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      <h1>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">2019-05-02</h4>
      
      
      <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"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb1-1" title="1">p5a &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p5a"</span>]])</a></code></pre></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"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb4-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p5a)</a></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p5a-1.png" width="700"></p>
<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb5-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p5a)</a></code></pre></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       3.41e-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 3.70e+11 2.03e+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"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb7-1" title="1">p5b &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p5b"</span>]])</a></code></pre></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"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb10-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p5b)</a></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p5b-1.png" width="700"></p>
<div class="sourceCode" id="cb11"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb11-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p5b)</a></code></pre></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       8.28e-12 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 1.37e+11 8.37e+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"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb13-1" title="1">p6 &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p6"</span>]])</a></code></pre></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"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb16-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p6)</a></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p6-1.png" width="700"></p>
<div class="sourceCode" id="cb17"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb17-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p6)</a></code></pre></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 92.3479 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       3.87e-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 8.43e+09 1.79e+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"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb19-1" title="1">p7 &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p7"</span>]])</a></code></pre></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"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb22-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p7)</a></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p7-1.png" width="700"></p>
<div class="sourceCode" id="cb23"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb23-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p7)</a></code></pre></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       2.46e-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 5.58e+09 2.82e+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"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb25-1" title="1">p8 &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p8"</span>]], <span class="dt">parms.ini =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="dt">k__iore_parent_sink =</span> <span class="fl">1e-3</span>))</a></code></pre></div>
<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
## singular system.

## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
## singular system.</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="cb29"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb29-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p8)</a></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p8-1.png" width="700"></p>
<div class="sourceCode" id="cb30"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb30-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p8)</a></code></pre></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     NA    NA    NA
## k__iore_parent_sink  0.00100     NA    NA    NA
## k_parent_sink        0.00803     NA    NA    NA
## sigma                7.44786     NA    NA    NA
## 
## $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     NA    NA    NA
## k__iore_parent_sink  0.00100     NA    NA    NA
## k1                   0.02500     NA    NA    NA
## k2                   0.00273     NA    NA    NA
## g                    0.58835     NA    NA    NA
## sigma                3.90001     NA    NA    NA
## 
## 
## 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="cb32"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb32-1" title="1">p9a &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p9a"</span>]])</a></code></pre></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="cb35"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb35-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p9a)</a></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p9a-1.png" width="700"></p>
<div class="sourceCode" id="cb36"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb36-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p9a)</a></code></pre></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       5.75e-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 2.17e+12 1.21e+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="cb38"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb38-1" title="1">p9b &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p9b"</span>]])</a></code></pre></div>
<pre><code>## Warning in sqrt(diag(covar_notrans)): NaNs wurden erzeugt</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="cb42"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb42-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p9b)</a></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p9b-1.png" width="700"></p>
<div class="sourceCode" id="cb43"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb43-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p9b)</a></code></pre></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      NaN  0.0306  0.0495
