Merge branch 'nlmixr'

author: Johannes Ranke <jranke@uni-bremen.de> 2022-02-08 17:17:29 +0100
committer: Johannes Ranke <jranke@uni-bremen.de> 2022-02-08 17:17:29 +0100
commit: 0fa8a770812775d697717ad723f7f61fb04b7fef (patch)
tree: 17473ddf787541745d47dab063bc643ec59a9557 /docs/dev/articles
parent: d081384ddcb75a9f92fad33e4e3f6d6796f98e67 (diff)
parent: c0638c84568d475b3b059e2c6e593e6f03b846bc (diff)
86 files changed, 1162 insertions, 251 deletions
diff --git a/docs/dev/articles/FOCUS_D.html b/docs/dev/articles/FOCUS_D.html
index dd86f677..a35a255a 100644
--- a/docs/dev/articles/FOCUS_D.html
+++ b/docs/dev/articles/FOCUS_D.html
@@ -32,7 +32,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">0.9.50.4</span>
+        <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">1.0.3.9000</span>
       </span>
     </div>
 
@@ -81,7 +81,7 @@
 <ul class="nav navbar-nav navbar-right">
 <li>
   <a href="https://github.com/jranke/mkin/">
-    <span class="fab fa fab fa-github fa-lg"></span>
+    <span class="fab fa-github fa-lg"></span>
      
   </a>
 </li>
@@ -95,14 +95,13 @@
 
       
 
-      </header><link href="FOCUS_D_files/anchor-sections-1.0/anchor-sections.css" rel="stylesheet">
-<script src="FOCUS_D_files/anchor-sections-1.0/anchor-sections.js"></script><div class="row">
+      </header><script src="FOCUS_D_files/header-attrs-2.6/header-attrs.js"></script><script src="FOCUS_D_files/accessible-code-block-0.0.1/empty-anchor.js"></script><div class="row">
   <div class="col-md-9 contents">
     <div class="page-header toc-ignore">
       <h1 data-toc-skip>Example evaluation of FOCUS Example Dataset D</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2020-11-30</h4>
+            <h4 class="date">Last change 31 January 2019 (rebuilt 2021-02-15)</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/master/vignettes/FOCUS_D.rmd"><code>vignettes/FOCUS_D.rmd</code></a></small>
       <div class="hidden name"><code>FOCUS_D.rmd</code></div>
@@ -187,10 +186,10 @@
 <p>A comprehensive report of the results is obtained using the <code>summary</code> method for <code>mkinfit</code> objects.</p>
 <div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html">summary</a></span><span class="op">(</span><span class="va">fit</span><span class="op">)</span></code></pre></div>
-<pre><code>## mkin version used for fitting:    0.9.50.4 
+<pre><code>## mkin version used for fitting:    1.0.3.9000 
 ## R version used for fitting:       4.0.3 
-## Date of fit:     Mon Nov 30 16:01:50 2020 
-## Date of summary: Mon Nov 30 16:01:50 2020 
+## Date of fit:     Mon Feb 15 17:13:36 2021 
+## Date of summary: Mon Feb 15 17:13:37 2021 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent * parent
@@ -241,11 +240,11 @@
 ## 
 ## Parameter correlation:
 ##                   parent_0 log_k_parent   log_k_m1 f_parent_qlogis      sigma
-## parent_0         1.000e+00    5.174e-01 -1.688e-01      -5.471e-01 -1.171e-06
-## log_k_parent     5.174e-01    1.000e+00 -3.263e-01      -5.426e-01 -8.481e-07
-## log_k_m1        -1.688e-01   -3.263e-01  1.000e+00       7.478e-01  8.209e-07
+## parent_0         1.000e+00    5.174e-01 -1.688e-01      -5.471e-01 -1.172e-06
+## log_k_parent     5.174e-01    1.000e+00 -3.263e-01      -5.426e-01 -8.483e-07
+## log_k_m1        -1.688e-01   -3.263e-01  1.000e+00       7.478e-01  8.205e-07
 ## f_parent_qlogis -5.471e-01   -5.426e-01  7.478e-01       1.000e+00  1.305e-06
-## sigma           -1.171e-06   -8.481e-07  8.209e-07       1.305e-06  1.000e+00
+## sigma           -1.172e-06   -8.483e-07  8.205e-07       1.305e-06  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
diff --git a/docs/dev/articles/FOCUS_D_files/accessible-code-block-0.0.1/empty-anchor.js b/docs/dev/articles/FOCUS_D_files/accessible-code-block-0.0.1/empty-anchor.js
new file mode 100644
index 00000000..ca349fd6
--- /dev/null
+++ b/docs/dev/articles/FOCUS_D_files/accessible-code-block-0.0.1/empty-anchor.js
@@ -0,0 +1,15 @@
+// Hide empty <a> tag within highlighted CodeBlock for screen reader accessibility (see https://github.com/jgm/pandoc/issues/6352#issuecomment-626106786) -->
+// v0.0.1
+// Written by JooYoung Seo (jooyoung@psu.edu) and Atsushi Yasumoto on June 1st, 2020.
+
+document.addEventListener('DOMContentLoaded', function() {
+  const codeList = document.getElementsByClassName("sourceCode");
+  for (var i = 0; i < codeList.length; i++) {
+    var linkList = codeList[i].getElementsByTagName('a');
+    for (var j = 0; j < linkList.length; j++) {
+      if (linkList[j].innerHTML === "") {
+        linkList[j].setAttribute('aria-hidden', 'true');
+      }
+    }
+  }
+});
diff --git a/docs/dev/articles/FOCUS_D_files/figure-html/plot-1.png b/docs/dev/articles/FOCUS_D_files/figure-html/plot-1.png
index 8ddca415..abf26715 100644
--- a/docs/dev/articles/FOCUS_D_files/figure-html/plot-1.png
+++ b/docs/dev/articles/FOCUS_D_files/figure-html/plot-1.png
diff --git a/docs/dev/articles/FOCUS_D_files/header-attrs-2.6/header-attrs.js b/docs/dev/articles/FOCUS_D_files/header-attrs-2.6/header-attrs.js
new file mode 100644
index 00000000..dd57d92e
--- /dev/null
+++ b/docs/dev/articles/FOCUS_D_files/header-attrs-2.6/header-attrs.js
@@ -0,0 +1,12 @@
+// Pandoc 2.9 adds attributes on both header and div. We remove the former (to
+// be compatible with the behavior of Pandoc < 2.8).
+document.addEventListener('DOMContentLoaded', function(e) {
+  var hs = document.querySelectorAll("div.section[class*='level'] > :first-child");
+  var i, h, a;
+  for (i = 0; i < hs.length; i++) {
+    h = hs[i];
+    if (!/^h[1-6]$/i.test(h.tagName)) continue;  // it should be a header h1-h6
+    a = h.attributes;
+    while (a.length > 0) h.removeAttribute(a[0].name);
+  }
+});
diff --git a/docs/dev/articles/FOCUS_L.html b/docs/dev/articles/FOCUS_L.html
index 2695db5e..547ec630 100644
--- a/docs/dev/articles/FOCUS_L.html
+++ b/docs/dev/articles/FOCUS_L.html
@@ -32,7 +32,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">0.9.50.4</span>
+        <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">1.0.3.9000</span>
       </span>
     </div>
 
@@ -81,7 +81,7 @@
 <ul class="nav navbar-nav navbar-right">
 <li>
   <a href="https://github.com/jranke/mkin/">
-    <span class="fab fa fab fa-github fa-lg"></span>
+    <span class="fab fa-github fa-lg"></span>
      
   </a>
 </li>
@@ -95,14 +95,13 @@
 
       
 
-      </header><link href="FOCUS_L_files/anchor-sections-1.0/anchor-sections.css" rel="stylesheet">
-<script src="FOCUS_L_files/anchor-sections-1.0/anchor-sections.js"></script><div class="row">
+      </header><script src="FOCUS_L_files/header-attrs-2.6/header-attrs.js"></script><script src="FOCUS_L_files/accessible-code-block-0.0.1/empty-anchor.js"></script><div class="row">
   <div class="col-md-9 contents">
     <div class="page-header toc-ignore">
       <h1 data-toc-skip>Example evaluation of FOCUS Laboratory Data L1 to L3</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2020-11-30</h4>
+            <h4 class="date">Last change 17 November 2016 (rebuilt 2021-02-15)</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/master/vignettes/FOCUS_L.rmd"><code>vignettes/FOCUS_L.rmd</code></a></small>
       <div class="hidden name"><code>FOCUS_L.rmd</code></div>
@@ -128,10 +127,10 @@
 <div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="va">m.L1.SFO</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="va">FOCUS_2006_L1_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>
 <span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html">summary</a></span><span class="op">(</span><span class="va">m.L1.SFO</span><span class="op">)</span></code></pre></div>
-<pre><code>## mkin version used for fitting:    0.9.50.4 
+<pre><code>## mkin version used for fitting:    1.0.3.9000 
 ## R version used for fitting:       4.0.3 
-## Date of fit:     Mon Nov 30 16:01:52 2020 
-## Date of summary: Mon Nov 30 16:01:52 2020 
+## Date of fit:     Mon Feb 15 17:13:39 2021 
+## Date of summary: Mon Feb 15 17:13:39 2021 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent * parent
@@ -234,17 +233,17 @@
 <pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
 <pre><code>## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
 ## doubtful</code></pre>
-<pre><code>## mkin version used for fitting:    0.9.50.4 
+<pre><code>## mkin version used for fitting:    1.0.3.9000 
 ## R version used for fitting:       4.0.3 
-## Date of fit:     Mon Nov 30 16:01:53 2020 
-## Date of summary: Mon Nov 30 16:01:53 2020 
+## Date of fit:     Mon Feb 15 17:13:40 2021 
+## Date of summary: Mon Feb 15 17:13:40 2021 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 380 model solutions performed in 0.087 s
+## Fitted using 369 model solutions performed in 0.084 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -272,22 +271,22 @@
 ## 
 ## Results:
 ## 
-##        AIC      BIC    logLik
-##   95.88778 99.44927 -43.94389
+##        AIC      BIC   logLik
+##   95.88781 99.44929 -43.9439
 ## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
 ##           Estimate Std. Error  Lower  Upper
 ## parent_0     92.47     1.2820 89.720 95.220
-## log_alpha    16.92        NaN    NaN    NaN
-## log_beta     19.26        NaN    NaN    NaN
-## sigma         2.78     0.4501  1.814  3.745
+## log_alpha    13.78        NaN    NaN    NaN
+## log_beta     16.13        NaN    NaN    NaN
+## sigma         2.78     0.4598  1.794  3.766
 ## 
 ## Parameter correlation:
-##           parent_0 log_alpha log_beta    sigma
-## parent_0  1.000000       NaN      NaN 0.002218
-## log_alpha      NaN         1      NaN      NaN
-## log_beta       NaN       NaN        1      NaN
-## sigma     0.002218       NaN      NaN 1.000000
+##            parent_0 log_alpha log_beta     sigma
+## parent_0  1.0000000       NaN      NaN 0.0001671
+## log_alpha       NaN         1      NaN       NaN
+## log_beta        NaN       NaN        1       NaN
+## sigma     0.0001671       NaN      NaN 1.0000000
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -295,9 +294,9 @@
 ## for estimators of untransformed parameters.
 ##           Estimate t value Pr(&gt;t)  Lower  Upper
 ## parent_0 9.247e+01      NA     NA 89.720 95.220
-## alpha    2.223e+07      NA     NA     NA     NA
-## beta     2.325e+08      NA     NA     NA     NA
-## sigma    2.780e+00      NA     NA  1.814  3.745
+## alpha    9.658e+05      NA     NA     NA     NA
+## beta     1.010e+07      NA     NA     NA     NA
+## sigma    2.780e+00      NA     NA  1.794  3.766
 ## 
 ## FOCUS Chi2 error levels in percent:
 ##          err.min n.optim df
@@ -346,10 +345,10 @@
 <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-9-1.png" width="672"></p>
 <div class="sourceCode" id="cb17"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html">summary</a></span><span class="op">(</span><span class="va">m.L2.FOMC</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></code></pre></div>
-<pre><code>## mkin version used for fitting:    0.9.50.4 
+<pre><code>## mkin version used for fitting:    1.0.3.9000 
 ## R version used for fitting:       4.0.3 
-## Date of fit:     Mon Nov 30 16:01:54 2020 
-## Date of summary: Mon Nov 30 16:01:54 2020 
+## Date of fit:     Mon Feb 15 17:13:40 2021 
+## Date of summary: Mon Feb 15 17:13:40 2021 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
@@ -391,10 +390,10 @@
 ## 
 ## Parameter correlation:
 ##             parent_0  log_alpha   log_beta      sigma
-## parent_0   1.000e+00 -1.151e-01 -2.085e-01 -7.436e-09
-## log_alpha -1.151e-01  1.000e+00  9.741e-01 -1.617e-07
-## log_beta  -2.085e-01  9.741e-01  1.000e+00 -1.386e-07
-## sigma     -7.436e-09 -1.617e-07 -1.386e-07  1.000e+00
+## parent_0   1.000e+00 -1.151e-01 -2.085e-01 -7.828e-09
+## log_alpha -1.151e-01  1.000e+00  9.741e-01 -1.602e-07
+## log_beta  -2.085e-01  9.741e-01  1.000e+00 -1.372e-07
+## sigma     -7.828e-09 -1.602e-07 -1.372e-07  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -427,10 +426,10 @@
 <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-10-1.png" width="672"></p>
 <div class="sourceCode" id="cb20"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html">summary</a></span><span class="op">(</span><span class="va">m.L2.DFOP</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></code></pre></div>
-<pre><code>## mkin version used for fitting:    0.9.50.4 
+<pre><code>## mkin version used for fitting:    1.0.3.9000 
 ## R version used for fitting:       4.0.3 
-## Date of fit:     Mon Nov 30 16:01:54 2020 
-## Date of summary: Mon Nov 30 16:01:54 2020 
+## Date of fit:     Mon Feb 15 17:13:41 2021 
+## Date of summary: Mon Feb 15 17:13:41 2021 
 ## 
 ## Equations:
 ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -439,7 +438,7 @@
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 581 model solutions performed in 0.136 s
+## Fitted using 581 model solutions performed in 0.134 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -470,18 +469,18 @@
 ## Optimised, transformed parameters with symmetric confidence intervals:
 ##          Estimate Std. Error      Lower     Upper
 ## parent_0   93.950  9.998e-01    91.5900   96.3100
-## log_k1      3.117  1.929e+03 -4558.0000 4564.0000
+## log_k1      3.112  1.842e+03 -4353.0000 4359.0000
 ## log_k2     -1.088  6.285e-02    -1.2370   -0.9394
 ## g_qlogis   -0.399  9.946e-02    -0.6342   -0.1638
 ## sigma       1.414  2.886e-01     0.7314    2.0960
 ## 
 ## Parameter correlation:
-##           parent_0     log_k1     log_k2   g_qlogis      sigma
-## parent_0 1.000e+00  6.459e-07  9.147e-11  2.665e-01  8.413e-11
-## log_k1   6.459e-07  1.000e+00  1.061e-04 -2.087e-04 -9.802e-06
-## log_k2   9.147e-11  1.061e-04  1.000e+00 -7.903e-01 -2.429e-09
-## g_qlogis 2.665e-01 -2.087e-04 -7.903e-01  1.000e+00  4.049e-09
-## sigma    8.413e-11 -9.802e-06 -2.429e-09  4.049e-09  1.000e+00
+##            parent_0     log_k1     log_k2   g_qlogis      sigma
+## parent_0  1.000e+00  6.783e-07 -3.390e-10  2.665e-01 -2.967e-10
+## log_k1    6.783e-07  1.000e+00  1.116e-04 -2.196e-04 -1.031e-05
+## log_k2   -3.390e-10  1.116e-04  1.000e+00 -7.903e-01  2.917e-09
+## g_qlogis  2.665e-01 -2.196e-04 -7.903e-01  1.000e+00 -4.408e-09
+## sigma    -2.967e-10 -1.031e-05  2.917e-09 -4.408e-09  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -489,7 +488,7 @@
 ## for estimators of untransformed parameters.
 ##          Estimate   t value    Pr(&gt;t)   Lower   Upper
 ## parent_0  93.9500 9.397e+01 2.036e-12 91.5900 96.3100
-## k1        22.5800 5.303e-04 4.998e-01  0.0000     Inf
+## k1        22.4800 5.553e-04 4.998e-01  0.0000     Inf
 ## k2         0.3369 1.591e+01 4.697e-07  0.2904  0.3909
 ## g          0.4016 1.680e+01 3.238e-07  0.3466  0.4591
 ## sigma      1.4140 4.899e+00 8.776e-04  0.7314  2.0960
@@ -501,7 +500,7 @@
 ## 
 ## Estimated disappearance times:
 ##          DT50  DT90 DT50back DT50_k1 DT50_k2
-## parent 0.5335 5.311    1.599  0.0307   2.058</code></pre>
+## parent 0.5335 5.311    1.599 0.03084   2.058</code></pre>
 <p>Here, the DFOP model is clearly the best-fit model for dataset L2 based on the chi^2 error level criterion. However, the failure to calculate the covariance matrix indicates that the parameter estimates correlate excessively. Therefore, the FOMC model may be preferred for this dataset.</p>
 </div>
 </div>
@@ -533,10 +532,10 @@
 <p>We can extract the summary and plot for <em>e.g.</em> the DFOP fit, using square brackets for indexing which will result in the use of the summary and plot functions working on mkinfit objects.</p>
 <div class="sourceCode" id="cb24"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html">summary</a></span><span class="op">(</span><span class="va">mm.L3</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="fl">1</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></code></pre></div>
-<pre><code>## mkin version used for fitting:    0.9.50.4 
+<pre><code>## mkin version used for fitting:    1.0.3.9000 
 ## R version used for fitting:       4.0.3 
-## Date of fit:     Mon Nov 30 16:01:55 2020 
-## Date of summary: Mon Nov 30 16:01:55 2020 
+## Date of fit:     Mon Feb 15 17:13:41 2021 
+## Date of summary: Mon Feb 15 17:13:42 2021 
 ## 
 ## Equations:
 ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -545,7 +544,7 @@
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 376 model solutions performed in 0.081 s
+## Fitted using 376 model solutions performed in 0.082 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -583,11 +582,11 @@
 ## 
 ## Parameter correlation:
 ##            parent_0     log_k1     log_k2   g_qlogis      sigma
-## parent_0  1.000e+00  1.732e-01  2.282e-02  4.009e-01 -9.671e-08
-## log_k1    1.732e-01  1.000e+00  4.945e-01 -5.809e-01  7.148e-07
+## parent_0  1.000e+00  1.732e-01  2.282e-02  4.009e-01 -9.664e-08
+## log_k1    1.732e-01  1.000e+00  4.945e-01 -5.809e-01  7.147e-07
 ## log_k2    2.282e-02  4.945e-01  1.000e+00 -6.812e-01  1.022e-06
-## g_qlogis  4.009e-01 -5.809e-01 -6.812e-01  1.000e+00 -7.929e-07
-## sigma    -9.671e-08  7.148e-07  1.022e-06 -7.929e-07  1.000e+00
+## g_qlogis  4.009e-01 -5.809e-01 -6.812e-01  1.000e+00 -7.926e-07
+## sigma    -9.664e-08  7.147e-07  1.022e-06 -7.926e-07  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -646,10 +645,10 @@
 <p>The <span class="math inline">\(\chi^2\)</span> error level of 3.3% as well as the plot suggest that the SFO model fits very well. The error level at which the <span class="math inline">\(\chi^2\)</span> test passes is slightly lower for the FOMC model. However, the difference appears negligible.</p>
 <div class="sourceCode" id="cb29"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html">summary</a></span><span class="op">(</span><span class="va">mm.L4</span><span class="op">[[</span><span class="st">"SFO"</span>, <span class="fl">1</span><span class="op">]</span><span class="op">]</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></code></pre></div>
-<pre><code>## mkin version used for fitting:    0.9.50.4 
+<pre><code>## mkin version used for fitting:    1.0.3.9000 
 ## R version used for fitting:       4.0.3 
-## Date of fit:     Mon Nov 30 16:01:55 2020 
-## Date of summary: Mon Nov 30 16:01:55 2020 
+## Date of fit:     Mon Feb 15 17:13:42 2021 
+## Date of summary: Mon Feb 15 17:13:42 2021 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent * parent
@@ -711,17 +710,17 @@
 ## parent  106  352</code></pre>
 <div class="sourceCode" id="cb31"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html">summary</a></span><span class="op">(</span><span class="va">mm.L4</span><span class="op">[[</span><span class="st">"FOMC"</span>, <span class="fl">1</span><span class="op">]</span><span class="op">]</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></code></pre></div>
-<pre><code>## mkin version used for fitting:    0.9.50.4 
+<pre><code>## mkin version used for fitting:    1.0.3.9000 
 ## R version used for fitting:       4.0.3 
-## Date of fit:     Mon Nov 30 16:01:55 2020 
-## Date of summary: Mon Nov 30 16:01:56 2020 
+## Date of fit:     Mon Feb 15 17:13:42 2021 
+## Date of summary: Mon Feb 15 17:13:42 2021 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 224 model solutions performed in 0.045 s
+## Fitted using 224 model solutions performed in 0.046 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -756,10 +755,10 @@
 ## 
 ## Parameter correlation:
 ##             parent_0  log_alpha   log_beta      sigma
-## parent_0   1.000e+00 -4.696e-01 -5.543e-01 -2.456e-07
-## log_alpha -4.696e-01  1.000e+00  9.889e-01  2.169e-08
-## log_beta  -5.543e-01  9.889e-01  1.000e+00  4.910e-08
-## sigma     -2.456e-07  2.169e-08  4.910e-08  1.000e+00
+## parent_0   1.000e+00 -4.696e-01 -5.543e-01 -2.468e-07
+## log_alpha -4.696e-01  1.000e+00  9.889e-01  2.478e-08
+## log_beta  -5.543e-01  9.889e-01  1.000e+00  5.211e-08
+## sigma     -2.468e-07  2.478e-08  5.211e-08  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -783,7 +782,7 @@
 <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="refs" class="references hanging-indent">
 <div id="ref-ranke2014">
 <p>Ranke, Johannes. 2014. “Prüfung und Validierung von Modellierungssoftware als Alternative zu ModelMaker 4.0.” Umweltbundesamt Projektnummer 27452.</p>
 </div>
diff --git a/docs/dev/articles/FOCUS_L_files/accessible-code-block-0.0.1/empty-anchor.js b/docs/dev/articles/FOCUS_L_files/accessible-code-block-0.0.1/empty-anchor.js
new file mode 100644
index 00000000..ca349fd6
--- /dev/null
+++ b/docs/dev/articles/FOCUS_L_files/accessible-code-block-0.0.1/empty-anchor.js
@@ -0,0 +1,15 @@
+// Hide empty <a> tag within highlighted CodeBlock for screen reader accessibility (see https://github.com/jgm/pandoc/issues/6352#issuecomment-626106786) -->
+// v0.0.1
+// Written by JooYoung Seo (jooyoung@psu.edu) and Atsushi Yasumoto on June 1st, 2020.
+
+document.addEventListener('DOMContentLoaded', function() {
+  const codeList = document.getElementsByClassName("sourceCode");
+  for (var i = 0; i < codeList.length; i++) {
+    var linkList = codeList[i].getElementsByTagName('a');
+    for (var j = 0; j < linkList.length; j++) {
+      if (linkList[j].innerHTML === "") {
+        linkList[j].setAttribute('aria-hidden', 'true');
+      }
+    }
+  }
+});
diff --git a/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-10-1.png b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-10-1.png
index 811c800e..e9c0b0a0 100644
--- a/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-10-1.png
+++ b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-10-1.png
diff --git a/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-12-1.png b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-12-1.png
index 4c02b097..3e03954d 100644
--- a/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-12-1.png
+++ b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-12-1.png
diff --git a/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-13-1.png b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-13-1.png
index 1aa97f8c..8c9e8fd4 100644
--- a/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-13-1.png
+++ b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-13-1.png
diff --git a/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-15-1.png b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-15-1.png
index 36e862f6..b3aa8334 100644
--- a/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-15-1.png
+++ b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-15-1.png
diff --git a/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-4-1.png b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-4-1.png
index 68b24b5e..477829a5 100644
--- a/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-4-1.png
+++ b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-4-1.png
diff --git a/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-6-1.png b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-6-1.png
index 53e33b68..c0e08884 100644
--- a/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-6-1.png
+++ b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-6-1.png
diff --git a/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-8-1.png b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-8-1.png
index 47d5b335..310b4f3b 100644
--- a/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-8-1.png
+++ b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-8-1.png
diff --git a/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-9-1.png b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-9-1.png
index f644c299..570f0026 100644
--- a/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-9-1.png
+++ b/docs/dev/articles/FOCUS_L_files/figure-html/unnamed-chunk-9-1.png
diff --git a/docs/dev/articles/FOCUS_L_files/header-attrs-2.6/header-attrs.js b/docs/dev/articles/FOCUS_L_files/header-attrs-2.6/header-attrs.js
new file mode 100644
index 00000000..dd57d92e
--- /dev/null
+++ b/docs/dev/articles/FOCUS_L_files/header-attrs-2.6/header-attrs.js
@@ -0,0 +1,12 @@
+// Pandoc 2.9 adds attributes on both header and div. We remove the former (to
+// be compatible with the behavior of Pandoc < 2.8).
+document.addEventListener('DOMContentLoaded', function(e) {
+  var hs = document.querySelectorAll("div.section[class*='level'] > :first-child");
+  var i, h, a;
+  for (i = 0; i < hs.length; i++) {
+    h = hs[i];
+    if (!/^h[1-6]$/i.test(h.tagName)) continue;  // it should be a header h1-h6
+    a = h.attributes;
+    while (a.length > 0) h.removeAttribute(a[0].name);
+  }
+});
diff --git a/docs/dev/articles/index.html b/docs/dev/articles/index.html
index 6daa6960..c0338df8 100644
--- a/docs/dev/articles/index.html
+++ b/docs/dev/articles/index.html
@@ -71,7 +71,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">0.9.50.4</span>
+        <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">1.1.0</span>
       </span>
     </div>
 
