3" class="anchor"></a>Metabolites Z2 and Z3</h1>
+<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"><html><body><pre class="r"><span class="no">Z.5</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="kw">Z0</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z1"</span>, <span class="kw">sink</span> <span class="kw">=</span> <span class="fl">FALSE</span>),
+               <span class="kw">Z1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z2"</span>, <span class="kw">sink</span> <span class="kw">=</span> <span class="fl">FALSE</span>),
+               <span class="kw">Z2</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>), <span class="kw">use_of_ff</span> <span class="kw">=</span> <span class="st">"max"</span>)</pre></body></html></div>
+<pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
+<div class="sourceCode" id="cb25"><html><body><pre class="r"><span class="no">m.Z.5</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">Z.5</span>, <span class="no">FOCUS_2006_Z_mkin</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)</pre></body></html></div>
+<pre><code>## Warning in mkinfit(Z.5, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with
+## value of zero were removed from the data</code></pre>
+<div class="sourceCode" id="cb27"><html><body><pre class="r"><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(<span class="no">m.Z.5</span>)</pre></body></html></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>
+<div class="sourceCode" id="cb28"><html><body><pre class="r"><span class="no">Z.FOCUS</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="kw">Z0</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z1"</span>, <span class="kw">sink</span> <span class="kw">=</span> <span class="fl">FALSE</span>),
+                   <span class="kw">Z1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z2"</span>, <span class="kw">sink</span> <span class="kw">=</span> <span class="fl">FALSE</span>),
+                   <span class="kw">Z2</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z3"</span>),
+                   <span class="kw">Z3</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>),
+                   <span class="kw">use_of_ff</span> <span class="kw">=</span> <span class="st">"max"</span>)</pre></body></html></div>
+<pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
+<div class="sourceCode" id="cb30"><html><body><pre class="r"><span class="no">m.Z.FOCUS</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">Z.FOCUS</span>, <span class="no">FOCUS_2006_Z_mkin</span>,
+                     <span class="kw">parms.ini</span> <span class="kw">=</span> <span class="no">m.Z.5</span>$<span class="no">bparms.ode</span>,
+                     <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)</pre></body></html></div>
+<pre><code>## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.5$bparms.ode, :
+## Observations with value of zero were removed from the data</code></pre>
+<pre><code>## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.5$bparms.ode, : Optimisation did not converge:
+## false convergence (8)</code></pre>
+<div class="sourceCode" id="cb33"><html><body><pre class="r"><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(<span class="no">m.Z.FOCUS</span>)</pre></body></html></div>
+<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png" width="700"></p>
+<div class="sourceCode" id="cb34"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">m.Z.FOCUS</span>, <span class="kw">data</span> <span class="kw">=</span> <span class="fl">FALSE</span>)$<span class="no">bpar</span></pre></body></html></div>
+<pre><code>##             Estimate se_notrans t value     Pr(&gt;t)     Lower     Upper
+## Z0_0       96.840695   1.994285 48.5591 4.0254e-42 92.828744 100.85265
+## k_Z0        2.215467   0.118463 18.7018 1.0417e-23  1.989524   2.46707
+## k_Z1        0.478325   0.028259 16.9265 6.2441e-22  0.424725   0.53869
+## k_Z2        0.451638   0.042139 10.7177 1.6309e-14  0.374346   0.54489
+## k_Z3        0.058692   0.015245  3.8498 1.7807e-04  0.034806   0.09897
+## f_Z2_to_Z3  0.471484   0.058348  8.0805 9.6599e-11  0.357736   0.58827
+## sigma       3.984431   0.383402 10.3923 4.5576e-14  3.213126   4.75574</code></pre>
+<div class="sourceCode" id="cb36"><html><body><pre class="r"><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span>(<span class="no">m.Z.FOCUS</span>)</pre></body></html></div>
+<pre><code>## $ff
+##   Z2_Z3 Z2_sink 
+## 0.47148 0.52852 
+## 
+## $distimes
+##        DT50    DT90
+## Z0  0.31287  1.0393
+## Z1  1.44911  4.8138
+## Z2  1.53474  5.0983
+## Z3 11.80989 39.2316</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>
+</div>
+<div id="using-the-sforb-model" class="section level1">
+<h1 class="hasAnchor">
+<a href="#using-the-sforb-model" class="anchor"></a>Using the SFORB model</h1>
+<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"><html><body><pre class="r"><span class="no">Z.mkin.1</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="kw">Z0</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z1"</span>, <span class="kw">sink</span> <span class="kw">=</span> <span class="fl">FALSE</span>),
+                    <span class="kw">Z1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z2"</span>, <span class="kw">sink</span> <span class="kw">=</span> <span class="fl">FALSE</span>),
+                    <span class="kw">Z2</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z3"</span>),
+                    <span class="kw">Z3</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFORB"</span>))</pre></body></html></div>
+<pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
+<div class="sourceCode" id="cb40"><html><body><pre class="r"><span class="no">m.Z.mkin.1</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">Z.mkin.1</span>, <span class="no">FOCUS_2006_Z_mkin</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)</pre></body></html></div>
+<pre><code>## Warning in mkinfit(Z.mkin.1, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with
+## value of zero were removed from the data</code></pre>
+<div class="sourceCode" id="cb42"><html><body><pre class="r"><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(<span class="no">m.Z.mkin.1</span>)</pre></body></html></div>
+<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png" width="700"></p>
+<div class="sourceCode" id="cb43"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">m.Z.mkin.1</span>, <span class="kw">data</span> <span class="kw">=</span> <span class="fl">FALSE</span>)$<span class="no">cov.unscaled</span></pre></body></html></div>
+<pre><code>## NULL</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>
+<div class="sourceCode" id="cb45"><html><body><pre class="r"><span class="no">Z.mkin.3</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="kw">Z0</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFORB"</span>, <span class="st">"Z1"</span>, <span class="kw">sink</span> <span class="kw">=</span> <span class="fl">FALSE</span>),
+                    <span class="kw">Z1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z2"</span>, <span class="kw">sink</span> <span class="kw">=</span> <span class="fl">FALSE</span>),
+                    <span class="kw">Z2</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>))</pre></body></html></div>
+<pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
+<div class="sourceCode" id="cb47"><html><body><pre class="r"><span class="no">m.Z.mkin.3</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">Z.mkin.3</span>, <span class="no">FOCUS_2006_Z_mkin</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)</pre></body></html></div>
+<pre><code>## Warning in mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with
+## value of zero were removed from the data</code></pre>
+<div class="sourceCode" id="cb49"><html><body><pre class="r"><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(<span class="no">m.Z.mkin.3</span>)</pre></body></html></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>
+<div class="sourceCode" id="cb50"><html><body><pre class="r"><span class="no">Z.mkin.4</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="kw">Z0</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFORB"</span>, <span class="st">"Z1"</span>, <span class="kw">sink</span> <span class="kw">=</span> <span class="fl">FALSE</span>),
+                    <span class="kw">Z1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z2"</span>, <span class="kw">sink</span> <span class="kw">=</span> <span class="fl">FALSE</span>),
+                    <span class="kw">Z2</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z3"</span>),
+                    <span class="kw">Z3</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>))</pre></body></html></div>
+<pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
+<div class="sourceCode" id="cb52"><html><body><pre class="r"><span class="no">m.Z.mkin.4</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">Z.mkin.4</span>, <span class="no">FOCUS_2006_Z_mkin</span>,
+                      <span class="kw">parms.ini</span> <span class="kw">=</span> <span class="no">m.Z.mkin.3</span>$<span class="no">bparms.ode</span>,
+                      <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)</pre></body></html></div>
+<pre><code>## Warning in mkinfit(Z.mkin.4, FOCUS_2006_Z_mkin, parms.ini = m.Z.mkin.
+## 3$bparms.ode, : Observations with value of zero were removed from the data</code></pre>
+<div class="sourceCode" id="cb54"><html><body><pre class="r"><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(<span class="no">m.Z.mkin.4</span>)</pre></body></html></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>
+<div class="sourceCode" id="cb55"><html><body><pre class="r"><span class="no">Z.mkin.5</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="kw">Z0</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFORB"</span>, <span class="st">"Z1"</span>, <span class="kw">sink</span> <span class="kw">=</span> <span class="fl">FALSE</span>),
+                    <span class="kw">Z1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z2"</span>, <span class="kw">sink</span> <span class="kw">=</span> <span class="fl">FALSE</span>),
+                    <span class="kw">Z2</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z3"</span>),
+                    <span class="kw">Z3</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFORB"</span>))</pre></body></html></div>
+<pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
+<div class="sourceCode" id="cb57"><html><body><pre class="r"><span class="no">m.Z.mkin.5</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">Z.mkin.5</span>, <span class="no">FOCUS_2006_Z_mkin</span>,
+                      <span class="kw">parms.ini</span> <span class="kw">=</span> <span class="no">m.Z.mkin.4</span>$<span class="no">bparms.ode</span>[<span class="fl">1</span>:<span class="fl">4</span>],
+                      <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)</pre></body></html></div>
+<pre><code>## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini = m.Z.mkin.
+## 4$bparms.ode[1:4], : Observations with value of zero were removed from the data</code></pre>
+<div class="sourceCode" id="cb59"><html><body><pre class="r"><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(<span class="no">m.Z.mkin.5</span>)</pre></body></html></div>
+<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png" width="700"></p>
+<p>The summary view of the backtransformed parameters shows that we get no confidence intervals due to overparameterisation. As the optimized  is excessively small, it seems reasonable to fix it to zero.</p>
+<div class="sourceCode" id="cb60"><html><body><pre class="r"><span class="no">m.Z.mkin.5a</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">Z.mkin.5</span>, <span class="no">FOCUS_2006_Z_mkin</span>,
+                       <span class="kw">parms.ini</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="no">m.Z.mkin.5</span>$<span class="no">bparms.ode</span>[<span class="fl">1</span>:<span class="fl">7</span>],
+                                     <span class="kw">k_Z3_bound_free</span> <span class="kw">=</span> <span class="fl">0</span>),
+                       <span class="kw">fixed_parms</span> <span class="kw">=</span> <span class="st">"k_Z3_bound_free"</span>,
+                       <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)</pre></body></html></div>
+<pre><code>## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini = c(m.Z.mkin.
