nlme	nlmixr_focei	saemix	nlmixr_saem
818.63	818.63	818.37	820.54
820.61	820.61	820.38	835.26
NA	728.11	725.91	842.84
687.84	687.82	683.64	684.51

Example evaluation of FOCUS Example Dataset D

Johannes Ranke

2020-11-30

Last change 31 January 2019 (rebuilt 2021-02-15)

Source: vignettes/FOCUS_D.rmd

FOCUS_D.rmd

@@ -187,10 +186,10 @@

A comprehensive report of the results is obtained using the summary method for mkinfit objects.

 summary(fit)

## mkin version used for fitting:    0.9.50.4 
+## 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  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
Binary files a/docs/dev/articles/FOCUS_D_files/figure-html/plot-1.png and b/docs/dev/articles/FOCUS_D_files/figure-html/plot-1.png differ
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 @@
       
       
         mkin
-        0.9.50.4
+        1.0.3.9000


 
@@ -81,7 +81,7 @@
 
 
   
-    
+    
      
   
 
@@ -95,14 +95,13 @@
 
       
 
-      
-
+      
   
     
       Example evaluation of FOCUS Laboratory Data L1 to L3
                         Johannes Ranke
             
-            2020-11-30
+            Last change 17 November 2016 (rebuilt 2021-02-15)
       
       Source: vignettes/FOCUS_L.rmd
       FOCUS_L.rmd
@@ -128,10 +127,10 @@
  m.L1.SFO <- mkinfit("SFO", FOCUS_2006_L1_mkin, quiet = TRUE)
 summary(m.L1.SFO)
-## mkin version used for fitting:    0.9.50.4 
+## 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 @@
 ## Warning in sqrt(1/diag(V)): NaNs produced
 ## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
 ## doubtful
-## mkin version used for fitting:    0.9.50.4 
+## 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(>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 @@
 
  summary(m.L2.FOMC, data = FALSE)
-## mkin version used for fitting:    0.9.50.4 
+## 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 @@
 
  summary(m.L2.DFOP, data = FALSE)
-## mkin version used for fitting:    0.9.50.4 
+## 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(>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
+## parent 0.5335 5.311    1.599 0.03084   2.058
 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.
 

 

@@ -533,10 +532,10 @@
 We can extract the summary and plot for e.g. the DFOP fit, using square brackets for indexing which will result in the use of the summary and plot functions working on mkinfit objects.
  summary(mm.L3[["DFOP", 1]])
-## mkin version used for fitting:    0.9.50.4 
+## 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 @@
 The \(\chi^2\) error level of 3.3% as well as the plot suggest that the SFO model fits very well. The error level at which the \(\chi^2\) test passes is slightly lower for the FOMC model. However, the difference appears negligible.
  summary(mm.L4[["SFO", 1]], data = FALSE)
-## mkin version used for fitting:    0.9.50.4 
+## 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
  summary(mm.L4[["FOMC", 1]], data = FALSE)
-## mkin version used for fitting:    0.9.50.4 
+## 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 @@
 
 
 References
-
+
 
 Ranke, Johannes. 2014. “Prüfung und Validierung von Modellierungssoftware als Alternative zu ModelMaker 4.0.” Umweltbundesamt Projektnummer 27452.
 
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  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');
+      }
+    }
+  }
+});
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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 57d0c0eb..17ee4a69 100644
--- a/docs/dev/articles/index.html
+++ b/docs/dev/articles/index.html
@@ -71,7 +71,7 @@
       
       
         mkin
-        1.0.2.9000
+        1.0.3.9000
       
     
 
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 @@
       
       
         mkin
-        0.9.50.4
+        1.0.3.9000
       
     
 
@@ -81,7 +81,7 @@
 
 
   
-    
+    
      
   
 
@@ -95,14 +95,13 @@
 
       
 
-      
-
+      
   
     
       Introduction to mkin
                         Johannes Ranke
             
-            2020-11-30
+            Last change 15 February 2021 (rebuilt 2021-02-15)
       
       Source: vignettes/mkin.rmd
       mkin.rmd
@@ -150,28 +149,34 @@
 
 
 Background
-Many approaches are possible regarding the evaluation of chemical degradation data.
-The mkin package (Ranke 2019) implements the approach recommended in the kinetics report provided by the FOrum for Co-ordination of pesticide fate models and their USe (FOCUS Work Group on Degradation Kinetics 2006, 2014) 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.
+The mkin package (Ranke 2021) 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 (FOCUS Work Group on Degradation Kinetics 2006, 2014). 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.
 When the first mkin code was published in 2010, the most commonly used tools for fitting more complex kinetic degradation models to experimental data were KinGUI (Schäfer et al. 2007), 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.
-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 e.g. the initial commit on 11 May 2010), where the code is still occasionally updated.
-At that time, the R package FME (Flexible Modelling Environment) (Soetaert and Petzoldt 2010) 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 \(\chi^2\) goodness-of-fit test as defined by the FOCUS kinetics workgroup would pass using an significance level \(\alpha\) of 0.05. This relative error, expressed as a percentage, is often termed \(\chi^2\) error level or similar.
-Also, mkin introduced using analytical solutions for parent only kinetics for improved optimization speed. Later, Eigenvalue based solutions were introduced to mkin for the case of linear differential equations (i.e. 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.
+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 e.g. the initial commit on 11 May 2010), where the code is still being updated.
+At that time, the R package FME (Flexible Modelling Environment) (Soetaert and Petzoldt 2010) 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 \(\chi^2\) error level as defined in this guidance.
+Also, mkin introduced using analytical solutions for parent only kinetics for improved optimization speed. Later, Eigenvalue based solutions were introduced to mkin for the case of linear differential equations (i.e. 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.
 The possibility to specify back-reactions and a biphasic model (SFORB) for metabolites were present in mkin from the very beginning.
 
 
 Derived software tools
-Soon after the publication of mkin, 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.
-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.
+Soon after the publication of mkin, 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.
+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).
 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.
 A further graphical user interface (GUI) that has recently been brought to a decent degree of maturity is the browser based GUI named gmkin. Please see its documentation page and manual for further information.
 A comparison of scope, usability and numerical results obtained with these tools has been recently been published by Ranke, Wöltjen, and Meinecke (2018).
 
-
-
-Recent developments
-Currently (July 2019), the main features available in mkin 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 mmkin function, and the estimation of parameter confidence intervals based on transformed parameters.
-In addition, the possibility to use two alternative error models to constant variance have been integrated. The variance by variable error model introduced by Gao et al. (2011) has been available via an iteratively reweighted least squares (IRLS) procedure since mkin version 0.9-22. With release 0.9.49.5, 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 two-component error model inspired by error models developed in analytical chemistry.
 