@@ -161,6 +161,8 @@
         <dd></dt>
         <dt><a href="web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a></dt>
         <dd></dt>
+        <dt><a href="web_only/dimethenamid_2018.html">Example evaluations of the dimethenamid data from 2018</a></dt>
+        <dd></dt>
       </dl>
     </div>
   </div>
diff --git a/docs/dev/articles/mkin.html b/docs/dev/articles/mkin.html
index 2de8b9f0..fed85a33 100644
--- a/docs/dev/articles/mkin.html
+++ b/docs/dev/articles/mkin.html
@@ -32,7 +32,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">0.9.50.4</span>
+        <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">1.0.3.9000</span>
       </span>
     </div>
 
@@ -81,7 +81,7 @@
 <ul class="nav navbar-nav navbar-right">
 <li>
   <a href="https://github.com/jranke/mkin/">
-    <span class="fab fa fab fa-github fa-lg"></span>
+    <span class="fab fa-github fa-lg"></span>
      
   </a>
 </li>
@@ -95,14 +95,13 @@
 
       
 
-      </header><link href="mkin_files/anchor-sections-1.0/anchor-sections.css" rel="stylesheet">
-<script src="mkin_files/anchor-sections-1.0/anchor-sections.js"></script><div class="row">
+      </header><script src="mkin_files/header-attrs-2.6/header-attrs.js"></script><script src="mkin_files/accessible-code-block-0.0.1/empty-anchor.js"></script><div class="row">
   <div class="col-md-9 contents">
     <div class="page-header toc-ignore">
       <h1 data-toc-skip>Introduction to mkin</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2020-11-30</h4>
+            <h4 class="date">Last change 15 February 2021 (rebuilt 2021-02-15)</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/master/vignettes/mkin.rmd"><code>vignettes/mkin.rmd</code></a></small>
       <div class="hidden name"><code>mkin.rmd</code></div>
@@ -150,28 +149,34 @@
 <div id="background" class="section level1">
 <h1 class="hasAnchor">
 <a href="#background" class="anchor"></a>Background</h1>
-<p>Many approaches are possible regarding the evaluation of chemical degradation data.</p>
-<p>The <code>mkin</code> package <span class="citation">(Ranke 2019)</span> implements the approach recommended in the kinetics report provided by the FOrum for Co-ordination of pesticide fate models and their USe <span class="citation">(FOCUS Work Group on Degradation Kinetics 2006, 2014)</span> for simple decline data series, data series with transformation products, commonly termed metabolites, and for data series for more than one compartment. It is also possible to include back reactions, so equilibrium reactions and equilibrium partitioning can be specified, although this oftentimes leads to an overparameterisation of the model.</p>
+<p>The <code>mkin</code> package <span class="citation">(Ranke 2021)</span> implements the approach to degradation kinetics recommended in the kinetics report provided by the FOrum for Co-ordination of pesticide fate models and their USe <span class="citation">(FOCUS Work Group on Degradation Kinetics 2006, 2014)</span>. It covers data series describing the decline of one compound, data series with transformation products (commonly termed metabolites) and data series for more than one compartment. It is possible to include back reactions. Therefore, equilibrium reactions and equilibrium partitioning can be specified, although this often leads to an overparameterisation of the model.</p>
 <p>When the first <code>mkin</code> code was published in 2010, the most commonly used tools for fitting more complex kinetic degradation models to experimental data were KinGUI <span class="citation">(Schäfer et al. 2007)</span>, a MATLAB based tool with a graphical user interface that was specifically tailored to the task and included some output as proposed by the FOCUS Kinetics Workgroup, and ModelMaker, a general purpose compartment based tool providing infrastructure for fitting dynamic simulation models based on differential equations to data.</p>
-<p>The code was first uploaded to the BerliOS platform. When this was taken down, the version control history was imported into the R-Forge site (see <em>e.g.</em> <a href="https://cgit.jrwb.de/mkin/commit/?id=30cbb4092f6d2d3beff5800603374a0d009ad770">the initial commit on 11 May 2010</a>), where the code is still occasionally updated.</p>
-<p>At that time, the R package <code>FME</code> (Flexible Modelling Environment) <span class="citation">(Soetaert and Petzoldt 2010)</span> was already available, and provided a good basis for developing a package specifically tailored to the task. The remaining challenge was to make it as easy as possible for the users (including the author of this vignette) to specify the system of differential equations and to include the output requested by the FOCUS guidance, such as the relative standard deviation that has to be assumed for the residuals, such that the <span class="math inline">\(\chi^2\)</span> goodness-of-fit test as defined by the FOCUS kinetics workgroup would pass using an significance level <span class="math inline">\(\alpha\)</span> of 0.05. This relative error, expressed as a percentage, is often termed <span class="math inline">\(\chi^2\)</span> error level or similar.</p>
-<p>Also, <code>mkin</code> introduced using analytical solutions for parent only kinetics for improved optimization speed. Later, Eigenvalue based solutions were introduced to <code>mkin</code> for the case of linear differential equations (<em>i.e.</em> where the FOMC or DFOP models were not used for the parent compound), greatly improving the optimization speed for these cases. This, however, has become somehow obsolete, as the use of compiled code described below gives even smaller execution times.</p>
+<p>The ‘mkin’ code was first uploaded to the BerliOS development platform. When this was taken down, the version control history was imported into the R-Forge site (see <em>e.g.</em> <a href="https://cgit.jrwb.de/mkin/commit/?id=30cbb4092f6d2d3beff5800603374a0d009ad770">the initial commit on 11 May 2010</a>), where the code is still being updated.</p>
+<p>At that time, the R package <code>FME</code> (Flexible Modelling Environment) <span class="citation">(Soetaert and Petzoldt 2010)</span> was already available, and provided a good basis for developing a package specifically tailored to the task. The remaining challenge was to make it as easy as possible for the users (including the author of this vignette) to specify the system of differential equations and to include the output requested by the FOCUS guidance, such as the <span class="math inline">\(\chi^2\)</span> error level as defined in this guidance.</p>
+<p>Also, <code>mkin</code> introduced using analytical solutions for parent only kinetics for improved optimization speed. Later, Eigenvalue based solutions were introduced to <code>mkin</code> for the case of linear differential equations (<em>i.e.</em> where the FOMC or DFOP models were not used for the parent compound), greatly improving the optimization speed for these cases. This, has become somehow obsolete, as the use of compiled code described below gives even faster execution times.</p>
 <p>The possibility to specify back-reactions and a biphasic model (SFORB) for metabolites were present in <code>mkin</code> from the very beginning.</p>
 <div id="derived-software-tools" class="section level2">
 <h2 class="hasAnchor">
 <a href="#derived-software-tools" class="anchor"></a>Derived software tools</h2>
-<p>Soon after the publication of <code>mkin</code>, two derived tools were published, namely KinGUII (available from Bayer Crop Science) and CAKE (commissioned to Tessella by Syngenta), which added a graphical user interface (GUI), and added fitting by iteratively reweighted least squares (IRLS) and characterisation of likely parameter distributions by Markov Chain Monte Carlo (MCMC) sampling.</p>
-<p>CAKE focuses on a smooth use experience, sacrificing some flexibility in the model definition, originally allowing only two primary metabolites in parallel. The current version 3.3 of CAKE release in March 2016 uses a basic scheme for up to six metabolites in a flexible arrangement, but does not support back-reactions (non-instantaneous equilibria) or biphasic kinetics for metabolites.</p>
+<p>Soon after the publication of <code>mkin</code>, two derived tools were published, namely KinGUII (developed at Bayer Crop Science) and CAKE (commissioned to Tessella by Syngenta), which added a graphical user interface (GUI), and added fitting by iteratively reweighted least squares (IRLS) and characterisation of likely parameter distributions by Markov Chain Monte Carlo (MCMC) sampling.</p>
+<p>CAKE focuses on a smooth use experience, sacrificing some flexibility in the model definition, originally allowing only two primary metabolites in parallel. The current version 3.4 of CAKE released in May 2020 uses a scheme for up to six metabolites in a flexible arrangement and supports biphasic modelling of metabolites, but does not support back-reactions (non-instantaneous equilibria).</p>
 <p>KinGUI offers an even more flexible widget for specifying complex kinetic models. Back-reactions (non-instantaneous equilibria) were supported early on, but until 2014, only simple first-order models could be specified for transformation products. Starting with KinGUII version 2.1, biphasic modelling of metabolites was also available in KinGUII.</p>
 <p>A further graphical user interface (GUI) that has recently been brought to a decent degree of maturity is the browser based GUI named <code>gmkin</code>. Please see its <a href="https://pkgdown.jrwb.de/gmkin/">documentation page</a> and <a href="https://pkgdown.jrwb.de/gmkin/articles/gmkin_manual.html">manual</a> for further information.</p>
 <p>A comparison of scope, usability and numerical results obtained with these tools has been recently been published by <span class="citation">Ranke, Wöltjen, and Meinecke (2018)</span>.</p>
 </div>
-<div id="recent-developments" class="section level2">
-<h2 class="hasAnchor">
-<a href="#recent-developments" class="anchor"></a>Recent developments</h2>
-<p>Currently (July 2019), the main features available in <code>mkin</code> which are not present in KinGUII or CAKE, are the speed increase by using compiled code when a compiler is present, parallel model fitting on multicore machines using the <code>mmkin</code> function, and the estimation of parameter confidence intervals based on transformed parameters.</p>
-<p>In addition, the possibility to use two alternative error models to constant variance have been integrated. The variance by variable error model introduced by <span class="citation">Gao et al. (2011)</span> has been available via an iteratively reweighted least squares (IRLS) procedure since mkin <a href="https://pkgdown.jrwb.de/mkin/news/index.html#mkin-0-9-22-2013-10-26">version 0.9-22</a>. With <a href="https://pkgdown.jrwb.de/mkin/news/index.html#mkin-0-9-49-5-2019-07-04">release 0.9.49.5</a>, the IRLS algorithm has been replaced by direct or step-wise maximisation of the likelihood function, which makes it possible not only to fit the variance by variable error model but also a <a href="https://pkgdown.jrwb.de/mkin/reference/sigma_twocomp.html">two-component error model</a> inspired by error models developed in analytical chemistry.</p>
 </div>
+<div id="unique-features" class="section level1">
+<h1 class="hasAnchor">
+<a href="#unique-features" class="anchor"></a>Unique features</h1>
+<p>Currently, the main unique features available in <code>mkin</code> are</p>
+<ul>
+<li>the <a href="https://pkgdown.jrwb.de/mkin/articles/web_only/compiled_models.html">speed increase</a> by using compiled code when a compiler is present,</li>
+<li>parallel model fitting on multicore machines using the <a href="https://pkgdown.jrwb.de/mkin/reference/mmkin.html"><code>mmkin</code> function</a>,</li>
+<li>the estimation of parameter confidence intervals based on transformed parameters (see below) and</li>
+<li>the possibility to use the <a href="https://pkgdown.jrwb.de/mkin/reference/sigma_twocomp.html">two-component error model</a>
+</li>
+</ul>
+<p>The iteratively reweighted least squares fitting of different variances for each variable as introduced by <span class="citation">Gao et al. (2011)</span> has been available in mkin since <a href="https://pkgdown.jrwb.de/mkin/news/index.html#mkin-0-9-22-2013-10-26">version 0.9-22</a>. With <a href="https://pkgdown.jrwb.de/mkin/news/index.html#mkin-0-9-49-5-2019-07-04">release 0.9.49.5</a>, the IRLS algorithm has been complemented by direct or step-wise maximisation of the likelihood function, which makes it possible not only to fit the variance by variable error model but also a <a href="https://pkgdown.jrwb.de/mkin/reference/sigma_twocomp.html">two-component error model</a> inspired by error models developed in analytical chemistry <span class="citation">(Ranke and Meinecke 2019)</span>.</p>
 </div>
 <div id="internal-parameter-transformations" class="section level1">
 <h1 class="hasAnchor">
@@ -179,13 +184,13 @@
 <p>For rate constants, the log transformation is used, as proposed by Bates and Watts <span class="citation">(1988, 77, 149)</span>. Approximate intervals are constructed for the transformed rate constants <span class="citation">(compare Bates and Watts 1988, 135)</span>, <em>i.e.</em> for their logarithms. Confidence intervals for the rate constants are then obtained using the appropriate backtransformation using the exponential function.</p>
 <p>In the first version of <code>mkin</code> allowing for specifying models using formation fractions, a home-made reparameterisation was used in order to ensure that the sum of formation fractions would not exceed unity.</p>
 <p>This method is still used in the current version of KinGUII (v2.1 from April 2014), with a modification that allows for fixing the pathway to sink to zero. CAKE uses penalties in the objective function in order to enforce this constraint.</p>
-<p>In 2012, an alternative reparameterisation of the formation fractions was proposed together with René Lehmann <span class="citation">(Ranke and Lehmann 2012)</span>, based on isometric logratio transformation (ILR). The aim was to improve the validity of the linear approximation of the objective function during the parameter estimation procedure as well as in the subsequent calculation of parameter confidence intervals.</p>
+<p>In 2012, an alternative reparameterisation of the formation fractions was proposed together with René Lehmann <span class="citation">(Ranke and Lehmann 2012)</span>, based on isometric logratio transformation (ILR). The aim was to improve the validity of the linear approximation of the objective function during the parameter estimation procedure as well as in the subsequent calculation of parameter confidence intervals. In the current version of mkin, a logit transformation is used for parameters that are bound between 0 and 1, such as the g parameter of the DFOP model.</p>
 <div id="confidence-intervals-based-on-transformed-parameters" class="section level2">
 <h2 class="hasAnchor">
 <a href="#confidence-intervals-based-on-transformed-parameters" class="anchor"></a>Confidence intervals based on transformed parameters</h2>
 <p>In the first attempt at providing improved parameter confidence intervals introduced to <code>mkin</code> in 2013, confidence intervals obtained from FME on the transformed parameters were simply all backtransformed one by one to yield asymmetric confidence intervals for the backtransformed parameters.</p>
 <p>However, while there is a 1:1 relation between the rate constants in the model and the transformed parameters fitted in the model, the parameters obtained by the isometric logratio transformation are calculated from the set of formation fractions that quantify the paths to each of the compounds formed from a specific parent compound, and no such 1:1 relation exists.</p>
-<p>Therefore, parameter confidence intervals for formation fractions obtained with this method only appear valid for the case of a single transformation product, where only one formation fraction is to be estimated, directly corresponding to one component of the ilr transformed parameter.</p>
+<p>Therefore, parameter confidence intervals for formation fractions obtained with this method only appear valid for the case of a single transformation product, where currently the logit transformation is used for the formation fraction.</p>
 <p>The confidence intervals obtained by backtransformation for the cases where a 1:1 relation between transformed and original parameter exist are considered by the author of this vignette to be more accurate than those obtained using a re-estimation of the Hessian matrix after backtransformation, as implemented in the FME package.</p>
 </div>
 <div id="parameter-t-test-based-on-untransformed-parameters" class="section level2">
@@ -200,36 +205,39 @@
 <h1 class="hasAnchor">
 <a href="#references" class="anchor"></a>References</h1>
 <!-- vim: set foldmethod=syntax: -->
-<div id="refs" class="references">
+<div id="refs" class="references hanging-indent">
 <div id="ref-bates1988">
 <p>Bates, D., and D. Watts. 1988. <em>Nonlinear Regression and Its Applications</em>. Wiley-Interscience.</p>
 </div>
 <div id="ref-FOCUS2006">
-<p>FOCUS Work Group on Degradation Kinetics. 2006. <em>Guidance Document on Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in Eu Registration. Report of the Focus Work Group on Degradation Kinetics</em>. <a href="http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics" class="uri">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>.</p>
+<p>FOCUS Work Group on Degradation Kinetics. 2006. <em>Guidance Document on Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in Eu Registration. Report of the Focus Work Group on Degradation Kinetics</em>. <a href="http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>.</p>
 </div>
 <div id="ref-FOCUSkinetics2014">
-<p>———. 2014. <em>Generic Guidance for Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in Eu Registration</em>. 1.1 ed. <a href="http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics" class="uri">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>.</p>
+<p>———. 2014. <em>Generic Guidance for Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in Eu Registration</em>. 1.1 ed. <a href="http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>.</p>
 </div>
 <div id="ref-gao11">
-<p>Gao, Z., J.W. Green, J. Vanderborght, and W. Schmitt. 2011. “Improving Uncertainty Analysis in Kinetic Evaluations Using Iteratively Reweighted Least Squares.” Journal. <em>Environmental Science and Technology</em> 45: 4429–37.</p>
+<p>Gao, Z., J. W. Green, J. Vanderborght, and W. Schmitt. 2011. “Improving Uncertainty Analysis in Kinetic Evaluations Using Iteratively Reweighted Least Squares.” Journal. <em>Environmental Science and Technology</em> 45: 4429–37.</p>
 </div>
 <div id="ref-pkg:mkin">
-<p>Ranke, J. 2019. <em>‘mkin‘: Kinetic Evaluation of Chemical Degradation Data</em>. <a href="https://CRAN.R-project.org/package=mkin" class="uri">https://CRAN.R-project.org/package=mkin</a>.</p>
+<p>Ranke, J. 2021. <em>‘mkin‘: Kinetic Evaluation of Chemical Degradation Data</em>. <a href="https://CRAN.R-project.org/package=mkin">https://CRAN.R-project.org/package=mkin</a>.</p>
 </div>
 <div id="ref-ranke2012">
 <p>Ranke, J., and R. Lehmann. 2012. “Parameter Reliability in Kinetic Evaluation of Environmental Metabolism Data - Assessment and the Influence of Model Specification.” In <em>SETAC World 20-24 May</em>. Berlin.</p>
 </div>
 <div id="ref-ranke2015">
-<p>———. 2015. “To T-Test or Not to T-Test, That Is the Question.” In <em>XV Symposium on Pesticide Chemistry 2-4 September 2015</em>. Piacenza. <a href="http://chem.uft.uni-bremen.de/ranke/posters/piacenza_2015.pdf" class="uri">http://chem.uft.uni-bremen.de/ranke/posters/piacenza_2015.pdf</a>.</p>
+<p>———. 2015. “To T-Test or Not to T-Test, That Is the Question.” In <em>XV Symposium on Pesticide Chemistry 2-4 September 2015</em>. Piacenza. <a href="http://chem.uft.uni-bremen.de/ranke/posters/piacenza_2015.pdf">http://chem.uft.uni-bremen.de/ranke/posters/piacenza_2015.pdf</a>.</p>
+</div>
+<div id="ref-ranke2019">
+<p>Ranke, Johannes, and Stefan Meinecke. 2019. “Error Models for the Kinetic Evaluation of Chemical Degradation Data.” <em>Environments</em> 6 (12). <a href="https://doi.org/10.3390/environments6120124">https://doi.org/10.3390/environments6120124</a>.</p>
 </div>
 <div id="ref-ranke2018">
-<p>Ranke, Johannes, Janina Wöltjen, and Stefan Meinecke. 2018. “Comparison of Software Tools for Kinetic Evaluation of Chemical Degradation Data.” <em>Environmental Sciences Europe</em> 30 (1): 17. <a href="https://doi.org/10.1186/s12302-018-0145-1" class="uri">https://doi.org/10.1186/s12302-018-0145-1</a>.</p>
+<p>Ranke, Johannes, Janina Wöltjen, and Stefan Meinecke. 2018. “Comparison of Software Tools for Kinetic Evaluation of Chemical Degradation Data.” <em>Environmental Sciences Europe</em> 30 (1): 17. <a href="https://doi.org/10.1186/s12302-018-0145-1">https://doi.org/10.1186/s12302-018-0145-1</a>.</p>
 </div>
 <div id="ref-schaefer2007">
 <p>Schäfer, D., B. Mikolasch, P. Rainbird, and B. Harvey. 2007. “KinGUI: A New Kinetic Software Tool for Evaluations According to FOCUS Degradation Kinetics.” In <em>Proceedings of the Xiii Symposium Pesticide Chemistry</em>, edited by Del Re A. A. M., Capri E., Fragoulis G., and Trevisan M., 916–23. Piacenza.</p>
 </div>
 <div id="ref-soetaert2010">
-<p>Soetaert, Karline, and Thomas Petzoldt. 2010. “Inverse Modelling, Sensitivity and Monte Carlo Analysis in R Using Package FME.” <em>Journal of Statistical Software</em> 33 (3): 1–28. <a href="https://www.jstatsoft.org/v33/i03/" class="uri">https://www.jstatsoft.org/v33/i03/</a>.</p>
+<p>Soetaert, Karline, and Thomas Petzoldt. 2010. “Inverse Modelling, Sensitivity and Monte Carlo Analysis in R Using Package FME.” <em>Journal of Statistical Software</em> 33 (3): 1–28. <a href="https://www.jstatsoft.org/v33/i03/">https://www.jstatsoft.org/v33/i03/</a>.</p>
 </div>
 </div>
 </div>
diff --git a/docs/dev/articles/mkin_files/accessible-code-block-0.0.1/empty-anchor.js b/docs/dev/articles/mkin_files/accessible-code-block-0.0.1/empty-anchor.js
new file mode 100644
index 00000000..ca349fd6
--- /dev/null
+++ b/docs/dev/articles/mkin_files/accessible-code-block-0.0.1/empty-anchor.js
@@ -0,0 +1,15 @@
+// Hide empty <a> tag within highlighted CodeBlock for screen reader accessibility (see https://github.com/jgm/pandoc/issues/6352#issuecomment-626106786) -->
+// v0.0.1
+// Written by JooYoung Seo (jooyoung@psu.edu) and Atsushi Yasumoto on June 1st, 2020.
+
+document.addEventListener('DOMContentLoaded', function() {
+  const codeList = document.getElementsByClassName("sourceCode");
+  for (var i = 0; i < codeList.length; i++) {
+    var linkList = codeList[i].getElementsByTagName('a');
+    for (var j = 0; j < linkList.length; j++) {
+      if (linkList[j].innerHTML === "") {
+        linkList[j].setAttribute('aria-hidden', 'true');
+      }
+    }
+  }
+});
diff --git a/docs/dev/articles/mkin_files/figure-html/unnamed-chunk-2-1.png b/docs/dev/articles/mkin_files/figure-html/unnamed-chunk-2-1.png
index 9b82cd62..bf38fdd7 100644
--- a/docs/dev/articles/mkin_files/figure-html/unnamed-chunk-2-1.png
+++ b/docs/dev/articles/mkin_files/figure-html/unnamed-chunk-2-1.png
diff --git a/docs/dev/articles/mkin_files/header-attrs-2.6/header-attrs.js b/docs/dev/articles/mkin_files/header-attrs-2.6/header-attrs.js
new file mode 100644
index 00000000..dd57d92e
--- /dev/null
+++ b/docs/dev/articles/mkin_files/header-attrs-2.6/header-attrs.js
@@ -0,0 +1,12 @@
+// Pandoc 2.9 adds attributes on both header and div. We remove the former (to
+// be compatible with the behavior of Pandoc < 2.8).
+document.addEventListener('DOMContentLoaded', function(e) {
+  var hs = document.querySelectorAll("div.section[class*='level'] > :first-child");
+  var i, h, a;
+  for (i = 0; i < hs.length; i++) {
+    h = hs[i];
+    if (!/^h[1-6]$/i.test(h.tagName)) continue;  // it should be a header h1-h6
+    a = h.attributes;
+    while (a.length > 0) h.removeAttribute(a[0].name);
+  }
+});
diff --git a/docs/dev/articles/twa.html b/docs/dev/articles/twa.html
index 42ed6fa5..30eeb5a6 100644
--- a/docs/dev/articles/twa.html
+++ b/docs/dev/articles/twa.html
@@ -32,7 +32,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">0.9.50.4</span>
+        <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">1.0.3.9000</span>
       </span>
     </div>
 
