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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 data-toc-skip class="author">Johannes
Ranke</h4>
<h4 data-toc-skip class="date">26 February 2019 (rebuilt
2023-05-19)</h4>
<small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/NAFTA_examples.rmd" class="external-link"><code>vignettes/web_only/NAFTA_examples.rmd</code></a></small>
<div class="hidden name"><code>NAFTA_examples.rmd</code></div>
</div>
<div class="section level2">
<h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#introduction"></a>
</h2>
<p>In this document, the example evaluations provided in Attachment 1 to
the SOP of US EPA for using the NAFTA guidance <span class="citation">(US EPA 2015)</span> are repeated using mkin. The
original evaluations reported in the attachment were performed using
PestDF in version 0.8.4. Note that PestDF 0.8.13 is the version
distributed at the US EPA website today (2019-02-26).</p>
<p>The datasets are now distributed with the mkin package.</p>
</div>
<div class="section level2">
<h2 id="examples-where-dfop-did-not-converge-with-pestdf-0-8-4">Examples where DFOP did not converge with PestDF 0.8.4<a class="anchor" aria-label="anchor" href="#examples-where-dfop-did-not-converge-with-pestdf-0-8-4"></a>
</h2>
<p>In attachment 1, it is reported that the DFOP model does not converge
for these datasets when PestDF 0.8.4 was used. For all four datasets,
the DFOP model can be fitted with mkin (see below). The negative
half-life given by PestDF 0.8.4 for these fits appears to be the result
of a bug. The results for the other two models (SFO and IORE) are the
same.</p>
<div class="section level3">
<h3 id="example-on-page-5-upper-panel">Example on page 5, upper panel<a class="anchor" aria-label="anchor" href="#example-on-page-5-upper-panel"></a>
</h3>
<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">p5a</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p5a"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre>
<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre>
<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p5a</span><span class="op">)</span></span></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p5a-1.png" width="700"></p>
<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p5a</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Sums of squares:</span></span>
<span><span class="co">## SFO IORE DFOP </span></span>
<span><span class="co">## 465.21753 56.27506 32.06401 </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span>
<span><span class="co">## [1] 64.4304</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Parameters:</span></span>
<span><span class="co">## $SFO</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 95.8401 4.67e-21 92.245 99.4357</span></span>
<span><span class="co">## k_parent 0.0102 3.92e-12 0.009 0.0117</span></span>
<span><span class="co">## sigma 4.8230 3.81e-06 3.214 6.4318</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $IORE</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 1.01e+02 NA 9.91e+01 1.02e+02</span></span>
<span><span class="co">## k__iore_parent 1.54e-05 NA 4.08e-06 5.84e-05</span></span>
<span><span class="co">## N_parent 2.57e+00 NA 2.25e+00 2.89e+00</span></span>
<span><span class="co">## sigma 1.68e+00 NA 1.12e+00 2.24e+00</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $DFOP</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 9.99e+01 1.41e-26 98.8116 101.0810</span></span>
<span><span class="co">## k1 2.67e-02 5.05e-06 0.0243 0.0295</span></span>
<span><span class="co">## k2 2.26e-12 5.00e-01 0.0000 Inf</span></span>
<span><span class="co">## g 6.47e-01 3.67e-06 0.6248 0.6677</span></span>
<span><span class="co">## sigma 1.27e+00 8.91e-06 0.8395 1.6929</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## DTx values:</span></span>
<span><span class="co">## DT50 DT90 DT50_rep</span></span>
<span><span class="co">## SFO 67.7 2.25e+02 6.77e+01</span></span>
<span><span class="co">## IORE 58.2 1.07e+03 3.22e+02</span></span>
<span><span class="co">## DFOP 55.5 5.59e+11 3.07e+11</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Representative half-life:</span></span>
<span><span class="co">## [1] 321.51</span></span></code></pre>
</div>
<div class="section level3">
<h3 id="example-on-page-5-lower-panel">Example on page 5, lower panel<a class="anchor" aria-label="anchor" href="#example-on-page-5-lower-panel"></a>
</h3>
<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">p5b</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p5b"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre>
<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre>
<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p5b</span><span class="op">)</span></span></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p5b-1.png" width="700"></p>
<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p5b</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Sums of squares:</span></span>
<span><span class="co">## SFO IORE DFOP </span></span>
<span><span class="co">## 94.81123 10.10936 7.55871 </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span>
<span><span class="co">## [1] 11.77879</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Parameters:</span></span>
<span><span class="co">## $SFO</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 96.497 2.32e-24 94.85271 98.14155</span></span>
<span><span class="co">## k_parent 0.008 3.42e-14 0.00737 0.00869</span></span>
<span><span class="co">## sigma 2.295 1.22e-05 1.47976 3.11036</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $IORE</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 9.85e+01 1.17e-28 9.79e+01 9.92e+01</span></span>
<span><span class="co">## k__iore_parent 1.53e-04 6.50e-03 7.21e-05 3.26e-04</span></span>
<span><span class="co">## N_parent 1.94e+00 5.88e-13 1.76e+00 2.12e+00</span></span>
<span><span class="co">## sigma 7.49e-01 1.63e-05 4.82e-01 1.02e+00</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $DFOP</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 9.84e+01 1.24e-27 97.8078 98.9187</span></span>
<span><span class="co">## k1 1.55e-02 4.10e-04 0.0143 0.0167</span></span>
<span><span class="co">## k2 8.63e-12 5.00e-01 0.0000 Inf</span></span>
<span><span class="co">## g 6.89e-01 2.92e-03 0.6626 0.7142</span></span>
<span><span class="co">## sigma 6.48e-01 2.38e-05 0.4147 0.8813</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## DTx values:</span></span>
<span><span class="co">## DT50 DT90 DT50_rep</span></span>