+
+
+Unique features
+Currently, the main unique features available in mkin are
+
+the speed increase by using compiled code when a compiler is present,
+parallel model fitting on multicore machines using the mmkin function,
+the estimation of parameter confidence intervals based on transformed parameters (see below) and
+the possibility to use the two-component error model
+
+
+The iteratively reweighted least squares fitting of different variances for each variable as introduced by Gao et al. (2011) has been available in mkin since version 0.9-22. With release 0.9.49.5, 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 two-component error model inspired by error models developed in analytical chemistry (Ranke and Meinecke 2019).
 
 
 
@@ -179,13 +184,13 @@
 For rate constants, the log transformation is used, as proposed by Bates and Watts (1988, 77, 149). Approximate intervals are constructed for the transformed rate constants (compare Bates and Watts 1988, 135), i.e. for their logarithms. Confidence intervals for the rate constants are then obtained using the appropriate backtransformation using the exponential function.
 In the first version of mkin 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.
 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.
-In 2012, an alternative reparameterisation of the formation fractions was proposed together with René Lehmann (Ranke and Lehmann 2012), 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 2012, an alternative reparameterisation of the formation fractions was proposed together with René Lehmann (Ranke and Lehmann 2012), 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.
 
 
 Confidence intervals based on transformed parameters
 In the first attempt at providing improved parameter confidence intervals introduced to mkin 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.
 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.
-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.
+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.
 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.
 
 
@@ -200,36 +205,39 @@
 
 References
 
-
+
 
 Bates, D., and D. Watts. 1988. Nonlinear Regression and Its Applications. Wiley-Interscience.
 
 
-FOCUS Work Group on Degradation Kinetics. 2006. 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. http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics.
+FOCUS Work Group on Degradation Kinetics. 2006. 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. http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics.
 
 
-———. 2014. Generic Guidance for Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in Eu Registration. 1.1 ed. http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics.
+———. 2014. Generic Guidance for Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in Eu Registration. 1.1 ed. http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics.
 
 
-Gao, Z., J.W. Green, J. Vanderborght, and W. Schmitt. 2011. “Improving Uncertainty Analysis in Kinetic Evaluations Using Iteratively Reweighted Least Squares.” Journal. Environmental Science and Technology 45: 4429–37.
+Gao, Z., J. W. Green, J. Vanderborght, and W. Schmitt. 2011. “Improving Uncertainty Analysis in Kinetic Evaluations Using Iteratively Reweighted Least Squares.” Journal. Environmental Science and Technology 45: 4429–37.
 
 
-Ranke, J. 2019. ‘mkin‘: Kinetic Evaluation of Chemical Degradation Data. https://CRAN.R-project.org/package=mkin.
+Ranke, J. 2021. ‘mkin‘: Kinetic Evaluation of Chemical Degradation Data. https://CRAN.R-project.org/package=mkin.
 
 
 Ranke, J., and R. Lehmann. 2012. “Parameter Reliability in Kinetic Evaluation of Environmental Metabolism Data - Assessment and the Influence of Model Specification.” In SETAC World 20-24 May. Berlin.
 
 
-———. 2015. “To T-Test or Not to T-Test, That Is the Question.” In XV Symposium on Pesticide Chemistry 2-4 September 2015. Piacenza. http://chem.uft.uni-bremen.de/ranke/posters/piacenza_2015.pdf.
+———. 2015. “To T-Test or Not to T-Test, That Is the Question.” In XV Symposium on Pesticide Chemistry 2-4 September 2015. Piacenza. http://chem.uft.uni-bremen.de/ranke/posters/piacenza_2015.pdf.
+
+
+Ranke, Johannes, and Stefan Meinecke. 2019. “Error Models for the Kinetic Evaluation of Chemical Degradation Data.” Environments 6 (12). https://doi.org/10.3390/environments6120124.
 
 
-Ranke, Johannes, Janina Wöltjen, and Stefan Meinecke. 2018. “Comparison of Software Tools for Kinetic Evaluation of Chemical Degradation Data.” Environmental Sciences Europe 30 (1): 17. https://doi.org/10.1186/s12302-018-0145-1.
+Ranke, Johannes, Janina Wöltjen, and Stefan Meinecke. 2018. “Comparison of Software Tools for Kinetic Evaluation of Chemical Degradation Data.” Environmental Sciences Europe 30 (1): 17. https://doi.org/10.1186/s12302-018-0145-1.
 
 
 Schäfer, D., B. Mikolasch, P. Rainbird, and B. Harvey. 2007. “KinGUI: A New Kinetic Software Tool for Evaluations According to FOCUS Degradation Kinetics.” In Proceedings of the Xiii Symposium Pesticide Chemistry, edited by Del Re A. A. M., Capri E., Fragoulis G., and Trevisan M., 916–23. Piacenza.
 
 
-Soetaert, Karline, and Thomas Petzoldt. 2010. “Inverse Modelling, Sensitivity and Monte Carlo Analysis in R Using Package FME.” Journal of Statistical Software 33 (3): 1–28. https://www.jstatsoft.org/v33/i03/.
+Soetaert, Karline, and Thomas Petzoldt. 2010. “Inverse Modelling, Sensitivity and Monte Carlo Analysis in R Using Package FME.” Journal of Statistical Software 33 (3): 1–28. https://www.jstatsoft.org/v33/i03/.
 
 
 
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  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
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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 @@
       
       
         mkin
-        0.9.50.4
+        1.0.3.9000
       
     
 
@@ -81,7 +81,7 @@
 
 
   
-    
+    
      
   
 
@@ -95,14 +95,13 @@
 
       
 
-      
-
+      
   
     
       Calculation of time weighted average concentrations with mkin
                         Johannes Ranke
             
-            2020-11-30
+            Last change 18 September 2019 (rebuilt 2021-02-15)
       
       Source: vignettes/twa.rmd
       twa.rmd
@@ -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) \]
 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 max_twa_parent() function. If the same is needed for metabolites, the function pfm::max_twa() from the ‘pfm’ package can be used.
-
+
 
-FOCUS Work Group on Degradation Kinetics. 2014. Generic Guidance for Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in Eu Registration. 1.1 ed. http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics.
+FOCUS Work Group on Degradation Kinetics. 2014. Generic Guidance for Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in Eu Registration. 1.1 ed. http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics.
 
 
   
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  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 @@
       
       
         mkin
-        0.9.50.4
+        1.0.3.9000
       
     
 
@@ -81,7 +81,7 @@
 
 
   
-    
+    
      
   
 
@@ -95,14 +95,13 @@
 
       
 
-      
-
+      
   
     
       Example evaluation of FOCUS dataset Z
                         Johannes Ranke
             
-            2020-11-30
+            Last change 16 January 2018 (rebuilt 2021-02-15)
       
       Source: vignettes/web_only/FOCUS_Z.rmd
       FOCUS_Z.rmd
@@ -239,12 +238,12 @@
  summary(m.Z.FOCUS, data = FALSE)$bpar
 ##             Estimate se_notrans t value     Pr(>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
  endpoints(m.Z.FOCUS)
@@ -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

+## Z3 11.80986 39.2315

 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.
 