@@ -81,7 +81,7 @@
 <ul class="nav navbar-nav navbar-right">
 <li>
   <a href="https://github.com/jranke/mkin/">
-    <span class="fab fa fab fa-github fa-lg"></span>
+    <span class="fab fa-github fa-lg"></span>
      
   </a>
 </li>
@@ -95,14 +95,13 @@
 
       
 
-      </header><link href="twa_files/anchor-sections-1.0/anchor-sections.css" rel="stylesheet">
-<script src="twa_files/anchor-sections-1.0/anchor-sections.js"></script><div class="row">
+      </header><script src="twa_files/header-attrs-2.6/header-attrs.js"></script><script src="twa_files/accessible-code-block-0.0.1/empty-anchor.js"></script><div class="row">
   <div class="col-md-9 contents">
     <div class="page-header toc-ignore">
       <h1 data-toc-skip>Calculation of time weighted average concentrations with mkin</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2020-11-30</h4>
+            <h4 class="date">Last change 18 September 2019 (rebuilt 2021-02-15)</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/master/vignettes/twa.rmd"><code>vignettes/twa.rmd</code></a></small>
       <div class="hidden name"><code>twa.rmd</code></div>
@@ -143,9 +142,9 @@
   \frac{1}{k_1} \left( 1 - e^{- k_1 t_b} \right) +
   \frac{e^{- k_1 t_b}}{k_2} \left( 1 - e^{- k_2 (t - t_b)} \right)  \right) \]</span></p>
 <p>Note that a method for calculating maximum moving window time weighted average concentrations for a model fitted by ‘mkinfit’ or from parent decline model parameters is included in the <code><a href="../reference/max_twa_parent.html">max_twa_parent()</a></code> function. If the same is needed for metabolites, the function <code><a href="https://pkgdown.jrwb.de/pfm/reference/max_twa.html">pfm::max_twa()</a></code> from the ‘pfm’ package can be used.</p>
-<div id="refs" class="references">
+<div id="refs" class="references hanging-indent">
 <div id="ref-FOCUSkinetics2014">
-<p>FOCUS Work Group on Degradation Kinetics. 2014. <em>Generic Guidance for Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in Eu Registration</em>. 1.1 ed. <a href="http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics" class="uri">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>.</p>
+<p>FOCUS Work Group on Degradation Kinetics. 2014. <em>Generic Guidance for Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in Eu Registration</em>. 1.1 ed. <a href="http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>.</p>
 </div>
 </div>
   </div>
diff --git a/docs/dev/articles/twa_files/accessible-code-block-0.0.1/empty-anchor.js b/docs/dev/articles/twa_files/accessible-code-block-0.0.1/empty-anchor.js
new file mode 100644
index 00000000..ca349fd6
--- /dev/null
+++ b/docs/dev/articles/twa_files/accessible-code-block-0.0.1/empty-anchor.js
@@ -0,0 +1,15 @@
+// Hide empty <a> tag within highlighted CodeBlock for screen reader accessibility (see https://github.com/jgm/pandoc/issues/6352#issuecomment-626106786) -->
+// v0.0.1
+// Written by JooYoung Seo (jooyoung@psu.edu) and Atsushi Yasumoto on June 1st, 2020.
+
+document.addEventListener('DOMContentLoaded', function() {
+  const codeList = document.getElementsByClassName("sourceCode");
+  for (var i = 0; i < codeList.length; i++) {
+    var linkList = codeList[i].getElementsByTagName('a');
+    for (var j = 0; j < linkList.length; j++) {
+      if (linkList[j].innerHTML === "") {
+        linkList[j].setAttribute('aria-hidden', 'true');
+      }
+    }
+  }
+});
diff --git a/docs/dev/articles/twa_files/header-attrs-2.6/header-attrs.js b/docs/dev/articles/twa_files/header-attrs-2.6/header-attrs.js
new file mode 100644
index 00000000..dd57d92e
--- /dev/null
+++ b/docs/dev/articles/twa_files/header-attrs-2.6/header-attrs.js
@@ -0,0 +1,12 @@
+// Pandoc 2.9 adds attributes on both header and div. We remove the former (to
+// be compatible with the behavior of Pandoc < 2.8).
+document.addEventListener('DOMContentLoaded', function(e) {
+  var hs = document.querySelectorAll("div.section[class*='level'] > :first-child");
+  var i, h, a;
+  for (i = 0; i < hs.length; i++) {
+    h = hs[i];
+    if (!/^h[1-6]$/i.test(h.tagName)) continue;  // it should be a header h1-h6
+    a = h.attributes;
+    while (a.length > 0) h.removeAttribute(a[0].name);
+  }
+});
diff --git a/docs/dev/articles/web_only/FOCUS_Z.html b/docs/dev/articles/web_only/FOCUS_Z.html
index 15c41eb7..694b33ca 100644
--- a/docs/dev/articles/web_only/FOCUS_Z.html
+++ b/docs/dev/articles/web_only/FOCUS_Z.html
@@ -32,7 +32,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../../index.html">mkin</a>
-        <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">0.9.50.4</span>
+        <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">1.0.3.9000</span>
       </span>
     </div>
 
@@ -81,7 +81,7 @@
 <ul class="nav navbar-nav navbar-right">
 <li>
   <a href="https://github.com/jranke/mkin/">
-    <span class="fab fa fab fa-github fa-lg"></span>
+    <span class="fab fa-github fa-lg"></span>
      
   </a>
 </li>
@@ -95,14 +95,13 @@
 
       
 