<span><span class="co">## SFO 86.6 2.88e+02 8.66e+01</span></span>
<span><span class="co">## IORE 85.5 7.17e+02 2.16e+02</span></span>
<span><span class="co">## DFOP 83.6 1.32e+11 8.04e+10</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Representative half-life:</span></span>
<span><span class="co">## [1] 215.87</span></span></code></pre>
</div>
<div class="section level3">
<h3 id="example-on-page-6">Example on page 6<a class="anchor" aria-label="anchor" href="#example-on-page-6"></a>
</h3>
<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">p6</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p6"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre>
<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre>
<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p6</span><span class="op">)</span></span></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p6-1.png" width="700"></p>
<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p6</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Sums of squares:</span></span>
<span><span class="co">## SFO IORE DFOP </span></span>
<span><span class="co">## 188.45361 51.00699 42.46931 </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span>
<span><span class="co">## [1] 58.39888</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Parameters:</span></span>
<span><span class="co">## $SFO</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 94.7759 7.29e-24 92.3478 97.2039</span></span>
<span><span class="co">## k_parent 0.0179 8.02e-16 0.0166 0.0194</span></span>
<span><span class="co">## sigma 3.0696 3.81e-06 2.0456 4.0936</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $IORE</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 97.12446 2.63e-26 95.62461 98.62431</span></span>
<span><span class="co">## k__iore_parent 0.00252 1.95e-03 0.00134 0.00472</span></span>
<span><span class="co">## N_parent 1.49587 4.07e-13 1.33896 1.65279</span></span>
<span><span class="co">## sigma 1.59698 5.05e-06 1.06169 2.13227</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $DFOP</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 9.66e+01 1.57e-25 95.3476 97.8979</span></span>
<span><span class="co">## k1 2.55e-02 7.33e-06 0.0233 0.0278</span></span>
<span><span class="co">## k2 3.22e-11 5.00e-01 0.0000 Inf</span></span>
<span><span class="co">## g 8.61e-01 7.55e-06 0.8314 0.8867</span></span>
<span><span class="co">## sigma 1.46e+00 6.93e-06 0.9661 1.9483</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## DTx values:</span></span>
<span><span class="co">## DT50 DT90 DT50_rep</span></span>
<span><span class="co">## SFO 38.6 1.28e+02 3.86e+01</span></span>
<span><span class="co">## IORE 34.0 1.77e+02 5.32e+01</span></span>
<span><span class="co">## DFOP 34.1 1.01e+10 2.15e+10</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Representative half-life:</span></span>
<span><span class="co">## [1] 53.17</span></span></code></pre>
</div>
<div class="section level3">
<h3 id="example-on-page-7">Example on page 7<a class="anchor" aria-label="anchor" href="#example-on-page-7"></a>
</h3>
<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">p7</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p7"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre>
<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre>
<div class="sourceCode" id="cb22"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p7</span><span class="op">)</span></span></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p7-1.png" width="700"></p>
<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p7</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Sums of squares:</span></span>
<span><span class="co">## SFO IORE DFOP </span></span>
<span><span class="co">## 3661.661 3195.030 3174.145 </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span>
<span><span class="co">## [1] 3334.194</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Parameters:</span></span>
<span><span class="co">## $SFO</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 96.41796 4.80e-53 93.32245 99.51347</span></span>
<span><span class="co">## k_parent 0.00735 7.64e-21 0.00641 0.00843</span></span>
<span><span class="co">## sigma 7.94557 1.83e-15 6.46713 9.42401</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $IORE</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 9.92e+01 NA 9.55e+01 1.03e+02</span></span>
<span><span class="co">## k__iore_parent 1.60e-05 NA 1.45e-07 1.77e-03</span></span>
<span><span class="co">## N_parent 2.45e+00 NA 1.35e+00 3.54e+00</span></span>
<span><span class="co">## sigma 7.42e+00 NA 6.04e+00 8.80e+00</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $DFOP</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 9.89e+01 9.44e-49 95.4640 102.2573</span></span>
<span><span class="co">## k1 1.81e-02 1.75e-01 0.0116 0.0281</span></span>
<span><span class="co">## k2 3.63e-10 5.00e-01 0.0000 Inf</span></span>
<span><span class="co">## g 6.06e-01 2.19e-01 0.4826 0.7178</span></span>
<span><span class="co">## sigma 7.40e+00 2.97e-15 6.0201 8.7754</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## DTx values:</span></span>
<span><span class="co">## DT50 DT90 DT50_rep</span></span>
<span><span class="co">## SFO 94.3 3.13e+02 9.43e+01</span></span>
<span><span class="co">## IORE 96.7 1.51e+03 4.55e+02</span></span>
<span><span class="co">## DFOP 96.4 3.77e+09 1.91e+09</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Representative half-life:</span></span>
<span><span class="co">## [1] 454.55</span></span></code></pre>
</div>
</div>
<div class="section level2">
<h2 id="examples-where-the-representative-half-life-deviates-from-the-observed-dt50">Examples where the representative half-life deviates from the
observed DT50<a class="anchor" aria-label="anchor" href="#examples-where-the-representative-half-life-deviates-from-the-observed-dt50"></a>
</h2>
<div class="section level3">
<h3 id="example-on-page-8">Example on page 8<a class="anchor" aria-label="anchor" href="#example-on-page-8"></a>
</h3>
<p>For this dataset, the IORE fit does not converge when the default
starting values used by mkin for the IORE model are used. Therefore, a
lower value for the rate constant is used here.</p>
<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">p8</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p8"</span><span class="op">]</span><span class="op">]</span>, parms.ini <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>k__iore_parent <span class="op">=</span> <span class="fl">1e-3</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre>
