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diff --git a/docs/articles/web_only/NAFTA_examples.html b/docs/articles/web_only/NAFTA_examples.html
index c614166d..b8a5215d 100644
--- a/docs/articles/web_only/NAFTA_examples.html
+++ b/docs/articles/web_only/NAFTA_examples.html
@@ -88,7 +88,7 @@
<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">2019-07-05</h4>
+ <h4 class="date">2019-07-09</h4>
<div class="hidden name"><code>NAFTA_examples.Rmd</code></div>
@@ -111,13 +111,11 @@
<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>## 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="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/graphics/topics/plot">plot</a></span>(p5a)</a></code></pre></div>
+<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="cb6"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb6-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p5a)</a></code></pre></div>
+<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
@@ -128,21 +126,24 @@
## Parameters:
## $SFO
## Estimate Pr(&gt;t) Lower Upper
-## parent_0 95.8401 1.10e-21 92.121 99.5597
-## k_parent_sink 0.0102 1.71e-12 0.009 0.0117
+## 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 2.37e-26 9.89e+01 1.03e+02
-## k__iore_parent_sink 1.54e-05 8.73e-02 3.48e-06 6.85e-05
-## N_parent 2.57e+00 1.14e-11 2.22e+00 2.92e+00
+## 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 4.33e-27 NA NA
-## k1 2.67e-02 3.17e-05 NA NA
-## k2 2.86e-12 5.00e-01 NA NA
-## g 6.47e-01 2.13e-05 NA NA
+## Estimate Pr(&gt;t) Lower Upper
+## parent_0 9.99e+01 1.41e-26 98.8116 101.0810
+## k1 2.67e-02 5.05e-06 0.0243 0.0295
+## k2 2.86e-12 5.00e-01 0.0000 Inf
+## g 6.47e-01 3.67e-06 0.6248 0.6677
+## sigma 1.27e+00 8.91e-06 0.8395 1.6929
##
##
## DTx values:
@@ -152,19 +153,17 @@
## DFOP 55.5 4.42e+11 2.42e+11
##
## Representative half-life:
-## [1] 321.5119</code></pre>
+## [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="cb8"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb8-1" 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>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.</code></pre>
+<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="cb12"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb12-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p5b)</a></code></pre></div>
+<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="cb13"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb13-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p5b)</a></code></pre></div>
+<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
@@ -175,21 +174,24 @@
## Parameters:
## $SFO
## Estimate Pr(&gt;t) Lower Upper
-## parent_0 96.497 2.62e-25 94.77653 98.21774
-## k_parent_sink 0.008 1.35e-14 0.00736 0.00871
+## 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 1.02e-29 9.78e+01 9.93e+01
-## k__iore_parent_sink 1.53e-04 1.15e-02 6.60e-05 3.56e-04
-## N_parent 1.94e+00 8.18e-13 1.74e+00 2.14e+00
+## 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 1.90e-28 NA NA
-## k1 1.55e-02 2.83e-03 NA NA
-## k2 1.16e-11 5.00e-01 NA NA
-## g 6.89e-01 1.31e-02 NA NA
+## Estimate Pr(&gt;t) Lower Upper
+## parent_0 9.84e+01 1.24e-27 97.8078 98.9187
+## k1 1.55e-02 4.10e-04 0.0143 0.0167
+## k2 1.16e-11 5.00e-01 0.0000 Inf
+## g 6.89e-01 2.92e-03 0.6626 0.7142
+## sigma 6.48e-01 2.38e-05 0.4147 0.8813
##
##
## DTx values:
@@ -199,19 +201,17 @@
## DFOP 83.6 9.80e+10 5.98e+10
##
## Representative half-life:
-## [1] 215.8655</code></pre>
+## [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="cb15"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb15-1" 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>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.</code></pre>
+<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="cb19"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb19-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p6)</a></code></pre></div>
+<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="cb20"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb20-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p6)</a></code></pre></div>
+<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
@@ -222,21 +222,24 @@
## Parameters:
## $SFO
## Estimate Pr(&gt;t) Lower Upper
-## parent_0 94.7759 1.25e-24 92.2558 97.2960
-## k_parent_sink 0.0179 2.35e-16 0.0166 0.0194
+## parent_0 94.7759 7.29e-24 92.3478 97.2039
+## k_parent_sink 0.0179 8.02e-16 0.0166 0.0194
+## sigma 3.0696 3.81e-06 2.0456 4.0936
##
## $IORE
## Estimate Pr(&gt;t) Lower Upper
-## parent_0 97.12446 5.62e-27 95.49343 98.75549