+## 5$bparms.ode[1:7], : Observations with value of zero were removed from the data</code></pre>
+<div class="sourceCode" id="cb62"><html><body><pre class="r"><span class="fu"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(<span class="no">m.Z.mkin.5a</span>)</pre></body></html></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>
+<div class="sourceCode" id="cb63"><html><body><pre class="r"><span class="fu"><a href="../../reference/mkinparplot.html">mkinparplot</a></span>(<span class="no">m.Z.mkin.5a</span>)</pre></body></html></div>
+<p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png" width="700"></p>
+<p>The endpoints obtained with this model are</p>
+<div class="sourceCode" id="cb64"><html><body><pre class="r"><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span>(<span class="no">m.Z.mkin.5a</span>)</pre></body></html></div>
+<pre><code>## $ff
+## Z0_free   Z2_Z3 Z2_sink Z3_free 
+## 1.00000 0.53656 0.46344 1.00000 
+## 
+## $SFORB
+##     Z0_b1     Z0_b2     Z3_b1     Z3_b2 
+## 2.4471337 0.0075125 0.0800071 0.0000000 
+## 
+## $distimes
+##      DT50   DT90 DT50_Z0_b1 DT50_Z0_b2 DT50_Z3_b1 DT50_Z3_b2
+## Z0 0.3043 1.1848    0.28325     92.266         NA         NA
+## Z1 1.5148 5.0320         NA         NA         NA         NA
+## Z2 1.6414 5.4526         NA         NA         NA         NA
+## Z3     NA     NA         NA         NA     8.6636        Inf</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>
+</div>
+<div id="references" class="section level1">
+<h1 class="hasAnchor">
+<a href="#references" class="anchor"></a>References</h1>
+<!-- vim: set foldmethod=syntax: -->
+<div id="refs" class="references">
+<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="uri">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>.</p>
+</div>
+</div>
+</div>
+  </div>
+
+  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
+
+        <nav id="toc" data-toggle="toc"><h2 data-toc-skip>Contents</h2>
+    </nav>
+</div>
+
+</div>
+
+
+
+      <footer><div class="copyright">
+  <p>Developed by Johannes Ranke.</p>
+</div>
+
+<div class="pkgdown">
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+</div>
+
+      </footer>
+</div>
+
+  
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+  </body>
+</html>
diff --git a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png
new file mode 100644
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diff --git a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png
new file mode 100644
index 00000000..96738dd0
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+      <h1 data-toc-skip>Evaluation of example datasets from Attachment 1 to the US EPA SOP for the NAFTA guidance</h1>
+                        <h4 class="author">Johannes Ranke</h4>
+            
+            <h4 class="date">2020-05-27</h4>
+      
+      <small class="dont-index">Source: <a href="http://github.com/jranke/mkin/blob/master/vignettes/web_only/NAFTA_examples.rmd"><code>vignettes/web_only/NAFTA_examples.rmd</code></a></small>
+      <div class="hidden name"><code>NAFTA_examples.rmd</code></div>
+
+    </div>
+
+    
+    
+<div id="introduction" class="section level1">
+<h1 class="hasAnchor">
+<a href="#introduction" class="anchor"></a>Introduction</h1>
+<p>In this document, the example evaluations provided in Attachment 1 to the SOP of US EPA for using the NAFTA guidance <span class="citation">(US EPA 2015)</span> are repeated using mkin. The original evaluations reported in the attachment were performed using PestDF in version 0.8.4. Note that PestDF 0.8.13 is the version distributed at the US EPA website today (2019-02-26).</p>
+<p>The datasets are now distributed with the mkin package.</p>
+</div>
+<div id="examples-where-dfop-did-not-converge-with-pestdf-0-8-4" class="section level1">
+<h1 class="hasAnchor">
+<a href="#examples-where-dfop-did-not-converge-with-pestdf-0-8-4" class="anchor"></a>Examples where DFOP did not converge with PestDF 0.8.4</h1>
+<p>In attachment 1, it is reported that the DFOP model does not converge for these datasets when PestDF 0.8.4 was used. For all four datasets, the DFOP model can be fitted with mkin (see below). The negative half-life given by PestDF 0.8.4 for these fits appears to be the result of a bug. The results for the other two models (SFO and IORE) are the same.</p>
+<div id="example-on-page-5-upper-panel" class="section level2">
+<h2 class="hasAnchor">
+<a href="#example-on-page-5-upper-panel" class="anchor"></a>Example on page 5, upper panel</h2>
+<div class="sourceCode" id="cb1"><html><body><pre class="r"><span class="no">p5a</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p5a"</span>]])</pre></body></html></div>
+<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
+<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
+<div class="sourceCode" id="cb4"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p5a</span>)</pre></body></html></div>
+<p><img src="NAFTA_examples_files/figure-html/p5a-1.png" width="700"></p>
+<div class="sourceCode" id="cb5"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p5a</span>)</pre></body></html></div>
+<pre><code>## Sums of squares:
+##       SFO      IORE      DFOP 
+## 465.21753  56.27506  32.06401 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 64.4304
+## 
+## Parameters:
+## $SFO
+##               Estimate   Pr(&gt;t)  Lower   Upper
+## parent_0       95.8401 4.67e-21 92.245 99.4357
+## k_parent_sink   0.0102 3.92e-12  0.009  0.0117
+## sigma           4.8230 3.81e-06  3.214  6.4318
+## 
+## $IORE
+##                     Estimate Pr(&gt;t)    Lower    Upper
+## parent_0            1.01e+02     NA 9.91e+01 1.02e+02
+## k__iore_parent_sink 1.54e-05     NA 4.08e-06 5.84e-05
+## N_parent            2.57e+00     NA 2.25e+00 2.89e+00
+## sigma               1.68e+00     NA 1.12e+00 2.24e+00
+## 
+## $DFOP
+##          Estimate   Pr(&gt;t)   Lower    Upper
+## parent_0 9.99e+01 1.41e-26 98.8116 101.0810
+## k1       2.67e-02 5.05e-06  0.0243   0.0295
+## k2       2.86e-12 5.00e-01  0.0000      Inf
+## g        6.47e-01 3.67e-06  0.6248   0.6677
+## sigma    1.27e+00 8.91e-06  0.8395   1.6929
+## 
+## 
+## DTx values:
+##      DT50     DT90 DT50_rep
+## SFO  67.7 2.25e+02 6.77e+01
+## IORE 58.2 1.07e+03 3.22e+02
+## DFOP 55.5 4.42e+11 2.42e+11
+## 
+## Representative half-life:
+## [1] 321.51</code></pre>
+</div>
+<div id="example-on-page-5-lower-panel" class="section level2">
+<h2 class="hasAnchor">
+<a href="#example-on-page-5-lower-panel" class="anchor"></a>Example on page 5, lower panel</h2>
+<div class="sourceCode" id="cb7"><html><body><pre class="r"><span class="no">p5b</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p5b"</span>]])</pre></body></html></div>
+<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
+<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
+<div class="sourceCode" id="cb10"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p5b</span>)</pre></body></html></div>
+<p><img src="NAFTA_examples_files/figure-html/p5b-1.png" width="700"></p>
+<div class="sourceCode" id="cb11"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p5b</span>)</pre></body></html></div>
+<pre><code>## Sums of squares:
+##      SFO     IORE     DFOP 
+## 94.81123 10.10936  7.55871 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 11.77879
+## 
+## Parameters:
+## $SFO
+##               Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0        96.497 2.32e-24 94.85271 98.14155
+## k_parent_sink    0.008 3.42e-14  0.00737  0.00869
+## sigma            2.295 1.22e-05  1.47976  3.11036
+## 
+## $IORE
+##                     Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0            9.85e+01 1.17e-28 9.79e+01 9.92e+01
+## k__iore_parent_sink 1.53e-04 6.50e-03 7.21e-05 3.26e-04
+## N_parent            1.94e+00 5.88e-13 1.76e+00 2.12e+00
+## sigma               7.49e-01 1.63e-05 4.82e-01 1.02e+00
+## 
+## $DFOP
+##          Estimate   Pr(&gt;t)   Lower   Upper
+## parent_0 9.84e+01 1.24e-27 97.8078 98.9187
+## k1       1.55e-02 4.10e-04  0.0143  0.0167
+## k2       1.16e-11 5.00e-01  0.0000     Inf
+## g        6.89e-01 2.92e-03  0.6626  0.7142
+## sigma    6.48e-01 2.38e-05  0.4147  0.8813
+## 
+## 
+## DTx values:
+##      DT50     DT90 DT50_rep
+## SFO  86.6 2.88e+02 8.66e+01
+## IORE 85.5 7.17e+02 2.16e+02
+## DFOP 83.6 9.80e+10 5.98e+10
+## 
+## Representative half-life:
+## [1] 215.87</code></pre>
+</div>
+<div id="example-on-page-6" class="section level2">
+<h2 class="hasAnchor">
+<a href="#example-on-page-6" class="anchor"></a>Example on page 6</h2>
+<div class="sourceCode" id="cb13"><html><body><pre class="r"><span class="no">p6</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p6"</span>]])</pre></body></html></div>
+<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
+<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
+<div class="sourceCode" id="cb16"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p6</span>)</pre></body></html></div>
+<p><img src="NAFTA_examples_files/figure-html/p6-1.png" width="700"></p>
+<div class="sourceCode" id="cb17"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p6</span>)</pre></body></html></div>
+<pre><code>## Sums of squares:
+##       SFO      IORE      DFOP 
+## 188.45361  51.00699  42.46931 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 58.39888
+## 
+## Parameters:
+## $SFO
+##               Estimate   Pr(&gt;t)   Lower   Upper
+## parent_0       94.7759 7.29e-24 92.3478 97.2039
+## k_parent_sink   0.0179 8.02e-16  0.0166  0.0194
+## sigma           3.0696 3.81e-06  2.0456  4.0936
+## 
+## $IORE
+##                     Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0            97.12446 2.63e-26 95.62461 98.62431
+## k__iore_parent_sink  0.00252 1.95e-03  0.00134  0.00472
+## N_parent             1.49587 4.07e-13  1.33896  1.65279
+## sigma                1.59698 5.05e-06  1.06169  2.13227
+## 
+## $DFOP
+##          Estimate   Pr(&gt;t)   Lower   Upper
+## parent_0 9.66e+01 1.57e-25 95.3476 97.8979
+## k1       2.55e-02 7.33e-06  0.0233  0.0278
+## k2       4.90e-11 5.00e-01  0.0000     Inf
+## g        8.61e-01 7.55e-06  0.8314  0.8867
+## sigma    1.46e+00 6.93e-06  0.9661  1.9483
+## 
+## 
+## DTx values:
+##      DT50     DT90 DT50_rep
+## SFO  38.6 1.28e+02 3.86e+01
+## IORE 34.0 1.77e+02 5.32e+01
+## DFOP 34.1 6.66e+09 1.41e+10
+## 
+## Representative half-life:
+## [1] 53.17</code></pre>
+</div>
+<div id="example-on-page-7" class="section level2">
+<h2 class="hasAnchor">
+<a href="#example-on-page-7" class="anchor"></a>Example on page 7</h2>