-      </header><link href="FOCUS_Z_files/anchor-sections-1.0/anchor-sections.css" rel="stylesheet">
-<script src="FOCUS_Z_files/anchor-sections-1.0/anchor-sections.js"></script><div class="row">
+      </header><script src="FOCUS_Z_files/header-attrs-2.6/header-attrs.js"></script><script src="FOCUS_Z_files/accessible-code-block-0.0.1/empty-anchor.js"></script><div class="row">
   <div class="col-md-9 contents">
     <div class="page-header toc-ignore">
       <h1 data-toc-skip>Example evaluation of FOCUS dataset Z</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2020-11-30</h4>
+            <h4 class="date">Last change 16 January 2018 (rebuilt 2021-02-15)</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/master/vignettes/web_only/FOCUS_Z.rmd"><code>vignettes/web_only/FOCUS_Z.rmd</code></a></small>
       <div class="hidden name"><code>FOCUS_Z.rmd</code></div>
@@ -239,12 +238,12 @@
 <div class="sourceCode" id="cb34"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html">summary</a></span><span class="op">(</span><span class="va">m.Z.FOCUS</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">$</span><span class="va">bpar</span></code></pre></div>
 <pre><code>##             Estimate se_notrans t value     Pr(&gt;t)     Lower      Upper
-## Z0_0       96.839001   1.994273 48.5585 4.0276e-42 92.827060 100.850943
-## k_Z0        2.215367   0.118456 18.7021 1.0410e-23  1.989432   2.466960
-## k_Z1        0.478310   0.028258 16.9265 6.2430e-22  0.424712   0.538673
-## k_Z2        0.451628   0.042139 10.7176 1.6313e-14  0.374337   0.544877
-## k_Z3        0.058692   0.015245  3.8498 1.7806e-04  0.034806   0.098972
-## f_Z2_to_Z3  0.471498   0.058350  8.0805 9.6614e-11  0.357741   0.588294
+## Z0_0       96.838822   1.994274 48.5584 4.0280e-42 92.826981 100.850664
+## k_Z0        2.215393   0.118458 18.7019 1.0413e-23  1.989456   2.466989
+## k_Z1        0.478305   0.028258 16.9266 6.2418e-22  0.424708   0.538666
+## k_Z2        0.451627   0.042139 10.7176 1.6314e-14  0.374339   0.544872
+## k_Z3        0.058692   0.015245  3.8499 1.7803e-04  0.034808   0.098965
+## f_Z2_to_Z3  0.471502   0.058351  8.0805 9.6608e-11  0.357769   0.588274
 ## sigma       3.984431   0.383402 10.3923 4.5575e-14  3.213126   4.755736</code></pre>
 <div class="sourceCode" id="cb36"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="../../reference/endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">m.Z.FOCUS</span><span class="op">)</span></code></pre></div>
@@ -255,9 +254,9 @@
 ## $distimes
 ##        DT50    DT90
 ## Z0  0.31288  1.0394
-## Z1  1.44916  4.8140
+## Z1  1.44917  4.8141
 ## Z2  1.53478  5.0984
-## Z3 11.80983 39.2314</code></pre>
+## Z3 11.80986 39.2315</code></pre>
 <p>This fit corresponds to the final result chosen in Appendix 7 of the FOCUS report. Confidence intervals returned by mkin are based on internally transformed parameters, however.</p>
 </div>
 <div id="using-the-sforb-model" class="section level1">
@@ -353,13 +352,13 @@
 ## 
 ## $SFORB
 ##     Z0_b1     Z0_b2     Z3_b1     Z3_b2 
-## 2.4471371 0.0075126 0.0800070 0.0000000 
+## 2.4471322 0.0075125 0.0800069 0.0000000 
 ## 
 ## $distimes
 ##      DT50   DT90 DT50back DT50_Z0_b1 DT50_Z0_b2 DT50_Z3_b1 DT50_Z3_b2
-## Z0 0.3043 1.1848  0.35666    0.28325     92.265         NA         NA
+## Z0 0.3043 1.1848  0.35666    0.28325     92.266         NA         NA
 ## Z1 1.5148 5.0320       NA         NA         NA         NA         NA
-## Z2 1.6414 5.4525       NA         NA         NA         NA         NA
+## Z2 1.6414 5.4526       NA         NA         NA         NA         NA
 ## Z3     NA     NA       NA         NA         NA     8.6636        Inf</code></pre>
 <p>It is clear the degradation rate of Z3 towards the end of the experiment is very low as DT50_Z3_b2 (the second Eigenvalue of the system of two differential equations representing the SFORB system for Z3, corresponding to the slower rate constant of the DFOP model) is reported to be infinity. However, this appears to be a feature of the data.</p>
 </div>
@@ -367,9 +366,9 @@
 <h1 class="hasAnchor">
 <a href="#references" class="anchor"></a>References</h1>
 <!-- vim: set foldmethod=syntax: -->
-<div id="refs" class="references">
+<div id="refs" class="references hanging-indent">
 <div id="ref-FOCUSkinetics2014">
-<p>FOCUS Work Group on Degradation Kinetics. 2014. <em>Generic Guidance for Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in Eu Registration</em>. 1.1 ed. <a href="http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics" class="uri">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>.</p>
+<p>FOCUS Work Group on Degradation Kinetics. 2014. <em>Generic Guidance for Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in Eu Registration</em>. 1.1 ed. <a href="http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>.</p>
 </div>
 </div>
 </div>
diff --git a/docs/dev/articles/web_only/FOCUS_Z_files/accessible-code-block-0.0.1/empty-anchor.js b/docs/dev/articles/web_only/FOCUS_Z_files/accessible-code-block-0.0.1/empty-anchor.js
new file mode 100644
index 00000000..ca349fd6
--- /dev/null
+++ b/docs/dev/articles/web_only/FOCUS_Z_files/accessible-code-block-0.0.1/empty-anchor.js
@@ -0,0 +1,15 @@
+// Hide empty <a> tag within highlighted CodeBlock for screen reader accessibility (see https://github.com/jgm/pandoc/issues/6352#issuecomment-626106786) -->
+// v0.0.1
+// Written by JooYoung Seo (jooyoung@psu.edu) and Atsushi Yasumoto on June 1st, 2020.
+
+document.addEventListener('DOMContentLoaded', function() {
+  const codeList = document.getElementsByClassName("sourceCode");
+  for (var i = 0; i < codeList.length; i++) {
+    var linkList = codeList[i].getElementsByTagName('a');
+    for (var j = 0; j < linkList.length; j++) {
+      if (linkList[j].innerHTML === "") {
+        linkList[j].setAttribute('aria-hidden', 'true');
+      }
+    }
+  }
+});
diff --git a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png
index 575def46..2213c446 100644
--- a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png
+++ b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png
diff --git a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png
index 22305ab1..61b04d3a 100644
--- a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png
+++ b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png
diff --git a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png
index 2213f493..409f1203 100644
--- a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png
+++ b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png
diff --git a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png
index fc5e5556..4d6820cd 100644
--- a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png
+++ b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png
diff --git a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png
index 5c29341c..2e504961 100644
--- a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png
+++ b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png
diff --git a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png
index 575def46..2213c446 100644
--- a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png
+++ b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png
diff --git a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png
index 98ce34a7..7ab743af 100644
--- a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png
+++ b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png
diff --git a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png
index d04a411e..2e0dce77 100644
--- a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png
+++ b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png
diff --git a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png
index 29a74490..458299c1 100644
--- a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png
+++ b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png
diff --git a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png
index 0acfa2a4..eb833066 100644
--- a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png
+++ b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png
diff --git a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png
index ca191b00..e7501cbb 100644
--- a/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png
+++ b/docs/dev/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png
diff --git a/docs/dev/articles/web_only/FOCUS_Z_files/header-attrs-2.6/header-attrs.js b/docs/dev/articles/web_only/FOCUS_Z_files/header-attrs-2.6/header-attrs.js
new file mode 100644
index 00000000..dd57d92e
--- /dev/null
+++ b/docs/dev/articles/web_only/FOCUS_Z_files/header-attrs-2.6/header-attrs.js
@@ -0,0 +1,12 @@
+// Pandoc 2.9 adds attributes on both header and div. We remove the former (to
+// be compatible with the behavior of Pandoc < 2.8).
+document.addEventListener('DOMContentLoaded', function(e) {
+  var hs = document.querySelectorAll("div.section[class*='level'] > :first-child");
+  var i, h, a;
+  for (i = 0; i < hs.length; i++) {
+    h = hs[i];
+    if (!/^h[1-6]$/i.test(h.tagName)) continue;  // it should be a header h1-h6
+    a = h.attributes;
+    while (a.length > 0) h.removeAttribute(a[0].name);
+  }
+});
diff --git a/docs/dev/articles/web_only/NAFTA_examples.html b/docs/dev/articles/web_only/NAFTA_examples.html
index fca15672..b9784415 100644
--- a/docs/dev/articles/web_only/NAFTA_examples.html
+++ b/docs/dev/articles/web_only/NAFTA_examples.html
@@ -32,7 +32,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../../index.html">mkin</a>
-        <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">0.9.50.4</span>
+        <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">1.0.3.9000</span>
       </span>
     </div>
 
@@ -81,7 +81,7 @@
 <ul class="nav navbar-nav navbar-right">
 <li>
   <a href="https://github.com/jranke/mkin/">
-    <span class="fab fa fab fa-github fa-lg"></span>
+    <span class="fab fa-github fa-lg"></span>
      
   </a>
 </li>
@@ -95,14 +95,13 @@
 
       
 
-      </header><link href="NAFTA_examples_files/anchor-sections-1.0/anchor-sections.css" rel="stylesheet">
-<script src="NAFTA_examples_files/anchor-sections-1.0/anchor-sections.js"></script><div class="row">
+      </header><script src="NAFTA_examples_files/header-attrs-2.6/header-attrs.js"></script><script src="NAFTA_examples_files/accessible-code-block-0.0.1/empty-anchor.js"></script><div class="row">
   <div class="col-md-9 contents">
     <div class="page-header toc-ignore">
       <h1 data-toc-skip>Evaluation of example datasets from Attachment 1 to the US EPA SOP for the NAFTA guidance</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2020-11-30</h4>
+            <h4 class="date">26 February 2019 (rebuilt 2021-02-15)</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/master/vignettes/web_only/NAFTA_examples.rmd"><code>vignettes/web_only/NAFTA_examples.rmd</code></a></small>
       <div class="hidden name"><code>NAFTA_examples.rmd</code></div>
@@ -158,7 +157,7 @@
 ##          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       2.42e-12 5.00e-01  0.0000      Inf
+## k2       2.26e-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
 ## 
@@ -167,7 +166,7 @@
 ##      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 5.22e+11 2.86e+11
+## DFOP 55.5 5.59e+11 3.07e+11
 ## 
 ## Representative half-life:
 ## [1] 321.51</code></pre>
@@ -209,7 +208,7 @@
 ##          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       1.10e-11 5.00e-01  0.0000     Inf
+## k2       8.63e-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
 ## 
@@ -218,7 +217,7 @@
 ##      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 1.03e+11 6.29e+10
+## DFOP 83.6 1.32e+11 8.04e+10
 ## 
 ## Representative half-life:
 ## [1] 215.87</code></pre>
@@ -260,7 +259,7 @@
 ##          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       3.60e-11 5.00e-01  0.0000     Inf
+## k2       3.22e-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
 ## 
@@ -269,7 +268,7 @@
 ##      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 9.07e+09 1.93e+10
+## DFOP 34.1 1.01e+10 2.15e+10
 ## 
 ## Representative half-life:
 ## [1] 53.17</code></pre>
@@ -311,7 +310,7 @@
 ##          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       2.89e-10 5.00e-01  0.0000      Inf
+## k2       3.63e-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
 ## 
@@ -320,7 +319,7 @@
 ##      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 4.75e+09 2.40e+09
+## DFOP 96.4 3.77e+09 1.91e+09
 ## 
 ## Representative half-life:
 ## [1] 454.55</code></pre>
@@ -422,7 +421,7 @@
 ##          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       9.03e-13 5.00e-01  0.000    Inf
+## k2       9.02e-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
 ## 
@@ -431,7 +430,7 @@
 ##      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 1.38e+12 7.67e+11
+## DFOP 10.5 1.38e+12 7.69e+11
 ## 
 ## Representative half-life:
 ## [1] 101.43</code></pre>
@@ -443,15 +442,16 @@
 <div class="sourceCode" id="cb37"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="va">p9b</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p9b"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></code></pre></div>
 <pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
+<pre><code>## Warning in sqrt(diag(covar_notrans)): NaNs produced</code></pre>
 <pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
 <pre><code>## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
 ## doubtful</code></pre>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb43"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb44"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-method.html">plot</a></span><span class="op">(</span><span class="va">p9b</span><span class="op">)</span></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p9b-1.png" width="700"></p>
-<div class="sourceCode" id="cb44"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb45"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p9b</span><span class="op">)</span></code></pre></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
@@ -475,12 +475,12 @@
 ## sigma             1.288 1.76e-04  0.7456  1.830
 ## 
 ## $DFOP
-##          Estimate Pr(&gt;t)   Lower   Upper
-## parent_0  94.7123     NA 93.1355 96.2891
-## k1         0.0389     NA  0.0266  0.0569
-## k2         0.0389     NA  0.0255  0.0592
-## g          0.5256     NA      NA      NA
-## sigma      1.5957     NA  0.9135  2.2779
+##          Estimate   Pr(&gt;t)   Lower   Upper
+## parent_0  94.7123 1.61e-16 93.1355 96.2891
+## k1         0.0389 1.08e-04  0.0266  0.0569
+## k2         0.0389 2.23e-04  0.0255  0.0592
+## g          0.5256      NaN      NA      NA
+## sigma      1.5957 2.50e-04  0.9135  2.2779
 ## 
 ## 
 ## DTx values:
@@ -496,15 +496,18 @@
 <div id="example-on-page-10" class="section level2">
 <h2 class="hasAnchor">
 <a href="#example-on-page-10" class="anchor"></a>Example on page 10</h2>
-<div class="sourceCode" id="cb46"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb47"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="va">p10</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p10"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></code></pre></div>
-<pre><code>## Warning in sqrt(diag(covar_notrans)): NaNs produced</code></pre>
+<pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
+<pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
+<pre><code>## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
+## doubtful</code></pre>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb50"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb53"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-method.html">plot</a></span><span class="op">(</span><span class="va">p10</span><span class="op">)</span></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p10-1.png" width="700"></p>
-<div class="sourceCode" id="cb51"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb54"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p10</span><span class="op">)</span></code></pre></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
@@ -530,9 +533,9 @@
 ## $DFOP
 ##          Estimate   Pr(&gt;t)   Lower    Upper
 ## parent_0 101.7315 1.41e-09 91.6534 111.8097
-## k1         0.0495 5.63e-03  0.0240   0.1020
-## k2         0.0495 1.93e-03  0.0272   0.0903
-## g          0.4487      NaN  0.0000   1.0000
+## k1         0.0495 6.58e-03  0.0303   0.0809
+## k2         0.0495 2.60e-03  0.0410   0.0598
+## g          0.4487 5.00e-01      NA       NA
 ## sigma      8.0152 2.50e-04  4.5886  11.4418
 ## 
 ## 
@@ -553,14 +556,14 @@
 <div id="example-on-page-11" class="section level2">
 <h2 class="hasAnchor">
 <a href="#example-on-page-11" class="anchor"></a>Example on page 11</h2>
-<div class="sourceCode" id="cb53"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb56"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="va">p11</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p11"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></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="cb56"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb59"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-method.html">plot</a></span><span class="op">(</span><span class="va">p11</span><span class="op">)</span></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p11-1.png" width="700"></p>
-<div class="sourceCode" id="cb57"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb60"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p11</span><span class="op">)</span></code></pre></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
@@ -596,10 +599,10 @@
 ##          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 3.07e+11 1.93e+12 6.97e+11
+## DFOP 3.07e+11 1.93e+12 6.98e+11
 ## 
 ## Representative half-life:
-## [1] 41148171</code></pre>
+## [1] 41148170</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>
@@ -610,19 +613,21 @@
 <div id="example-on-page-12-upper-panel" class="section level2">
 <h2 class="hasAnchor">
 <a href="#example-on-page-12-upper-panel" class="anchor"></a>Example on page 12, upper panel</h2>
-<div class="sourceCode" id="cb59"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb62"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="va">p12a</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p12a"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></code></pre></div>
 <pre><code>## Warning in summary.mkinfit(x): Could not calculate correlation; no covariance
-## matrix
-
-## Warning in summary.mkinfit(x): Could not calculate correlation; no covariance
 ## matrix</code></pre>
+<pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
+<pre><code>## Warning in sqrt(diag(covar_notrans)): NaNs produced</code></pre>
+<pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
+<pre><code>## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
+## doubtful</code></pre>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb63"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb70"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-method.html">plot</a></span><span class="op">(</span><span class="va">p12a</span><span class="op">)</span></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p12a-1.png" width="700"></p>
-<div class="sourceCode" id="cb64"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb71"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p12a</span><span class="op">)</span></code></pre></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
@@ -646,12 +651,12 @@
 ## sigma             3.965     NA    NA    NA
 ## 
 ## $DFOP
-##          Estimate   Pr(&gt;t) Lower Upper
-## parent_0  100.521 2.74e-10    NA    NA
-## k1          0.124 2.53e-05    NA    NA
-## k2          0.124 2.52e-02    NA    NA
-## g           0.793 5.00e-01    NA    NA
-## sigma       7.048 2.50e-04    NA    NA
+##          Estimate   Pr(&gt;t)   Lower   Upper
+## parent_0  100.521 2.74e-10 92.2366 108.805
+## k1          0.124 2.53e-05  0.0908   0.170
+## k2          0.124 2.52e-02  0.0456   0.339
+## g           0.793      NaN      NA      NA
+## sigma       7.048 2.50e-04  4.0349  10.061
 ## 
 ## 
 ## DTx values:
@@ -666,20 +671,18 @@
 <div id="example-on-page-12-lower-panel" class="section level2">
 <h2 class="hasAnchor">
 <a href="#example-on-page-12-lower-panel" class="anchor"></a>Example on page 12, lower panel</h2>
-<div class="sourceCode" id="cb66"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb73"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="va">p12b</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p12b"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></code></pre></div>
-<pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
 <pre><code>## Warning in qt(alpha/2, rdf): NaNs produced</code></pre>
 <pre><code>## Warning in qt(1 - alpha/2, rdf): NaNs produced</code></pre>
-<pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
-<pre><code>## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
-## doubtful</code></pre>
+<pre><code>## Warning in sqrt(diag(covar_notrans)): NaNs produced</code></pre>
+<pre><code>## Warning in pt(abs(tval), rdf, lower.tail = FALSE): NaNs produced</code></pre>
 <pre><code>## 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="cb74"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb80"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-method.html">plot</a></span><span class="op">(</span><span class="va">p12b</span><span class="op">)</span></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p12b-1.png" width="700"></p>
-<div class="sourceCode" id="cb75"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb81"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p12b</span><span class="op">)</span></code></pre></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
@@ -704,11 +707,11 @@
 ## 
 ## $DFOP
 ##          Estimate Pr(&gt;t) Lower Upper
-## parent_0  97.6840     NA   NaN   NaN
-## k1         0.0589     NA    NA    NA
-## k2         0.0589     NA    NA    NA
-## g          0.6473     NA    NA    NA
-## sigma      3.4323     NA   NaN   NaN
+## parent_0  97.6840    NaN   NaN   NaN
+## k1         0.0589    NaN    NA    NA
+## k2         0.0589    NaN    NA    NA
+## g          0.6473    NaN    NA    NA
+## sigma      3.4323    NaN   NaN   NaN
 ## 
 ## 
 ## DTx values:
@@ -723,18 +726,14 @@
 <div id="example-on-page-13" class="section level2">
 <h2 class="hasAnchor">
 <a href="#example-on-page-13" class="anchor"></a>Example on page 13</h2>
-<div class="sourceCode" id="cb77"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb83"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="va">p13</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p13"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></code></pre></div>
-<pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
-<pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
-<pre><code>## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
-## doubtful</code></pre>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb83"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb86"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-method.html">plot</a></span><span class="op">(</span><span class="va">p13</span><span class="op">)</span></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p13-1.png" width="700"></p>
-<div class="sourceCode" id="cb84"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb87"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p13</span><span class="op">)</span></code></pre></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
@@ -760,9 +759,9 @@
 ## $DFOP
 ##          Estimate Pr(&gt;t)    Lower    Upper
 ## parent_0 92.73500     NA 8.95e+01 95.92118
-## k1        0.00258     NA 4.25e-04  0.01569
-## k2        0.00258     NA 1.76e-03  0.00379
-## g         0.16452     NA       NA       NA
+## k1        0.00258     NA 4.14e-04  0.01611
+## k2        0.00258     NA 1.74e-03  0.00383
+## g         0.16452     NA 0.00e+00  1.00000
 ## sigma     3.41172     NA 2.02e+00  4.79960
 ## 
 ## 
@@ -779,7 +778,7 @@
 <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="cb86"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb89"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="va">p14</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p14"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></code></pre></div>
 <pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
 <pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
@@ -787,10 +786,10 @@
 ## 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="cb92"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb95"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-method.html">plot</a></span><span class="op">(</span><span class="va">p14</span><span class="op">)</span></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p14-1.png" width="700"></p>
-<div class="sourceCode" id="cb93"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb96"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p14</span><span class="op">)</span></code></pre></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
@@ -817,7 +816,7 @@
 ##          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       5.33e-12 5.00e-01  0.00000      Inf
+## k2       6.08e-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
 ## 
@@ -826,7 +825,7 @@
 ##          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 3.48e+10 3.37e+11 1.30e+11
+## DFOP 3.05e+10 2.95e+11 1.14e+11
 ## 
 ## Representative half-life:
 ## [1] 6697.44</code></pre>
@@ -835,14 +834,14 @@
 <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="cb95"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb98"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="va">p15a</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p15a"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></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="cb98"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb101"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-method.html">plot</a></span><span class="op">(</span><span class="va">p15a</span><span class="op">)</span></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p15a-1.png" width="700"></p>
-<div class="sourceCode" id="cb99"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb102"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p15a</span><span class="op">)</span></code></pre></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
@@ -866,12 +865,12 @@
 ## sigma             3.105 1.78e-04  1.795  4.416
 ## 
 ## $DFOP
-##          Estimate Pr(&gt;t)    Lower    Upper
-## parent_0 97.96751     NA 94.21913 101.7159
-## k1        0.00952     NA  0.00221   0.0411
-## k2        0.00952     NA  0.00626   0.0145
-## g         0.21241     NA  0.00000   1.0000
-## sigma     4.18778     NA  2.39747   5.9781
+##          Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0 97.96751 2.85e-13 94.21913 101.7159
+## k1        0.00952 6.28e-02  0.00250   0.0363
+## k2        0.00952 1.27e-04  0.00646   0.0140
+## g         0.21241 5.00e-01  0.00000   1.0000
+## sigma     4.18778 2.50e-04  2.39747   5.9781
 ## 
 ## 
 ## DTx values:
@@ -882,7 +881,7 @@
 ## 
 ## Representative half-life:
 ## [1] 41.33</code></pre>
-<div class="sourceCode" id="cb101"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb104"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="va">p15b</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p15b"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></code></pre></div>
 <pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
 <pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
@@ -890,10 +889,10 @@
 ## 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="cb107"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb110"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-method.html">plot</a></span><span class="op">(</span><span class="va">p15b</span><span class="op">)</span></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p15b-1.png" width="700"></p>
-<div class="sourceCode" id="cb108"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb111"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p15b</span><span class="op">)</span></code></pre></div>
 <pre><code>## Sums of squares:
 ##       SFO      IORE      DFOP 
@@ -911,7 +910,7 @@
 ## 
 ## $IORE
 ##                Estimate   Pr(&gt;t)    Lower  Upper
-## parent_0          99.83 1.81e-16 97.51348 102.14
+## parent_0          99.83 1.81e-16 97.51349 102.14
 ## k__iore_parent     0.38 3.22e-01  0.00352  41.05
 ## N_parent           0.00 5.00e-01 -1.07696   1.08
 ## sigma              2.21 2.57e-04  1.23245   3.19
@@ -938,16 +937,16 @@
 <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="cb110"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb113"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="va">p16</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p16"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></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="cb115"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb118"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-method.html">plot</a></span><span class="op">(</span><span class="va">p16</span><span class="op">)</span></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p16-1.png" width="700"></p>
-<div class="sourceCode" id="cb116"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb119"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p16</span><span class="op">)</span></code></pre></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
@@ -998,7 +997,7 @@
 <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="refs" class="references hanging-indent">
 <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>
diff --git a/docs/dev/articles/web_only/NAFTA_examples_files/accessible-code-block-0.0.1/empty-anchor.js b/docs/dev/articles/web_only/NAFTA_examples_files/accessible-code-block-0.0.1/empty-anchor.js
new file mode 100644
index 00000000..ca349fd6
--- /dev/null
+++ b/docs/dev/articles/web_only/NAFTA_examples_files/accessible-code-block-0.0.1/empty-anchor.js
@@ -0,0 +1,15 @@
+// Hide empty <a> tag within highlighted CodeBlock for screen reader accessibility (see https://github.com/jgm/pandoc/issues/6352#issuecomment-626106786) -->
+// v0.0.1
+// Written by JooYoung Seo (jooyoung@psu.edu) and Atsushi Yasumoto on June 1st, 2020.
+
+document.addEventListener('DOMContentLoaded', function() {
+  const codeList = document.getElementsByClassName("sourceCode");
+  for (var i = 0; i < codeList.length; i++) {
+    var linkList = codeList[i].getElementsByTagName('a');
+    for (var j = 0; j < linkList.length; j++) {
+      if (linkList[j].innerHTML === "") {
+        linkList[j].setAttribute('aria-hidden', 'true');
+      }
+    }
+  }
+});
diff --git a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p10-1.png b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p10-1.png
index 38b251ea..f5420ce8 100644
--- a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p10-1.png
+++ b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p10-1.png
diff --git a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p11-1.png b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p11-1.png
index 77463495..0ae4bd9f 100644
--- a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p11-1.png
+++ b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p11-1.png
diff --git a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p12a-1.png b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p12a-1.png
index ccf8f77a..57a48119 100644
--- a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p12a-1.png
+++ b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p12a-1.png
diff --git a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p12b-1.png b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p12b-1.png
index 6b0dcaf2..c42d45f0 100644
--- a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p12b-1.png
+++ b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p12b-1.png
diff --git a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p13-1.png b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p13-1.png
index ce177190..52dea51e 100644
--- a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p13-1.png
+++ b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p13-1.png
diff --git a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p14-1.png b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p14-1.png
index f2f59ff7..ca1f29be 100644
--- a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p14-1.png
+++ b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p14-1.png
diff --git a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p15a-1.png b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p15a-1.png
index c5759a5b..f69e6d3b 100644
--- a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p15a-1.png
+++ b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p15a-1.png
diff --git a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p15b-1.png b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p15b-1.png
index 3640ea68..71fcd257 100644
--- a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p15b-1.png
+++ b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p15b-1.png
diff --git a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p16-1.png b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p16-1.png
index b61f28e2..820501a3 100644
--- a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p16-1.png
+++ b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p16-1.png
diff --git a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p5a-1.png b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p5a-1.png
index 8d38b89c..e264d2ea 100644
--- a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p5a-1.png
+++ b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p5a-1.png
diff --git a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p5b-1.png b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p5b-1.png
index 3f2da285..e5b656a4 100644
--- a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p5b-1.png
+++ b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p5b-1.png
diff --git a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p6-1.png b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p6-1.png
index 37274769..c9664c77 100644
--- a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p6-1.png
+++ b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p6-1.png
diff --git a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p7-1.png b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p7-1.png
index 515e9095..a81f814c 100644
--- a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p7-1.png
+++ b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p7-1.png
diff --git a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p8-1.png b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p8-1.png
index ebcc326c..75d72e7c 100644
--- a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p8-1.png
+++ b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p8-1.png
diff --git a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p9a-1.png b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p9a-1.png
index a6f4e763..3ce13a97 100644
--- a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p9a-1.png
+++ b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p9a-1.png
diff --git a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p9b-1.png b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p9b-1.png
index 2a8cf947..e2cf2f83 100644
--- a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p9b-1.png
+++ b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p9b-1.png
diff --git a/docs/dev/articles/web_only/NAFTA_examples_files/header-attrs-2.6/header-attrs.js b/docs/dev/articles/web_only/NAFTA_examples_files/header-attrs-2.6/header-attrs.js
new file mode 100644
index 00000000..dd57d92e
--- /dev/null
+++ b/docs/dev/articles/web_only/NAFTA_examples_files/header-attrs-2.6/header-attrs.js
@@ -0,0 +1,12 @@
+// Pandoc 2.9 adds attributes on both header and div. We remove the former (to
+// be compatible with the behavior of Pandoc < 2.8).
+document.addEventListener('DOMContentLoaded', function(e) {
+  var hs = document.querySelectorAll("div.section[class*='level'] > :first-child");
+  var i, h, a;
+  for (i = 0; i < hs.length; i++) {
+    h = hs[i];
+    if (!/^h[1-6]$/i.test(h.tagName)) continue;  // it should be a header h1-h6
+    a = h.attributes;
+    while (a.length > 0) h.removeAttribute(a[0].name);
+  }
+});
diff --git a/docs/dev/articles/web_only/benchmarks.html b/docs/dev/articles/web_only/benchmarks.html
index 8e157c0f..a6d52649 100644
--- a/docs/dev/articles/web_only/benchmarks.html
+++ b/docs/dev/articles/web_only/benchmarks.html
@@ -32,7 +32,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../../index.html">mkin</a>
-        <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">0.9.50.4</span>
+        <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">1.0.3.9000</span>
       </span>
     </div>
 