 
@@ -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
 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.
 
@@ -367,9 +366,9 @@
 
 References
 
-
+
 
-FOCUS Work Group on Degradation Kinetics. 2014. Generic Guidance for Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in Eu Registration. 1.1 ed. http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics.
+FOCUS Work Group on Degradation Kinetics. 2014. Generic Guidance for Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in Eu Registration. 1.1 ed. http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics.
 
 
 
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  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');
+      }
+    }
+  }
+});
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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 @@
       
       
         mkin
-        0.9.50.4
+        1.0.3.9000
       
     
 
@@ -81,7 +81,7 @@
 
 
   
-    
+    
      
   
 
@@ -95,14 +95,13 @@
 
       
 
-      
-
+      
   
     
       Evaluation of example datasets from Attachment 1 to the US EPA SOP for the NAFTA guidance
                         Johannes Ranke
             
-            2020-11-30
+            26 February 2019 (rebuilt 2021-02-15)
       
       Source: vignettes/web_only/NAFTA_examples.rmd
       NAFTA_examples.rmd
@@ -158,7 +157,7 @@
 ##          Estimate   Pr(>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
@@ -209,7 +208,7 @@
 ##          Estimate   Pr(>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
@@ -260,7 +259,7 @@
 ##          Estimate   Pr(>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
@@ -311,7 +310,7 @@
 ##          Estimate   Pr(>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
@@ -422,7 +421,7 @@
 ##          Estimate   Pr(>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
@@ -443,15 +442,16 @@
  p9b <- nafta(NAFTA_SOP_Attachment[["p9b"]])
 ## Warning in sqrt(diag(covar)): NaNs produced
+## Warning in sqrt(diag(covar_notrans)): NaNs produced
 ## Warning in sqrt(1/diag(V)): NaNs produced
 ## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
 ## doubtful
 ## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
 ## The half-life obtained from the IORE model may be used
-+ plot(p9b)
 
-+ print(p9b)
 ## Sums of squares:
 ##      SFO     IORE     DFOP 
@@ -475,12 +475,12 @@
 ## sigma             1.288 1.76e-04  0.7456  1.830
 ## 
 ## $DFOP
-##          Estimate Pr(>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(>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 @@
 
 
 Example on page 10
-+ p10 <- nafta(NAFTA_SOP_Attachment[["p10"]])
-## Warning in sqrt(diag(covar_notrans)): NaNs produced
+## Warning in sqrt(diag(covar)): NaNs produced
+## Warning in sqrt(1/diag(V)): NaNs produced
+## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
+## doubtful
 ## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
 ## The half-life obtained from the IORE model may be used
-+ plot(p10)
 
-+ print(p10)
 ## Sums of squares:
 ##      SFO     IORE     DFOP 
@@ -530,9 +533,9 @@
 ## $DFOP
 ##          Estimate   Pr(>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 @@
 
 
 Example on page 11
-+ p11 <- nafta(NAFTA_SOP_Attachment[["p11"]])
 ## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
 ## The half-life obtained from the IORE model may be used
-+ plot(p11)
 
-+ print(p11)
 ## 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
+## [1] 41148170
 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.
 
 
@@ -610,19 +613,21 @@
 
 
 Example on page 12, upper panel
-+ p12a <- nafta(NAFTA_SOP_Attachment[["p12a"]])
 ## Warning in summary.mkinfit(x): Could not calculate correlation; no covariance
-## matrix
-
-## Warning in summary.mkinfit(x): Could not calculate correlation; no covariance
 ## matrix
+## Warning in sqrt(diag(covar)): NaNs produced
+## Warning in sqrt(diag(covar_notrans)): NaNs produced
+## Warning in sqrt(1/diag(V)): NaNs produced
+## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
+## doubtful
 ## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
 ## The half-life obtained from the IORE model may be used
-+ plot(p12a)
 
-+ print(p12a)
 ## Sums of squares:
 ##      SFO     IORE     DFOP 
@@ -646,12 +651,12 @@
 ## sigma             3.965     NA    NA    NA
 ## 
 ## $DFOP
-##          Estimate   Pr(>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(>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 @@
 
 
 Example on page 12, lower panel
-+ p12b <- nafta(NAFTA_SOP_Attachment[["p12b"]])
-## Warning in sqrt(diag(covar)): NaNs produced
 ## Warning in qt(alpha/2, rdf): NaNs produced
 ## Warning in qt(1 - alpha/2, rdf): NaNs produced
-## Warning in sqrt(1/diag(V)): NaNs produced
-## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
-## doubtful
+## Warning in sqrt(diag(covar_notrans)): NaNs produced
+## Warning in pt(abs(tval), rdf, lower.tail = FALSE): NaNs produced
 ## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
 ## The half-life obtained from the IORE model may be used
-+ plot(p12b)
 
-+ print(p12b)
 ## Sums of squares:
 ##      SFO     IORE     DFOP 
@@ -704,11 +707,11 @@
 ## 
 ## $DFOP
 ##          Estimate Pr(>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 @@
 
 
 Example on page 13
-+ p13 <- nafta(NAFTA_SOP_Attachment[["p13"]])
-## Warning in sqrt(diag(covar)): NaNs produced
-## Warning in sqrt(1/diag(V)): NaNs produced
-## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
-## doubtful
 ## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
 ## The half-life obtained from the IORE model may be used
-+ plot(p13)
 
-+ print(p13)
 ## Sums of squares:
 ##      SFO     IORE     DFOP 
@@ -760,9 +759,9 @@
 ## $DFOP
 ##          Estimate Pr(>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 @@
 
 
 DT50 not observed in the study and DFOP problems in PestDF
-+ p14 <- nafta(NAFTA_SOP_Attachment[["p14"]])
 ## Warning in sqrt(diag(covar)): NaNs produced
 ## Warning in sqrt(1/diag(V)): NaNs produced
@@ -787,10 +786,10 @@
 ## doubtful
 ## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
 ## The half-life obtained from the IORE model may be used
-+ plot(p14)
 
-+ print(p14)
 ## Sums of squares:
 ##      SFO     IORE     DFOP 
@@ -817,7 +816,7 @@
 ##          Estimate   Pr(>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
@@ -835,14 +834,14 @@
 
 
 N is less than 1 and DFOP fraction parameter is below zero
-+ p15a <- nafta(NAFTA_SOP_Attachment[["p15a"]])
 ## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
 ## The half-life obtained from the IORE model may be used
-+ plot(p15a)
 