-## k__iore_parent_sink 0.00252 3.54e-03 0.00126 0.00502
-## N_parent 1.49587 6.13e-13 1.32380 1.66794
+## 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 4.17e-26 NA NA
-## k1 2.55e-02 2.12e-05 NA NA
-## k2 4.90e-11 5.00e-01 NA NA
-## g 8.61e-01 2.10e-05 NA NA
+## Estimate Pr(&gt;t) Lower Upper
+## parent_0 9.66e+01 1.57e-25 95.3476 97.8979
+## k1 2.55e-02 7.33e-06 0.0233 0.0278
+## k2 4.90e-11 5.00e-01 0.0000 Inf
+## g 8.61e-01 7.55e-06 0.8314 0.8867
+## sigma 1.46e+00 6.93e-06 0.9661 1.9483
##
##
## DTx values:
@@ -246,19 +249,17 @@
## DFOP 34.1 6.66e+09 1.41e+10
##
## Representative half-life:
-## [1] 53.16582</code></pre>
+## [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="cb22"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb22-1" 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>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.</code></pre>
+<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="cb26"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb26-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p7)</a></code></pre></div>
+<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="cb27"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb27-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p7)</a></code></pre></div>
+<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
@@ -269,21 +270,24 @@
## Parameters:
## $SFO
## Estimate Pr(&gt;t) Lower Upper
-## parent_0 96.41796 1.52e-53 93.29554 99.54038
-## k_parent_sink 0.00735 3.59e-21 0.00641 0.00842
+## 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 7.33e-49 9.53e+01 1.03e+02
-## k__iore_parent_sink 1.60e-05 3.47e-01 9.98e-08 2.57e-03
-## N_parent 2.45e+00 6.14e-05 1.26e+00 3.63e+00
+## 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 8.13e-48 NA NA
-## k1 1.81e-02 2.20e-01 NA NA
-## k2 1.97e-10 5.00e-01 NA NA
-## g 6.06e-01 2.60e-01 NA NA
+## Estimate Pr(&gt;t) Lower Upper
+## parent_0 9.89e+01 9.44e-49 95.4640 102.2573
+## k1 1.81e-02 1.75e-01 0.0116 0.0281
+## k2 1.97e-10 5.00e-01 0.0000 Inf
+## g 6.06e-01 2.19e-01 0.4826 0.7178
+## sigma 7.40e+00 2.97e-15 6.0201 8.7754
##
##
## DTx values:
@@ -293,7 +297,7 @@
## DFOP 96.4 6.97e+09 3.52e+09
##
## Representative half-life:
-## [1] 454.5528</code></pre>
+## [1] 454.55</code></pre>
</div>
</div>
<div id="examples-where-the-representative-half-life-deviates-from-the-observed-dt50" class="section level1">
@@ -303,17 +307,12 @@
<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="cb29"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb29-1" 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>
+<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>## 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="cb33"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb33-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p8)</a></code></pre></div>
+<div class="sourceCode" id="cb28"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb28-1" 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="cb34"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb34-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p8)</a></code></pre></div>
+<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/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
@@ -323,24 +322,25 @@
##
## 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
+## Estimate Pr(&gt;t) Lower Upper
+## parent_0 88.16549 6.53e-29 83.37344 92.95754
+## k_parent_sink 0.00803 1.67e-13 0.00674 0.00957
+## sigma 7.44786 4.17e-10 5.66209 9.23363
##
## $IORE
## Estimate Pr(&gt;t) Lower Upper
-## parent_0 9.77e+01 1.05e-35 9.44e+01 1.01e+02
-## k__iore_parent_sink 6.14e-05 2.76e-02 2.21e-05 1.71e-04
-## N_parent 2.27e+00 6.00e-19 2.02e+00 2.53e+00
+## 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
+## Estimate Pr(&gt;t) Lower Upper
+## parent_0 95.70619 8.99e-32 91.87941 99.53298
+## k1 0.02500 5.25e-04 0.01422 0.04394
+## k2 0.00273 6.84e-03 0.00125 0.00597
+## g 0.58835 2.84e-06 0.36595 0.77970
+## sigma 3.90001 6.94e-10 2.96260 4.83741
##
##
## DTx values:
@@ -350,7 +350,7 @@
## DFOP 55.6 517 253.0
##
## Representative half-life:
-## [1] 201.0316</code></pre>
+## [1] 201.03</code></pre>
</div>
</div>
<div id="examples-where-sfo-was-not-selected-for-an-abiotic-study" class="section level1">
@@ -359,14 +359,12 @@
<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="cb36"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb36-1" 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>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.</code></pre>