@@ -81,7 +81,7 @@
 <ul class="nav navbar-nav navbar-right">
 <li>
   <a href="https://github.com/jranke/mkin/">
-    <span class="fab fa fab fa-github fa-lg"></span>
+    <span class="fab fa-github fa-lg"></span>
      
   </a>
 </li>
@@ -95,14 +95,13 @@
 
       
 
-      </header><link href="benchmarks_files/anchor-sections-1.0/anchor-sections.css" rel="stylesheet">
-<script src="benchmarks_files/anchor-sections-1.0/anchor-sections.js"></script><div class="row">
+      </header><script src="benchmarks_files/header-attrs-2.6/header-attrs.js"></script><script src="benchmarks_files/accessible-code-block-0.0.1/empty-anchor.js"></script><div class="row">
   <div class="col-md-9 contents">
     <div class="page-header toc-ignore">
       <h1 data-toc-skip>Benchmark timings for mkin</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2020-11-30</h4>
+            <h4 class="date">Last change 13 May 2020 (rebuilt 2021-02-15)</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/master/vignettes/web_only/benchmarks.rmd"><code>vignettes/web_only/benchmarks.rmd</code></a></small>
       <div class="hidden name"><code>benchmarks.rmd</code></div>
@@ -137,17 +136,11 @@
   m1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span><span class="op">)</span>
 <span class="va">t3</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOMC_SFO</span>, <span class="va">DFOP_SFO</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">FOCUS_D</span><span class="op">)</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span>
 <span class="va">t4</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOMC_SFO</span>, <span class="va">DFOP_SFO</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">FOCUS_D</span><span class="op">)</span>,
-    error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></code></pre></div>
-<pre><code>## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...): Optimisation did not converge:
-## iteration limit reached without convergence (10)
-
-## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...): Optimisation did not converge:
-## iteration limit reached without convergence (10)</code></pre>
-<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span class="va">t5</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOMC_SFO</span>, <span class="va">DFOP_SFO</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">FOCUS_D</span><span class="op">)</span>,
+    error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span>
+<span class="va">t5</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOMC_SFO</span>, <span class="va">DFOP_SFO</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">FOCUS_D</span><span class="op">)</span>,
     error_model <span class="op">=</span> <span class="st">"obs"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></code></pre></div>
 <p>Two metabolites, synthetic data:</p>
-<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="va">m_synth_SFO_lin</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>parent <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M1"</span><span class="op">)</span>,
                            M1 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M2"</span><span class="op">)</span>,
                            M2 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,
@@ -174,7 +167,7 @@
     error_model <span class="op">=</span> <span class="st">"obs"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span>
 <span class="va">t11</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html">system.time</a></span><span class="op">(</span><span class="fu">mmkin_bench</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">m_synth_DFOP_par</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">DFOP_par_c</span><span class="op">)</span>,
     error_model <span class="op">=</span> <span class="st">"obs"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></code></pre></div>
-<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span class="va">mkin_benchmarks</span><span class="op">[</span><span class="va">system_string</span>, <span class="fu"><a href="https://rdrr.io/r/base/paste.html">paste0</a></span><span class="op">(</span><span class="st">"t"</span>, <span class="fl">1</span><span class="op">:</span><span class="fl">11</span><span class="op">)</span><span class="op">]</span> <span class="op">&lt;-</span>
   <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="va">t1</span>, <span class="va">t2</span>, <span class="va">t3</span>, <span class="va">t4</span>, <span class="va">t5</span>, <span class="va">t6</span>, <span class="va">t7</span>, <span class="va">t8</span>, <span class="va">t9</span>, <span class="va">t10</span>, <span class="va">t11</span><span class="op">)</span>
 <span class="fu"><a href="https://rdrr.io/r/base/save.html">save</a></span><span class="op">(</span><span class="va">mkin_benchmarks</span>, file <span class="op">=</span> <span class="st">"~/git/mkin/vignettes/web_only/mkin_benchmarks.rda"</span><span class="op">)</span></code></pre></div>
@@ -235,6 +228,16 @@
 <td align="right">1.786</td>
 <td align="right">3.729</td>
 </tr>
+<tr class="odd">
+<td align="left">1.0.3</td>
+<td align="right">1.722</td>
+<td align="right">3.419</td>
+</tr>
+<tr class="even">
+<td align="left">1.0.3.9000</td>
+<td align="right">2.770</td>
+<td align="right">3.458</td>
+</tr>
 </tbody>
 </table>
 </div>
@@ -298,13 +301,25 @@
 <td align="right">7.251</td>
 <td align="right">2.810</td>
 </tr>
+<tr class="odd">
+<td align="left">1.0.3</td>
+<td align="right">1.402</td>
+<td align="right">6.343</td>
+<td align="right">2.802</td>
+</tr>
+<tr class="even">
+<td align="left">1.0.3.9000</td>
+<td align="right">1.405</td>
+<td align="right">6.417</td>
+<td align="right">2.824</td>
+</tr>
 </tbody>
 </table>
 </div>
 <div id="two-metabolites" class="section level3">
 <h3 class="hasAnchor">
 <a href="#two-metabolites" class="anchor"></a>Two metabolites</h3>
-<p>Constant variance (t6 and t7), two-component error model (t8 and t9), and variance by variable (t10 and t11) for one model fitted to one dataset, i.e. one fit for each test.</p>
+<p>Constant variance (t6 and t7), two-component error model (t8 and t9), and variance by variable (t10 and t11) for one model fitted to one dataset, i.e. one fit for each test.</p>
 <table class="table">
 <thead><tr class="header">
 <th align="left">mkin version</th>
@@ -388,6 +403,24 @@
 <td align="right">1.958</td>
 <td align="right">3.105</td>
 </tr>
+<tr class="odd">
+<td align="left">1.0.3</td>
+<td align="right">0.771</td>
+<td align="right">1.251</td>
+<td align="right">1.464</td>
+<td align="right">3.074</td>
+<td align="right">1.940</td>
+<td align="right">2.831</td>
+</tr>
+<tr class="even">
+<td align="left">1.0.3.9000</td>
+<td align="right">0.772</td>
+<td align="right">1.263</td>
+<td align="right">1.483</td>
+<td align="right">3.101</td>
+<td align="right">1.958</td>
+<td align="right">2.843</td>
+</tr>
 </tbody>
 </table>
 </div>
diff --git a/docs/dev/articles/web_only/benchmarks_files/accessible-code-block-0.0.1/empty-anchor.js b/docs/dev/articles/web_only/benchmarks_files/accessible-code-block-0.0.1/empty-anchor.js
new file mode 100644
index 00000000..ca349fd6
--- /dev/null
+++ b/docs/dev/articles/web_only/benchmarks_files/accessible-code-block-0.0.1/empty-anchor.js
@@ -0,0 +1,15 @@
+// Hide empty <a> tag within highlighted CodeBlock for screen reader accessibility (see https://github.com/jgm/pandoc/issues/6352#issuecomment-626106786) -->
+// v0.0.1
+// Written by JooYoung Seo (jooyoung@psu.edu) and Atsushi Yasumoto on June 1st, 2020.
+
+document.addEventListener('DOMContentLoaded', function() {
+  const codeList = document.getElementsByClassName("sourceCode");
+  for (var i = 0; i < codeList.length; i++) {
+    var linkList = codeList[i].getElementsByTagName('a');
+    for (var j = 0; j < linkList.length; j++) {
+      if (linkList[j].innerHTML === "") {
+        linkList[j].setAttribute('aria-hidden', 'true');
+      }
+    }
+  }
+});
diff --git a/docs/dev/articles/web_only/benchmarks_files/header-attrs-2.6/header-attrs.js b/docs/dev/articles/web_only/benchmarks_files/header-attrs-2.6/header-attrs.js
new file mode 100644
index 00000000..dd57d92e
--- /dev/null
+++ b/docs/dev/articles/web_only/benchmarks_files/header-attrs-2.6/header-attrs.js
@@ -0,0 +1,12 @@
+// Pandoc 2.9 adds attributes on both header and div. We remove the former (to
+// be compatible with the behavior of Pandoc < 2.8).
+document.addEventListener('DOMContentLoaded', function(e) {
+  var hs = document.querySelectorAll("div.section[class*='level'] > :first-child");
+  var i, h, a;
+  for (i = 0; i < hs.length; i++) {
+    h = hs[i];
+    if (!/^h[1-6]$/i.test(h.tagName)) continue;  // it should be a header h1-h6
+    a = h.attributes;
+    while (a.length > 0) h.removeAttribute(a[0].name);
+  }
+});
diff --git a/docs/dev/articles/web_only/compiled_models.html b/docs/dev/articles/web_only/compiled_models.html
index a444f4bc..49a579fc 100644
--- a/docs/dev/articles/web_only/compiled_models.html
+++ b/docs/dev/articles/web_only/compiled_models.html
@@ -32,7 +32,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../../index.html">mkin</a>
-        <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">0.9.50.4</span>
+        <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">1.0.3.9000</span>
       </span>
     </div>
 
@@ -81,7 +81,7 @@
 <ul class="nav navbar-nav navbar-right">
 <li>
   <a href="https://github.com/jranke/mkin/">
-    <span class="fab fa fab fa-github fa-lg"></span>
+    <span class="fab fa-github fa-lg"></span>
      
   </a>
 </li>
@@ -95,14 +95,13 @@
 
       
 