<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre>
<div class="sourceCode" id="cb28"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p8</span><span class="op">)</span></span></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p8-1.png" width="700"></p>
<div class="sourceCode" id="cb29"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p8</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Sums of squares:</span></span>
<span><span class="co">## SFO IORE DFOP </span></span>
<span><span class="co">## 1996.9408 444.9237 547.5616 </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span>
<span><span class="co">## [1] 477.4924</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Parameters:</span></span>
<span><span class="co">## $SFO</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 88.16549 6.53e-29 83.37344 92.95754</span></span>
<span><span class="co">## k_parent 0.00803 1.67e-13 0.00674 0.00957</span></span>
<span><span class="co">## sigma 7.44786 4.17e-10 5.66209 9.23363</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $IORE</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 9.77e+01 7.03e-35 9.44e+01 1.01e+02</span></span>
<span><span class="co">## k__iore_parent 6.14e-05 3.20e-02 2.12e-05 1.78e-04</span></span>
<span><span class="co">## N_parent 2.27e+00 4.23e-18 2.00e+00 2.54e+00</span></span>
<span><span class="co">## sigma 3.52e+00 5.36e-10 2.67e+00 4.36e+00</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $DFOP</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 95.70619 8.99e-32 91.87941 99.53298</span></span>
<span><span class="co">## k1 0.02500 5.25e-04 0.01422 0.04394</span></span>
<span><span class="co">## k2 0.00273 6.84e-03 0.00125 0.00597</span></span>
<span><span class="co">## g 0.58835 2.84e-06 0.36595 0.77970</span></span>
<span><span class="co">## sigma 3.90001 6.94e-10 2.96260 4.83741</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## DTx values:</span></span>
<span><span class="co">## DT50 DT90 DT50_rep</span></span>
<span><span class="co">## SFO 86.3 287 86.3</span></span>
<span><span class="co">## IORE 53.4 668 201.0</span></span>
<span><span class="co">## DFOP 55.6 517 253.0</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Representative half-life:</span></span>
<span><span class="co">## [1] 201.03</span></span></code></pre>
</div>
</div>
<div class="section level2">
<h2 id="examples-where-sfo-was-not-selected-for-an-abiotic-study">Examples where SFO was not selected for an abiotic study<a class="anchor" aria-label="anchor" href="#examples-where-sfo-was-not-selected-for-an-abiotic-study"></a>
</h2>
<div class="section level3">
<h3 id="example-on-page-9-upper-panel">Example on page 9, upper panel<a class="anchor" aria-label="anchor" href="#example-on-page-9-upper-panel"></a>
</h3>
<div class="sourceCode" id="cb31"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">p9a</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p9a"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre>
<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre>
<div class="sourceCode" id="cb34"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p9a</span><span class="op">)</span></span></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p9a-1.png" width="700"></p>
<div class="sourceCode" id="cb35"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p9a</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Sums of squares:</span></span>
<span><span class="co">## SFO IORE DFOP </span></span>
<span><span class="co">## 839.35238 88.57064 9.93363 </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span>
<span><span class="co">## [1] 105.5678</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Parameters:</span></span>
<span><span class="co">## $SFO</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 88.1933 3.06e-12 79.9447 96.4419</span></span>
<span><span class="co">## k_parent 0.0409 2.07e-07 0.0324 0.0516</span></span>
<span><span class="co">## sigma 7.2429 3.92e-05 4.4768 10.0090</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $IORE</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 9.89e+01 1.12e-16 9.54e+01 1.02e+02</span></span>
<span><span class="co">## k__iore_parent 1.93e-05 1.13e-01 3.49e-06 1.06e-04</span></span>
<span><span class="co">## N_parent 2.91e+00 1.45e-09 2.50e+00 3.32e+00</span></span>
<span><span class="co">## sigma 2.35e+00 5.31e-05 1.45e+00 3.26e+00</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $DFOP</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 9.85e+01 2.54e-20 97.390 99.672</span></span>
<span><span class="co">## k1 1.38e-01 3.52e-05 0.131 0.146</span></span>
<span><span class="co">## k2 9.02e-13 5.00e-01 0.000 Inf</span></span>
<span><span class="co">## g 6.52e-01 8.13e-06 0.642 0.661</span></span>
<span><span class="co">## sigma 7.88e-01 6.13e-02 0.481 1.095</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## DTx values:</span></span>
<span><span class="co">## DT50 DT90 DT50_rep</span></span>
<span><span class="co">## SFO 16.9 5.63e+01 1.69e+01</span></span>
<span><span class="co">## IORE 11.6 3.37e+02 1.01e+02</span></span>
<span><span class="co">## DFOP 10.5 1.38e+12 7.69e+11</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Representative half-life:</span></span>
<span><span class="co">## [1] 101.43</span></span></code></pre>
<p>In this example, the residuals of the SFO indicate a lack of fit of
this model, so even if it was an abiotic experiment, the data do not
suggest a simple exponential decline.</p>
</div>
<div class="section level3">
<h3 id="example-on-page-9-lower-panel">Example on page 9, lower panel<a class="anchor" aria-label="anchor" href="#example-on-page-9-lower-panel"></a>
</h3>
<div class="sourceCode" id="cb37"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">p9b</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p9b"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Warning in sqrt(diag(covar)): NaNs produced</span></span></code></pre>
<pre><code><span><span class="co">## Warning in sqrt(diag(covar_notrans)): NaNs produced</span></span></code></pre>
<pre><code><span><span class="co">## Warning in sqrt(1/diag(V)): NaNs produced</span></span></code></pre>
<pre><code><span><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result</span></span>
<span><span class="co">## is doubtful</span></span></code></pre>
<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre>
<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre>
<div class="sourceCode" id="cb44"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p9b</span><span class="op">)</span></span></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p9b-1.png" width="700"></p>