+<div class="sourceCode" id="cb19"><html><body><pre class="r"><span class="no">p7</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p7"</span>]])</pre></body></html></div>
+<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
+<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
+<div class="sourceCode" id="cb22"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p7</span>)</pre></body></html></div>
+<p><img src="NAFTA_examples_files/figure-html/p7-1.png" width="700"></p>
+<div class="sourceCode" id="cb23"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p7</span>)</pre></body></html></div>
+<pre><code>## Sums of squares:
+##      SFO     IORE     DFOP 
+## 3661.661 3195.030 3174.145 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 3334.194
+## 
+## Parameters:
+## $SFO
+##               Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0      96.41796 4.80e-53 93.32245 99.51347
+## k_parent_sink  0.00735 7.64e-21  0.00641  0.00843
+## sigma          7.94557 1.83e-15  6.46713  9.42401
+## 
+## $IORE
+##                     Estimate Pr(&gt;t)    Lower    Upper
+## parent_0            9.92e+01     NA 9.55e+01 1.03e+02
+## k__iore_parent_sink 1.60e-05     NA 1.45e-07 1.77e-03
+## N_parent            2.45e+00     NA 1.35e+00 3.54e+00
+## sigma               7.42e+00     NA 6.04e+00 8.80e+00
+## 
+## $DFOP
+##          Estimate   Pr(&gt;t)   Lower    Upper
+## parent_0 9.89e+01 9.44e-49 95.4640 102.2573
+## k1       1.81e-02 1.75e-01  0.0116   0.0281
+## k2       1.97e-10 5.00e-01  0.0000      Inf
+## g        6.06e-01 2.19e-01  0.4826   0.7178
+## sigma    7.40e+00 2.97e-15  6.0201   8.7754
+## 
+## 
+## DTx values:
+##      DT50     DT90 DT50_rep
+## SFO  94.3 3.13e+02 9.43e+01
+## IORE 96.7 1.51e+03 4.55e+02
+## DFOP 96.4 6.97e+09 3.52e+09
+## 
+## Representative half-life:
+## [1] 454.55</code></pre>
+</div>
+</div>
+<div id="examples-where-the-representative-half-life-deviates-from-the-observed-dt50" class="section level1">
+<h1 class="hasAnchor">
+<a href="#examples-where-the-representative-half-life-deviates-from-the-observed-dt50" class="anchor"></a>Examples where the representative half-life deviates from the observed DT50</h1>
+<div id="example-on-page-8" class="section level2">
+<h2 class="hasAnchor">
+<a href="#example-on-page-8" class="anchor"></a>Example on page 8</h2>
+<p>For this dataset, the IORE fit does not converge when the default starting values used by mkin for the IORE model are used. Therefore, a lower value for the rate constant is used here.</p>
+<div class="sourceCode" id="cb25"><html><body><pre class="r"><span class="no">p8</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p8"</span>]], <span class="kw">parms.ini</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="kw">k__iore_parent_sink</span> <span class="kw">=</span> <span class="fl">1e-3</span>))</pre></body></html></div>
+<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
+<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
+<div class="sourceCode" id="cb28"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p8</span>)</pre></body></html></div>
+<p><img src="NAFTA_examples_files/figure-html/p8-1.png" width="700"></p>
+<div class="sourceCode" id="cb29"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p8</span>)</pre></body></html></div>
+<pre><code>## Sums of squares:
+##       SFO      IORE      DFOP 
+## 1996.9408  444.9237  547.5616 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 477.4924
+## 
+## Parameters:
+## $SFO
+##               Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0      88.16549 6.53e-29 83.37344 92.95754
+## k_parent_sink  0.00803 1.67e-13  0.00674  0.00957
+## sigma          7.44786 4.17e-10  5.66209  9.23363
+## 
+## $IORE
+##                     Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0            9.77e+01 7.03e-35 9.44e+01 1.01e+02
+## k__iore_parent_sink 6.14e-05 3.20e-02 2.12e-05 1.78e-04
+## N_parent            2.27e+00 4.23e-18 2.00e+00 2.54e+00
+## sigma               3.52e+00 5.36e-10 2.67e+00 4.36e+00
+## 
+## $DFOP
+##          Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0 95.70619 8.99e-32 91.87941 99.53298
+## k1        0.02500 5.25e-04  0.01422  0.04394
+## k2        0.00273 6.84e-03  0.00125  0.00597
+## g         0.58835 2.84e-06  0.36595  0.77970
+## sigma     3.90001 6.94e-10  2.96260  4.83741
+## 
+## 
+## DTx values:
+##      DT50 DT90 DT50_rep
+## SFO  86.3  287     86.3
+## IORE 53.4  668    201.0
+## DFOP 55.6  517    253.0
+## 
+## Representative half-life:
+## [1] 201.03</code></pre>
+</div>
+</div>
+<div id="examples-where-sfo-was-not-selected-for-an-abiotic-study" class="section level1">
+<h1 class="hasAnchor">
+<a href="#examples-where-sfo-was-not-selected-for-an-abiotic-study" class="anchor"></a>Examples where SFO was not selected for an abiotic study</h1>
+<div id="example-on-page-9-upper-panel" class="section level2">
+<h2 class="hasAnchor">
+<a href="#example-on-page-9-upper-panel" class="anchor"></a>Example on page 9, upper panel</h2>
+<div class="sourceCode" id="cb31"><html><body><pre class="r"><span class="no">p9a</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p9a"</span>]])</pre></body></html></div>
+<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
+<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
+<div class="sourceCode" id="cb34"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p9a</span>)</pre></body></html></div>
+<p><img src="NAFTA_examples_files/figure-html/p9a-1.png" width="700"></p>
+<div class="sourceCode" id="cb35"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p9a</span>)</pre></body></html></div>
+<pre><code>## Sums of squares:
+##       SFO      IORE      DFOP 
+## 839.35238  88.57064   9.93363 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 105.5678
+## 
+## Parameters:
+## $SFO
+##               Estimate   Pr(&gt;t)   Lower   Upper
+## parent_0       88.1933 3.06e-12 79.9447 96.4419
+## k_parent_sink   0.0409 2.07e-07  0.0324  0.0516
+## sigma           7.2429 3.92e-05  4.4768 10.0090
+## 
+## $IORE
+##                     Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0            9.89e+01 1.12e-16 9.54e+01 1.02e+02
+## k__iore_parent_sink 1.93e-05 1.13e-01 3.49e-06 1.06e-04
+## N_parent            2.91e+00 1.45e-09 2.50e+00 3.32e+00
+## sigma               2.35e+00 5.31e-05 1.45e+00 3.26e+00
+## 
+## $DFOP
+##          Estimate   Pr(&gt;t)  Lower  Upper
+## parent_0 9.85e+01 2.54e-20 97.390 99.672
+## k1       1.38e-01 3.52e-05  0.131  0.146
+## k2       6.02e-13 5.00e-01  0.000    Inf
+## g        6.52e-01 8.13e-06  0.642  0.661
+## sigma    7.88e-01 6.13e-02  0.481  1.095
+## 
+## 
+## DTx values:
+##      DT50     DT90 DT50_rep
+## SFO  16.9 5.63e+01 1.69e+01
+## IORE 11.6 3.37e+02 1.01e+02
+## DFOP 10.5 2.07e+12 1.15e+12
+## 
+## Representative half-life:
+## [1] 101.43</code></pre>
+<p>In this example, the residuals of the SFO indicate a lack of fit of this model, so even if it was an abiotic experiment, the data do not suggest a simple exponential decline.</p>
+</div>
+<div id="example-on-page-9-lower-panel" class="section level2">
+<h2 class="hasAnchor">
+<a href="#example-on-page-9-lower-panel" class="anchor"></a>Example on page 9, lower panel</h2>
+<div class="sourceCode" id="cb37"><html><body><pre class="r"><span class="no">p9b</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p9b"</span>]])</pre></body></html></div>
+<pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
+<pre><code>## Warning in sqrt(diag(covar_notrans)): NaNs produced</code></pre>
+<pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
+<pre><code>## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
+## doubtful</code></pre>
+<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
+<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
+<div class="sourceCode" id="cb44"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p9b</span>)</pre></body></html></div>
+<p><img src="NAFTA_examples_files/figure-html/p9b-1.png" width="700"></p>
+<div class="sourceCode" id="cb45"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p9b</span>)</pre></body></html></div>
+<pre><code>## Sums of squares:
+##      SFO     IORE     DFOP 
+## 35.64867 23.22334 35.64867 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 28.54188
+## 
+## Parameters:
+## $SFO
+##               Estimate   Pr(&gt;t)  Lower   Upper
+## parent_0       94.7123 2.15e-19 93.178 96.2464
+## k_parent_sink   0.0389 4.47e-14  0.037  0.0408
+## sigma           1.5957 1.28e-04  0.932  2.2595
+## 
+## $IORE
+##                     Estimate   Pr(&gt;t)   Lower  Upper
+## parent_0              93.863 2.32e-18 92.4565 95.269
+## k__iore_parent_sink    0.127 1.85e-02  0.0504  0.321
+## N_parent               0.711 1.88e-05  0.4843  0.937
+## sigma                  1.288 1.76e-04  0.7456  1.830
+## 
+## $DFOP
+##          Estimate   Pr(&gt;t)   Lower   Upper
+## parent_0  94.7123 1.61e-16 93.1355 96.2891
+## k1         0.0389 1.43e-06  0.0312  0.0485
+## k2         0.0389 6.67e-03  0.0186  0.0812
+## g          0.7742      NaN      NA      NA
+## sigma      1.5957 2.50e-04  0.9135  2.2779
+## 
+## 
+## DTx values:
+##      DT50 DT90 DT50_rep
+## SFO  17.8 59.2     17.8
+## IORE 18.4 49.2     14.8
+## DFOP 17.8 59.2     17.8
+## 
+## Representative half-life:
+## [1] 14.8</code></pre>
+<p>Here, mkin gives a longer slow DT50 for the DFOP model (17.8 days) than PestDF (13.5 days). Presumably, this is related to the fact that PestDF gives a negative value for the proportion of the fast degradation which should be between 0 and 1, inclusive. This parameter is called f in PestDF and g in mkin. In mkin, it is restricted to the interval from 0 to 1.</p>
+</div>
+<div id="example-on-page-10" class="section level2">
+<h2 class="hasAnchor">
+<a href="#example-on-page-10" class="anchor"></a>Example on page 10</h2>
+<div class="sourceCode" id="cb47"><html><body><pre class="r"><span class="no">p10</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p10"</span>]])</pre></body></html></div>
+<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
+<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
+<div class="sourceCode" id="cb50"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p10</span>)</pre></body></html></div>
+<p><img src="NAFTA_examples_files/figure-html/p10-1.png" width="700"></p>
+<div class="sourceCode" id="cb51"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p10</span>)</pre></body></html></div>
+<pre><code>## Sums of squares:
+##      SFO     IORE     DFOP 
+## 899.4089 336.4348 899.4089 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 413.4841
+## 
+## Parameters:
+## $SFO