-      </header><link href="compiled_models_files/anchor-sections-1.0/anchor-sections.css" rel="stylesheet">
-<script src="compiled_models_files/anchor-sections-1.0/anchor-sections.js"></script><div class="row">
+      </header><script src="compiled_models_files/header-attrs-2.6/header-attrs.js"></script><script src="compiled_models_files/accessible-code-block-0.0.1/empty-anchor.js"></script><div class="row">
   <div class="col-md-9 contents">
     <div class="page-header toc-ignore">
       <h1 data-toc-skip>Performance benefit by using compiled model definitions in mkin</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2020-11-30</h4>
+            <h4 class="date">2021-02-15</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/master/vignettes/web_only/compiled_models.rmd"><code>vignettes/web_only/compiled_models.rmd</code></a></small>
       <div class="hidden name"><code>compiled_models.rmd</code></div>
@@ -160,10 +159,10 @@
   <span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="st">"R package rbenchmark is not available"</span><span class="op">)</span>
 <span class="op">}</span></code></pre></div>
 <pre><code>##                    test replications relative elapsed
-## 4            analytical            1    1.000   0.187
-## 3     deSolve, compiled            1    1.807   0.338
-## 2      Eigenvalue based            1    2.032   0.380
-## 1 deSolve, not compiled            1   43.048   8.050</code></pre>
+## 4            analytical            1    1.000   0.182
+## 3     deSolve, compiled            1    1.824   0.332
+## 2      Eigenvalue based            1    2.082   0.379
+## 1 deSolve, not compiled            1   46.181   8.405</code></pre>
 <p>We see that using the compiled model is by more than a factor of 10 faster than using deSolve without compiled code.</p>
 </div>
 <div id="model-without-analytical-solution" class="section level2">
@@ -190,13 +189,13 @@
 <span class="op">}</span></code></pre></div>
 <pre><code>## Temporary DLL for differentials generated and loaded</code></pre>
 <pre><code>##                    test replications relative elapsed
-## 2     deSolve, compiled            1    1.000   0.483
-## 1 deSolve, not compiled            1   29.969  14.475</code></pre>
-<p>Here we get a performance benefit of a factor of 30 using the version of the differential equation model compiled from C code!</p>
-<p>This vignette was built with mkin 0.9.50.4 on</p>
+## 2     deSolve, compiled            1    1.000   0.541
+## 1 deSolve, not compiled            1   29.091  15.738</code></pre>
+<p>Here we get a performance benefit of a factor of 29 using the version of the differential equation model compiled from C code!</p>
+<p>This vignette was built with mkin 1.0.3.9000 on</p>
 <pre><code>## R version 4.0.3 (2020-10-10)
 ## Platform: x86_64-pc-linux-gnu (64-bit)
-## Running under: Debian GNU/Linux 10 (buster)</code></pre>
+## Running under: Debian GNU/Linux bullseye/sid</code></pre>
 <pre><code>## CPU model: AMD Ryzen 7 1700 Eight-Core Processor</code></pre>
 </div>
   </div>
diff --git a/docs/dev/articles/web_only/compiled_models_files/accessible-code-block-0.0.1/empty-anchor.js b/docs/dev/articles/web_only/compiled_models_files/accessible-code-block-0.0.1/empty-anchor.js
new file mode 100644
index 00000000..ca349fd6
--- /dev/null
+++ b/docs/dev/articles/web_only/compiled_models_files/accessible-code-block-0.0.1/empty-anchor.js
@@ -0,0 +1,15 @@
+// Hide empty <a> tag within highlighted CodeBlock for screen reader accessibility (see https://github.com/jgm/pandoc/issues/6352#issuecomment-626106786) -->
+// v0.0.1
+// Written by JooYoung Seo (jooyoung@psu.edu) and Atsushi Yasumoto on June 1st, 2020.
+
+document.addEventListener('DOMContentLoaded', function() {
+  const codeList = document.getElementsByClassName("sourceCode");
+  for (var i = 0; i < codeList.length; i++) {
+    var linkList = codeList[i].getElementsByTagName('a');
+    for (var j = 0; j < linkList.length; j++) {
+      if (linkList[j].innerHTML === "") {
+        linkList[j].setAttribute('aria-hidden', 'true');
+      }
+    }
+  }
+});
diff --git a/docs/dev/articles/web_only/compiled_models_files/header-attrs-2.6/header-attrs.js b/docs/dev/articles/web_only/compiled_models_files/header-attrs-2.6/header-attrs.js
new file mode 100644
index 00000000..dd57d92e
--- /dev/null
+++ b/docs/dev/articles/web_only/compiled_models_files/header-attrs-2.6/header-attrs.js
@@ -0,0 +1,12 @@
+// Pandoc 2.9 adds attributes on both header and div. We remove the former (to
+// be compatible with the behavior of Pandoc < 2.8).
+document.addEventListener('DOMContentLoaded', function(e) {
+  var hs = document.querySelectorAll("div.section[class*='level'] > :first-child");
+  var i, h, a;
+  for (i = 0; i < hs.length; i++) {
+    h = hs[i];
+    if (!/^h[1-6]$/i.test(h.tagName)) continue;  // it should be a header h1-h6
+    a = h.attributes;
+    while (a.length > 0) h.removeAttribute(a[0].name);
+  }
+});
diff --git a/docs/dev/articles/web_only/dimethenamid_2018.html b/docs/dev/articles/web_only/dimethenamid_2018.html
new file mode 100644
index 00000000..a2ea5c8d
--- /dev/null
+++ b/docs/dev/articles/web_only/dimethenamid_2018.html
@@ -0,0 +1,619 @@
+<!DOCTYPE html>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en">
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
+<meta charset="utf-8">
+<meta http-equiv="X-UA-Compatible" content="IE=edge">
+<meta name="viewport" content="width=device-width, initial-scale=1.0">
+<title>Example evaluations of the dimethenamid data from 2018 • mkin</title>
+<!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous">
+<script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../../bootstrap-toc.css">
+<script src="../../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous">
+<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous">
+<!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../../pkgdown.css" rel="stylesheet">
+<script src="../../pkgdown.js"></script><meta property="og:title" content="Example evaluations of the dimethenamid data from 2018">
+<meta property="og:description" content="mkin">
+<meta name="robots" content="noindex">
+<!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
+<script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script>
+<script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
+<![endif]-->
+</head>
+<body data-spy="scroll" data-target="#toc">
+    <div class="container template-article">
+      <header><div class="navbar navbar-default navbar-fixed-top" role="navigation">
+  <div class="container">
+    <div class="navbar-header">
+      <button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#navbar" aria-expanded="false">
+        <span class="sr-only">Toggle navigation</span>
+        <span class="icon-bar"></span>
+        <span class="icon-bar"></span>
+        <span class="icon-bar"></span>
+      </button>
+      <span class="navbar-brand">
+        <a class="navbar-link" href="../../index.html">mkin</a>
+        <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">1.1.0</span>
+      </span>
+    </div>
+
+    <div id="navbar" class="navbar-collapse collapse">
+      <ul class="nav navbar-nav">
+<li>
+  <a href="../../reference/index.html">Functions and data</a>
+</li>
+<li class="dropdown">
+  <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" aria-expanded="false">
+    Articles
+     
+    <span class="caret"></span>
+  </a>
+  <ul class="dropdown-menu" role="menu">
+<li>
+      <a href="../../articles/mkin.html">Introduction to mkin</a>
+    </li>
+    <li>
+      <a href="../../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a>
+    </li>
+    <li>
+      <a href="../../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a>
+    </li>
+    <li>
+      <a href="../../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a>
+    </li>
+    <li>
+      <a href="../../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a>
+    </li>
+    <li>
+      <a href="../../articles/twa.html">Calculation of time weighted average concentrations with mkin</a>
+    </li>
+    <li>
+      <a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
+    </li>
+    <li>
+      <a href="../../articles/web_only/benchmarks.html">Some benchmark timings</a>
+    </li>
+  </ul>
+</li>
+<li>
+  <a href="../../news/index.html">News</a>
+</li>
+      </ul>
+<ul class="nav navbar-nav navbar-right">
+<li>
+  <a href="https://github.com/jranke/mkin/">
+    <span class="fab fa-github fa-lg"></span>
+     
+  </a>
+</li>
+      </ul>
+</div>
+<!--/.nav-collapse -->
+  </div>
+<!--/.container -->
+</div>
+<!--/.navbar -->
+
+      
+
+      </header><script src="dimethenamid_2018_files/header-attrs-2.11/header-attrs.js"></script><script src="dimethenamid_2018_files/accessible-code-block-0.0.1/empty-anchor.js"></script><div class="row">
+  <div class="col-md-9 contents">
+    <div class="page-header toc-ignore">
+      <h1 data-toc-skip>Example evaluations of the dimethenamid data from 2018</h1>
+                        <h4 class="author">Johannes Ranke</h4>
+            
+            <h4 class="date">Last change 11 January 2022, built on 11 Jan 2022</h4>
+      
+      <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/master/vignettes/web_only/dimethenamid_2018.rmd"><code>vignettes/web_only/dimethenamid_2018.rmd</code></a></small>
+      <div class="hidden name"><code>dimethenamid_2018.rmd</code></div>
+
+    </div>
+
+    
+    
+<p><a href="http://www.jrwb.de">Wissenschaftlicher Berater, Kronacher Str. 12, 79639 Grenzach-Wyhlen, Germany</a></p>
+<div id="introduction" class="section level1">
+<h1 class="hasAnchor">
+<a href="#introduction" class="anchor"></a>Introduction</h1>
+<p>During the preparation of the journal article on nonlinear mixed-effects models in degradation kinetics <span class="citation">(Ranke et al. 2021)</span> and the analysis of the dimethenamid degradation data analysed therein, a need for a more detailed analysis using not only nlme and saemix, but also nlmixr for fitting the mixed-effects models was identified, as many model variants do not converge when fitted with nlme, and not all relevant error models can be fitted with saemix.</p>
+<p>This vignette is an attempt to satisfy this need.</p>
+</div>
+<div id="data" class="section level1">
+<h1 class="hasAnchor">
+<a href="#data" class="anchor"></a>Data</h1>
+<p>Residue data forming the basis for the endpoints derived in the conclusion on the peer review of the pesticide risk assessment of dimethenamid-P published by the European Food Safety Authority (EFSA) in 2018 <span class="citation">(EFSA 2018)</span> were transcribed from the risk assessment report <span class="citation">(Rapporteur Member State Germany, Co-Rapporteur Member State Bulgaria 2018)</span> which can be downloaded from the Open EFSA repository <a href="https://open.efsa.europa.eu">https://open.efsa.europa.eu/study-inventory/EFSA-Q-2014-00716</a>.</p>
+<p>The data are <a href="https://pkgdown.jrwb.de/mkin/reference/dimethenamid_2018.html">available in the mkin package</a>. The following code (hidden by default, please use the button to the right to show it) treats the data available for the racemic mixture dimethenamid (DMTA) and its enantiomer dimethenamid-P (DMTAP) in the same way, as no difference between their degradation behaviour was identified in the EU risk assessment. The observation times of each dataset are multiplied with the corresponding normalisation factor also available in the dataset, in order to make it possible to describe all datasets with a single set of parameters.</p>
+<p>Also, datasets observed in the same soil are merged, resulting in dimethenamid (DMTA) data from six soils.</p>
+<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="kw"><a href="https://rdrr.io/r/base/library.html">library</a></span><span class="op">(</span><span class="va"><a href="https://pkgdown.jrwb.de/mkin/">mkin</a></span>, quietly <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>
+<span class="va">dmta_ds</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html">lapply</a></span><span class="op">(</span><span class="fl">1</span><span class="op">:</span><span class="fl">7</span>, <span class="kw">function</span><span class="op">(</span><span class="va">i</span><span class="op">)</span> <span class="op">{</span>
+  <span class="va">ds_i</span> <span class="op">&lt;-</span> <span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">ds</span><span class="op">[[</span><span class="va">i</span><span class="op">]</span><span class="op">]</span><span class="op">$</span><span class="va">data</span>
+  <span class="va">ds_i</span><span class="op">[</span><span class="va">ds_i</span><span class="op">$</span><span class="va">name</span> <span class="op">==</span> <span class="st">"DMTAP"</span>, <span class="st">"name"</span><span class="op">]</span> <span class="op">&lt;-</span>  <span class="st">"DMTA"</span>
+  <span class="va">ds_i</span><span class="op">$</span><span class="va">time</span> <span class="op">&lt;-</span> <span class="va">ds_i</span><span class="op">$</span><span class="va">time</span> <span class="op">*</span> <span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">f_time_norm</span><span class="op">[</span><span class="va">i</span><span class="op">]</span>
+  <span class="va">ds_i</span>
+<span class="op">}</span><span class="op">)</span>
+<span class="fu"><a href="https://rdrr.io/r/base/names.html">names</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">)</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html">sapply</a></span><span class="op">(</span><span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">ds</span>, <span class="kw">function</span><span class="op">(</span><span class="va">ds</span><span class="op">)</span> <span class="va">ds</span><span class="op">$</span><span class="va">title</span><span class="op">)</span>
+<span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot"</span><span class="op">]</span><span class="op">]</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/cbind.html">rbind</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 1"</span><span class="op">]</span><span class="op">]</span>, <span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 2"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span>
+<span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 1"</span><span class="op">]</span><span class="op">]</span> <span class="op">&lt;-</span> <span class="cn">NULL</span>
+<span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 2"</span><span class="op">]</span><span class="op">]</span> <span class="op">&lt;-</span> <span class="cn">NULL</span></code></pre></div>
+</div>
+<div id="parent-degradation" class="section level1">
+<h1 class="hasAnchor">
+<a href="#parent-degradation" class="anchor"></a>Parent degradation</h1>
+<p>We evaluate the observed degradation of the parent compound using simple exponential decline (SFO) and biexponential decline (DFOP), using constant variance (const) and a two-component variance (tc) as error models.</p>
+<div id="separate-evaluations" class="section level2">
+<h2 class="hasAnchor">
+<a href="#separate-evaluations" class="anchor"></a>Separate evaluations</h2>
+<p>As a first step, to get a visual impression of the fit of the different models, we do separate evaluations for each soil using the mmkin function from the mkin package:</p>
+<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="va">f_parent_mkin_const</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"DFOP"</span><span class="op">)</span>, <span class="va">dmta_ds</span>,
+  error_model <span class="op">=</span> <span class="st">"const"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>
+<span class="va">f_parent_mkin_tc</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"DFOP"</span><span class="op">)</span>, <span class="va">dmta_ds</span>,
+  error_model <span class="op">=</span> <span class="st">"tc"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></code></pre></div>
+<p>The plot of the individual SFO fits shown below suggests that at least in some datasets the degradation slows down towards later time points, and that the scatter of the residuals error is smaller for smaller values (panel to the right):</p>
+<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="fu"><a href="../../reference/mixed.html">mixed</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span><span class="op">)</span><span class="op">)</span></code></pre></div>
+<p><img src="dimethenamid_2018_files/figure-html/f_parent_mkin_sfo_const-1.png" width="700"></p>
+<p>Using biexponential decline (DFOP) results in a slightly more random scatter of the residuals:</p>
+<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="fu"><a href="../../reference/mixed.html">mixed</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span><span class="op">)</span><span class="op">)</span></code></pre></div>
+<p><img src="dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const-1.png" width="700"></p>
+<p>The population curve (bold line) in the above plot results from taking the mean of the individual transformed parameters, i.e. of log k1 and log k2, as well as of the logit of the g parameter of the DFOP model). Here, this procedure does not result in parameters that represent the degradation well, because in some datasets the fitted value for k2 is extremely close to zero, leading to a log k2 value that dominates the average. This is alleviated if only rate constants that pass the t-test for significant difference from zero (on the untransformed scale) are considered in the averaging:</p>
+<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="fu"><a href="../../reference/mixed.html">mixed</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span><span class="op">)</span>, test_log_parms <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></code></pre></div>
+<p><img src="dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const_test-1.png" width="700"></p>
+<p>While this is visually much more satisfactory, such an average procedure could introduce a bias, as not all results from the individual fits enter the population curve with the same weight. This is where nonlinear mixed-effects models can help out by treating all datasets with equally by fitting a parameter distribution model together with the degradation model and the error model (see below).</p>
+<p>The remaining trend of the residuals to be higher for higher predicted residues is reduced by using the two-component error model:</p>
+<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="fu"><a href="../../reference/mixed.html">mixed</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span><span class="op">)</span>, test_log_parms <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></code></pre></div>
+<p><img src="dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_tc_test-1.png" width="700"></p>
+</div>
+<div id="nonlinear-mixed-effects-models" class="section level2">
+<h2 class="hasAnchor">
+<a href="#nonlinear-mixed-effects-models" class="anchor"></a>Nonlinear mixed-effects models</h2>
+<p>Instead of taking a model selection decision for each of the individual fits, we fit nonlinear mixed-effects models (using different fitting algorithms as implemented in different packages) and do model selection using all available data at the same time. In order to make sure that these decisions are not unduly influenced by the type of algorithm used, by implementation details or by the use of wrong control parameters, we compare the model selection results obtained with different R packages, with different algorithms and checking control parameters.</p>
+<div id="nlme" class="section level3">
+<h3 class="hasAnchor">
+<a href="#nlme" class="anchor"></a>nlme</h3>
+<p>The nlme package was the first R extension providing facilities to fit nonlinear mixed-effects models. We would like to do model selection from all four combinations of degradation models and error models based on the AIC. However, fitting the DFOP model with constant variance and using default control parameters results in an error, signalling that the maximum number of 50 iterations was reached, potentially indicating overparameterisation. Nevertheless, the algorithm converges when the two-component error model is used in combination with the DFOP model. This can be explained by the fact that the smaller residues observed at later sampling times get more weight when using the two-component error model which will counteract the tendency of the algorithm to try parameter combinations unsuitable for fitting these data.</p>
+<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="kw"><a href="https://rdrr.io/r/base/library.html">library</a></span><span class="op">(</span><span class="va"><a href="https://svn.r-project.org/R-packages/trunk/nlme/">nlme</a></span><span class="op">)</span>
+<span class="va">f_parent_nlme_sfo_const</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlme/man/nlme.html">nlme</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span><span class="op">)</span>
+<span class="co"># f_parent_nlme_dfop_const &lt;- nlme(f_parent_mkin_const["DFOP", ])</span>
+<span class="va">f_parent_nlme_sfo_tc</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlme/man/nlme.html">nlme</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span><span class="op">)</span>
+<span class="va">f_parent_nlme_dfop_tc</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlme/man/nlme.html">nlme</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span><span class="op">)</span></code></pre></div>
+<p>Note that a certain degree of overparameterisation is also indicated by a warning obtained when fitting DFOP with the two-component error model (‘false convergence’ in the ‘LME step’ in iteration 3). However, as this warning does not occur in later iterations, and specifically not in the last of the 6 iterations, we can ignore this warning.</p>
+<p>The model comparison function of the nlme package can directly be applied to these fits showing a much lower AIC for the DFOP model fitted with the two-component error model. Also, the likelihood ratio test indicates that this difference is significant as the p-value is below 0.0001.</p>
+<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/stats/anova.html">anova</a></span><span class="op">(</span>
+  <span class="va">f_parent_nlme_sfo_const</span>, <span class="va">f_parent_nlme_sfo_tc</span>, <span class="va">f_parent_nlme_dfop_tc</span>
+<span class="op">)</span></code></pre></div>
+<pre><code>                        Model df    AIC    BIC  logLik   Test L.Ratio p-value
+f_parent_nlme_sfo_const     1  5 796.60 811.82 -393.30                       
+f_parent_nlme_sfo_tc        2  6 798.60 816.86 -393.30 1 vs 2    0.00   0.998
+f_parent_nlme_dfop_tc       3 10 671.91 702.34 -325.96 2 vs 3  134.69  &lt;.0001</code></pre>
+<p>In addition to these fits, attempts were also made to include correlations between random effects by using the log Cholesky parameterisation of the matrix specifying them. The code used for these attempts can be made visible below.</p>
+<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="va">f_parent_nlme_sfo_const_logchol</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlme/man/nlme.html">nlme</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span>,
+  random <span class="op">=</span> <span class="fu">nlme</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/nlme/man/pdLogChol.html">pdLogChol</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">DMTA_0</span> <span class="op">~</span> <span class="fl">1</span>, <span class="va">log_k_DMTA</span> <span class="op">~</span> <span class="fl">1</span><span class="op">)</span><span class="op">)</span><span class="op">)</span>
+<span class="fu"><a href="https://rdrr.io/r/stats/anova.html">anova</a></span><span class="op">(</span><span class="va">f_parent_nlme_sfo_const</span>, <span class="va">f_parent_nlme_sfo_const_logchol</span><span class="op">)</span>
+<span class="va">f_parent_nlme_sfo_tc_logchol</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlme/man/nlme.html">nlme</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span>,
+  random <span class="op">=</span> <span class="fu">nlme</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/nlme/man/pdLogChol.html">pdLogChol</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">DMTA_0</span> <span class="op">~</span> <span class="fl">1</span>, <span class="va">log_k_DMTA</span> <span class="op">~</span> <span class="fl">1</span><span class="op">)</span><span class="op">)</span><span class="op">)</span>