+<div class="sourceCode" id="cb31"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb31-1" 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="cb40"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb40-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p9a)</a></code></pre></div>
+<div class="sourceCode" id="cb34"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb34-1" 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="cb41"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb41-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p9a)</a></code></pre></div>
+<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/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
@@ -377,21 +375,24 @@
## Parameters:
## $SFO
## Estimate Pr(&gt;t) Lower Upper
-## parent_0 88.1933 1.12e-12 79.7671 96.6195
-## k_parent_sink 0.0409 9.50e-08 0.0326 0.0513
+## 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 5.16e-17 9.50e+01 1.03e+02
-## k__iore_parent_sink 1.93e-05 1.48e-01 2.65e-06 1.40e-04
-## N_parent 2.91e+00 3.74e-09 2.43e+00 3.39e+00
+## 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
##
## $DFOP
-## Estimate Pr(&gt;t) Lower Upper
-## parent_0 9.85e+01 1.31e-21 NA NA
-## k1 1.38e-01 3.63e-09 NA NA
-## k2 6.02e-13 5.00e-01 NA NA
-## g 6.52e-01 1.50e-10 NA NA
+## Estimate Pr(&gt;t) Lower Upper
+## parent_0 9.85e+01 2.54e-20 97.390 99.672
+## k1 1.38e-01 3.52e-05 0.131 0.146
+## k2 6.02e-13 5.00e-01 0.000 Inf
+## g 6.52e-01 8.13e-06 0.642 0.661
+## sigma 7.88e-01 6.13e-02 0.481 1.095
##
##
## DTx values:
@@ -401,20 +402,23 @@
## DFOP 10.5 2.07e+12 1.15e+12
##
## Representative half-life:
-## [1] 101.4264</code></pre>
+## [1] 101.43</code></pre>
<p>In this example, the residuals of the SFO indicate a lack of fit of this model, so even if it was an abiotic experiment, the data do not suggest a simple exponential decline.</p>
</div>
<div id="example-on-page-9-lower-panel" class="section level2">
<h2 class="hasAnchor">
<a href="#example-on-page-9-lower-panel" class="anchor"></a>Example on page 9, lower panel</h2>
-<div class="sourceCode" id="cb43"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb43-1" title="1">p9b &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p9b"</span>]])</a></code></pre></div>
-<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.</code></pre>
+<div class="sourceCode" id="cb37"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb37-1" title="1">p9b &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p9b"</span>]])</a></code></pre></div>
+<pre><code>## Warning in sqrt(diag(covar)): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in sqrt(diag(covar_notrans)): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in cov2cor(ans$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="cb47"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb47-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p9b)</a></code></pre></div>
+<div class="sourceCode" id="cb44"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb44-1" 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="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/base/topics/print">print</a></span>(p9b)</a></code></pre></div>
+<div class="sourceCode" id="cb45"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb45-1" 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
@@ -424,22 +428,25 @@
##
## Parameters:
## $SFO
-## Estimate Pr(&gt;t) Lower Upper
-## parent_0 94.7123 2.21e-20 93.0673 96.357
-## k_parent_sink 0.0389 1.48e-14 0.0369 0.041
+## 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 2.91e-19 92.2996 95.426
-## k__iore_parent_sink 0.127 2.73e-02 0.0457 0.354
-## N_parent 0.711 3.13e-05 0.4605 0.961
+## 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 NA NA NA
-## k1 0.0389 NA NA NA
-## k2 0.0389 NA NA NA
-## g 0.7742 NA NA NA
+## Estimate Pr(&gt;t) Lower Upper
+## parent_0 94.7123 1.61e-16 93.1355 96.2891
+## k1 0.0389 1.43e-06 0.0312 0.0485
+## k2 0.0389 6.67e-03 0.0186 0.0812
+## g 0.7742 NaN NA NA
+## sigma 1.5957 2.50e-04 0.9135 2.2779
##
##
## DTx values:
@@ -449,20 +456,18 @@
## DFOP 17.8 59.2 17.8
##
## Representative half-life:
-## [1] 14.80012</code></pre>
+## [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="cb50"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb50-1" 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>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.</code></pre>
+<div class="sourceCode" id="cb47"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb47-1" 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="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>(p10)</a></code></pre></div>