+##               Estimate   Pr(&gt;t)   Lower    Upper
+## parent_0      101.7315 6.42e-11 91.9259 111.5371
+## k_parent_sink   0.0495 1.70e-07  0.0404   0.0607
+## sigma           8.0152 1.28e-04  4.6813  11.3491
+## 
+## $IORE
+##                     Estimate   Pr(&gt;t)  Lower   Upper
+## parent_0               96.86 3.32e-12 90.848 102.863
+## k__iore_parent_sink     2.96 7.91e-02  0.687  12.761
+## N_parent                0.00 5.00e-01 -0.372   0.372
+## sigma                   4.90 1.77e-04  2.837   6.968
+## 
+## $DFOP
+##          Estimate   Pr(&gt;t)   Lower    Upper
+## parent_0 101.7315 1.41e-09 91.6534 111.8097
+## k1         0.0495 6.42e-04  0.0301   0.0814
+## k2         0.0495 1.66e-02  0.0200   0.1225
+## g          0.6634 5.00e-01  0.0000   1.0000
+## sigma      8.0152 2.50e-04  4.5886  11.4418
+## 
+## 
+## DTx values:
+##      DT50 DT90 DT50_rep
+## SFO  14.0 46.5    14.00
+## IORE 16.4 29.4     8.86
+## DFOP 14.0 46.5    14.00
+## 
+## Representative half-life:
+## [1] 8.86</code></pre>
+<p>Here, a value below N is given for the IORE model, because the data suggests a faster decline towards the end of the experiment, which appears physically rather unlikely in the case of a photolysis study. It seems PestDF does not constrain N to values above zero, thus the slight difference in IORE model parameters between PestDF and mkin.</p>
+</div>
+</div>
+<div id="the-dt50-was-not-observed-during-the-study" class="section level1">
+<h1 class="hasAnchor">
+<a href="#the-dt50-was-not-observed-during-the-study" class="anchor"></a>The DT50 was not observed during the study</h1>
+<div id="example-on-page-11" class="section level2">
+<h2 class="hasAnchor">
+<a href="#example-on-page-11" class="anchor"></a>Example on page 11</h2>
+<div class="sourceCode" id="cb53"><html><body><pre class="r"><span class="no">p11</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p11"</span>]])</pre></body></html></div>
+<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
+<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
+<div class="sourceCode" id="cb56"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p11</span>)</pre></body></html></div>
+<p><img src="NAFTA_examples_files/figure-html/p11-1.png" width="700"></p>
+<div class="sourceCode" id="cb57"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p11</span>)</pre></body></html></div>
+<pre><code>## Sums of squares:
+##      SFO     IORE     DFOP 
+## 579.6805 204.7932 144.7783 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 251.6944
+## 
+## Parameters:
+## $SFO
+##               Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0      96.15820 4.83e-13 90.24934 1.02e+02
+## k_parent_sink  0.00321 4.71e-05  0.00222 4.64e-03
+## sigma          6.43473 1.28e-04  3.75822 9.11e+00
+## 
+## $IORE
+##                     Estimate Pr(&gt;t)    Lower    Upper
+## parent_0            1.05e+02     NA 9.90e+01 1.10e+02
+## k__iore_parent_sink 3.11e-17     NA 1.35e-20 7.18e-14
+## N_parent            8.36e+00     NA 6.62e+00 1.01e+01
+## sigma               3.82e+00     NA 2.21e+00 5.44e+00
+## 
+## $DFOP
+##          Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0 1.05e+02 9.47e-13  99.9990 109.1224
+## k1       4.41e-02 5.95e-03   0.0296   0.0658
+## k2       7.25e-13 5.00e-01   0.0000      Inf
+## g        3.22e-01 1.45e-03   0.2814   0.3650
+## sigma    3.22e+00 3.52e-04   1.8410   4.5906
+## 
+## 
+## DTx values:
+##          DT50     DT90 DT50_rep
+## SFO  2.16e+02 7.18e+02 2.16e+02
+## IORE 9.73e+02 1.37e+08 4.11e+07
+## DFOP 4.21e+11 2.64e+12 9.56e+11
+## 
+## Representative half-life:
+## [1] 41148169</code></pre>
+<p>In this case, the DFOP fit reported for PestDF resulted in a negative value for the slower rate constant, which is not possible in mkin. The other results are in agreement.</p>
+</div>
+</div>
+<div id="n-is-less-than-1-and-the-dfop-rate-constants-are-like-the-sfo-rate-constant" class="section level1">
+<h1 class="hasAnchor">
+<a href="#n-is-less-than-1-and-the-dfop-rate-constants-are-like-the-sfo-rate-constant" class="anchor"></a>N is less than 1 and the DFOP rate constants are like the SFO rate constant</h1>
+<p>In the following three examples, the same results are obtained with mkin as reported for PestDF. As in the case on page 10, the N values below 1 are deemed unrealistic and appear to be the result of an overparameterisation.</p>
+<div id="example-on-page-12-upper-panel" class="section level2">
+<h2 class="hasAnchor">
+<a href="#example-on-page-12-upper-panel" class="anchor"></a>Example on page 12, upper panel</h2>
+<div class="sourceCode" id="cb59"><html><body><pre class="r"><span class="no">p12a</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p12a"</span>]])</pre></body></html></div>
+<pre><code>## Warning in summary.mkinfit(x): Could not calculate correlation; no covariance
+## matrix</code></pre>
+<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
+<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
+<div class="sourceCode" id="cb63"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p12a</span>)</pre></body></html></div>
+<p><img src="NAFTA_examples_files/figure-html/p12a-1.png" width="700"></p>
+<div class="sourceCode" id="cb64"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p12a</span>)</pre></body></html></div>
+<pre><code>## Sums of squares:
+##      SFO     IORE     DFOP 
+## 695.4440 220.0685 695.4440 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 270.4679
+## 
+## Parameters:
+## $SFO
+##               Estimate   Pr(&gt;t)  Lower   Upper
+## parent_0       100.521 8.75e-12 92.461 108.581
+## k_parent_sink    0.124 3.61e-08  0.104   0.148
+## sigma            7.048 1.28e-04  4.116   9.980
+## 
+## $IORE
+##                     Estimate Pr(&gt;t) Lower Upper
+## parent_0              96.823     NA    NA    NA
+## k__iore_parent_sink    2.436     NA    NA    NA
+## N_parent               0.263     NA    NA    NA
+## sigma                  3.965     NA    NA    NA
+## 
+## $DFOP
+##          Estimate   Pr(&gt;t)   Lower   Upper
+## parent_0  100.521 2.74e-10 92.2366 108.805
+## k1          0.124 5.74e-06  0.0958   0.161
+## k2          0.124 6.61e-02  0.0319   0.484
+## g           0.877 5.00e-01  0.0000   1.000
+## sigma       7.048 2.50e-04  4.0349  10.061
+## 
+## 
+## DTx values:
+##      DT50 DT90 DT50_rep
+## SFO  5.58 18.5     5.58
+## IORE 6.49 13.2     3.99
+## DFOP 5.58 18.5     5.58
+## 
+## Representative half-life:
+## [1] 3.99</code></pre>
+</div>
+<div id="example-on-page-12-lower-panel" class="section level2">
+<h2 class="hasAnchor">
+<a href="#example-on-page-12-lower-panel" class="anchor"></a>Example on page 12, lower panel</h2>
+<div class="sourceCode" id="cb66"><html><body><pre class="r"><span class="no">p12b</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p12b"</span>]])</pre></body></html></div>
+<pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
+<pre><code>## Warning in qt(alpha/2, rdf): NaNs produced</code></pre>
+<pre><code>## Warning in qt(1 - alpha/2, rdf): NaNs produced</code></pre>
+<pre><code>## Warning in sqrt(diag(covar_notrans)): NaNs produced</code></pre>
+<pre><code>## Warning in pt(abs(tval), rdf, lower.tail = FALSE): NaNs produced</code></pre>
+<pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
+<pre><code>## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
+## doubtful</code></pre>
+<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
+<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
+<div class="sourceCode" id="cb76"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p12b</span>)</pre></body></html></div>
+<p><img src="NAFTA_examples_files/figure-html/p12b-1.png" width="700"></p>
+<div class="sourceCode" id="cb77"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p12b</span>)</pre></body></html></div>
+<pre><code>## Sums of squares:
+##      SFO     IORE     DFOP 
+## 58.90242 19.06353 58.90242 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 51.51756
+## 
+## Parameters:
+## $SFO
+##               Estimate  Pr(&gt;t)   Lower    Upper
+## parent_0       97.6840 0.00039 85.9388 109.4292
+## k_parent_sink   0.0589 0.00261  0.0431   0.0805
+## sigma           3.4323 0.04356 -1.2377   8.1023
+## 
+## $IORE
+##                     Estimate Pr(&gt;t)     Lower  Upper
+## parent_0              95.523 0.0055 74.539157 116.51
+## k__iore_parent_sink    0.333 0.1433  0.000717 154.57
+## N_parent               0.568 0.0677 -0.989464   2.13
+## sigma                  1.953 0.0975 -5.893100   9.80
+## 
+## $DFOP
+##          Estimate Pr(&gt;t) Lower Upper
+## parent_0  97.6840    NaN   NaN   NaN
+## k1         0.0589    NaN    NA    NA
+## k2         0.0589    NaN    NA    NA
+## g          0.6902    NaN    NA    NA
+## sigma      3.4323    NaN   NaN   NaN
+## 
+## 
+## DTx values:
+##      DT50 DT90 DT50_rep
+## SFO  11.8 39.1    11.80
+## IORE 12.9 31.4     9.46
+## DFOP 11.8 39.1    11.80
+## 
+## Representative half-life:
+## [1] 9.46</code></pre>
+</div>
+<div id="example-on-page-13" class="section level2">
+<h2 class="hasAnchor">
+<a href="#example-on-page-13" class="anchor"></a>Example on page 13</h2>
+<div class="sourceCode" id="cb79"><html><body><pre class="r"><span class="no">p13</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p13"</span>]])</pre></body></html></div>
+<pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
+<pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
+<pre><code>## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
+## doubtful</code></pre>
+<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
+<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
+<div class="sourceCode" id="cb85"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p13</span>)</pre></body></html></div>
+<p><img src="NAFTA_examples_files/figure-html/p13-1.png" width="700"></p>
+<div class="sourceCode" id="cb86"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p13</span>)</pre></body></html></div>
+<pre><code>## Sums of squares:
+##      SFO     IORE     DFOP 
+## 174.5971 142.3951 174.5971 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 172.131
+## 
+## Parameters:
+## $SFO
+##               Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0      92.73500 5.99e-17 89.61936 95.85065
+## k_parent_sink  0.00258 2.42e-09  0.00223  0.00299
+## sigma          3.41172 7.07e-05  2.05455  4.76888
+## 
+## $IORE
+##                     Estimate   Pr(&gt;t)    Lower  Upper
+## parent_0             91.6016 6.34e-16 88.53086 94.672
+## k__iore_parent_sink   0.0396 2.36e-01  0.00207  0.759
+## N_parent              0.3541 1.46e-01 -0.35153  1.060