-+ print(p15a)
 ## Sums of squares:
 ##      SFO     IORE     DFOP 
@@ -866,12 +865,12 @@
 ## sigma             3.105 1.78e-04  1.795  4.416
 ## 
 ## $DFOP
-##          Estimate Pr(>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(>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
-+ p15b <- nafta(NAFTA_SOP_Attachment[["p15b"]])
 ## Warning in sqrt(diag(covar)): NaNs produced
 ## Warning in sqrt(1/diag(V)): NaNs produced
@@ -890,10 +889,10 @@
 ## doubtful
 ## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
 ## The half-life obtained from the IORE model may be used
-+ plot(p15b)
 
-+ print(p15b)
 ## Sums of squares:
 ##       SFO      IORE      DFOP 
@@ -911,7 +910,7 @@
 ## 
 ## $IORE
 ##                Estimate   Pr(>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 @@
 
 
 The DFOP fraction parameter is greater than 1
-+ p16 <- nafta(NAFTA_SOP_Attachment[["p16"]])
 ## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
 ## The representative half-life of the IORE model is longer than the one corresponding
 ## to the terminal degradation rate found with the DFOP model.
 ## The representative half-life obtained from the DFOP model may be used
-+ plot(p16)
 
-+ print(p16)
 ## Sums of squares:
 ##      SFO     IORE     DFOP 
@@ -998,7 +997,7 @@
 
 
 References
-
+
 
 US EPA. 2015. “Standard Operating Procedure for Using the NAFTA Guidance to Calculate Representative Half-Life Values and Characterizing Pesticide Degradation.”
 
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  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
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index 6b0dcaf2..c42d45f0 100644
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index ce177190..52dea51e 100644
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index f2f59ff7..ca1f29be 100644
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index c5759a5b..f69e6d3b 100644
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index 3640ea68..71fcd257 100644
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diff --git a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p16-1.png b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p16-1.png
index b61f28e2..820501a3 100644
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index 8d38b89c..e264d2ea 100644
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index 37274769..c9664c77 100644
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index 515e9095..a81f814c 100644
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index ebcc326c..75d72e7c 100644
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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
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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
Binary files a/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p9b-1.png and b/docs/dev/articles/web_only/NAFTA_examples_files/figure-html/p9b-1.png differ
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 @@
       
       
         mkin
-        0.9.50.4
+        1.0.3.9000
       
     
 
@@ -81,7 +81,7 @@
 
 
   
-    
+    
      
   
 
@@ -95,14 +95,13 @@
 
       
 
-      
-
+      
   
     
       Benchmark timings for mkin
                         Johannes Ranke
             
-            2020-11-30
+            Last change 13 May 2020 (rebuilt 2021-02-15)
       
       Source: vignettes/web_only/benchmarks.rmd
       benchmarks.rmd
@@ -137,17 +136,11 @@
   m1 = mkinsub("SFO"))
 t3 <- system.time(mmkin_bench(list(SFO_SFO, FOMC_SFO, DFOP_SFO), list(FOCUS_D)))[["elapsed"]]
 t4 <- system.time(mmkin_bench(list(SFO_SFO, FOMC_SFO, DFOP_SFO), list(FOCUS_D),
-    error_model = "tc"))[["elapsed"]]
-## 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)
--t5 <- system.time(mmkin_bench(list(SFO_SFO, FOMC_SFO, DFOP_SFO), list(FOCUS_D),
+    error_model = "tc"))[["elapsed"]]
+t5 <- system.time(mmkin_bench(list(SFO_SFO, FOMC_SFO, DFOP_SFO), list(FOCUS_D),
     error_model = "obs"))[["elapsed"]]
 Two metabolites, synthetic data:
-+ m_synth_SFO_lin <- mkinmod(parent = mkinsub("SFO", "M1"),
                            M1 = mkinsub("SFO", "M2"),
                            M2 = mkinsub("SFO"),
@@ -174,7 +167,7 @@
     error_model = "obs"))[["elapsed"]]
 t11 <- system.time(mmkin_bench(list(m_synth_DFOP_par), list(DFOP_par_c),
     error_model = "obs"))[["elapsed"]]
-+ mkin_benchmarks[system_string, paste0("t", 1:11)] <-
   c(t1, t2, t3, t4, t5, t6, t7, t8, t9, t10, t11)
 save(mkin_benchmarks, file = "~/git/mkin/vignettes/web_only/mkin_benchmarks.rda")
@@ -235,6 +228,16 @@
 1.786
 3.729
 
+
+1.0.3
+1.722
+3.419
+
+
+1.0.3.9000
+2.770
+3.458
+
 
 
 
@@ -298,13 +301,25 @@
 7.251
 2.810
 
+
+1.0.3
+1.402
+6.343
+2.802
+
+
+1.0.3.9000
+1.405
+6.417
+2.824
+
 
 
 
 
 
 Two metabolites
-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.
+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.
 
@@ -388,6 +403,24 @@
 
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
 
 mkin version 1.958
 3.105
 
1.0.3 0.771 1.251 1.464 3.074 1.940 2.831
1.0.3.9000 0.772 1.263 1.483 3.101 1.958 2.843
 
 
 
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  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 @@
       
       
         mkin
-        0.9.50.4
+        1.0.3.9000
       
     
 
@@ -81,7 +81,7 @@
 
 
   
-    
+    
      
   
 
@@ -95,14 +95,13 @@
 
       
 
-      
-
+      
   
     
       Performance benefit by using compiled model definitions in mkin
                         Johannes Ranke
             
-            2020-11-30
+            2021-02-15
       
       Source: vignettes/web_only/compiled_models.rmd
       compiled_models.rmd
@@ -160,10 +159,10 @@
   print("R package rbenchmark is not available")
 }

 ##                    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
+## 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
 We see that using the compiled model is by more than a factor of 10 faster than using deSolve without compiled code.
 
 
@@ -190,13 +189,13 @@
 }
 ## Temporary DLL for differentials generated and loaded
 ##                    test replications relative elapsed
-## 2     deSolve, compiled            1    1.000   0.483
-## 1 deSolve, not compiled            1   29.969  14.475
-Here we get a performance benefit of a factor of 30 using the version of the differential equation model compiled from C code!
-This vignette was built with mkin 0.9.50.4 on
+## 2     deSolve, compiled            1    1.000   0.541
+## 1 deSolve, not compiled            1   29.091  15.738
+Here we get a performance benefit of a factor of 29 using the version of the differential equation model compiled from C code!
+This vignette was built with mkin 1.0.3.9000 on
 ## R version 4.0.3 (2020-10-10)
 ## Platform: x86_64-pc-linux-gnu (64-bit)
-## Running under: Debian GNU/Linux 10 (buster)
+## Running under: Debian GNU/Linux bullseye/sid
 ## CPU model: AMD Ryzen 7 1700 Eight-Core Processor
 
   
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  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);
+  }
+});
-- 
cgit v1.2.1


From c73b2f30ec836c949885784ab576e814eb8070a9 Mon Sep 17 00:00:00 2001
From: Johannes Ranke 
Date: Tue, 9 Mar 2021 17:35:47 +0100
Subject: Some improvements for borderline cases