+<div class="sourceCode" id="cb50"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb50-1" 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="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>(p10)</a></code></pre></div>
+<div class="sourceCode" id="cb51"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb51-1" 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
@@ -473,21 +478,24 @@
## Parameters:
## $SFO
## Estimate Pr(&gt;t) Lower Upper
-## parent_0 101.7315 4.95e-11 90.9683 112.4947
-## k_parent_sink 0.0495 3.40e-07 0.0393 0.0624
+## 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 2.71e-12 89.884 103.826
-## k__iore_parent_sink 2.96 1.31e-01 0.461 19.020
-## N_parent 0.00 5.00e-01 -0.473 0.473
+## 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 NA NA NA
-## k1 0.0495 NA NA NA
-## k2 0.0495 NA NA NA
-## g 0.6634 NA NA NA
+## Estimate Pr(&gt;t) Lower Upper
+## parent_0 101.7315 1.41e-09 91.6534 111.8097
+## k1 0.0495 6.42e-04 0.0301 0.0814
+## k2 0.0495 1.66e-02 0.0200 0.1225
+## g 0.6634 5.00e-01 0.0000 1.0000
+## sigma 8.0152 2.50e-04 4.5886 11.4418
##
##
## DTx values:
@@ -497,7 +505,7 @@
## DFOP 14.0 46.5 14.00
##
## Representative half-life:
-## [1] 8.862193</code></pre>
+## [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>
@@ -507,14 +515,12 @@
<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="cb57"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb57-1" 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>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.</code></pre>
+<div class="sourceCode" id="cb53"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb53-1" 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="cb61"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb61-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p11)</a></code></pre></div>
+<div class="sourceCode" id="cb56"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb56-1" 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="cb62"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb62-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p11)</a></code></pre></div>
+<div class="sourceCode" id="cb57"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb57-1" 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
@@ -525,21 +531,24 @@
## Parameters:
## $SFO
## Estimate Pr(&gt;t) Lower Upper
-## parent_0 96.15820 1.56e-13 89.91373 1.02e+02
-## k_parent_sink 0.00321 5.27e-05 0.00218 4.71e-03
+## 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 9.80e+01 1.11e+02
-## k__iore_parent_sink 3.11e-17 NA 6.88e-25 1.41e-09
-## N_parent 8.36e+00 NA 4.40e+00 1.23e+01
+## 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 7.50e-13 NA NA
-## k1 4.41e-02 3.34e-02 NA NA
-## k2 7.25e-13 5.00e-01 NA NA
-## g 3.22e-01 7.87e-03 NA NA
+## Estimate Pr(&gt;t) Lower Upper
+## parent_0 1.05e+02 9.47e-13 99.9990 109.1224
+## k1 4.41e-02 5.95e-03 0.0296 0.0658
+## k2 7.25e-13 5.00e-01 0.0000 Inf
+## g 3.22e-01 1.45e-03 0.2814 0.3650
+## sigma 3.22e+00 3.52e-04 1.8410 4.5906
##
##
## DTx values:
@@ -560,14 +569,14 @@
<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="cb64"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb64-1" 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>
+<div class="sourceCode" id="cb59"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb59-1" 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 calculate correlation; no
+## covariance matrix</code></pre>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb68"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb68-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p12a)</a></code></pre></div>
+<div class="sourceCode" id="cb63"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb63-1" 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="cb69"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb69-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p12a)</a></code></pre></div>
+<div class="sourceCode" id="cb64"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb64-1" 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
@@ -578,21 +587,24 @@
## Parameters:
## $SFO
## Estimate Pr(&gt;t) Lower Upper
-## parent_0 100.521 5.61e-12 91.687 109.355
-## k_parent_sink 0.124 7.24e-08 0.102 0.152
+## 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 1.24e-13 91.5691 102.078
-## k__iore_parent_sink 2.436 3.89e-02 0.7854 7.556
-## N_parent 0.263 3.64e-02 -0.0288 0.554
+## 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
##
## $DFOP
-## Estimate Pr(&gt;t) Lower Upper