+## sigma                 3.0811 9.64e-05  1.84296  4.319
+## 
+## $DFOP
+##          Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0 92.73500 9.25e-15 8.95e+01 9.59e+01
+## k1        0.00258 4.28e-01 1.70e-08 3.92e+02
+## k2        0.00258 3.69e-08 2.20e-03 3.03e-03
+## g         0.00442 5.00e-01       NA       NA
+## sigma     3.41172 1.35e-04 2.02e+00 4.80e+00
+## 
+## 
+## DTx values:
+##      DT50 DT90 DT50_rep
+## SFO   269  892      269
+## IORE  261  560      169
+## DFOP  269  892      269
+## 
+## Representative half-life:
+## [1] 168.51</code></pre>
+</div>
+</div>
+<div id="dt50-not-observed-in-the-study-and-dfop-problems-in-pestdf" class="section level1">
+<h1 class="hasAnchor">
+<a href="#dt50-not-observed-in-the-study-and-dfop-problems-in-pestdf" class="anchor"></a>DT50 not observed in the study and DFOP problems in PestDF</h1>
+<div class="sourceCode" id="cb88"><html><body><pre class="r"><span class="no">p14</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p14"</span>]])</pre></body></html></div>
+<pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
+<pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
+<pre><code>## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
+## doubtful</code></pre>
+<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
+<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
+<div class="sourceCode" id="cb94"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p14</span>)</pre></body></html></div>
+<p><img src="NAFTA_examples_files/figure-html/p14-1.png" width="700"></p>
+<div class="sourceCode" id="cb95"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p14</span>)</pre></body></html></div>
+<pre><code>## Sums of squares:
+##      SFO     IORE     DFOP 
+## 48.43249 28.67746 27.26248 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 32.83337
+## 
+## Parameters:
+## $SFO
+##               Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0      99.47124 2.06e-30 98.42254 1.01e+02
+## k_parent_sink  0.00279 3.75e-15  0.00256 3.04e-03
+## sigma          1.55616 3.81e-06  1.03704 2.08e+00
+## 
+## $IORE
+##                     Estimate Pr(&gt;t) Lower Upper
+## parent_0            1.00e+02     NA   NaN   NaN
+## k__iore_parent_sink 9.44e-08     NA   NaN   NaN
+## N_parent            3.31e+00     NA   NaN   NaN
+## sigma               1.20e+00     NA 0.796   1.6
+## 
+## $DFOP
+##          Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0 1.00e+02 2.96e-28 99.40280 101.2768
+## k1       9.53e-03 1.20e-01  0.00638   0.0143
+## k2       7.29e-12 5.00e-01  0.00000      Inf
+## g        3.98e-01 2.19e-01  0.30481   0.4998
+## sigma    1.17e+00 7.68e-06  0.77406   1.5610
+## 
+## 
+## DTx values:
+##          DT50     DT90 DT50_rep
+## SFO  2.48e+02 8.25e+02 2.48e+02
+## IORE 4.34e+02 2.22e+04 6.70e+03
+## DFOP 2.54e+10 2.46e+11 9.51e+10
+## 
+## Representative half-life:
+## [1] 6697.44</code></pre>
+<p>The slower rate constant reported by PestDF is negative, which is not physically realistic, and not possible in mkin. The other fits give the same results in mkin and PestDF.</p>
+</div>
+<div id="n-is-less-than-1-and-dfop-fraction-parameter-is-below-zero" class="section level1">
+<h1 class="hasAnchor">
+<a href="#n-is-less-than-1-and-dfop-fraction-parameter-is-below-zero" class="anchor"></a>N is less than 1 and DFOP fraction parameter is below zero</h1>
+<div class="sourceCode" id="cb97"><html><body><pre class="r"><span class="no">p15a</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p15a"</span>]])</pre></body></html></div>
+<pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
+<pre><code>## Warning in sqrt(diag(covar_notrans)): NaNs produced</code></pre>
+<pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
+<pre><code>## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
+## doubtful</code></pre>
+<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
+<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
+<div class="sourceCode" id="cb104"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p15a</span>)</pre></body></html></div>
+<p><img src="NAFTA_examples_files/figure-html/p15a-1.png" width="700"></p>
+<div class="sourceCode" id="cb105"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p15a</span>)</pre></body></html></div>
+<pre><code>## Sums of squares:
+##      SFO     IORE     DFOP 
+## 245.5248 135.0132 245.5248 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 165.9335
+## 
+## Parameters:
+## $SFO
+##               Estimate   Pr(&gt;t)    Lower   Upper
+## parent_0      97.96751 2.00e-15 94.32049 101.615
+## k_parent_sink  0.00952 4.93e-09  0.00824   0.011
+## sigma          4.18778 1.28e-04  2.44588   5.930
+## 
+## $IORE
+##                     Estimate   Pr(&gt;t)  Lower  Upper
+## parent_0              95.874 2.94e-15 92.937 98.811
+## k__iore_parent_sink    0.629 2.11e-01  0.044  8.982
+## N_parent               0.000 5.00e-01 -0.642  0.642
+## sigma                  3.105 1.78e-04  1.795  4.416
+## 
+## $DFOP
+##          Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0 97.96752 2.85e-13 94.21914 101.7159
+## k1        0.00952 6.80e-02  0.00277   0.0327
+## k2        0.00952 3.82e-06  0.00902   0.0100
+## g         0.17247      NaN       NA       NA
+## sigma     4.18778 2.50e-04  2.39747   5.9781
+## 
+## 
+## DTx values:
+##      DT50 DT90 DT50_rep
+## SFO  72.8  242     72.8
+## IORE 76.3  137     41.3
+## DFOP 72.8  242     72.8
+## 
+## Representative half-life:
+## [1] 41.33</code></pre>
+<div class="sourceCode" id="cb107"><html><body><pre class="r"><span class="no">p15b</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p15b"</span>]])</pre></body></html></div>
+<pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
+<pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
+<pre><code>## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
+## doubtful</code></pre>
+<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
+<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
+<div class="sourceCode" id="cb113"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p15b</span>)</pre></body></html></div>
+<p><img src="NAFTA_examples_files/figure-html/p15b-1.png" width="700"></p>
+<div class="sourceCode" id="cb114"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p15b</span>)</pre></body></html></div>
+<pre><code>## Sums of squares:
+##       SFO      IORE      DFOP 
+## 106.91629  68.55574 106.91629 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 84.25618
+## 
+## Parameters:
+## $SFO
+##               Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0      1.01e+02 3.06e-17 98.31594 1.03e+02
+## k_parent_sink 4.86e-03 2.48e-10  0.00435 5.42e-03
+## sigma         2.76e+00 1.28e-04  1.61402 3.91e+00
+## 
+## $IORE
+##                     Estimate   Pr(&gt;t)    Lower  Upper
+## parent_0               99.83 1.81e-16 97.51349 102.14
+## k__iore_parent_sink     0.38 3.22e-01  0.00352  41.05
+## N_parent                0.00 5.00e-01 -1.07695   1.08
+## sigma                   2.21 2.57e-04  1.23245   3.19
+## 
+## $DFOP
+##          Estimate Pr(&gt;t)    Lower    Upper
+## parent_0 1.01e+02     NA 9.82e+01 1.04e+02
+## k1       4.86e-03     NA 6.75e-04 3.49e-02
+## k2       4.86e-03     NA 3.37e-03 6.99e-03
+## g        1.50e-01     NA       NA       NA
+## sigma    2.76e+00     NA 1.58e+00 3.94e+00
+## 
+## 
+## DTx values:
+##      DT50 DT90 DT50_rep
+## SFO   143  474    143.0
+## IORE  131  236     71.2
+## DFOP  143  474    143.0
+## 
+## Representative half-life:
+## [1] 71.18</code></pre>
+<p>In mkin, only the IORE fit is affected (deemed unrealistic), as the fraction parameter of the DFOP model is restricted to the interval between 0 and 1 in mkin. The SFO fits give the same results for both mkin and PestDF.</p>
+</div>
+<div id="the-dfop-fraction-parameter-is-greater-than-1" class="section level1">
+<h1 class="hasAnchor">
+<a href="#the-dfop-fraction-parameter-is-greater-than-1" class="anchor"></a>The DFOP fraction parameter is greater than 1</h1>
+<div class="sourceCode" id="cb116"><html><body><pre class="r"><span class="no">p16</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span>(<span class="no">NAFTA_SOP_Attachment</span><span class="kw">[[</span><span class="st">"p16"</span>]])</pre></body></html></div>
+<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
+<pre><code>## The representative half-life of the IORE model is longer than the one corresponding</code></pre>
+<pre><code>## to the terminal degradation rate found with the DFOP model.</code></pre>
+<pre><code>## The representative half-life obtained from the DFOP model may be used</code></pre>
+<div class="sourceCode" id="cb121"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">p16</span>)</pre></body></html></div>
+<p><img src="NAFTA_examples_files/figure-html/p16-1.png" width="700"></p>
+<div class="sourceCode" id="cb122"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">p16</span>)</pre></body></html></div>
+<pre><code>## Sums of squares:
+##      SFO     IORE     DFOP 
+## 3831.804 2062.008 1550.980 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 2247.348
+## 
+## Parameters:
+## $SFO
+##               Estimate   Pr(&gt;t)  Lower Upper
+## parent_0        71.953 2.33e-13 60.509 83.40
+## k_parent_sink    0.159 4.86e-05  0.102  0.25
+## sigma           11.302 1.25e-08  8.308 14.30
+## 
+## $IORE
+##                     Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0            8.74e+01 2.48e-16 7.72e+01 97.52972
+## k__iore_parent_sink 4.55e-04 2.16e-01 3.48e-05  0.00595
+## N_parent            2.70e+00 1.21e-08 1.99e+00  3.40046
+## sigma               8.29e+00 1.61e-08 6.09e+00 10.49062
+## 
+## $DFOP
+##          Estimate   Pr(&gt;t)   Lower  Upper
+## parent_0  88.5333 7.40e-18 79.9836 97.083
+## k1        18.5561 5.00e-01  0.0000    Inf
+## k2         0.0776 1.41e-05  0.0518  0.116
+## g          0.4733 1.41e-09  0.3674  0.582
+## sigma      7.1902 2.11e-08  5.2785  9.102
+## 
+## 
+## DTx values:
+##      DT50 DT90 DT50_rep
+## SFO  4.35 14.4     4.35
+## IORE 1.48 32.1     9.67
+## DFOP 0.67 21.4     8.93
+## 
+## Representative half-life:
+## [1] 8.93</code></pre>
+<p>In PestDF, the DFOP fit seems to have stuck in a local minimum, as mkin finds a solution with a much lower <span class="math inline">\(\chi^2\)</span> error level. As the half-life from the slower rate constant of the DFOP model is larger than the IORE derived half-life, the NAFTA recommendation obtained with mkin is to use the DFOP representative half-life of 8.9 days.</p>
+</div>
+<div id="conclusions" class="section level1">
+<h1 class="hasAnchor">