- fit_with_errors for saem()
- test_log_parms for mean_degparms() and saem()
---
 docs/dev/articles/index.html | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

(limited to 'docs/dev/articles')

diff --git a/docs/dev/articles/index.html b/docs/dev/articles/index.html
index 17ee4a69..3c00526e 100644
--- a/docs/dev/articles/index.html
+++ b/docs/dev/articles/index.html
@@ -71,7 +71,7 @@
       
       
         mkin
-        1.0.3.9000
+        1.0.4.9000
       
     
 
-- 
cgit v1.2.1


From 0c9b2f0e3c8ce65cb790c9e048476784cbbea070 Mon Sep 17 00:00:00 2001
From: Johannes Ranke 
Date: Fri, 11 Jun 2021 11:14:45 +0200
Subject: Finished 'summary.nlmixr.mmkin', checks, docs

---
 docs/dev/articles/index.html | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

(limited to 'docs/dev/articles')

diff --git a/docs/dev/articles/index.html b/docs/dev/articles/index.html
index 3c00526e..3896120a 100644
--- a/docs/dev/articles/index.html
+++ b/docs/dev/articles/index.html
@@ -71,7 +71,7 @@
       
       
         mkin
-        1.0.4.9000
+        1.0.5
       
     
 
-- 
cgit v1.2.1


From 0b754ffa91b9496bdd2f892cf3ca2bd887028dea Mon Sep 17 00:00:00 2001
From: Johannes Ranke 
Date: Tue, 27 Jul 2021 18:22:01 +0200
Subject: Fix dimethenamid vignette problems and update docs

---
 docs/dev/articles/index.html                       |   4 +-
 docs/dev/articles/web_only/dimethenamid_2018.html  | 420 +++++++++++++++++++++
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diff --git a/docs/dev/articles/index.html b/docs/dev/articles/index.html
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         mkin
-        1.0.5
+        1.1.0
       
     
 
@@ -161,6 +161,8 @@
         
         
Performance benefit by using compiled model definitions in mkin
         
+        
Example evaluations of the dimethenamid data from 2018
+        
       
     
   
diff --git a/docs/dev/articles/web_only/dimethenamid_2018.html b/docs/dev/articles/web_only/dimethenamid_2018.html
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+
+
+Example evaluations of the dimethenamid data from 2018 • mkin
+
+
+
+
+
+
+
+
+
+
+
+    
+      
+  
+    
+      
+      
+        mkin
+        1.1.0
+      
+    
+
+    
+      
+
+  Functions and data
+
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+  
+    Articles
+     
+    
+  
+  
+
+      Introduction to mkin
+    
+    
+      Example evaluation of FOCUS Example Dataset D
+    
+    
+      Example evaluation of FOCUS Laboratory Data L1 to L3
+    
+    
+      Example evaluation of FOCUS Example Dataset Z
+    
+    
+      Performance benefit by using compiled model definitions in mkin
+    
+    
+      Calculation of time weighted average concentrations with mkin
+    
+    
+      Example evaluation of NAFTA SOP Attachment examples
+    
+    
+      Some benchmark timings
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+      
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+      
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+      