+<span class="fu"><a href="https://rdrr.io/r/stats/anova.html">anova</a></span><span class="op">(</span><span class="va">f_parent_nlme_sfo_tc</span>, <span class="va">f_parent_nlme_sfo_tc_logchol</span><span class="op">)</span>
+<span class="va">f_parent_nlme_dfop_tc_logchol</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlme/man/nlme.html">nlme</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>,
+  random <span class="op">=</span> <span class="fu">nlme</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/nlme/man/pdLogChol.html">pdLogChol</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">DMTA_0</span> <span class="op">~</span> <span class="fl">1</span>, <span class="va">log_k1</span> <span class="op">~</span> <span class="fl">1</span>, <span class="va">log_k2</span> <span class="op">~</span> <span class="fl">1</span>, <span class="va">g_qlogis</span> <span class="op">~</span> <span class="fl">1</span><span class="op">)</span><span class="op">)</span><span class="op">)</span>
+<span class="fu"><a href="https://rdrr.io/r/stats/anova.html">anova</a></span><span class="op">(</span><span class="va">f_parent_nlme_dfop_tc</span>, <span class="va">f_parent_nlme_dfop_tc_logchol</span><span class="op">)</span></code></pre></div>
+<p>While the SFO variants converge fast, the additional parameters introduced by this lead to convergence warnings for the DFOP model. The model comparison clearly show that adding correlations between random effects does not improve the fits.</p>
+<p>The selected model (DFOP with two-component error) fitted to the data assuming no correlations between random effects is shown below.</p>
+<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">f_parent_nlme_dfop_tc</span><span class="op">)</span></code></pre></div>
+<p><img src="dimethenamid_2018_files/figure-html/plot_parent_nlme-1.png" width="700"></p>
+</div>
+<div id="saemix" class="section level3">
+<h3 class="hasAnchor">
+<a href="#saemix" class="anchor"></a>saemix</h3>
+<p>The saemix package provided the first Open Source implementation of the Stochastic Approximation to the Expectation Maximisation (SAEM) algorithm. SAEM fits of degradation models can be conveniently performed using an interface to the saemix package available in current development versions of the mkin package.</p>
+<p>The corresponding SAEM fits of the four combinations of degradation and error models are fitted below. As there is no convergence criterion implemented in the saemix package, the convergence plots need to be manually checked for every fit. As we will compare the SAEM implementation of saemix to the results obtained using the nlmixr package later, we define control settings that work well for all the parent data fits shown in this vignette.</p>
+<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="kw"><a href="https://rdrr.io/r/base/library.html">library</a></span><span class="op">(</span><span class="va">saemix</span><span class="op">)</span>
+<span class="va">saemix_control</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/saemix/man/saemixControl.html">saemixControl</a></span><span class="op">(</span>nbiter.saemix <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="fl">800</span>, <span class="fl">300</span><span class="op">)</span>, nb.chains <span class="op">=</span> <span class="fl">15</span>,
+    print <span class="op">=</span> <span class="cn">FALSE</span>, save <span class="op">=</span> <span class="cn">FALSE</span>, save.graphs <span class="op">=</span> <span class="cn">FALSE</span>, displayProgress <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>
+<span class="va">saemix_control_moreiter</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/saemix/man/saemixControl.html">saemixControl</a></span><span class="op">(</span>nbiter.saemix <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="fl">1600</span>, <span class="fl">300</span><span class="op">)</span>, nb.chains <span class="op">=</span> <span class="fl">15</span>,
+    print <span class="op">=</span> <span class="cn">FALSE</span>, save <span class="op">=</span> <span class="cn">FALSE</span>, save.graphs <span class="op">=</span> <span class="cn">FALSE</span>, displayProgress <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></code></pre></div>
+<p>The convergence plot for the SFO model using constant variance is shown below.</p>
+<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="va">f_parent_saemix_sfo_const</span> <span class="op">&lt;-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,
+  control <span class="op">=</span> <span class="va">saemix_control</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span>
+<span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html">plot</a></span><span class="op">(</span><span class="va">f_parent_saemix_sfo_const</span><span class="op">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></code></pre></div>
+<p><img src="dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_const-1.png" width="700"></p>
+<p>Obviously the default number of iterations is sufficient to reach convergence. This can also be said for the SFO fit using the two-component error model.</p>
+<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="va">f_parent_saemix_sfo_tc</span> <span class="op">&lt;-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,
+  control <span class="op">=</span> <span class="va">saemix_control</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span>
+<span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html">plot</a></span><span class="op">(</span><span class="va">f_parent_saemix_sfo_tc</span><span class="op">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></code></pre></div>
+<p><img src="dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_tc-1.png" width="700"></p>
+<p>When fitting the DFOP model with constant variance (see below), parameter convergence is not as unambiguous.</p>
+<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="va">f_parent_saemix_dfop_const</span> <span class="op">&lt;-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,
+  control <span class="op">=</span> <span class="va">saemix_control</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span>
+<span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html">plot</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_const</span><span class="op">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></code></pre></div>
+<p><img src="dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_const-1.png" width="700"></p>
+<p>This is improved when the DFOP model is fitted with the two-component error model. Convergence of the variance of k2 is enhanced, it remains more or less stable already after 200 iterations of the first phase.</p>
+<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="va">f_parent_saemix_dfop_tc</span> <span class="op">&lt;-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,
+  control <span class="op">=</span> <span class="va">saemix_control</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span>
+<span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html">plot</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></code></pre></div>
+<p><img src="dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc-1.png" width="700"></p>
+<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="co"># The last time I tried (2022-01-11) this gives an error in solve.default(omega.eta)</span>
+<span class="co"># system is computationally singular: reciprocal condition number = 5e-17</span>
+<span class="co">#f_parent_saemix_dfop_tc_10k &lt;- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,</span>
+<span class="co">#  control = saemix_control_10k, transformations = "saemix")</span>
+<span class="co"># Now we do not get a significant improvement by using twice the number of iterations</span>
+<span class="va">f_parent_saemix_dfop_tc_moreiter</span> <span class="op">&lt;-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,
+  control <span class="op">=</span> <span class="va">saemix_control_moreiter</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span>
+<span class="co">#plot(f_parent_saemix_dfop_tc_moreiter$so, plot.type = "convergence")</span></code></pre></div>
+<p>An alternative way to fit DFOP in combination with the two-component error model is to use the model formulation with transformed parameters as used per default in mkin.</p>
+<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="va">f_parent_saemix_dfop_tc_mkin</span> <span class="op">&lt;-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,
+  control <span class="op">=</span> <span class="va">saemix_control</span>, transformations <span class="op">=</span> <span class="st">"mkin"</span><span class="op">)</span>
+<span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html">plot</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc_mkin</span><span class="op">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></code></pre></div>
+<p><img src="dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc_mkin-1.png" width="700"> As the convergence plots do not clearly indicate that the algorithm has converged, we again use four times the number of iterations, which leads to almost satisfactory convergence (see below).</p>
+<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="va">saemix_control_muchmoreiter</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/saemix/man/saemixControl.html">saemixControl</a></span><span class="op">(</span>nbiter.saemix <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="fl">3200</span>, <span class="fl">300</span><span class="op">)</span>, nb.chains <span class="op">=</span> <span class="fl">15</span>,
+    print <span class="op">=</span> <span class="cn">FALSE</span>, save <span class="op">=</span> <span class="cn">FALSE</span>, save.graphs <span class="op">=</span> <span class="cn">FALSE</span>, displayProgress <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>
+<span class="va">f_parent_saemix_dfop_tc_mkin_muchmoreiter</span> <span class="op">&lt;-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,
+  control <span class="op">=</span> <span class="va">saemix_control_muchmoreiter</span>, transformations <span class="op">=</span> <span class="st">"mkin"</span><span class="op">)</span>
+<span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html">plot</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc_mkin_muchmoreiter</span><span class="op">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></code></pre></div>
+<p><img src="dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc_mkin_moreiter-1.png" width="700"></p>
+<p>The four combinations (SFO/const, SFO/tc, DFOP/const and DFOP/tc), including the variations of the DFOP/tc combination can be compared using the model comparison function of the saemix package:</p>
+<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="va">AIC_parent_saemix</span> <span class="op">&lt;-</span> <span class="fu">saemix</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/compare.saemix.html">compare.saemix</a></span><span class="op">(</span>
+  <span class="va">f_parent_saemix_sfo_const</span><span class="op">$</span><span class="va">so</span>,
+  <span class="va">f_parent_saemix_sfo_tc</span><span class="op">$</span><span class="va">so</span>,
+  <span class="va">f_parent_saemix_dfop_const</span><span class="op">$</span><span class="va">so</span>,
+  <span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span>,
+  <span class="va">f_parent_saemix_dfop_tc_moreiter</span><span class="op">$</span><span class="va">so</span>,
+  <span class="va">f_parent_saemix_dfop_tc_mkin</span><span class="op">$</span><span class="va">so</span>,
+  <span class="va">f_parent_saemix_dfop_tc_mkin_muchmoreiter</span><span class="op">$</span><span class="va">so</span><span class="op">)</span></code></pre></div>
+<pre><code>Likelihoods calculated by importance sampling</code></pre>
+<div class="sourceCode" id="cb22"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/colnames.html">rownames</a></span><span class="op">(</span><span class="va">AIC_parent_saemix</span><span class="op">)</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span>
+  <span class="st">"SFO const"</span>, <span class="st">"SFO tc"</span>, <span class="st">"DFOP const"</span>, <span class="st">"DFOP tc"</span>, <span class="st">"DFOP tc more iterations"</span>,
+  <span class="st">"DFOP tc mkintrans"</span>, <span class="st">"DFOP tc mkintrans more iterations"</span><span class="op">)</span>
+<span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">AIC_parent_saemix</span><span class="op">)</span></code></pre></div>
+<pre><code>                                     AIC    BIC
+SFO const                         796.38 795.34
+SFO tc                            798.38 797.13
+DFOP const                        705.75 703.88
+DFOP tc                           665.65 663.57
+DFOP tc more iterations           665.88 663.80
+DFOP tc mkintrans                 674.02 671.94
+DFOP tc mkintrans more iterations 667.94 665.86</code></pre>
+<p>As in the case of nlme fits, the DFOP model fitted with two-component error (number 4) gives the lowest AIC. Using a much larger number of iterations does not significantly change the AIC. When the mkin transformations are used instead of the saemix transformations, we need four times the number of iterations to obtain a goodness of fit that almost as good as the result obtained with saemix transformations.</p>
+<p>In order to check the influence of the likelihood calculation algorithms implemented in saemix, the likelihood from Gaussian quadrature is added to the best fit, and the AIC values obtained from the three methods are compared.</p>
+<div class="sourceCode" id="cb24"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span> <span class="op">&lt;-</span>
+  <span class="fu">saemix</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/llgq.saemix.html">llgq.saemix</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span><span class="op">)</span>
+<span class="va">AIC_parent_saemix_methods</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span>
+  is <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/AIC.html">AIC</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span>, method <span class="op">=</span> <span class="st">"is"</span><span class="op">)</span>,
+  gq <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/AIC.html">AIC</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span>, method <span class="op">=</span> <span class="st">"gq"</span><span class="op">)</span>,
+  lin <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/AIC.html">AIC</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span>, method <span class="op">=</span> <span class="st">"lin"</span><span class="op">)</span>
+<span class="op">)</span>
+<span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">AIC_parent_saemix_methods</span><span class="op">)</span></code></pre></div>
+<pre><code>    is     gq    lin 
+665.65 665.68 665.11 </code></pre>
+<p>The AIC values based on importance sampling and Gaussian quadrature are very similar. Using linearisation is known to be less accurate, but still gives a similar value.</p>
+</div>
+<div id="nlmixr" class="section level3">
+<h3 class="hasAnchor">
+<a href="#nlmixr" class="anchor"></a>nlmixr</h3>
+<p>In the last years, a lot of effort has been put into the nlmixr package which is designed for pharmacokinetics, where nonlinear mixed-effects models are routinely used, but which can also be used for related data like chemical degradation data. A current development branch of the mkin package provides an interface between mkin and nlmixr. Here, we check if we get equivalent results when using a refined version of the First Order Conditional Estimation (FOCE) algorithm used in nlme, namely the First Order Conditional Estimation with Interaction (FOCEI), and the SAEM algorithm as implemented in nlmixr.</p>
+<p>First, the focei algorithm is used for the four model combinations. A number of warnings are produced with unclear significance.</p>
+<div class="sourceCode" id="cb26"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="kw"><a href="https://rdrr.io/r/base/library.html">library</a></span><span class="op">(</span><span class="va"><a href="https://github.com/nlmixrdevelopment/nlmixr">nlmixr</a></span><span class="op">)</span>
+<span class="va">f_parent_nlmixr_focei_sfo_const</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/nlmixr.html">nlmixr</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span>, est <span class="op">=</span> <span class="st">"focei"</span><span class="op">)</span>
+<span class="va">f_parent_nlmixr_focei_sfo_tc</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/nlmixr.html">nlmixr</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span>, est <span class="op">=</span> <span class="st">"focei"</span><span class="op">)</span>
+<span class="va">f_parent_nlmixr_focei_dfop_const</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/nlmixr.html">nlmixr</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, est <span class="op">=</span> <span class="st">"focei"</span><span class="op">)</span>
+<span class="va">f_parent_nlmixr_focei_dfop_tc</span><span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/nlmixr.html">nlmixr</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, est <span class="op">=</span> <span class="st">"focei"</span><span class="op">)</span></code></pre></div>
+<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="va">aic_nlmixr_focei</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html">sapply</a></span><span class="op">(</span>
+  <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">f_parent_nlmixr_focei_sfo_const</span><span class="op">$</span><span class="va">nm</span>, <span class="va">f_parent_nlmixr_focei_sfo_tc</span><span class="op">$</span><span class="va">nm</span>,
+    <span class="va">f_parent_nlmixr_focei_dfop_const</span><span class="op">$</span><span class="va">nm</span>, <span class="va">f_parent_nlmixr_focei_dfop_tc</span><span class="op">$</span><span class="va">nm</span><span class="op">)</span>,
+  <span class="va">AIC</span><span class="op">)</span></code></pre></div>
+<p>The AIC values are very close to the ones obtained with nlme which are repeated below for convenience.</p>
+<div class="sourceCode" id="cb28"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="va">aic_nlme</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html">sapply</a></span><span class="op">(</span>
+  <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">f_parent_nlme_sfo_const</span>, <span class="cn">NA</span>, <span class="va">f_parent_nlme_sfo_tc</span>, <span class="va">f_parent_nlme_dfop_tc</span><span class="op">)</span>,
+  <span class="kw">function</span><span class="op">(</span><span class="va">x</span><span class="op">)</span> <span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/NA.html">is.na</a></span><span class="op">(</span><span class="va">x</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span><span class="op">)</span><span class="op">)</span> <span class="cn">NA</span> <span class="kw">else</span> <span class="fu"><a href="https://rdrr.io/r/stats/AIC.html">AIC</a></span><span class="op">(</span><span class="va">x</span><span class="op">)</span><span class="op">)</span>
+<span class="va">aic_nlme_nlmixr_focei</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html">data.frame</a></span><span class="op">(</span>
+  <span class="st">"Degradation model"</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"SFO"</span>, <span class="st">"DFOP"</span>, <span class="st">"DFOP"</span><span class="op">)</span>,
+  <span class="st">"Error model"</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/rep.html">rep</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="st">"constant variance"</span>, <span class="st">"two-component"</span><span class="op">)</span>, <span class="fl">2</span><span class="op">)</span>,
+  <span class="st">"AIC (nlme)"</span> <span class="op">=</span> <span class="va">aic_nlme</span>,
+  <span class="st">"AIC (nlmixr with FOCEI)"</span> <span class="op">=</span> <span class="va">aic_nlmixr_focei</span>,
+  check.names <span class="op">=</span> <span class="cn">FALSE</span>
+<span class="op">)</span>
+<span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">aic_nlme_nlmixr_focei</span><span class="op">)</span></code></pre></div>
+<pre><code>  Degradation model       Error model AIC (nlme) AIC (nlmixr with FOCEI)
+1               SFO constant variance     796.60                  796.60
+2               SFO     two-component         NA                  798.64
+3              DFOP constant variance     798.60                  745.87
+4              DFOP     two-component     671.91                  740.42</code></pre>
+<p>Secondly, we use the SAEM estimation routine and check the convergence plots. The control parameters also used for the saemix fits are defined beforehand.</p>
+<div class="sourceCode" id="cb30"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="va">nlmixr_saem_control_800</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/saemControl.html">saemControl</a></span><span class="op">(</span>logLik <span class="op">=</span> <span class="cn">TRUE</span>,
+  nBurn <span class="op">=</span> <span class="fl">800</span>, nEm <span class="op">=</span> <span class="fl">300</span>, nmc <span class="op">=</span> <span class="fl">15</span><span class="op">)</span>
+<span class="va">nlmixr_saem_control_1000</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/saemControl.html">saemControl</a></span><span class="op">(</span>logLik <span class="op">=</span> <span class="cn">TRUE</span>,
+  nBurn <span class="op">=</span> <span class="fl">1000</span>, nEm <span class="op">=</span> <span class="fl">300</span>, nmc <span class="op">=</span> <span class="fl">15</span><span class="op">)</span>
+<span class="va">nlmixr_saem_control_10k</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/saemControl.html">saemControl</a></span><span class="op">(</span>logLik <span class="op">=</span> <span class="cn">TRUE</span>,
+  nBurn <span class="op">=</span> <span class="fl">10000</span>, nEm <span class="op">=</span> <span class="fl">1000</span>, nmc <span class="op">=</span> <span class="fl">15</span><span class="op">)</span></code></pre></div>
+<p>Then we fit SFO with constant variance</p>
+<div class="sourceCode" id="cb31"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="va">f_parent_nlmixr_saem_sfo_const</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/nlmixr.html">nlmixr</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span>, est <span class="op">=</span> <span class="st">"saem"</span>,
+  control <span class="op">=</span> <span class="va">nlmixr_saem_control_800</span><span class="op">)</span>
+<span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/traceplot.html">traceplot</a></span><span class="op">(</span><span class="va">f_parent_nlmixr_saem_sfo_const</span><span class="op">$</span><span class="va">nm</span><span class="op">)</span></code></pre></div>
+<p><img src="dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_sfo_const-1.png" width="700"></p>
+<p>and SFO with two-component error.</p>
+<div class="sourceCode" id="cb32"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="va">f_parent_nlmixr_saem_sfo_tc</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/nlmixr.html">nlmixr</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span>, est <span class="op">=</span> <span class="st">"saem"</span>,
+  control <span class="op">=</span> <span class="va">nlmixr_saem_control_800</span><span class="op">)</span>
+<span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/traceplot.html">traceplot</a></span><span class="op">(</span><span class="va">f_parent_nlmixr_saem_sfo_tc</span><span class="op">$</span><span class="va">nm</span><span class="op">)</span></code></pre></div>
+<p><img src="dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_sfo_tc-1.png" width="700"></p>
+<p>For DFOP with constant variance, the convergence plots show considerable instability of the fit, which indicates overparameterisation which was already observed above for this model combination.</p>
+<div class="sourceCode" id="cb33"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="va">f_parent_nlmixr_saem_dfop_const</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/nlmixr.html">nlmixr</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, est <span class="op">=</span> <span class="st">"saem"</span>,