+<a href="#conclusions" class="anchor"></a>Conclusions</h1>
+<p>The results obtained with mkin deviate from the results obtained with PestDF either in cases where one of the interpretive rules would apply, i.e. the IORE parameter N is less than one or the DFOP k values obtained with PestDF are equal to the SFO k values, or in cases where the DFOP model did not converge, which often lead to negative rate constants returned by PestDF.</p>
+<p>Therefore, mkin appears to suitable for kinetic evaluations according to the NAFTA guidance.</p>
+</div>
+<div id="references" class="section level1 unnumbered">
+<h1 class="hasAnchor">
+<a href="#references" class="anchor"></a>References</h1>
+<div id="refs" class="references">
+<div id="ref-usepa2015">
+<p>US EPA. 2015. “Standard Operating Procedure for Using the NAFTA Guidance to Calculate Representative Half-Life Values and Characterizing Pesticide Degradation.”</p>
+</div>
+</div>
+</div>
+  </div>
+
+  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
+
+        <nav id="toc" data-toggle="toc"><h2 data-toc-skip>Contents</h2>
+    </nav>
+</div>
+
+</div>
+
+
+
+      <footer><div class="copyright">
+  <p>Developed by Johannes Ranke.</p>
+</div>
+
+<div class="pkgdown">
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+</div>
+
+      </footer>
+</div>
+
+  
+
+
+  </body>
+</html>
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diff --git a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p16-1.png b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p16-1.png
new file mode 100644
index 00000000..36999356
--- /dev/null
+++ b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p16-1.png
diff --git a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p5a-1.png b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p5a-1.png
new file mode 100644
index 00000000..596a33b2
--- /dev/null
+++ b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p5a-1.png
diff --git a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p5b-1.png b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p5b-1.png
new file mode 100644
index 00000000..e6f9716e
--- /dev/null
+++ b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p5b-1.png
diff --git a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p6-1.png b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p6-1.png
new file mode 100644
index 00000000..f8576168
--- /dev/null
+++ b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p6-1.png
diff --git a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p7-1.png b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p7-1.png
new file mode 100644
index 00000000..218a790f
--- /dev/null
+++ b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p7-1.png
diff --git a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p8-1.png b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p8-1.png
new file mode 100644
index 00000000..fa8621e7
--- /dev/null
+++ b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p8-1.png
diff --git a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p9a-1.png b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p9a-1.png
new file mode 100644
index 00000000..aac3600b
--- /dev/null
+++ b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p9a-1.png
diff --git a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p9b-1.png b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p9b-1.png
new file mode 100644
index 00000000..cb52aecd
--- /dev/null
+++ b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p9b-1.png
diff --git a/docs/dev/articles/web_only/benchmarks.html b/docs/dev/articles/web_only/benchmarks.html
new file mode 100644
index 00000000..b46b873c
--- /dev/null
+++ b/docs/dev/articles/web_only/benchmarks.html
@@ -0,0 +1,391 @@
+<!DOCTYPE html>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en">
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+      <h1 data-toc-skip>Benchmark timings for mkin</h1>
+                        <h4 class="author">Johannes Ranke</h4>
+            
+            <h4 class="date">2020-05-27</h4>
+      
+      <small class="dont-index">Source: <a href="http://github.com/jranke/mkin/blob/master/vignettes/web_only/benchmarks.rmd"><code>vignettes/web_only/benchmarks.rmd</code></a></small>
+      <div class="hidden name"><code>benchmarks.rmd</code></div>
+
+    </div>
+
+    
+    
+<p>Each system is characterized by its CPU type, the operating system type and the mkin version. Currently only values for one system are available. A compiler was available, so if no analytical solution was available, compiled ODE models are used.</p>
+<div id="test-cases" class="section level2">
+<h2 class="hasAnchor">
+<a href="#test-cases" class="anchor"></a>Test cases</h2>
+<p>Parent only:</p>
+<div class="sourceCode" id="cb1"><html><body><pre class="r"><span class="no">FOCUS_C</span> <span class="kw">&lt;-</span> <span class="no">FOCUS_2006_C</span>
+<span class="no">FOCUS_D</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/subset.html">subset</a></span>(<span class="no">FOCUS_2006_D</span>, <span class="no">value</span> <span class="kw">!=</span> <span class="fl">0</span>)
+<span class="no">parent_datasets</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">FOCUS_C</span>, <span class="no">FOCUS_D</span>)
+
+<span class="no">t1</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>, <span class="st">"HS"</span>), <span class="no">parent_datasets</span>))<span class="kw">[[</span><span class="st">"elapsed"</span>]]
+<span class="no">t2</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>, <span class="st">"HS"</span>), <span class="no">parent_datasets</span>,
+    <span class="kw">error_model</span> <span class="kw">=</span> <span class="st">"tc"</span>))<span class="kw">[[</span><span class="st">"elapsed"</span>]]</pre></body></html></div>
+<p>One metabolite:</p>
+<div class="sourceCode" id="cb2"><html><body><pre class="r"><span class="no">SFO_SFO</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(
+  <span class="kw">parent</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"m1"</span>),
+  <span class="kw">m1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>))
+<span class="no">FOMC_SFO</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(
+  <span class="kw">parent</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"FOMC"</span>, <span class="st">"m1"</span>),
+  <span class="kw">m1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>))
+<span class="no">DFOP_SFO</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(
+  <span class="kw">parent</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"FOMC"</span>, <span class="st">"m1"</span>),
+  <span class="kw">m1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>))
+<span class="no">t3</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">SFO_SFO</span>, <span class="no">FOMC_SFO</span>, <span class="no">DFOP_SFO</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">FOCUS_D</span>)))<span class="kw">[[</span><span class="st">"elapsed"</span>]]
+<span class="no">t4</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">SFO_SFO</span>, <span class="no">FOMC_SFO</span>, <span class="no">DFOP_SFO</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">FOCUS_D</span>),
+    <span class="kw">error_model</span> <span class="kw">=</span> <span class="st">"tc"</span>))<span class="kw">[[</span><span class="st">"elapsed"</span>]]
+<span class="no">t5</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">SFO_SFO</span>, <span class="no">FOMC_SFO</span>, <span class="no">DFOP_SFO</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">FOCUS_D</span>),
+    <span class="kw">error_model</span> <span class="kw">=</span> <span class="st">"obs"</span>))<span class="kw">[[</span><span class="st">"elapsed"</span>]]</pre></body></html></div>
+<p>Two metabolites, synthetic data:</p>
+<div class="sourceCode" id="cb3"><html><body><pre class="r"><span class="no">m_synth_SFO_lin</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="kw">parent</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"M1"</span>),
+                           <span class="kw">M1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"M2"</span>),
+                           <span class="kw">M2</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>),
+                           <span class="kw">use_of_ff</span> <span class="kw">=</span> <span class="st">"max"</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)
+
+<span class="no">m_synth_DFOP_par</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="kw">parent</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"DFOP"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="st">"M1"</span>, <span class="st">"M2"</span>)),
+                           <span class="kw">M1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>),
+                           <span class="kw">M2</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>),
+                           <span class="kw">use_of_ff</span> <span class="kw">=</span> <span class="st">"max"</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)
+
+<span class="no">SFO_lin_a</span> <span class="kw">&lt;-</span> <span class="no">synthetic_data_for_UBA_2014</span><span class="kw">[[</span><span class="fl">1</span>]]$<span class="no">data</span>
+
+<span class="no">DFOP_par_c</span> <span class="kw">&lt;-</span> <span class="no">synthetic_data_for_UBA_2014</span><span class="kw">[[</span><span class="fl">12</span>]]$<span class="no">data</span>
+
+<span class="no">t6</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">m_synth_SFO_lin</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">SFO_lin_a</span>)))<span class="kw">[[</span><span class="st">"elapsed"</span>]]
+<span class="no">t7</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">m_synth_DFOP_par</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">DFOP_par_c</span>)))<span class="kw">[[</span><span class="st">"elapsed"</span>]]
+
+<span class="no">t8</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">m_synth_SFO_lin</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">SFO_lin_a</span>),
+    <span class="kw">error_model</span> <span class="kw">=</span> <span class="st">"tc"</span>))<span class="kw">[[</span><span class="st">"elapsed"</span>]]
+<span class="no">t9</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">m_synth_DFOP_par</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">DFOP_par_c</span>),
+    <span class="kw">error_model</span> <span class="kw">=</span> <span class="st">"tc"</span>))<span class="kw">[[</span><span class="st">"elapsed"</span>]]