<div class="sourceCode" id="cb45"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p9b</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Sums of squares:</span></span>
<span><span class="co">## SFO IORE DFOP </span></span>
<span><span class="co">## 35.64867 23.22334 35.64867 </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span>
<span><span class="co">## [1] 28.54188</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Parameters:</span></span>
<span><span class="co">## $SFO</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 94.7123 2.15e-19 93.178 96.2464</span></span>
<span><span class="co">## k_parent 0.0389 4.47e-14 0.037 0.0408</span></span>
<span><span class="co">## sigma 1.5957 1.28e-04 0.932 2.2595</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $IORE</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 93.863 2.32e-18 92.4565 95.269</span></span>
<span><span class="co">## k__iore_parent 0.127 1.85e-02 0.0504 0.321</span></span>
<span><span class="co">## N_parent 0.711 1.88e-05 0.4843 0.937</span></span>
<span><span class="co">## sigma 1.288 1.76e-04 0.7456 1.830</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $DFOP</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 94.7123 1.61e-16 93.1355 96.2891</span></span>
<span><span class="co">## k1 0.0389 1.08e-04 0.0266 0.0569</span></span>
<span><span class="co">## k2 0.0389 2.23e-04 0.0255 0.0592</span></span>
<span><span class="co">## g 0.5256 NaN NA NA</span></span>
<span><span class="co">## sigma 1.5957 2.50e-04 0.9135 2.2779</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## DTx values:</span></span>
<span><span class="co">## DT50 DT90 DT50_rep</span></span>
<span><span class="co">## SFO 17.8 59.2 17.8</span></span>
<span><span class="co">## IORE 18.4 49.2 14.8</span></span>
<span><span class="co">## DFOP 17.8 59.2 17.8</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Representative half-life:</span></span>
<span><span class="co">## [1] 14.8</span></span></code></pre>
<p>Here, mkin gives a longer slow DT50 for the DFOP model (17.8 days)
than PestDF (13.5 days). Presumably, this is related to the fact that
PestDF gives a negative value for the proportion of the fast degradation
which should be between 0 and 1, inclusive. This parameter is called f
in PestDF and g in mkin. In mkin, it is restricted to the interval from
0 to 1.</p>
</div>
<div class="section level3">
<h3 id="example-on-page-10">Example on page 10<a class="anchor" aria-label="anchor" href="#example-on-page-10"></a>
</h3>
<div class="sourceCode" id="cb47"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">p10</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p10"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Warning in sqrt(diag(covar)): NaNs produced</span></span></code></pre>
<pre><code><span><span class="co">## Warning in sqrt(1/diag(V)): NaNs produced</span></span></code></pre>
<pre><code><span><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result</span></span>
<span><span class="co">## is doubtful</span></span></code></pre>
<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre>
<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre>
<div class="sourceCode" id="cb53"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p10</span><span class="op">)</span></span></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p10-1.png" width="700"></p>
<div class="sourceCode" id="cb54"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p10</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Sums of squares:</span></span>
<span><span class="co">## SFO IORE DFOP </span></span>
<span><span class="co">## 899.4089 336.4348 899.4089 </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span>
<span><span class="co">## [1] 413.4841</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Parameters:</span></span>
<span><span class="co">## $SFO</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 101.7315 6.42e-11 91.9259 111.5371</span></span>
<span><span class="co">## k_parent 0.0495 1.70e-07 0.0404 0.0607</span></span>
<span><span class="co">## sigma 8.0152 1.28e-04 4.6813 11.3491</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $IORE</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 96.86 3.32e-12 90.848 102.863</span></span>
<span><span class="co">## k__iore_parent 2.96 7.91e-02 0.687 12.761</span></span>
<span><span class="co">## N_parent 0.00 5.00e-01 -0.372 0.372</span></span>
<span><span class="co">## sigma 4.90 1.77e-04 2.837 6.968</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $DFOP</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 101.7315 1.41e-09 91.6534 111.8097</span></span>
<span><span class="co">## k1 0.0495 6.58e-03 0.0303 0.0809</span></span>
<span><span class="co">## k2 0.0495 2.60e-03 0.0410 0.0598</span></span>
<span><span class="co">## g 0.4487 5.00e-01 NA NA</span></span>
<span><span class="co">## sigma 8.0152 2.50e-04 4.5886 11.4418</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## DTx values:</span></span>
<span><span class="co">## DT50 DT90 DT50_rep</span></span>
<span><span class="co">## SFO 14.0 46.5 14.00</span></span>
<span><span class="co">## IORE 16.4 29.4 8.86</span></span>
<span><span class="co">## DFOP 14.0 46.5 14.00</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Representative half-life:</span></span>
<span><span class="co">## [1] 8.86</span></span></code></pre>
<p>Here, a value below N is given for the IORE model, because the data
suggests a faster decline towards the end of the experiment, which
appears physically rather unlikely in the case of a photolysis study. It
seems PestDF does not constrain N to values above zero, thus the slight
difference in IORE model parameters between PestDF and mkin.</p>
</div>
</div>
<div class="section level2">
<h2 id="the-dt50-was-not-observed-during-the-study">The DT50 was not observed during the study<a class="anchor" aria-label="anchor" href="#the-dt50-was-not-observed-during-the-study"></a>
</h2>
<div class="section level3">
<h3 id="example-on-page-11">Example on page 11<a class="anchor" aria-label="anchor" href="#example-on-page-11"></a>
</h3>
<div class="sourceCode" id="cb56"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">p11</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p11"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre>
<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre>
<div class="sourceCode" id="cb59"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p11</span><span class="op">)</span></span></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p11-1.png" width="700"></p>