-## parent_0 100.521 NA NA NA
-## k1 0.124 NA NA NA
-## k2 0.124 NA NA NA
-## g 0.877 NA NA NA
+## Estimate Pr(&gt;t) Lower Upper
+## parent_0 100.521 2.74e-10 92.2366 108.805
+## k1 0.124 5.74e-06 0.0958 0.161
+## k2 0.124 6.61e-02 0.0319 0.484
+## g 0.877 5.00e-01 0.0000 1.000
+## sigma 7.048 2.50e-04 4.0349 10.061
##
##
## DTx values:
@@ -602,19 +614,25 @@
## DFOP 5.58 18.5 5.58
##
## Representative half-life:
-## [1] 3.987308</code></pre>
+## [1] 3.99</code></pre>
</div>
<div id="example-on-page-12-lower-panel" class="section level2">
<h2 class="hasAnchor">
<a href="#example-on-page-12-lower-panel" class="anchor"></a>Example on page 12, lower panel</h2>
-<div class="sourceCode" id="cb71"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb71-1" title="1">p12b &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p12b"</span>]])</a></code></pre></div>
-<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.</code></pre>
+<div class="sourceCode" id="cb66"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb66-1" title="1">p12b &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p12b"</span>]])</a></code></pre></div>
+<pre><code>## Warning in sqrt(diag(covar)): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in qt(alpha/2, rdf): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in qt(1 - alpha/2, rdf): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in sqrt(diag(covar_notrans)): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in pt(abs(tval), rdf, lower.tail = FALSE): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in cov2cor(ans$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="cb75"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb75-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p12b)</a></code></pre></div>
+<div class="sourceCode" id="cb76"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb76-1" 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="cb76"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb76-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p12b)</a></code></pre></div>
+<div class="sourceCode" id="cb77"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb77-1" 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
@@ -624,22 +642,25 @@
##
## Parameters:
## $SFO
-## Estimate Pr(&gt;t) Lower Upper
-## parent_0 97.6840 5.36e-05 86.3205 109.0475
-## k_parent_sink 0.0589 9.87e-04 0.0432 0.0803
+## 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 0.000386 84.0963 106.95
-## k__iore_parent_sink 0.333 0.170886 0.0103 10.80
-## N_parent 0.568 0.054881 -0.3161 1.45
+## 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
##
## $DFOP
## Estimate Pr(&gt;t) Lower Upper
-## parent_0 97.6840 NA NA NA
-## k1 0.0589 NA NA NA
-## k2 0.0589 NA NA NA
-## g 0.6902 NA NA NA
+## parent_0 97.6840 NaN NaN NaN
+## k1 0.0589 NaN NA NA
+## k2 0.0589 NaN NA NA
+## g 0.6902 NaN NA NA
+## sigma 3.4323 NaN NaN NaN
##
##
## DTx values:
@@ -649,19 +670,21 @@
## DFOP 11.8 39.1 11.80
##
## Representative half-life:
-## [1] 9.461912</code></pre>
+## [1] 9.46</code></pre>
</div>
<div id="example-on-page-13" class="section level2">
<h2 class="hasAnchor">
<a href="#example-on-page-13" class="anchor"></a>Example on page 13</h2>
-<div class="sourceCode" id="cb78"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb78-1" title="1">p13 &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p13"</span>]])</a></code></pre></div>
-<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.</code></pre>
+<div class="sourceCode" id="cb79"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb79-1" title="1">p13 &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p13"</span>]])</a></code></pre></div>
+<pre><code>## Warning in sqrt(diag(covar)): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in cov2cor(ans$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="cb82"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb82-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p13)</a></code></pre></div>
+<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/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="cb83"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb83-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p13)</a></code></pre></div>
+<div class="sourceCode" id="cb86"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb86-1" 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
@@ -671,22 +694,25 @@
##
## Parameters:
## $SFO
-## Estimate Pr(&gt;t) Lower Upper
-## parent_0 92.73500 1.45e-17 89.3891 96.08094
-## k_parent_sink 0.00258 2.63e-09 0.0022 0.00303