+
+<span class="no">t10</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">m_synth_SFO_lin</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">SFO_lin_a</span>),
+    <span class="kw">error_model</span> <span class="kw">=</span> <span class="st">"obs"</span>))<span class="kw">[[</span><span class="st">"elapsed"</span>]]
+<span class="no">t11</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span>(<span class="fu">mmkin_bench</span>(<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">m_synth_DFOP_par</span>), <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="no">DFOP_par_c</span>),
+    <span class="kw">error_model</span> <span class="kw">=</span> <span class="st">"obs"</span>))<span class="kw">[[</span><span class="st">"elapsed"</span>]]</pre></body></html></div>
+<div class="sourceCode" id="cb4"><html><body><pre class="r"><span class="no">mkin_benchmarks</span>[<span class="no">system_string</span>, <span class="fu"><a href="https://rdrr.io/r/base/paste.html">paste0</a></span>(<span class="st">"t"</span>, <span class="fl">1</span>:<span class="fl">11</span>)] <span class="kw">&lt;-</span>
+  <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="no">t1</span>, <span class="no">t2</span>, <span class="no">t3</span>, <span class="no">t4</span>, <span class="no">t5</span>, <span class="no">t6</span>, <span class="no">t7</span>, <span class="no">t8</span>, <span class="no">t9</span>, <span class="no">t10</span>, <span class="no">t11</span>)
+<span class="fu"><a href="https://rdrr.io/r/base/save.html">save</a></span>(<span class="no">mkin_benchmarks</span>, <span class="kw">file</span> <span class="kw">=</span> <span class="st">"~/git/mkin/vignettes/web_only/mkin_benchmarks.rda"</span>)</pre></body></html></div>
+</div>
+<div id="results" class="section level2">
+<h2 class="hasAnchor">
+<a href="#results" class="anchor"></a>Results</h2>
+<p>Currently, we only have benchmark information on one system, therefore only the mkin version is shown with the results below. Timings are in seconds, shorter is better. All results were obtained by serial, i.e. not using multiple computing cores.</p>
+<p>Benchmarks for all available error models are shown.</p>
+<div id="parent-only" class="section level3">
+<h3 class="hasAnchor">
+<a href="#parent-only" class="anchor"></a>Parent only</h3>
+<p>Constant variance (t1) and two-component error model (t2) for four models fitted to two datasets, i.e. eight fits for each test.</p>
+<table class="table">
+<thead><tr class="header">
+<th align="left">mkin version</th>
+<th align="right">t1 [s]</th>
+<th align="right">t2 [s]</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">0.9.48.1</td>
+<td align="right">3.610</td>
+<td align="right">11.019</td>
+</tr>
+<tr class="even">
+<td align="left">0.9.49.1</td>
+<td align="right">8.184</td>
+<td align="right">22.889</td>
+</tr>
+<tr class="odd">
+<td align="left">0.9.49.2</td>
+<td align="right">7.064</td>
+<td align="right">12.558</td>
+</tr>
+<tr class="even">
+<td align="left">0.9.49.3</td>
+<td align="right">7.296</td>
+<td align="right">21.239</td>
+</tr>
+<tr class="odd">
+<td align="left">0.9.49.4</td>
+<td align="right">5.936</td>
+<td align="right">20.545</td>
+</tr>
+<tr class="even">
+<td align="left">0.9.50.2</td>
+<td align="right">1.714</td>
+<td align="right">3.971</td>
+</tr>
+<tr class="odd">
+<td align="left">0.9.50.3</td>
+<td align="right">1.752</td>
+<td align="right">3.728</td>
+</tr>
+</tbody>
+</table>
+</div>
+<div id="one-metabolite" class="section level3">
+<h3 class="hasAnchor">
+<a href="#one-metabolite" class="anchor"></a>One metabolite</h3>
+<p>Constant variance (t3), two-component error model (t4), and variance by variable (t5) for three models fitted to one dataset, i.e. three fits for each test.</p>
+<table class="table">
+<thead><tr class="header">
+<th align="left">mkin version</th>
+<th align="right">t3 [s]</th>
+<th align="right">t4 [s]</th>
+<th align="right">t5 [s]</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">0.9.48.1</td>
+<td align="right">3.764</td>
+<td align="right">14.347</td>
+<td align="right">9.495</td>
+</tr>
+<tr class="even">
+<td align="left">0.9.49.1</td>
+<td align="right">4.649</td>
+<td align="right">13.789</td>
+<td align="right">6.395</td>
+</tr>
+<tr class="odd">
+<td align="left">0.9.49.2</td>
+<td align="right">4.786</td>
+<td align="right">8.461</td>
+<td align="right">5.675</td>
+</tr>
+<tr class="even">
+<td align="left">0.9.49.3</td>
+<td align="right">4.510</td>
+<td align="right">13.805</td>
+<td align="right">7.386</td>
+</tr>
+<tr class="odd">
+<td align="left">0.9.49.4</td>
+<td align="right">4.446</td>
+<td align="right">15.335</td>
+<td align="right">6.002</td>
+</tr>
+<tr class="even">
+<td align="left">0.9.50.2</td>
+<td align="right">1.402</td>
+<td align="right">6.174</td>
+<td align="right">2.764</td>
+</tr>
+<tr class="odd">
+<td align="left">0.9.50.3</td>
+<td align="right">1.389</td>
+<td align="right">6.579</td>
+<td align="right">2.740</td>
+</tr>
+</tbody>
+</table>
+</div>
+<div id="two-metabolites" class="section level3">
+<h3 class="hasAnchor">
+<a href="#two-metabolites" class="anchor"></a>Two metabolites</h3>
+<p>Constant variance (t6 and t7), two-component error model (t8 and t9), and variance by variable (t10 and t11) for one model fitted to one dataset, i.e. one fit for each test.</p>
+<table class="table">
+<thead><tr class="header">
+<th align="left">mkin version</th>
+<th align="right">t6 [s]</th>
+<th align="right">t7 [s]</th>
+<th align="right">t8 [s]</th>
+<th align="right">t9 [s]</th>
+<th align="right">t10 [s]</th>
+<th align="right">t11 [s]</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">0.9.48.1</td>
+<td align="right">2.623</td>
+<td align="right">4.587</td>
+<td align="right">7.525</td>
+<td align="right">16.621</td>
+<td align="right">8.576</td>
+<td align="right">31.267</td>
+</tr>
+<tr class="even">
+<td align="left">0.9.49.1</td>
+<td align="right">2.542</td>
+<td align="right">4.128</td>
+<td align="right">4.632</td>
+<td align="right">8.171</td>
+<td align="right">3.676</td>
+<td align="right">5.636</td>
+</tr>
+<tr class="odd">
+<td align="left">0.9.49.2</td>
+<td align="right">2.723</td>
+<td align="right">4.478</td>
+<td align="right">4.862</td>
+<td align="right">7.618</td>
+<td align="right">3.579</td>
+<td align="right">5.574</td>
+</tr>
+<tr class="even">
+<td align="left">0.9.49.3</td>
+<td align="right">2.643</td>
+<td align="right">4.374</td>
+<td align="right">7.020</td>
+<td align="right">11.124</td>
+<td align="right">5.388</td>
+<td align="right">7.365</td>
+</tr>
+<tr class="odd">
+<td align="left">0.9.49.4</td>
+<td align="right">2.635</td>
+<td align="right">4.259</td>
+<td align="right">4.737</td>
+<td align="right">7.763</td>
+<td align="right">3.427</td>
+<td align="right">5.626</td>
+</tr>
+<tr class="even">
+<td align="left">0.9.50.2</td>
+<td align="right">0.777</td>
+<td align="right">1.236</td>
+<td align="right">1.332</td>
+<td align="right">2.872</td>
+<td align="right">2.069</td>
+<td align="right">2.987</td>
+</tr>
+<tr class="odd">
+<td align="left">0.9.50.3</td>
+<td align="right">0.760</td>
+<td align="right">1.252</td>
+<td align="right">1.457</td>
+<td align="right">4.201</td>
+<td align="right">2.007</td>
+<td align="right">2.979</td>
+</tr>
+</tbody>
+</table>
+</div>
+</div>
+  </div>
+
+  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
+
+        <nav id="toc" data-toggle="toc"><h2 data-toc-skip>Contents</h2>
+    </nav>
+</div>
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+</div>
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+  <p>Developed by Johannes Ranke.</p>
+</div>
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diff --git a/docs/dev/articles/web_only/compiled_models.html b/docs/dev/articles/web_only/compiled_models.html
new file mode 100644
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--- /dev/null
+++ b/docs/dev/articles/web_only/compiled_models.html
@@ -0,0 +1,221 @@
+<!DOCTYPE html>
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+<script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
+<![endif]-->
+</head>
+<body data-spy="scroll" data-target="#toc">
+    <div class="container template-article">
+      <header><div class="navbar navbar-default navbar-fixed-top" role="navigation">
+  <div class="container">
+    <div class="navbar-header">
+      <button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#navbar" aria-expanded="false">
+        <span class="sr-only">Toggle navigation</span>
+        <span class="icon-bar"></span>
+        <span class="icon-bar"></span>
+        <span class="icon-bar"></span>
+      </button>
+      <span class="navbar-brand">
+        <a class="navbar-link" href="../../index.html">mkin</a>
+        <span class="version label label-danger" data-toggle="tooltip" data-placement="bottom" title="In-development version">0.9.50.3</span>
+      </span>
+    </div>
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+    <div id="navbar" class="navbar-collapse collapse">
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+<li>
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+<li>
+      <a href="../../articles/mkin.html">Introduction to mkin</a>
+    </li>
+    <li>
+      <a href="../../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a>
+    </li>
+    <li>
+      <a href="../../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a>
+    </li>
+    <li>
+      <a href="../../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a>
+    </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/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>
+    <li>
+      <a href="../../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
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+    <div class="page-header toc-ignore">
+      <h1 data-toc-skip>Performance benefit by using compiled model definitions in mkin</h1>
+                        <h4 class="author">Johannes Ranke</h4>
+            
+            <h4 class="date">2020-05-27</h4>
+      
+      <small class="dont-index">Source: <a href="http://github.com/jranke/mkin/blob/master/vignettes/web_only/compiled_models.rmd"><code>vignettes/web_only/compiled_models.rmd</code></a></small>
+      <div class="hidden name"><code>compiled_models.rmd</code></div>
+
+    </div>
+
+    
+    
+<div id="how-to-benefit-from-compiled-models" class="section level2">
+<h2 class="hasAnchor">
+<a href="#how-to-benefit-from-compiled-models" class="anchor"></a>How to benefit from compiled models</h2>