+  control <span class="op">=</span> <span class="va">nlmixr_saem_control_800</span><span class="op">)</span>
+<span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/traceplot.html">traceplot</a></span><span class="op">(</span><span class="va">f_parent_nlmixr_saem_dfop_const</span><span class="op">$</span><span class="va">nm</span><span class="op">)</span></code></pre></div>
+<p><img src="dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_dfop_const-1.png" width="700"></p>
+<p>For DFOP with two-component error, a less erratic convergence is seen.</p>
+<div class="sourceCode" id="cb34"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="va">f_parent_nlmixr_saem_dfop_tc</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/nlmixr.html">nlmixr</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, est <span class="op">=</span> <span class="st">"saem"</span>,
+  control <span class="op">=</span> <span class="va">nlmixr_saem_control_800</span><span class="op">)</span>
+<span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/traceplot.html">traceplot</a></span><span class="op">(</span><span class="va">f_parent_nlmixr_saem_dfop_tc</span><span class="op">$</span><span class="va">nm</span><span class="op">)</span></code></pre></div>
+<p><img src="dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_dfop_tc-1.png" width="700"></p>
+<p>To check if an increase in the number of iterations improves the fit, we repeat the fit with 1000 iterations for the burn in phase and 300 iterations for the second phase.</p>
+<div class="sourceCode" id="cb35"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="va">f_parent_nlmixr_saem_dfop_tc_1000</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/nlmixr.html">nlmixr</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, est <span class="op">=</span> <span class="st">"saem"</span>,
+  control <span class="op">=</span> <span class="va">nlmixr_saem_control_1000</span><span class="op">)</span>
+<span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/traceplot.html">traceplot</a></span><span class="op">(</span><span class="va">f_parent_nlmixr_saem_dfop_tc_1000</span><span class="op">$</span><span class="va">nm</span><span class="op">)</span></code></pre></div>
+<p><img src="dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_dfop_tc_1k-1.png" width="700"></p>
+<p>Here the fit looks very similar, but we will see below that it shows a higher AIC than the fit with 800 iterations in the burn in phase. Next we choose 10 000 iterations for the burn in phase and 1000 iterations for the second phase for comparison with saemix.</p>
+<div class="sourceCode" id="cb36"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="va">f_parent_nlmixr_saem_dfop_tc_10k</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/nlmixr.html">nlmixr</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, est <span class="op">=</span> <span class="st">"saem"</span>,
+  control <span class="op">=</span> <span class="va">nlmixr_saem_control_10k</span><span class="op">)</span>
+<span class="fu"><a href="https://rdrr.io/pkg/nlmixr/man/traceplot.html">traceplot</a></span><span class="op">(</span><span class="va">f_parent_nlmixr_saem_dfop_tc_10k</span><span class="op">$</span><span class="va">nm</span><span class="op">)</span></code></pre></div>
+<p><img src="dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_dfop_tc_10k-1.png" width="700"></p>
+<p>In the above convergence plot, the time course of ‘eta.DMTA_0’ and ‘log_k2’ indicate a false convergence.</p>
+<p>The AIC values are internally calculated using Gaussian quadrature.</p>
+<div class="sourceCode" id="cb37"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/stats/AIC.html">AIC</a></span><span class="op">(</span><span class="va">f_parent_nlmixr_saem_sfo_const</span><span class="op">$</span><span class="va">nm</span>, <span class="va">f_parent_nlmixr_saem_sfo_tc</span><span class="op">$</span><span class="va">nm</span>,
+  <span class="va">f_parent_nlmixr_saem_dfop_const</span><span class="op">$</span><span class="va">nm</span>, <span class="va">f_parent_nlmixr_saem_dfop_tc</span><span class="op">$</span><span class="va">nm</span>,
+  <span class="va">f_parent_nlmixr_saem_dfop_tc_1000</span><span class="op">$</span><span class="va">nm</span>,
+  <span class="va">f_parent_nlmixr_saem_dfop_tc_10k</span><span class="op">$</span><span class="va">nm</span><span class="op">)</span></code></pre></div>
+<pre><code>                                     df     AIC
+f_parent_nlmixr_saem_sfo_const$nm     5  798.71
+f_parent_nlmixr_saem_sfo_tc$nm        6  808.64
+f_parent_nlmixr_saem_dfop_const$nm    9 1995.96
+f_parent_nlmixr_saem_dfop_tc$nm      10  664.96
+f_parent_nlmixr_saem_dfop_tc_1000$nm 10  667.39
+f_parent_nlmixr_saem_dfop_tc_10k$nm  10     Inf</code></pre>
+<p>We can see that again, the DFOP/tc model shows the best goodness of fit. However, increasing the number of burn-in iterations from 800 to 1000 results in a higher AIC. If we further increase the number of iterations to 10 000 (burn-in) and 1000 (second phase), the AIC cannot be calculated for the nlmixr/saem fit, supporting that the fit did not converge properly.</p>
+</div>
+<div id="comparison" class="section level3">
+<h3 class="hasAnchor">
+<a href="#comparison" class="anchor"></a>Comparison</h3>
+<p>The following table gives the AIC values obtained with the three packages using the same control parameters (800 iterations burn-in, 300 iterations second phase, 15 chains).</p>
+<div class="sourceCode" id="cb39"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="va">AIC_all</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html">data.frame</a></span><span class="op">(</span>
+  check.names <span class="op">=</span> <span class="cn">FALSE</span>,
+  <span class="st">"Degradation model"</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"SFO"</span>, <span class="st">"DFOP"</span>, <span class="st">"DFOP"</span><span class="op">)</span>,
+  <span class="st">"Error model"</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="st">"const"</span>, <span class="st">"tc"</span>, <span class="st">"const"</span>, <span class="st">"tc"</span><span class="op">)</span>,
+  nlme <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/stats/AIC.html">AIC</a></span><span class="op">(</span><span class="va">f_parent_nlme_sfo_const</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/stats/AIC.html">AIC</a></span><span class="op">(</span><span class="va">f_parent_nlme_sfo_tc</span><span class="op">)</span>, <span class="cn">NA</span>, <span class="fu"><a href="https://rdrr.io/r/stats/AIC.html">AIC</a></span><span class="op">(</span><span class="va">f_parent_nlme_dfop_tc</span><span class="op">)</span><span class="op">)</span>,
+  nlmixr_focei <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html">sapply</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">f_parent_nlmixr_focei_sfo_const</span><span class="op">$</span><span class="va">nm</span>, <span class="va">f_parent_nlmixr_focei_sfo_tc</span><span class="op">$</span><span class="va">nm</span>,
+  <span class="va">f_parent_nlmixr_focei_dfop_const</span><span class="op">$</span><span class="va">nm</span>, <span class="va">f_parent_nlmixr_focei_dfop_tc</span><span class="op">$</span><span class="va">nm</span><span class="op">)</span>, <span class="va">AIC</span><span class="op">)</span>,
+  saemix <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html">sapply</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">f_parent_saemix_sfo_const</span><span class="op">$</span><span class="va">so</span>, <span class="va">f_parent_saemix_sfo_tc</span><span class="op">$</span><span class="va">so</span>,
+    <span class="va">f_parent_saemix_dfop_const</span><span class="op">$</span><span class="va">so</span>, <span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span><span class="op">)</span>, <span class="va">AIC</span><span class="op">)</span>,
+  nlmixr_saem <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html">sapply</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span><span class="op">(</span><span class="va">f_parent_nlmixr_saem_sfo_const</span><span class="op">$</span><span class="va">nm</span>, <span class="va">f_parent_nlmixr_saem_sfo_tc</span><span class="op">$</span><span class="va">nm</span>,
+  <span class="va">f_parent_nlmixr_saem_dfop_const</span><span class="op">$</span><span class="va">nm</span>, <span class="va">f_parent_nlmixr_saem_dfop_tc</span><span class="op">$</span><span class="va">nm</span><span class="op">)</span>, <span class="va">AIC</span><span class="op">)</span>
+<span class="op">)</span>
+<span class="fu">kable</span><span class="op">(</span><span class="va">AIC_all</span><span class="op">)</span></code></pre></div>
+<table class="table">
+<thead><tr class="header">
+<th align="left">Degradation model</th>
+<th align="left">Error model</th>
+<th align="right">nlme</th>
+<th align="right">nlmixr_focei</th>
+<th align="right">saemix</th>
+<th align="right">nlmixr_saem</th>
+</tr></thead>
+<tbody>
+<tr class="odd">
+<td align="left">SFO</td>
+<td align="left">const</td>
+<td align="right">796.60</td>
+<td align="right">796.60</td>
+<td align="right">796.38</td>
+<td align="right">798.71</td>
+</tr>
+<tr class="even">
+<td align="left">SFO</td>
+<td align="left">tc</td>
+<td align="right">798.60</td>
+<td align="right">798.64</td>
+<td align="right">798.38</td>
+<td align="right">808.64</td>
+</tr>
+<tr class="odd">
+<td align="left">DFOP</td>
+<td align="left">const</td>
+<td align="right">NA</td>
+<td align="right">745.87</td>
+<td align="right">705.75</td>
+<td align="right">1995.96</td>
+</tr>
+<tr class="even">
+<td align="left">DFOP</td>
+<td align="left">tc</td>
+<td align="right">671.91</td>
+<td align="right">740.42</td>
+<td align="right">665.65</td>
+<td align="right">664.96</td>
+</tr>
+</tbody>
+</table>
+<div class="sourceCode" id="cb40"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/nlme/man/intervals.html">intervals</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc</span><span class="op">)</span></code></pre></div>
+<pre><code>Approximate 95% confidence intervals
+
+ Fixed effects:
+            lower       est.      upper
+DMTA_0 96.3087887 98.2761715 100.243554
+k1      0.0336893  0.0643651   0.095041
+k2      0.0062993  0.0088001   0.011301
+g       0.9100426  0.9524920   0.994941
+
+ Random effects:
+               lower      est.    upper
+sd(DMTA_0)   0.41868 2.0607469  3.70281
+sd(k1)       0.25611 0.5935653  0.93102
+sd(k2)     -10.29603 0.0029188 10.30187
+sd(g)        0.38083 1.0572543  1.73368
+
+ 
+      lower     est.    upper
+a.1 0.86253 1.061610 1.260690
+b.1 0.02262 0.029666 0.036712</code></pre>
+<div class="sourceCode" id="cb42"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/nlme/man/intervals.html">intervals</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc</span><span class="op">)</span></code></pre></div>
+<pre><code>Approximate 95% confidence intervals
+
+ Fixed effects:
+            lower       est.      upper
+DMTA_0 96.3087887 98.2761715 100.243554
+k1      0.0336893  0.0643651   0.095041
+k2      0.0062993  0.0088001   0.011301
+g       0.9100426  0.9524920   0.994941
+
+ Random effects:
+               lower      est.    upper
+sd(DMTA_0)   0.41868 2.0607469  3.70281
+sd(k1)       0.25611 0.5935653  0.93102
+sd(k2)     -10.29603 0.0029188 10.30187
+sd(g)        0.38083 1.0572543  1.73368
+
+ 
+      lower     est.    upper
+a.1 0.86253 1.061610 1.260690
+b.1 0.02262 0.029666 0.036712</code></pre>
+<div class="sourceCode" id="cb44"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/nlme/man/intervals.html">intervals</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc_mkin_muchmoreiter</span><span class="op">)</span></code></pre></div>
+<pre><code>Approximate 95% confidence intervals
+
+ Fixed effects:
+            lower       est.      upper
+DMTA_0 96.3402070 98.2789378 100.217669
+k1      0.0397896  0.0641976   0.103578
+k2      0.0041987  0.0084427   0.016977
+g       0.8656257  0.9521509   0.983992
+
+ Random effects:
+                lower    est.   upper
+sd(DMTA_0)    0.38907 2.01821 3.64735
+sd(log_k1)    0.25653 0.59512 0.93371
+sd(log_k2)   -0.20501 0.37610 0.95721
+sd(g_qlogis)  0.39712 1.18296 1.96879
+
+ 
+       lower     est.    upper
+a.1 0.868558 1.070260 1.271963
+b.1 0.022461 0.029505 0.036548</code></pre>
+<div class="sourceCode" id="cb46"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/nlme/man/intervals.html">intervals</a></span><span class="op">(</span><span class="va">f_parent_nlmixr_saem_dfop_tc</span><span class="op">)</span></code></pre></div>
+<pre><code>Approximate 95% confidence intervals
+
+ Fixed effects:
+            lower       est.      upper
+DMTA_0 96.3224806 98.2941093 100.265738
+k1      0.0402270  0.0648200   0.104448
+k2      0.0068547  0.0093928   0.012871
+g       0.8764066  0.9501419   0.980848
+
+ Random effects:
+             lower     est. upper
+sd(DMTA_0)      NA 1.686509    NA
+sd(log_k1)      NA 0.592805    NA
+sd(log_k2)      NA 0.009766    NA
+sd(g_qlogis)    NA 1.082616    NA
+
+ 
+          lower     est. upper
+sigma_low    NA 1.081677    NA
+rsd_high     NA 0.032073    NA</code></pre>
+<div class="sourceCode" id="cb48"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/nlme/man/intervals.html">intervals</a></span><span class="op">(</span><span class="va">f_parent_nlmixr_saem_dfop_tc_10k</span><span class="op">)</span></code></pre></div>
+<pre><code>Approximate 95% confidence intervals
+
+ Fixed effects:
+            lower       est.      upper
+DMTA_0 96.2302085 98.1641090 100.098010
+k1      0.0398514  0.0643909   0.104041
+k2      0.0066292  0.0090784   0.012432
+g       0.8831478  0.9527284   0.981734
+
+ Random effects:
+             lower       est. upper
+sd(DMTA_0)      NA 1.6257e+00    NA
+sd(log_k1)      NA 5.9627e-01    NA
+sd(log_k2)      NA 5.8400e-07    NA
+sd(g_qlogis)    NA 1.0676e+00    NA
+
+ 
+          lower     est. upper
+sigma_low    NA 1.087722    NA
+rsd_high     NA 0.031883    NA</code></pre>
+</div>
+</div>
+</div>
+<div id="references" class="section level1">
+<h1 class="hasAnchor">
+<a href="#references" class="anchor"></a>References</h1>
+<!-- vim: set foldmethod=syntax: -->
+<div id="refs" class="references hanging-indent">
+<div id="ref-efsa_2018_dimethenamid">
+<p>EFSA. 2018. “Peer Review of the Pesticide Risk Assessment of the Active Substance Dimethenamid-P.” <em>EFSA Journal</em> 16 (4): 5211.</p>
+</div>
+<div id="ref-ranke2021">
+<p>Ranke, Johannes, Janina Wöltjen, Jana Schmidt, and Emmanuelle Comets. 2021. “Taking Kinetic Evaluations of Degradation Data to the Next Level with Nonlinear Mixed-Effects Models.” <em>Environments</em> 8 (8). <a href="https://doi.org/10.3390/environments8080071">https://doi.org/10.3390/environments8080071</a>.</p>
+</div>
+<div id="ref-dimethenamid_rar_2018_b8">
+<p>Rapporteur Member State Germany, Co-Rapporteur Member State Bulgaria. 2018. “Renewal Assessment Report Dimethenamid-P Volume 3 - B.8 Environmental fate and behaviour, Rev. 2 - November 2017.” <a href="https://open.efsa.europa.eu/study-inventory/EFSA-Q-2014-00716">https://open.efsa.europa.eu/study-inventory/EFSA-Q-2014-00716</a>.</p>
+</div>
+</div>
+</div>
+  </div>
+
+  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
+
+        <nav id="toc" data-toggle="toc"><h2 data-toc-skip>Contents</h2>
+    </nav>
+</div>
+
+</div>
+
+
+
+      <footer><div class="copyright">
+  <p>Developed by Johannes Ranke.</p>
+</div>
+
+<div class="pkgdown">
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
+</div>
+
+      </footer>
+</div>
+
+  
+
+
+  </body>
+</html>
diff --git a/docs/dev/articles/web_only/dimethenamid_2018_files/accessible-code-block-0.0.1/empty-anchor.js b/docs/dev/articles/web_only/dimethenamid_2018_files/accessible-code-block-0.0.1/empty-anchor.js
new file mode 100644
index 00000000..ca349fd6
--- /dev/null
+++ b/docs/dev/articles/web_only/dimethenamid_2018_files/accessible-code-block-0.0.1/empty-anchor.js
@@ -0,0 +1,15 @@
+// Hide empty <a> tag within highlighted CodeBlock for screen reader accessibility (see https://github.com/jgm/pandoc/issues/6352#issuecomment-626106786) -->
+// v0.0.1
+// Written by JooYoung Seo (jooyoung@psu.edu) and Atsushi Yasumoto on June 1st, 2020.
+
+document.addEventListener('DOMContentLoaded', function() {
+  const codeList = document.getElementsByClassName("sourceCode");
+  for (var i = 0; i < codeList.length; i++) {
+    var linkList = codeList[i].getElementsByTagName('a');
+    for (var j = 0; j < linkList.length; j++) {
+      if (linkList[j].innerHTML === "") {
+        linkList[j].setAttribute('aria-hidden', 'true');
+      }
+    }
+  }
+});
diff --git a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const-1.png b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const-1.png
new file mode 100644
index 00000000..8eb464d1
--- /dev/null
+++ b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const-1.png
diff --git a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const_test-1.png b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const_test-1.png
new file mode 100644
index 00000000..9e4b951a
--- /dev/null
+++ b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_const_test-1.png
diff --git a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_tc_test-1.png b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_tc_test-1.png
new file mode 100644
index 00000000..830fec65
--- /dev/null
+++ b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_dfop_tc_test-1.png
diff --git a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_sfo_const-1.png b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_sfo_const-1.png
new file mode 100644
index 00000000..133249a4
--- /dev/null
+++ b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_mkin_sfo_const-1.png
diff --git a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_dfop_const-1.png b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_dfop_const-1.png
new file mode 100644
index 00000000..27546d8d
--- /dev/null
+++ b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_dfop_const-1.png
diff --git a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_dfop_tc-1.png b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_dfop_tc-1.png
new file mode 100644
index 00000000..dcb8a2f0
--- /dev/null
+++ b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_dfop_tc-1.png
diff --git a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_dfop_tc_10k-1.png b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_dfop_tc_10k-1.png
new file mode 100644
index 00000000..7871ef69
--- /dev/null
+++ b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_dfop_tc_10k-1.png
diff --git a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_dfop_tc_1k-1.png b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_dfop_tc_1k-1.png
new file mode 100644
index 00000000..69aaae8e
--- /dev/null
+++ b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_dfop_tc_1k-1.png
diff --git a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_sfo_const-1.png b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_sfo_const-1.png
new file mode 100644
index 00000000..4316ed0b
--- /dev/null
+++ b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_sfo_const-1.png
diff --git a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_sfo_tc-1.png b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_sfo_tc-1.png
new file mode 100644
index 00000000..fb6dd51c
--- /dev/null
+++ b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_sfo_tc-1.png
diff --git a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_const-1.png b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_const-1.png
new file mode 100644
index 00000000..fd4a686d
--- /dev/null
+++ b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_const-1.png
diff --git a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc-1.png b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc-1.png
new file mode 100644
index 00000000..25a82cbe
--- /dev/null
+++ b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc-1.png
diff --git a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc_10k-1.png b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc_10k-1.png
new file mode 100644
index 00000000..0975126f
--- /dev/null
+++ b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc_10k-1.png
diff --git a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc_mkin-1.png b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc_mkin-1.png
new file mode 100644
index 00000000..9a6547a2
--- /dev/null
+++ b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc_mkin-1.png
diff --git a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc_mkin_10k-1.png b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc_mkin_10k-1.png
new file mode 100644
index 00000000..ae8c1555
--- /dev/null
+++ b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc_mkin_10k-1.png
diff --git a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc_mkin_moreiter-1.png b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc_mkin_moreiter-1.png
new file mode 100644
index 00000000..30ee4ea0
--- /dev/null
+++ b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc_mkin_moreiter-1.png
diff --git a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc_moreiter-1.png b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc_moreiter-1.png
new file mode 100644
index 00000000..1c8fc837
--- /dev/null
+++ b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc_moreiter-1.png
diff --git a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_const-1.png b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_const-1.png
new file mode 100644
index 00000000..c406f3f2
--- /dev/null
+++ b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_const-1.png
diff --git a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_tc-1.png b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_tc-1.png
new file mode 100644
index 00000000..aaf2e0c8
--- /dev/null
+++ b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_tc-1.png
diff --git a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/plot_parent_nlme-1.png b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/plot_parent_nlme-1.png
new file mode 100644
index 00000000..ed978664
--- /dev/null
+++ b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/plot_parent_nlme-1.png
diff --git a/docs/dev/articles/web_only/dimethenamid_2018_files/header-attrs-2.11/header-attrs.js b/docs/dev/articles/web_only/dimethenamid_2018_files/header-attrs-2.11/header-attrs.js
new file mode 100644
index 00000000..dd57d92e
--- /dev/null
+++ b/docs/dev/articles/web_only/dimethenamid_2018_files/header-attrs-2.11/header-attrs.js
@@ -0,0 +1,12 @@
+// Pandoc 2.9 adds attributes on both header and div. We remove the former (to
+// be compatible with the behavior of Pandoc < 2.8).
+document.addEventListener('DOMContentLoaded', function(e) {
+  var hs = document.querySelectorAll("div.section[class*='level'] > :first-child");
+  var i, h, a;
+  for (i = 0; i < hs.length; i++) {
+    h = hs[i];
+    if (!/^h[1-6]$/i.test(h.tagName)) continue;  // it should be a header h1-h6
+    a = h.attributes;
+    while (a.length > 0) h.removeAttribute(a[0].name);
+  }
+});
diff --git a/docs/dev/articles/web_only/dimethenamid_2018_files/header-attrs-2.9/header-attrs.js b/docs/dev/articles/web_only/dimethenamid_2018_files/header-attrs-2.9/header-attrs.js
new file mode 100644
index 00000000..dd57d92e
--- /dev/null
+++ b/docs/dev/articles/web_only/dimethenamid_2018_files/header-attrs-2.9/header-attrs.js
@@ -0,0 +1,12 @@
+// Pandoc 2.9 adds attributes on both header and div. We remove the former (to
+// be compatible with the behavior of Pandoc < 2.8).
+document.addEventListener('DOMContentLoaded', function(e) {
+  var hs = document.querySelectorAll("div.section[class*='level'] > :first-child");
+  var i, h, a;
+  for (i = 0; i < hs.length; i++) {
+    h = hs[i];
+    if (!/^h[1-6]$/i.test(h.tagName)) continue;  // it should be a header h1-h6
+    a = h.attributes;
+    while (a.length > 0) h.removeAttribute(a[0].name);
+  }
+});
author	Johannes Ranke <jranke@uni-bremen.de>	2022-02-08 17:17:29 +0100
committer	Johannes Ranke <jranke@uni-bremen.de>	2022-02-08 17:17:29 +0100
commit	0fa8a770812775d697717ad723f7f61fb04b7fef (patch)
tree	17473ddf787541745d47dab063bc643ec59a9557 /docs/dev/articles
parent	d081384ddcb75a9f92fad33e4e3f6d6796f98e67 (diff)
parent	c0638c84568d475b3b059e2c6e593e6f03b846bc (diff)