+## 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 2.93e-16 88.08711 95.12
-## k__iore_parent_sink 0.0396 2.81e-01 0.00102 1.53
-## N_parent 0.3541 1.97e-01 -0.51943 1.23
+## 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
##
## $DFOP
-## Estimate Pr(&gt;t) Lower Upper
-## parent_0 92.73500 NA NA NA
-## k1 0.00258 NA NA NA
-## k2 0.00258 NA NA NA
-## g 0.00442 NA NA NA
+## Estimate Pr(&gt;t) Lower Upper
+## parent_0 92.73500 9.25e-15 8.95e+01 9.59e+01
+## k1 0.00258 4.28e-01 1.70e-08 3.92e+02
+## k2 0.00258 3.69e-08 2.20e-03 3.03e-03
+## g 0.00442 5.00e-01 NA NA
+## sigma 3.41172 1.35e-04 2.02e+00 4.80e+00
##
##
## DTx values:
@@ -696,20 +722,22 @@
## DFOP 269 892 269
##
## Representative half-life:
-## [1] 168.5123</code></pre>
+## [1] 168.51</code></pre>
</div>
</div>
<div id="dt50-not-observed-in-the-study-and-dfop-problems-in-pestdf" class="section level1">
<h1 class="hasAnchor">
<a href="#dt50-not-observed-in-the-study-and-dfop-problems-in-pestdf" class="anchor"></a>DT50 not observed in the study and DFOP problems in PestDF</h1>
-<div class="sourceCode" id="cb85"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb85-1" title="1">p14 &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p14"</span>]])</a></code></pre></div>
-<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.</code></pre>
+<div class="sourceCode" id="cb88"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb88-1" title="1">p14 &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p14"</span>]])</a></code></pre></div>
+<pre><code>## Warning in sqrt(diag(covar)): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in cov2cor(ans$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="cb89"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb89-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p14)</a></code></pre></div>
+<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/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="cb90"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb90-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p14)</a></code></pre></div>
+<div class="sourceCode" id="cb95"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb95-1" 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
@@ -720,21 +748,24 @@
## Parameters:
## $SFO
## Estimate Pr(&gt;t) Lower Upper
-## parent_0 99.47124 1.71e-31 98.37313 1.01e+02
-## k_parent_sink 0.00279 2.22e-15 0.00255 3.05e-03
+## 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 9.93e+01 1.01e+02
-## k__iore_parent_sink 9.44e-08 NA 6.81e-11 1.31e-04
-## N_parent 3.31e+00 NA 1.69e+00 4.93e+00
+## 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 2.70e-28 NA NA
-## k1 9.53e-03 3.39e-01 NA NA
-## k2 7.29e-12 5.00e-01 NA NA
-## g 3.98e-01 3.92e-01 NA NA
+## Estimate Pr(&gt;t) Lower Upper
+## parent_0 1.00e+02 2.96e-28 99.40280 101.2768
+## k1 9.53e-03 1.20e-01 0.00638 0.0143
+## k2 7.29e-12 5.00e-01 0.00000 Inf
+## g 3.98e-01 2.19e-01 0.30481 0.4998
+## sigma 1.17e+00 7.68e-06 0.77406 1.5610
##
##
## DTx values:
@@ -744,20 +775,23 @@
## DFOP 2.54e+10 2.46e+11 9.51e+10
##
## Representative half-life:
-## [1] 6697.437</code></pre>
+## [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="cb92"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb92-1" 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 summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.</code></pre>
+<div class="sourceCode" id="cb97"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb97-1" 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="cb96"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb96-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p15a)</a></code></pre></div>
+<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/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="cb97"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb97-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p15a)</a></code></pre></div>
+<div class="sourceCode" id="cb105"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb105-1" 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
@@ -767,22 +801,25 @@
##
## Parameters:
## $SFO
-## Estimate Pr(&gt;t) Lower Upper
-## parent_0 97.96751 4.98e-16 94.03829 101.8967
-## k_parent_sink 0.00952 5.24e-09 0.00813 0.0112
+## 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 8.30e-16 92.5802 99.167
-## k__iore_parent_sink 0.629 2.39e-01 0.0316 12.519
-## N_parent 0.000 5.00e-01 -0.7219 0.722
+## Estimate Pr(&gt;t) Lower Upper
+## parent_0 95.874 2.94e-15 92.937 98.811
+## k__iore_parent_sink 0.629 2.11e-01 0.044 8.982