+<p>When using an mkin version equal to or greater than 0.9-36 and a C compiler is available, you will see a message that the model is being compiled from autogenerated C code when defining a model using mkinmod. Starting from version 0.9.49.9, the <code><a href="../../reference/mkinmod.html">mkinmod()</a></code> function checks for presence of a compiler using</p>
+<div class="sourceCode" id="cb1"><html><body><pre class="r"><span class="kw pkg">pkgbuild</span><span class="kw ns">::</span><span class="fu"><a href="https://rdrr.io/pkg/pkgbuild/man/has_compiler.html">has_compiler</a></span>()</pre></body></html></div>
+<p>In previous versions, it used <code><a href="https://rdrr.io/r/base/Sys.which.html">Sys.which("gcc")</a></code> for this check.</p>
+<p>On Linux, you need to have the essential build tools like make and gcc or clang installed. On Debian based linux distributions, these will be pulled in by installing the build-essential package.</p>
+<p>On MacOS, which I do not use personally, I have had reports that a compiler is available by default.</p>
+<p>On Windows, you need to install Rtools and have the path to its bin directory in your PATH variable. You do not need to modify the PATH variable when installing Rtools. Instead, I would recommend to put the line</p>
+<div class="sourceCode" id="cb2"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/Sys.setenv.html">Sys.setenv</a></span>(<span class="kw">PATH</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html">paste</a></span>(<span class="st">"C:/Rtools/bin"</span>, <span class="fu"><a href="https://rdrr.io/r/base/Sys.getenv.html">Sys.getenv</a></span>(<span class="st">"PATH"</span>), <span class="kw">sep</span><span class="kw">=</span><span class="st">";"</span>))</pre></body></html></div>
+<p>into your .Rprofile startup file. This is just a text file with some R code that is executed when your R session starts. It has to be named .Rprofile and has to be located in your home directory, which will generally be your Documents folder. You can check the location of the home directory used by R by issuing</p>
+<div class="sourceCode" id="cb3"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/Sys.getenv.html">Sys.getenv</a></span>(<span class="st">"HOME"</span>)</pre></body></html></div>
+</div>
+<div id="comparison-with-other-solution-methods" class="section level2">
+<h2 class="hasAnchor">
+<a href="#comparison-with-other-solution-methods" class="anchor"></a>Comparison with other solution methods</h2>
+<p>First, we build a simple degradation model for a parent compound with one metabolite, and we remove zero values from the dataset.</p>
+<div class="sourceCode" id="cb4"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/library.html">library</a></span>(<span class="st">"mkin"</span>, <span class="kw">quietly</span> <span class="kw">=</span> <span class="fl">TRUE</span>)
+<span class="no">SFO_SFO</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(
+  <span class="kw">parent</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"m1"</span>),
+  <span class="kw">m1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>))</pre></body></html></div>
+<pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
+<div class="sourceCode" id="cb6"><html><body><pre class="r"><span class="no">FOCUS_D</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/subset.html">subset</a></span>(<span class="no">FOCUS_2006_D</span>, <span class="no">value</span> <span class="kw">!=</span> <span class="fl">0</span>)</pre></body></html></div>
+<p>We can compare the performance of the Eigenvalue based solution against the compiled version and the R implementation of the differential equations using the benchmark package. In the output of below code, the warnings about zero being removed from the FOCUS D dataset are suppressed. Since mkin version 0.9.49.11, an analytical solution is also implemented, which is included in the tests below.</p>
+<div class="sourceCode" id="cb7"><html><body><pre class="r"><span class="kw">if</span> (<span class="fu"><a href="https://rdrr.io/r/base/library.html">require</a></span>(<span class="no">rbenchmark</span>)) {
+  <span class="no">b.1</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/rbenchmark/man/benchmark.html">benchmark</a></span>(
+    <span class="st">"deSolve, not compiled"</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">SFO_SFO</span>, <span class="no">FOCUS_D</span>,
+       <span class="kw">solution_type</span> <span class="kw">=</span> <span class="st">"deSolve"</span>,
+       <span class="kw">use_compiled</span> <span class="kw">=</span> <span class="fl">FALSE</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>),
+    <span class="st">"Eigenvalue based"</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">SFO_SFO</span>, <span class="no">FOCUS_D</span>,
+       <span class="kw">solution_type</span> <span class="kw">=</span> <span class="st">"eigen"</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>),
+    <span class="st">"deSolve, compiled"</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">SFO_SFO</span>, <span class="no">FOCUS_D</span>,
+       <span class="kw">solution_type</span> <span class="kw">=</span> <span class="st">"deSolve"</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>),
+    <span class="st">"analytical"</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">SFO_SFO</span>, <span class="no">FOCUS_D</span>,
+       <span class="kw">solution_type</span> <span class="kw">=</span> <span class="st">"analytical"</span>,
+       <span class="kw">use_compiled</span> <span class="kw">=</span> <span class="fl">FALSE</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>),
+    <span class="kw">replications</span> <span class="kw">=</span> <span class="fl">1</span>, <span class="kw">order</span> <span class="kw">=</span> <span class="st">"relative"</span>,
+    <span class="kw">columns</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="st">"test"</span>, <span class="st">"replications"</span>, <span class="st">"relative"</span>, <span class="st">"elapsed"</span>))
+  <span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">b.1</span>)
+} <span class="kw">else</span> {
+  <span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="st">"R package rbenchmark is not available"</span>)
+}</pre></body></html></div>
+<pre><code>##                    test replications relative elapsed
+## 4            analytical            1    1.000   0.202
+## 3     deSolve, compiled            1    1.703   0.344
+## 2      Eigenvalue based            1    1.990   0.402
+## 1 deSolve, not compiled            1   40.173   8.115</code></pre>
+<p>We see that using the compiled model is by more than a factor of 10 faster than using deSolve without compiled code.</p>
+</div>
+<div id="model-without-analytical-solution" class="section level2">
+<h2 class="hasAnchor">
+<a href="#model-without-analytical-solution" class="anchor"></a>Model without analytical solution</h2>
+<p>This evaluation is also taken from the example section of mkinfit. No analytical solution is available for this system, and now Eigenvalue based solution is possible, so only deSolve using with or without compiled code is available.</p>
+<div class="sourceCode" id="cb9"><html><body><pre class="r"><span class="kw">if</span> (<span class="fu"><a href="https://rdrr.io/r/base/library.html">require</a></span>(<span class="no">rbenchmark</span>)) {
+  <span class="no">FOMC_SFO</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span>(
+    <span class="kw">parent</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"FOMC"</span>, <span class="st">"m1"</span>),
+    <span class="kw">m1</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinsub.html">mkinsub</a></span>( <span class="st">"SFO"</span>))
+
+  <span class="no">b.2</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/rbenchmark/man/benchmark.html">benchmark</a></span>(
+    <span class="st">"deSolve, not compiled"</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">FOMC_SFO</span>, <span class="no">FOCUS_D</span>,
+                                      <span class="kw">use_compiled</span> <span class="kw">=</span> <span class="fl">FALSE</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>),
+    <span class="st">"deSolve, compiled"</span> <span class="kw">=</span> <span class="fu"><a href="../../reference/mkinfit.html">mkinfit</a></span>(<span class="no">FOMC_SFO</span>, <span class="no">FOCUS_D</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>),
+    <span class="kw">replications</span> <span class="kw">=</span> <span class="fl">1</span>, <span class="kw">order</span> <span class="kw">=</span> <span class="st">"relative"</span>,
+    <span class="kw">columns</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="st">"test"</span>, <span class="st">"replications"</span>, <span class="st">"relative"</span>, <span class="st">"elapsed"</span>))
+  <span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="no">b.2</span>)
+  <span class="no">factor_FOMC_SFO</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/Round.html">round</a></span>(<span class="no">b.2</span>[<span class="st">"1"</span>, <span class="st">"relative"</span>])
+} <span class="kw">else</span> {
+  <span class="no">factor_FOMC_SFO</span> <span class="kw">&lt;-</span> <span class="fl">NA</span>
+  <span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span>(<span class="st">"R package benchmark is not available"</span>)
+}</pre></body></html></div>
+<pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
+<pre><code>##                    test replications relative elapsed
+## 2     deSolve, compiled            1    1.000   0.469
+## 1 deSolve, not compiled            1   30.384  14.250</code></pre>
+<p>Here we get a performance benefit of a factor of 30 using the version of the differential equation model compiled from C code!</p>
+<p>This vignette was built with mkin 0.9.50.3 on</p>
+<pre><code>## R version 4.0.0 (2020-04-24)
+## Platform: x86_64-pc-linux-gnu (64-bit)
+## Running under: Debian GNU/Linux 10 (buster)</code></pre>
+<pre><code>## CPU model: AMD Ryzen 7 1700 Eight-Core Processor</code></pre>
+</div>
+  </div>
+
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+  <p>Developed by Johannes Ranke.</p>
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author	Johannes Ranke <jranke@uni-bremen.de>	2020-05-27 06:06:08 +0200
committer	Johannes Ranke <jranke@uni-bremen.de>	2020-05-27 06:06:08 +0200
commit	a77a10ea6c607346778ba0700b3b66ac393101a2 (patch)
tree	e91f627fba0580ef237ecbc8f24d6294a59597d3 /docs/dev/articles/web_only
parent	675a733fa2acc08daabb9b8b571c7d658f281f73 (diff)