+  
+    
+      Example evaluations of the dimethenamid data from 2018
+                        Johannes Ranke
+            
+            Last change 27 July 2021, built on 27 Jul 2021
+      
+      Source: vignettes/web_only/dimethenamid_2018.rmd
+      dimethenamid_2018.rmd
+
+    
+
+    
+    
+Wissenschaftlicher Berater, Kronacher Str. 12, 79639 Grenzach-Wyhlen, Germany
Privatdozent at the University of Bremen
+
+
+Introduction
+During the preparation of the journal article on nonlinear mixed-effects models in degradation kinetics (submitted) 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.
+This vignette is an attempt to satisfy this need.
+
+
+
+Data
+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 (EFSA 2018) were transcribed from the risk assessment report (Rapporteur Member State Germany, Co-Rapporteur Member State Bulgaria 2018) which can be downloaded from the EFSA register of questions.
+The data are available in the mkin package. 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.
+Also, datasets observed in the same soil are merged, resulting in dimethenamid (DMTA) data from six soils.
++library(mkin)
+dmta_ds <- lapply(1:8, function(i) {
+  ds_i <- dimethenamid_2018$ds[[i]]$data
+  ds_i[ds_i$name == "DMTAP", "name"] <-  "DMTA"
+  ds_i$time <- ds_i$time * dimethenamid_2018$f_time_norm[i]
+  ds_i
+})
+names(dmta_ds) <- sapply(dimethenamid_2018$ds, function(ds) ds$title)
+dmta_ds[["Borstel"]] <- rbind(dmta_ds[["Borstel 1"]], dmta_ds[["Borstel 2"]])
+dmta_ds[["Borstel 1"]] <- NULL
+dmta_ds[["Borstel 2"]] <- NULL
+dmta_ds[["Elliot"]] <- rbind(dmta_ds[["Elliot 1"]], dmta_ds[["Elliot 2"]])
+dmta_ds[["Elliot 1"]] <- NULL
+dmta_ds[["Elliot 2"]] <- NULL
+
+
+
+Parent degradation
+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.
+
+
+Separate evaluations
+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:
++f_parent_mkin_const <- mmkin(c("SFO", "DFOP"), dmta_ds,
+  error_model = "const", quiet = TRUE)
+f_parent_mkin_tc <- mmkin(c("SFO", "DFOP"), dmta_ds,
+  error_model = "tc", quiet = TRUE)
+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):
++plot(mixed(f_parent_mkin_const["SFO", ]))
+
+Using biexponential decline (DFOP) results in a slightly more random scatter of the residuals:
++plot(mixed(f_parent_mkin_const["DFOP", ]))
+
+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:
++plot(mixed(f_parent_mkin_const["DFOP", ]), test_log_parms = TRUE)
+
+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).
+The remaining trend of the residuals to be higher for higher predicted residues is reduced by using the two-component error model:
++plot(mixed(f_parent_mkin_tc["DFOP", ]), test_log_parms = TRUE)
+
+
+
+
+Nonlinear mixed-effects models
+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.
+
+
+nlme
+The nlme package was the first R extension providing facilities to fit nonlinear mixed-effects models. We use 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. However, 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.
++library(nlme)
+f_parent_nlme_sfo_const <- nlme(f_parent_mkin_const["SFO", ])
+#f_parent_nlme_dfop_const <- nlme(f_parent_mkin_const["DFOP", ])
+# maxIter = 50 reached
+f_parent_nlme_sfo_tc <- nlme(f_parent_mkin_tc["SFO", ])
+f_parent_nlme_dfop_tc <- nlme(f_parent_mkin_tc["DFOP", ])
+Note that overparameterisation is also indicated by warnings obtained when fitting SFO or DFOP with the two-component error model (‘false convergence’ in the ‘LME step’ in some iterations). 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.
++f_parent_nlme_sfo_const_logchol <- nlme(f_parent_mkin_const["SFO", ],
+  random = pdLogChol(list(DMTA_0 ~ 1, log_k_DMTA ~ 1)))
+anova(f_parent_nlme_sfo_const, f_parent_nlme_sfo_const_logchol) # not better
+#f_parent_nlme_dfop_tc_logchol <- update(f_parent_nlme_dfop_tc,
+#  random = pdLogChol(list(DMTA_0 ~ 1, log_k1 ~ 1, log_k2 ~ 1, g_qlogis ~ 1)))
+# using log Cholesky parameterisation for random effects (nlme default) does
+# not converge here and gives lots of warnings about the LME step not converging
+The model comparison function of the nlme package can directly be applied to these fits showing a similar goodness-of-fit of the SFO model, but 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.
++anova(
+  f_parent_nlme_sfo_const, f_parent_nlme_sfo_tc, f_parent_nlme_dfop_tc
+)
+                        Model df    AIC    BIC  logLik   Test L.Ratio p-value
+f_parent_nlme_sfo_const     1  5 818.63 834.00 -404.31                       
+f_parent_nlme_sfo_tc        2  6 820.61 839.06 -404.31 1 vs 2   0.014  0.9049
+f_parent_nlme_dfop_tc       3 10 687.84 718.59 -333.92 2 vs 3 140.771  <.0001
+The selected model (DFOP with two-component error) fitted to the data assuming no correlations between random effects is shown below.
++plot(f_parent_nlme_dfop_tc)
+
+
+
+
+saemix
+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 performed using an interface to the saemix package available in current development versions of the mkin package.
+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.
+The convergence plot for the SFO model using constant variance is shown below.
++library(saemix)
+f_parent_saemix_sfo_const <- mkin::saem(f_parent_mkin_const["SFO", ], quiet = TRUE,
+  transformations = "saemix")
+plot(f_parent_saemix_sfo_const$so, plot.type = "convergence")
+
+Obviously the default number of iterations is sufficient to reach convergence. This can also be said for the SFO fit using the two-component error model.
++f_parent_saemix_sfo_tc <- mkin::saem(f_parent_mkin_tc["SFO", ], quiet = TRUE,
+  transformations = "saemix")
+plot(f_parent_saemix_sfo_tc$so, plot.type = "convergence")
+
+When fitting the DFOP model with constant variance, parameter convergence is not as unambiguous (see the failure of nlme with the default number of iterations above). Therefore, the number of iterations in the first phase of the algorithm was increased, leading to visually satisfying convergence.
++f_parent_saemix_dfop_const <- mkin::saem(f_parent_mkin_const["DFOP", ], quiet = TRUE,
+  control = saemixControl(nbiter.saemix = c(800, 200), print = FALSE,
+    save = FALSE, save.graphs = FALSE, displayProgress = FALSE),
+  transformations = "saemix")
+plot(f_parent_saemix_dfop_const$so, plot.type = "convergence")
+
+The same applies to the case where the DFOP model is fitted with the two-component error model. Convergence of the variance of k2 is enhanced by using the two-component error, it remains more or less stable already after 200 iterations of the first phase.
++f_parent_saemix_dfop_tc_moreiter <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
+  control = saemixControl(nbiter.saemix = c(800, 200), print = FALSE,
+    save = FALSE, save.graphs = FALSE, displayProgress = FALSE),
+  transformations = "saemix")
+plot(f_parent_saemix_dfop_tc_moreiter$so, plot.type = "convergence")
+
+The four combinations can be compared using the model comparison function from the saemix package:
++compare.saemix(f_parent_saemix_sfo_const$so, f_parent_saemix_sfo_tc$so,
+  f_parent_saemix_dfop_const$so, f_parent_saemix_dfop_tc_moreiter$so)
+Likelihoods calculated by importance sampling
+     AIC    BIC
+1 818.37 817.33
+2 820.38 819.14
+3 725.91 724.04
+4 683.64 681.55
+As in the case of nlme fits, the DFOP model fitted with two-component error (number 4) gives the lowest AIC. The numeric values are reasonably close to the ones obtained using nlme, considering that the algorithms for fitting the model and for the likelihood calculation are quite different.
+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.
++f_parent_saemix_dfop_tc_moreiter$so <-
+  llgq.saemix(f_parent_saemix_dfop_tc_moreiter$so)
+AIC(f_parent_saemix_dfop_tc_moreiter$so)
+[1] 683.64
++AIC(f_parent_saemix_dfop_tc_moreiter$so, method = "gq")
+[1] 683.7
++AIC(f_parent_saemix_dfop_tc_moreiter$so, method = "lin")
+[1] 683.17
+The AIC values based on importance sampling and Gaussian quadrature are quite similar. Using linearisation is less accurate, but still gives a similar value.
+
+
+
+nlmixr
+In the last years, a lot of effort has been put into the nlmixr package which is designed for pharmacokinetics, where nonlinear mixed-effects models are routinely used, but which can also be used for related data like chemical degradation data. A current development branch of the mkin package provides an interface between mkin and nlmixr. Here, we check if we get equivalent results when using a refined version of the First Order Conditional Estimation (FOCE) algorithm used in nlme, namely First Order Conditional Estimation with Interaction (FOCEI), and the SAEM algorithm as implemented in nlmixr.
+First, the focei algorithm is used for the four model combinations and the goodness of fit of the results is compared.
++library(nlmixr)
+f_parent_nlmixr_focei_sfo_const <- nlmixr(f_parent_mkin_const["SFO", ], est = "focei")
+f_parent_nlmixr_focei_sfo_tc <- nlmixr(f_parent_mkin_tc["SFO", ], est = "focei")
+f_parent_nlmixr_focei_dfop_const <- nlmixr(f_parent_mkin_const["DFOP", ], est = "focei")
+f_parent_nlmixr_focei_dfop_tc<- nlmixr(f_parent_mkin_tc["DFOP", ], est = "focei")
++AIC(f_parent_nlmixr_focei_sfo_const$nm, f_parent_nlmixr_focei_sfo_tc$nm,
+  f_parent_nlmixr_focei_dfop_const$nm, f_parent_nlmixr_focei_dfop_tc$nm)
+                                    df    AIC
+f_parent_nlmixr_focei_sfo_const$nm   5 818.63
+f_parent_nlmixr_focei_sfo_tc$nm      6 820.61
+f_parent_nlmixr_focei_dfop_const$nm  9 728.11
+f_parent_nlmixr_focei_dfop_tc$nm    10 687.82
+The AIC values are very close to the ones obtained with nlme which are repeated below for convenience.
++AIC(
+  f_parent_nlme_sfo_const, f_parent_nlme_sfo_tc, f_parent_nlme_dfop_tc
+)
+                        df    AIC
+f_parent_nlme_sfo_const  5 818.63
+f_parent_nlme_sfo_tc     6 820.61
+f_parent_nlme_dfop_tc   10 687.84
+Secondly, we use the SAEM estimation routine and check the convergence plots for SFO with constant variance
++f_parent_nlmixr_saem_sfo_const <- nlmixr(f_parent_mkin_const["SFO", ], est = "saem",
+  control = nlmixr::saemControl(logLik = TRUE))
+traceplot(f_parent_nlmixr_saem_sfo_const$nm)
+
+for SFO with two-component error
++f_parent_nlmixr_saem_sfo_tc <- nlmixr(f_parent_mkin_tc["SFO", ], est = "saem",
+  control = nlmixr::saemControl(logLik = TRUE))
+traceplot(f_parent_nlmixr_saem_sfo_tc$nm)
+
+For DFOP with constant variance, the convergence plots show considerable instability of the fit, which can be alleviated by increasing the number of iterations and the number of parallel chains for the first phase of algorithm.
++f_parent_nlmixr_saem_dfop_const <- nlmixr(f_parent_mkin_const["DFOP", ], est = "saem",
+  control = nlmixr::saemControl(logLik = TRUE, nBurn = 1000), nmc = 15)
+traceplot(f_parent_nlmixr_saem_dfop_const$nm)
+
+For DFOP with two-component error, the same increase in iterations and parallel chains was used, but using the two-component error appears to lead to a less erratic convergence, so this may not be necessary to this degree.
++f_parent_nlmixr_saem_dfop_tc <- nlmixr(f_parent_mkin_tc["DFOP", ], est = "saem",
+  control = nlmixr::saemControl(logLik = TRUE, nBurn = 1000, nmc = 15))
+traceplot(f_parent_nlmixr_saem_dfop_tc$nm)
+
+The AIC values are internally calculated using Gaussian quadrature. For an unknown reason, the AIC value obtained for the DFOP fit using the two-component error model is given as Infinity.
++AIC(f_parent_nlmixr_saem_sfo_const$nm, f_parent_nlmixr_saem_sfo_tc$nm,
+  f_parent_nlmixr_saem_dfop_const$nm, f_parent_nlmixr_saem_dfop_tc$nm)
+                                   df    AIC
+f_parent_nlmixr_saem_sfo_const$nm   5 820.54
+f_parent_nlmixr_saem_sfo_tc$nm      6 835.26
+f_parent_nlmixr_saem_dfop_const$nm  9 842.84
+f_parent_nlmixr_saem_dfop_tc$nm    10 684.51
+The following table gives the AIC values obtained with the three packages.
++AIC_all <- data.frame(
+  nlme = c(AIC(f_parent_nlme_sfo_const), AIC(f_parent_nlme_sfo_tc), NA, AIC(f_parent_nlme_dfop_tc)),
+  nlmixr_focei = sapply(list(f_parent_nlmixr_focei_sfo_const$nm, f_parent_nlmixr_focei_sfo_tc$nm,
+  f_parent_nlmixr_focei_dfop_const$nm, f_parent_nlmixr_focei_dfop_tc$nm), AIC),
+  saemix = sapply(list(f_parent_saemix_sfo_const$so, f_parent_saemix_sfo_tc$so,
+    f_parent_saemix_dfop_const$so, f_parent_saemix_dfop_tc_moreiter$so), AIC),
+  nlmixr_saem = sapply(list(f_parent_nlmixr_saem_sfo_const$nm, f_parent_nlmixr_saem_sfo_tc$nm,
+  f_parent_nlmixr_saem_dfop_const$nm, f_parent_nlmixr_saem_dfop_tc$nm), AIC)
+)
+kable(AIC_all)
+
+
+
+
+
+
+
+
+
+
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+
+nlme nlmixr_focei saemix nlmixr_saem
818.63 818.63 818.37 820.54
820.61 820.61 820.38 835.26
NA 728.11 725.91 842.84
687.84 687.82 683.64 684.51
+
+
+
+
+
+References
+
+
+
+EFSA. 2018. “Peer Review of the Pesticide Risk Assessment of the Active Substance Dimethenamid-P.” EFSA Journal 16 (4): 5211.
+
+
+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.” https://open.efsa.europa.eu/study-inventory/EFSA-Q-2014-00716.
+
+
+
+  
+
+  
+
+        Contents
+    
+
+
+
+
+
+
+      
+  Developed by Johannes Ranke.
+
+
+
+  Site built with pkgdown 1.6.1.
+
+
+      
+
+
+  
+
+
+  
+
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
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+// Hide empty  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
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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
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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
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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
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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
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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
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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
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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
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index 00000000..a4695eea
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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
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index 00000000..1c8fc837
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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
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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..d26bcc09
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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..6edeb794
Binary files /dev/null and b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/plot_parent_nlme-1.png differ
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);
+  }
+});
-- 
cgit v1.2.1