<div class="sourceCode" id="cb60"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p11</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Sums of squares:</span></span>
<span><span class="co">## SFO IORE DFOP </span></span>
<span><span class="co">## 579.6805 204.7932 144.7783 </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span>
<span><span class="co">## [1] 251.6944</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Parameters:</span></span>
<span><span class="co">## $SFO</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 96.15820 4.83e-13 90.24934 1.02e+02</span></span>
<span><span class="co">## k_parent 0.00321 4.71e-05 0.00222 4.64e-03</span></span>
<span><span class="co">## sigma 6.43473 1.28e-04 3.75822 9.11e+00</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $IORE</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 1.05e+02 NA 9.90e+01 1.10e+02</span></span>
<span><span class="co">## k__iore_parent 3.11e-17 NA 1.35e-20 7.18e-14</span></span>
<span><span class="co">## N_parent 8.36e+00 NA 6.62e+00 1.01e+01</span></span>
<span><span class="co">## sigma 3.82e+00 NA 2.21e+00 5.44e+00</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $DFOP</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 1.05e+02 9.47e-13 99.9990 109.1224</span></span>
<span><span class="co">## k1 4.41e-02 5.95e-03 0.0296 0.0658</span></span>
<span><span class="co">## k2 9.94e-13 5.00e-01 0.0000 Inf</span></span>
<span><span class="co">## g 3.22e-01 1.45e-03 0.2814 0.3650</span></span>
<span><span class="co">## sigma 3.22e+00 3.52e-04 1.8410 4.5906</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## DTx values:</span></span>
<span><span class="co">## DT50 DT90 DT50_rep</span></span>
<span><span class="co">## SFO 2.16e+02 7.18e+02 2.16e+02</span></span>
<span><span class="co">## IORE 9.73e+02 1.37e+08 4.11e+07</span></span>
<span><span class="co">## DFOP 3.07e+11 1.93e+12 6.98e+11</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Representative half-life:</span></span>
<span><span class="co">## [1] 41148170</span></span></code></pre>
<p>In this case, the DFOP fit reported for PestDF resulted in a negative
value for the slower rate constant, which is not possible in mkin. The
other results are in agreement.</p>
</div>
</div>
<div class="section level2">
<h2 id="n-is-less-than-1-and-the-dfop-rate-constants-are-like-the-sfo-rate-constant">N is less than 1 and the DFOP rate constants are like the SFO rate
constant<a class="anchor" aria-label="anchor" href="#n-is-less-than-1-and-the-dfop-rate-constants-are-like-the-sfo-rate-constant"></a>
</h2>
<p>In the following three examples, the same results are obtained with
mkin as reported for PestDF. As in the case on page 10, the N values
below 1 are deemed unrealistic and appear to be the result of an
overparameterisation.</p>
<div class="section level3">
<h3 id="example-on-page-12-upper-panel">Example on page 12, upper panel<a class="anchor" aria-label="anchor" href="#example-on-page-12-upper-panel"></a>
</h3>
<div class="sourceCode" id="cb62"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">p12a</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p12a"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Warning in summary.mkinfit(x): Could not calculate correlation; no covariance</span></span>
<span><span class="co">## matrix</span></span></code></pre>
<pre><code><span><span class="co">## Warning in sqrt(diag(covar)): NaNs produced</span></span></code></pre>
<pre><code><span><span class="co">## Warning in sqrt(diag(covar_notrans)): NaNs produced</span></span></code></pre>
<pre><code><span><span class="co">## Warning in sqrt(1/diag(V)): NaNs produced</span></span></code></pre>
<pre><code><span><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result</span></span>
<span><span class="co">## is doubtful</span></span></code></pre>
<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre>
<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre>
<div class="sourceCode" id="cb70"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p12a</span><span class="op">)</span></span></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p12a-1.png" width="700"></p>
<div class="sourceCode" id="cb71"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p12a</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Sums of squares:</span></span>
<span><span class="co">## SFO IORE DFOP </span></span>
<span><span class="co">## 695.4440 220.0685 695.4440 </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span>
<span><span class="co">## [1] 270.4679</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Parameters:</span></span>
<span><span class="co">## $SFO</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 100.521 8.75e-12 92.461 108.581</span></span>
<span><span class="co">## k_parent 0.124 3.61e-08 0.104 0.148</span></span>
<span><span class="co">## sigma 7.048 1.28e-04 4.116 9.980</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $IORE</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 96.823 NA NA NA</span></span>
<span><span class="co">## k__iore_parent 2.436 NA NA NA</span></span>
<span><span class="co">## N_parent 0.263 NA NA NA</span></span>
<span><span class="co">## sigma 3.965 NA NA NA</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $DFOP</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 100.521 2.74e-10 92.2366 108.805</span></span>
<span><span class="co">## k1 0.124 2.53e-05 0.0908 0.170</span></span>
<span><span class="co">## k2 0.124 2.52e-02 0.0456 0.339</span></span>
<span><span class="co">## g 0.793 NaN NA NA</span></span>
<span><span class="co">## sigma 7.048 2.50e-04 4.0349 10.061</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## DTx values:</span></span>
<span><span class="co">## DT50 DT90 DT50_rep</span></span>
<span><span class="co">## SFO 5.58 18.5 5.58</span></span>
<span><span class="co">## IORE 6.49 13.2 3.99</span></span>
<span><span class="co">## DFOP 5.58 18.5 5.58</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Representative half-life:</span></span>
<span><span class="co">## [1] 3.99</span></span></code></pre>
</div>
<div class="section level3">
<h3 id="example-on-page-12-lower-panel">Example on page 12, lower panel<a class="anchor" aria-label="anchor" href="#example-on-page-12-lower-panel"></a>
</h3>
<div class="sourceCode" id="cb73"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">p12b</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p12b"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Warning in qt(alpha/2, rdf): NaNs produced</span></span></code></pre>