## k2         0.0389 1.10e-06  0.0186  0.0812
## g          0.7598      NaN  0.0000  1.0000
## 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="cb45"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb45-1" title="1">p10 &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p10"</span>]])</a></code></pre></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="cb48"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb48-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p10)</a></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p10-1.png" width="700"></p>
<div class="sourceCode" id="cb49"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb49-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p10)</a></code></pre></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 6.41e-04  0.0303   0.0809
## k2         0.0495 1.66e-02  0.0201   0.1219
## 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="cb51"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb51-1" title="1">p11 &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p11"</span>]])</a></code></pre></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="cb54"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb54-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p11)</a></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p11-1.png" width="700"></p>
<div class="sourceCode" id="cb55"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb55-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p11)</a></code></pre></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       9.20e-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 3.31e+11 2.08e+12 7.53e+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="cb57"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb57-1" title="1">p12a &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p12a"</span>]])</a></code></pre></div>
<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
## singular system.</code></pre>
<pre><code>## Warning in sqrt(diag(covar)): NaNs wurden erzeugt</code></pre>
<pre><code>## Warning in sqrt(diag(covar_notrans)): NaNs wurden erzeugt</code></pre>
<pre><code>## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt</code></pre>
<pre><code>## Warning in cov2cor(ans$cov.unscaled): 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="cb65"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb65-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p12a)</a></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p12a-1.png" width="700"></p>
<div class="sourceCode" id="cb66"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb66-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p12a)</a></code></pre></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
## 
## $DFOP
##          Estimate   Pr(&gt;t)   Lower   Upper
## parent_0  100.521 2.74e-10 92.2366 108.805
## k1          0.124 5.43e-06  0.0959   0.161
## k2          0.124 6.45e-02  0.0315   0.490
## g           0.880      NaN      NA      NA
## sigma       7.048 2.50e-04  4.0349  10.061
## 
## 
## DTx values:
##      DT50 DT90 DT50_rep
## SFO  5.58 18.5     5.58
## IORE 6.49 13.2     3.99
## DFOP 5.58 18.5     5.58
## 
## Representative half-life:
## [1] 3.99</code></pre>
</div>
<div id="example-on-page-12-lower-panel" class="section level2">
<h2 class="hasAnchor">
<a href="#example-on-page-12-lower-panel" class="anchor"></a>Example on page 12, lower panel</h2>
<div class="sourceCode" id="cb68"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb68-1" title="1">p12b &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p12b"</span>]])</a></code></pre></div>
<pre><code>## Warning in sqrt(diag(covar)): NaNs wurden erzeugt</code></pre>
<pre><code>## Warning in qt(alpha/2, rdf): NaNs wurden erzeugt</code></pre>
<pre><code>## Warning in qt(1 - alpha/2, rdf): NaNs wurden erzeugt</code></pre>
<pre><code>## Warning in sqrt(diag(covar_notrans)): NaNs wurden erzeugt</code></pre>
<pre><code>## Warning in pt(abs(tval), rdf, lower.tail = FALSE): NaNs wurden erzeugt</code></pre>
<pre><code>## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt</code></pre>
<pre><code>## Warning in cov2cor(ans$cov.unscaled): 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="cb78"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb78-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p12b)</a></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p12b-1.png" width="700"></p>
<div class="sourceCode" id="cb79"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb79-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p12b)</a></code></pre></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          0.8275    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="cb81"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb81-1" title="1">p13 &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p13"</span>]])</a></code></pre></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="cb84"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb84-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p13)</a></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p13-1.png" width="700"></p>
<div class="sourceCode" id="cb85"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb85-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p13)</a></code></pre></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
## 
## $DFOP
##          Estimate   Pr(&gt;t)    Lower    Upper
## parent_0 92.73500 9.25e-15 8.95e+01 9.59e+01
## k1        0.00258 4.28e-01 1.25e-08 5.31e+02
## k2        0.00258 3.69e-08 2.20e-03 3.03e-03
## g         0.00442 5.00e-01 0.00e+00 1.00e+00
## sigma     3.41172 1.35e-04 2.02e+00 4.80e+00
## 
## 
## DTx values:
##      DT50 DT90 DT50_rep
## SFO   269  892      269
## IORE  261  560      169
## DFOP  269  892      269
## 
## Representative half-life:
## [1] 168.51</code></pre>
</div>
</div>
<div id="dt50-not-observed-in-the-study-and-dfop-problems-in-pestdf" class="section level1">
<h1 class="hasAnchor">
<a href="#dt50-not-observed-in-the-study-and-dfop-problems-in-pestdf" class="anchor"></a>DT50 not observed in the study and DFOP problems in PestDF</h1>
<div class="sourceCode" id="cb87"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb87-1" title="1">p14 &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p14"</span>]])</a></code></pre></div>
<pre><code>## Warning in sqrt(diag(covar)): NaNs wurden erzeugt</code></pre>
<pre><code>## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt</code></pre>
<pre><code>## Warning in cov2cor(ans$cov.unscaled): 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="cb93"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb93-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p14)</a></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p14-1.png" width="700"></p>