From 137612045c23198f10d6e8612c32e266c2a6c00e Mon Sep 17 00:00:00 2001
From: Johannes Ranke 
Date: Thu, 29 Jul 2021 12:17:56 +0200
Subject: Go back to 1.0.x version, update docs

---
 docs/dev/articles/index.html                      |  2 +-
 docs/dev/articles/web_only/dimethenamid_2018.html | 14 +++++++-------
 2 files changed, 8 insertions(+), 8 deletions(-)

(limited to 'docs/dev/articles')

diff --git a/docs/dev/articles/index.html b/docs/dev/articles/index.html
index c0338df8..99ce950b 100644
--- a/docs/dev/articles/index.html
+++ b/docs/dev/articles/index.html
@@ -71,7 +71,7 @@
       
       
         mkin
-        1.1.0
+        1.0.5
       
     
 
diff --git a/docs/dev/articles/web_only/dimethenamid_2018.html b/docs/dev/articles/web_only/dimethenamid_2018.html
index 7648f75a..34d882a4 100644
--- a/docs/dev/articles/web_only/dimethenamid_2018.html
+++ b/docs/dev/articles/web_only/dimethenamid_2018.html
@@ -32,7 +32,7 @@
       
       
         mkin
-        1.1.0
+        1.0.5
       
     
 
@@ -101,7 +101,7 @@
       Example evaluations of the dimethenamid data from 2018
                         Johannes Ranke
             
-            Last change 27 July 2021, built on 27 Jul 2021
+            Last change 27 July 2021, built on 29 Jul 2021
       
       Source: vignettes/web_only/dimethenamid_2018.rmd
       dimethenamid_2018.rmd
@@ -154,20 +154,20 @@
   error_model = "tc", quiet = TRUE)
 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):
 -plot(mixed(f_parent_mkin_const["SFO", ]))
+plot(mixed(f_parent_mkin_const["SFO", ]))
 
 Using biexponential decline (DFOP) results in a slightly more random scatter of the residuals:
 -plot(mixed(f_parent_mkin_const["DFOP", ]))
+plot(mixed(f_parent_mkin_const["DFOP", ]))
 