<pre><code><span><span class="co">## Warning in qt(1 - alpha/2, rdf): NaNs produced</span></span></code></pre>
<pre><code><span><span class="co">## Warning in sqrt(diag(covar_notrans)): NaNs produced</span></span></code></pre>
<pre><code><span><span class="co">## Warning in pt(abs(tval), rdf, lower.tail = FALSE): NaNs produced</span></span></code></pre>
<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre>
<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre>
<div class="sourceCode" id="cb80"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p12b</span><span class="op">)</span></span></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p12b-1.png" width="700"></p>
<div class="sourceCode" id="cb81"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p12b</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Sums of squares:</span></span>
<span><span class="co">## SFO IORE DFOP </span></span>
<span><span class="co">## 58.90242 19.06353 58.90242 </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span>
<span><span class="co">## [1] 51.51756</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Parameters:</span></span>
<span><span class="co">## $SFO</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 97.6840 0.00039 85.9388 109.4292</span></span>
<span><span class="co">## k_parent 0.0589 0.00261 0.0431 0.0805</span></span>
<span><span class="co">## sigma 3.4323 0.04356 -1.2377 8.1023</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $IORE</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 95.523 0.0055 74.539157 116.51</span></span>
<span><span class="co">## k__iore_parent 0.333 0.1433 0.000717 154.57</span></span>
<span><span class="co">## N_parent 0.568 0.0677 -0.989464 2.13</span></span>
<span><span class="co">## sigma 1.953 0.0975 -5.893100 9.80</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $DFOP</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 97.6840 NaN NaN NaN</span></span>
<span><span class="co">## k1 0.0589 NaN NA NA</span></span>
<span><span class="co">## k2 0.0589 NaN NA NA</span></span>
<span><span class="co">## g 0.6473 NaN NA NA</span></span>
<span><span class="co">## sigma 3.4323 NaN NaN NaN</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## DTx values:</span></span>
<span><span class="co">## DT50 DT90 DT50_rep</span></span>
<span><span class="co">## SFO 11.8 39.1 11.80</span></span>
<span><span class="co">## IORE 12.9 31.4 9.46</span></span>
<span><span class="co">## DFOP 11.8 39.1 11.80</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Representative half-life:</span></span>
<span><span class="co">## [1] 9.46</span></span></code></pre>
</div>
<div class="section level3">
<h3 id="example-on-page-13">Example on page 13<a class="anchor" aria-label="anchor" href="#example-on-page-13"></a>
</h3>
<div class="sourceCode" id="cb83"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">p13</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p13"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre>
<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre>
<div class="sourceCode" id="cb86"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p13</span><span class="op">)</span></span></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p13-1.png" width="700"></p>
<div class="sourceCode" id="cb87"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p13</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Sums of squares:</span></span>
<span><span class="co">## SFO IORE DFOP </span></span>
<span><span class="co">## 174.5971 142.3951 174.5971 </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span>
<span><span class="co">## [1] 172.131</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Parameters:</span></span>
<span><span class="co">## $SFO</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 92.73500 5.99e-17 89.61936 95.85065</span></span>
<span><span class="co">## k_parent 0.00258 2.42e-09 0.00223 0.00299</span></span>
<span><span class="co">## sigma 3.41172 7.07e-05 2.05455 4.76888</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $IORE</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 91.6016 6.34e-16 88.53086 94.672</span></span>
<span><span class="co">## k__iore_parent 0.0396 2.36e-01 0.00207 0.759</span></span>
<span><span class="co">## N_parent 0.3541 1.46e-01 -0.35153 1.060</span></span>
<span><span class="co">## sigma 3.0811 9.64e-05 1.84296 4.319</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $DFOP</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 92.73500 NA 8.95e+01 95.92118</span></span>
<span><span class="co">## k1 0.00258 NA 4.14e-04 0.01611</span></span>
<span><span class="co">## k2 0.00258 NA 1.74e-03 0.00383</span></span>
<span><span class="co">## g 0.16452 NA 0.00e+00 1.00000</span></span>
<span><span class="co">## sigma 3.41172 NA 2.02e+00 4.79960</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## DTx values:</span></span>
<span><span class="co">## DT50 DT90 DT50_rep</span></span>
<span><span class="co">## SFO 269 892 269</span></span>
<span><span class="co">## IORE 261 560 169</span></span>
<span><span class="co">## DFOP 269 892 269</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Representative half-life:</span></span>
<span><span class="co">## [1] 168.51</span></span></code></pre>
</div>
</div>
<div class="section level2">
<h2 id="dt50-not-observed-in-the-study-and-dfop-problems-in-pestdf">DT50 not observed in the study and DFOP problems in PestDF<a class="anchor" aria-label="anchor" href="#dt50-not-observed-in-the-study-and-dfop-problems-in-pestdf"></a>
</h2>
<div class="sourceCode" id="cb89"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">p14</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p14"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Warning in sqrt(diag(covar)): NaNs produced</span></span></code></pre>
<pre><code><span><span class="co">## Warning in sqrt(1/diag(V)): NaNs produced</span></span></code></pre>
<pre><code><span><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result</span></span>
<span><span class="co">## is doubtful</span></span></code></pre>
<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre>
<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre>
<div class="sourceCode" id="cb95"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p14</span><span class="op">)</span></span></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p14-1.png" width="700"></p>