<div class="sourceCode" id="cb94"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb94-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p14)</a></code></pre></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
## 
## $DFOP
##          Estimate   Pr(&gt;t)    Lower    Upper
## parent_0 1.00e+02 2.96e-28 99.40280 101.2768
## k1       9.53e-03 1.20e-01  0.00638   0.0143
## k2       5.42e-12 5.00e-01  0.00000      Inf
## g        3.98e-01 2.19e-01  0.30481   0.4998
## sigma    1.17e+00 7.68e-06  0.77406   1.5610
## 
## 
## DTx values:
##          DT50     DT90 DT50_rep
## SFO  2.48e+02 8.25e+02 2.48e+02
## IORE 4.34e+02 2.22e+04 6.70e+03
## DFOP 3.41e+10 3.31e+11 1.28e+11
## 
## Representative half-life:
## [1] 6697.44</code></pre>
<p>The slower rate constant reported by PestDF is negative, which is not physically realistic, and not possible in mkin. The other fits give the same results in mkin and PestDF.</p>
</div>
<div id="n-is-less-than-1-and-dfop-fraction-parameter-is-below-zero" class="section level1">
<h1 class="hasAnchor">
<a href="#n-is-less-than-1-and-dfop-fraction-parameter-is-below-zero" class="anchor"></a>N is less than 1 and DFOP fraction parameter is below zero</h1>
<div class="sourceCode" id="cb96"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb96-1" title="1">p15a &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p15a"</span>]])</a></code></pre></div>
<pre><code>## Warning in sqrt(diag(covar)): NaNs wurden erzeugt</code></pre>
<pre><code>## Warning in sqrt(diag(covar_notrans)): NaNs wurden erzeugt</code></pre>
<pre><code>## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt</code></pre>
<pre><code>## Warning in cov2cor(ans$cov.unscaled): 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="cb103"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb103-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p15a)</a></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p15a-1.png" width="700"></p>
<div class="sourceCode" id="cb104"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb104-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p15a)</a></code></pre></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 97.96751 2.85e-13 94.21913 101.7159
## k1        0.00952 5.68e-02  0.00262   0.0347
## k2        0.00952 1.52e-04  0.00639   0.0142
## g         0.22357      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="cb106"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb106-1" title="1">p15b &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p15b"</span>]])</a></code></pre></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="cb109"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb109-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p15b)</a></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p15b-1.png" width="700"></p>
<div class="sourceCode" id="cb110"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb110-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p15b)</a></code></pre></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 6.49e-04 3.64e-02
## k2       4.86e-03     NA 3.36e-03 7.03e-03
## g        1.50e-01     NA 0.00e+00 1.00e+00
## 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="cb112"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb112-1" title="1">p16 &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p16"</span>]])</a></code></pre></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="cb117"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb117-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p16)</a></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p16-1.png" width="700"></p>
<div class="sourceCode" id="cb118"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb118-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p16)</a></code></pre></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        18.6315 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="sidebar">
        <div id="tocnav">
      <h2 class="hasAnchor">
<a href="#tocnav" class="anchor"></a>Contents</h2>
      <ul class="nav nav-pills nav-stacked">
<li><a href="#introduction">Introduction</a></li>
      <li>
<a href="#examples-where-dfop-did-not-converge-with-pestdf-0-8-4">Examples where DFOP did not converge with PestDF 0.8.4</a><ul class="nav nav-pills nav-stacked">
<li><a href="#example-on-page-5-upper-panel">Example on page 5, upper panel</a></li>
      <li><a href="#example-on-page-5-lower-panel">Example on page 5, lower panel</a></li>
      <li><a href="#example-on-page-6">Example on page 6</a></li>
      <li><a href="#example-on-page-7">Example on page 7</a></li>
      </ul>
</li>
      <li>
<a href="#examples-where-the-representative-half-life-deviates-from-the-observed-dt50">Examples where the representative half-life deviates from the observed DT50</a><ul class="nav nav-pills nav-stacked">
<li><a href="#example-on-page-8">Example on page 8</a></li>
      </ul>
</li>
      <li>
<a href="#examples-where-sfo-was-not-selected-for-an-abiotic-study">Examples where SFO was not selected for an abiotic study</a><ul class="nav nav-pills nav-stacked">
<li><a href="#example-on-page-9-upper-panel">Example on page 9, upper panel</a></li>
      <li><a href="#example-on-page-9-lower-panel">Example on page 9, lower panel</a></li>
      <li><a href="#example-on-page-10">Example on page 10</a></li>
      </ul>
</li>
      <li>
<a href="#the-dt50-was-not-observed-during-the-study">The DT50 was not observed during the study</a><ul class="nav nav-pills nav-stacked">
<li><a href="#example-on-page-11">Example on page 11</a></li>
      </ul>
</li>
      <li>
<a href="#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><ul class="nav nav-pills nav-stacked">
<li><a href="#example-on-page-12-upper-panel">Example on page 12, upper panel</a></li>
      <li><a href="#example-on-page-12-lower-panel">Example on page 12, lower panel</a></li>
      <li><a href="#example-on-page-13">Example on page 13</a></li>
      </ul>
</li>
      <li><a href="#dt50-not-observed-in-the-study-and-dfop-problems-in-pestdf">DT50 not observed in the study and DFOP problems in PestDF</a></li>
      <li><a href="#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></li>
      <li><a href="#the-dfop-fraction-parameter-is-greater-than-1">The DFOP fraction parameter is greater than 1</a></li>
      <li><a href="#conclusions">Conclusions</a></li>
      <li><a href="#references">References</a></li>
      </ul>
</div>
      </div>

</div>


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