+## N_parent 0.000 5.00e-01 -0.642 0.642
+## sigma 3.105 1.78e-04 1.795 4.416
##
## $DFOP
-## Estimate Pr(&gt;t) Lower Upper
-## parent_0 97.96752 NA NA NA
-## k1 0.00952 NA NA NA
-## k2 0.00952 NA NA NA
-## g 0.17247 NA NA NA
+## Estimate Pr(&gt;t) Lower Upper
+## parent_0 97.96752 2.85e-13 94.21914 101.7159
+## k1 0.00952 6.80e-02 0.00277 0.0327
+## k2 0.00952 3.82e-06 0.00902 0.0100
+## g 0.17247 NaN NA NA
+## sigma 4.18778 2.50e-04 2.39747 5.9781
##
##
## DTx values:
@@ -792,15 +829,17 @@
## DFOP 72.8 242 72.8
##
## Representative half-life:
-## [1] 41.32749</code></pre>
-<div class="sourceCode" id="cb99"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb99-1" title="1">p15b &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p15b"</span>]])</a></code></pre></div>
-<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.</code></pre>
+## [1] 41.33</code></pre>
+<div class="sourceCode" id="cb107"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb107-1" title="1">p15b &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p15b"</span>]])</a></code></pre></div>
+<pre><code>## Warning in sqrt(diag(covar)): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in cov2cor(ans$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="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>(p15b)</a></code></pre></div>
+<div class="sourceCode" id="cb113"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb113-1" 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="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>(p15b)</a></code></pre></div>
+<div class="sourceCode" id="cb114"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb114-1" 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
@@ -811,21 +850,24 @@
## Parameters:
## $SFO
## Estimate Pr(&gt;t) Lower Upper
-## parent_0 1.01e+02 4.99e-18 98.12761 1.04e+02
-## k_parent_sink 4.86e-03 1.76e-10 0.00432 5.46e-03
+## 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 4.49e-17 97.19753 102.5
-## k__iore_parent_sink 0.38 3.41e-01 0.00206 70.0
-## N_parent 0.00 5.00e-01 -1.20105 1.2
+## 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 NA NA
-## k1 4.86e-03 NA NA NA
-## k2 4.86e-03 NA NA NA
-## g 1.50e-01 NA NA NA
+## Estimate Pr(&gt;t) Lower Upper
+## parent_0 1.01e+02 NA 9.82e+01 1.04e+02
+## k1 4.86e-03 NA 6.75e-04 3.49e-02
+## k2 4.86e-03 NA 3.37e-03 6.99e-03
+## g 1.50e-01 NA NA NA
+## sigma 2.76e+00 NA 1.58e+00 3.94e+00
##
##
## DTx values:
@@ -835,20 +877,20 @@
## DFOP 143 474 143.0
##
## Representative half-life:
-## [1] 71.18014</code></pre>
+## [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="cb106"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb106-1" 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>
+<div class="sourceCode" id="cb116"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb116-1" 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="cb111"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb111-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p16)</a></code></pre></div>
+<div class="sourceCode" id="cb121"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb121-1" 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="cb112"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb112-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p16)</a></code></pre></div>
+<div class="sourceCode" id="cb122"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb122-1" 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
@@ -858,22 +900,25 @@
##
## Parameters:
## $SFO
-## Estimate Pr(&gt;t) Lower Upper
-## parent_0 71.953 3.92e-14 61.087 82.819
-## k_parent_sink 0.159 2.27e-06 0.111 0.229
+## 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 1.74e-16 7.71e+01 97.70701
-## k__iore_parent_sink 4.55e-04 2.28e-01 3.01e-05 0.00688
-## N_parent 2.70e+00 1.87e-08 1.97e+00 3.42611
+## 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 NA 79.3673 97.699
-## k1 18.5561 NA 0.0000 Inf
-## k2 0.0776 NA 0.0471 0.128
-## g 0.4733 NA 0.3138 0.639
+## Estimate Pr(&gt;t) Lower Upper
+## parent_0 88.5333 7.40e-18 79.9836 97.083
+## k1 18.5561 5.00e-01 0.0000 Inf
+## k2 0.0776 1.41e-05 0.0518 0.116
+## g 0.4733 1.41e-09 0.3674 0.582
+## sigma 7.1902 2.11e-08 5.2785 9.102
##
##
## DTx values:
@@ -883,7 +928,7 @@
## DFOP 0.67 21.4 8.93
##
## Representative half-life:
-## [1] 8.932679</code></pre>
+## [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>
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<div id="conclusions" class="section level1">

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