<div class="sourceCode" id="cb96"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p14</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Sums of squares:</span></span>
<span><span class="co">## SFO IORE DFOP </span></span>
<span><span class="co">## 48.43249 28.67746 27.26248 </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span>
<span><span class="co">## [1] 32.83337</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Parameters:</span></span>
<span><span class="co">## $SFO</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 99.47124 2.06e-30 98.42254 1.01e+02</span></span>
<span><span class="co">## k_parent 0.00279 3.75e-15 0.00256 3.04e-03</span></span>
<span><span class="co">## sigma 1.55616 3.81e-06 1.03704 2.08e+00</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $IORE</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 1.00e+02 NA NaN NaN</span></span>
<span><span class="co">## k__iore_parent 9.44e-08 NA NaN NaN</span></span>
<span><span class="co">## N_parent 3.31e+00 NA NaN NaN</span></span>
<span><span class="co">## sigma 1.20e+00 NA 0.796 1.6</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $DFOP</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 1.00e+02 2.96e-28 99.40280 101.2768</span></span>
<span><span class="co">## k1 9.53e-03 1.20e-01 0.00638 0.0143</span></span>
<span><span class="co">## k2 6.08e-12 5.00e-01 0.00000 Inf</span></span>
<span><span class="co">## g 3.98e-01 2.19e-01 0.30481 0.4998</span></span>
<span><span class="co">## sigma 1.17e+00 7.68e-06 0.77406 1.5610</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## DTx values:</span></span>
<span><span class="co">## DT50 DT90 DT50_rep</span></span>
<span><span class="co">## SFO 2.48e+02 8.25e+02 2.48e+02</span></span>
<span><span class="co">## IORE 4.34e+02 2.22e+04 6.70e+03</span></span>
<span><span class="co">## DFOP 3.05e+10 2.95e+11 1.14e+11</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Representative half-life:</span></span>
<span><span class="co">## [1] 6697.44</span></span></code></pre>
<p>The slower rate constant reported by PestDF is negative, which is not
physically realistic, and not possible in mkin. The other fits give the
same results in mkin and PestDF.</p>
</div>
<div class="section level2">
<h2 id="n-is-less-than-1-and-dfop-fraction-parameter-is-below-zero">N is less than 1 and DFOP fraction parameter is below zero<a class="anchor" aria-label="anchor" href="#n-is-less-than-1-and-dfop-fraction-parameter-is-below-zero"></a>
</h2>
<div class="sourceCode" id="cb98"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">p15a</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p15a"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre>
<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre>
<div class="sourceCode" id="cb101"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p15a</span><span class="op">)</span></span></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p15a-1.png" width="700"></p>
<div class="sourceCode" id="cb102"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p15a</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Sums of squares:</span></span>
<span><span class="co">## SFO IORE DFOP </span></span>
<span><span class="co">## 245.5248 135.0132 245.5248 </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span>
<span><span class="co">## [1] 165.9335</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Parameters:</span></span>
<span><span class="co">## $SFO</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 97.96751 2.00e-15 94.32049 101.615</span></span>
<span><span class="co">## k_parent 0.00952 4.93e-09 0.00824 0.011</span></span>
<span><span class="co">## sigma 4.18778 1.28e-04 2.44588 5.930</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $IORE</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 95.874 2.94e-15 92.937 98.811</span></span>
<span><span class="co">## k__iore_parent 0.629 2.11e-01 0.044 8.982</span></span>
<span><span class="co">## N_parent 0.000 5.00e-01 -0.642 0.642</span></span>
<span><span class="co">## sigma 3.105 1.78e-04 1.795 4.416</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $DFOP</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 97.96751 2.85e-13 94.21913 101.7159</span></span>
<span><span class="co">## k1 0.00952 6.28e-02 0.00250 0.0363</span></span>
<span><span class="co">## k2 0.00952 1.27e-04 0.00646 0.0140</span></span>
<span><span class="co">## g 0.21241 5.00e-01 0.00000 1.0000</span></span>
<span><span class="co">## sigma 4.18778 2.50e-04 2.39747 5.9781</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## DTx values:</span></span>
<span><span class="co">## DT50 DT90 DT50_rep</span></span>
<span><span class="co">## SFO 72.8 242 72.8</span></span>
<span><span class="co">## IORE 76.3 137 41.3</span></span>
<span><span class="co">## DFOP 72.8 242 72.8</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Representative half-life:</span></span>
<span><span class="co">## [1] 41.33</span></span></code></pre>
<div class="sourceCode" id="cb104"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">p15b</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p15b"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Warning in sqrt(diag(covar)): NaNs produced</span></span></code></pre>
<pre><code><span><span class="co">## Warning in sqrt(1/diag(V)): NaNs produced</span></span></code></pre>
<pre><code><span><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result</span></span>
<span><span class="co">## is doubtful</span></span></code></pre>
<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre>
<pre><code><span><span class="co">## The half-life obtained from the IORE model may be used</span></span></code></pre>
<div class="sourceCode" id="cb110"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p15b</span><span class="op">)</span></span></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p15b-1.png" width="700"></p>
<div class="sourceCode" id="cb111"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p15b</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Sums of squares:</span></span>
<span><span class="co">## SFO IORE DFOP </span></span>
<span><span class="co">## 106.91629 68.55574 106.91629 </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span>
<span><span class="co">## [1] 84.25618</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Parameters:</span></span>
<span><span class="co">## $SFO</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 1.01e+02 3.06e-17 98.31594 1.03e+02</span></span>
<span><span class="co">## k_parent 4.86e-03 2.48e-10 0.00435 5.42e-03</span></span>
<span><span class="co">## sigma 2.76e+00 1.28e-04 1.61402 3.91e+00</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $IORE</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 99.83 1.81e-16 97.51349 102.14</span></span>
<span><span class="co">## k__iore_parent 0.38 3.22e-01 0.00352 41.05</span></span>
<span><span class="co">## N_parent 0.00 5.00e-01 -1.07696 1.08</span></span>
<span><span class="co">## sigma 2.21 2.57e-04 1.23245 3.19</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $DFOP</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 1.01e+02 NA 9.82e+01 1.04e+02</span></span>
<span><span class="co">## k1 4.86e-03 NA 8.63e-04 2.73e-02</span></span>
<span><span class="co">## k2 4.86e-03 NA 3.21e-03 7.35e-03</span></span>
<span><span class="co">## g 1.88e-01 NA NA NA</span></span>
<span><span class="co">## sigma 2.76e+00 NA 1.58e+00 3.94e+00</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## DTx values:</span></span>
<span><span class="co">## DT50 DT90 DT50_rep</span></span>
<span><span class="co">## SFO 143 474 143.0</span></span>
<span><span class="co">## IORE 131 236 71.2</span></span>
<span><span class="co">## DFOP 143 474 143.0</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Representative half-life:</span></span>
<span><span class="co">## [1] 71.18</span></span></code></pre>
<p>In mkin, only the IORE fit is affected (deemed unrealistic), as the
fraction parameter of the DFOP model is restricted to the interval
between 0 and 1 in mkin. The SFO fits give the same results for both
mkin and PestDF.</p>
</div>
<div class="section level2">
<h2 id="the-dfop-fraction-parameter-is-greater-than-1">The DFOP fraction parameter is greater than 1<a class="anchor" aria-label="anchor" href="#the-dfop-fraction-parameter-is-greater-than-1"></a>
</h2>
<div class="sourceCode" id="cb113"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">p16</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p16"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</span></span></code></pre>
<pre><code><span><span class="co">## The representative half-life of the IORE model is longer than the one corresponding</span></span></code></pre>
<pre><code><span><span class="co">## to the terminal degradation rate found with the DFOP model.</span></span></code></pre>
<pre><code><span><span class="co">## The representative half-life obtained from the DFOP model may be used</span></span></code></pre>
<div class="sourceCode" id="cb118"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">p16</span><span class="op">)</span></span></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p16-1.png" width="700"></p>
<div class="sourceCode" id="cb119"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">p16</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## Sums of squares:</span></span>
<span><span class="co">## SFO IORE DFOP </span></span>
<span><span class="co">## 3831.804 2062.008 1550.980 </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Critical sum of squares for checking the SFO model:</span></span>
<span><span class="co">## [1] 2247.348</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Parameters:</span></span>
<span><span class="co">## $SFO</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 71.953 2.33e-13 60.509 83.40</span></span>
<span><span class="co">## k_parent 0.159 4.86e-05 0.102 0.25</span></span>
<span><span class="co">## sigma 11.302 1.25e-08 8.308 14.30</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $IORE</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 8.74e+01 2.48e-16 7.72e+01 97.52972</span></span>
<span><span class="co">## k__iore_parent 4.55e-04 2.16e-01 3.48e-05 0.00595</span></span>
<span><span class="co">## N_parent 2.70e+00 1.21e-08 1.99e+00 3.40046</span></span>
<span><span class="co">## sigma 8.29e+00 1.61e-08 6.09e+00 10.49062</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## $DFOP</span></span>
<span><span class="co">## Estimate Pr(>t) Lower Upper</span></span>
<span><span class="co">## parent_0 88.5333 7.40e-18 79.9836 97.083</span></span>
<span><span class="co">## k1 18.8461 5.00e-01 0.0000 Inf</span></span>
<span><span class="co">## k2 0.0776 1.41e-05 0.0518 0.116</span></span>
<span><span class="co">## g 0.4733 1.41e-09 0.3674 0.582</span></span>
<span><span class="co">## sigma 7.1902 2.11e-08 5.2785 9.102</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## </span></span>
<span><span class="co">## DTx values:</span></span>
<span><span class="co">## DT50 DT90 DT50_rep</span></span>
<span><span class="co">## SFO 4.35 14.4 4.35</span></span>
<span><span class="co">## IORE 1.48 32.1 9.67</span></span>
<span><span class="co">## DFOP 0.67 21.4 8.93</span></span>
<span><span class="co">## </span></span>
<span><span class="co">## Representative half-life:</span></span>
<span><span class="co">## [1] 8.93</span></span></code></pre>
<p>In PestDF, the DFOP fit seems to have stuck in a local minimum, as
mkin finds a solution with a much lower <span class="math inline">\(\chi^2\)</span> error level. As the half-life from
the slower rate constant of the DFOP model is larger than the IORE
derived half-life, the NAFTA recommendation obtained with mkin is to use
the DFOP representative half-life of 8.9 days.</p>
</div>
<div class="section level2">
<h2 id="conclusions">Conclusions<a class="anchor" aria-label="anchor" href="#conclusions"></a>
</h2>
<p>The results obtained with mkin deviate from the results obtained with
PestDF either in cases where one of the interpretive rules would apply,
i.e. the IORE parameter N is less than one or the DFOP k values obtained
with PestDF are equal to the SFO k values, or in cases where the DFOP
model did not converge, which often lead to negative rate constants
returned by PestDF.</p>
<p>Therefore, mkin appears to suitable for kinetic evaluations according
to the NAFTA guidance.</p>
</div>
<div class="section level2">
<h2 class="unnumbered" id="references">References<a class="anchor" aria-label="anchor" href="#references"></a>
</h2>
<div id="refs" class="references csl-bib-body hanging-indent">
<div id="ref-usepa2015" class="csl-entry">
US EPA. 2015. <span>“Standard Operating Procedure for Using the NAFTA
Guidance to Calculate Representative Half-Life Values and Characterizing
Pesticide Degradation.”</span> <a href="https://www.epa.gov/pesticide-science-and-assessing-pesticide-risks/standard-operating-procedure-using-nafta-guidance" class="external-link">https://www.epa.gov/pesticide-science-and-assessing-pesticide-risks/standard-operating-procedure-using-nafta-guidance</a>.
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