 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:
 -plot(mixed(f_parent_mkin_const["DFOP", ]), test_log_parms = TRUE)
+plot(mixed(f_parent_mkin_const["DFOP", ]), test_log_parms = TRUE)
 
 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).
 The remaining trend of the residuals to be higher for higher predicted residues is reduced by using the two-component error model:
 -plot(mixed(f_parent_mkin_tc["DFOP", ]), test_log_parms = TRUE)
+plot(mixed(f_parent_mkin_tc["DFOP", ]), test_log_parms = TRUE)
 
 
 
@@ -205,7 +205,7 @@ f_parent_nlme_sfo_tc        2  6 820.61 839.06 -404.31 1 vs 2   0.014  0.9049
 f_parent_nlme_dfop_tc       3 10 687.84 718.59 -333.92 2 vs 3 140.771  <.0001
 The selected model (DFOP with two-component error) fitted to the data assuming no correlations between random effects is shown below.
 -plot(f_parent_nlme_dfop_tc)
+plot(f_parent_nlme_dfop_tc)
 
 
 
-- 
cgit v1.2.1


From 51fab94230e926cec690dc455964bd797a97b7c7 Mon Sep 17 00:00:00 2001
From: Johannes Ranke 
Date: Wed, 4 Aug 2021 16:37:52 +0200
Subject: Improve AIC table in vignette

---
 docs/dev/articles/web_only/dimethenamid_2018.html | 14 +++++++++++++-
 1 file changed, 13 insertions(+), 1 deletion(-)

(limited to 'docs/dev/articles')

diff --git a/docs/dev/articles/web_only/dimethenamid_2018.html b/docs/dev/articles/web_only/dimethenamid_2018.html
index 34d882a4..9a6d8388 100644
--- a/docs/dev/articles/web_only/dimethenamid_2018.html
+++ b/docs/dev/articles/web_only/dimethenamid_2018.html
@@ -101,7 +101,7 @@
       Example evaluations of the dimethenamid data from 2018
                         Johannes Ranke
             
-            Last change 27 July 2021, built on 29 Jul 2021
+            Last change 4 August 2021, built on 04 Aug 2021
       
       Source: vignettes/web_only/dimethenamid_2018.rmd
       dimethenamid_2018.rmd
@@ -331,6 +331,8 @@ f_parent_nlmixr_saem_dfop_tc$nm    10 684.51
 The following table gives the AIC values obtained with the three packages.
  AIC_all <- data.frame(
+  "Degradation model" = c("SFO", "SFO", "DFOP", "DFOP"),
+  "Error model" = c("const", "tc", "const", "tc"),
   nlme = c(AIC(f_parent_nlme_sfo_const), AIC(f_parent_nlme_sfo_tc), NA, AIC(f_parent_nlme_dfop_tc)),
   nlmixr_focei = sapply(list(f_parent_nlmixr_focei_sfo_const$nm, f_parent_nlmixr_focei_sfo_tc$nm,
   f_parent_nlmixr_focei_dfop_const$nm, f_parent_nlmixr_focei_dfop_tc$nm), AIC),
@@ -342,6 +344,8 @@ f_parent_nlmixr_saem_dfop_tc$nm    10 684.51
 kable(AIC_all)
 
+
+
@@ -349,24 +353,32 @@ f_parent_nlmixr_saem_dfop_tc$nm    10 684.51
+
+
+
+
+
+
+
+
-- 
cgit v1.2.1


From c41381a961263c28d60976e68923157916c78b15 Mon Sep 17 00:00:00 2001
From: Johannes Ranke 
Date: Thu, 16 Sep 2021 15:31:13 +0200
Subject: Adapt and improve the dimethenamid vignette

Adapt to the corrected data and unify control parameters for saemix and
nlmixr with saem. Update docs
---
 docs/dev/articles/index.html                       |   2 +-
 docs/dev/articles/web_only/dimethenamid_2018.html  | 245 +++++++++++----------
 .../figure-html/f_parent_mkin_dfop_const-1.png     | Bin 145534 -> 141661 bytes
 .../f_parent_mkin_dfop_const_test-1.png            | Bin 146181 -> 141889 bytes
 .../figure-html/f_parent_mkin_dfop_tc_test-1.png   | Bin 150274 -> 144254 bytes
 .../figure-html/f_parent_mkin_sfo_const-1.png      | Bin 141499 -> 137650 bytes
 .../f_parent_nlmixr_saem_dfop_const-1.png          | Bin 180061 -> 174055 bytes
 .../figure-html/f_parent_nlmixr_saem_dfop_tc-1.png | Bin 151832 -> 162039 bytes
 .../f_parent_nlmixr_saem_sfo_const-1.png           | Bin 124946 -> 142453 bytes
 .../figure-html/f_parent_nlmixr_saem_sfo_tc-1.png  | Bin 140491 -> 144010 bytes
 .../figure-html/f_parent_saemix_dfop_const-1.png   | Bin 58759 -> 55927 bytes
 .../figure-html/f_parent_saemix_dfop_tc-1.png      | Bin 0 -> 43674 bytes
 .../figure-html/f_parent_saemix_sfo_const-1.png    | Bin 59913 -> 55667 bytes
 .../figure-html/f_parent_saemix_sfo_tc-1.png       | Bin 53550 -> 50848 bytes
 .../figure-html/plot_parent_nlme-1.png             | Bin 147409 -> 143978 bytes
 .../header-attrs-2.11/header-attrs.js              |  12 +
 16 files changed, 140 insertions(+), 119 deletions(-)
 create mode 100644 docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc-1.png
 create mode 100644 docs/dev/articles/web_only/dimethenamid_2018_files/header-attrs-2.11/header-attrs.js

(limited to 'docs/dev/articles')

diff --git a/docs/dev/articles/index.html b/docs/dev/articles/index.html
index 99ce950b..c0338df8 100644
--- a/docs/dev/articles/index.html
+++ b/docs/dev/articles/index.html
@@ -71,7 +71,7 @@
       
       
         mkin
-        1.0.5
+        1.1.0
       
     
 
diff --git a/docs/dev/articles/web_only/dimethenamid_2018.html b/docs/dev/articles/web_only/dimethenamid_2018.html
index 9a6d8388..b35d8210 100644
--- a/docs/dev/articles/web_only/dimethenamid_2018.html
+++ b/docs/dev/articles/web_only/dimethenamid_2018.html
@@ -32,7 +32,7 @@
       
       
         mkin
-        1.0.5
+        1.1.0
       
     
 
@@ -95,13 +95,13 @@
 
       
 
-      
+      
   
     
       Example evaluations of the dimethenamid data from 2018
                         Johannes Ranke
             
-            Last change 4 August 2021, built on 04 Aug 2021
+            Last change 16 September 2021, built on 16 Sep 2021
       
       Source: vignettes/web_only/dimethenamid_2018.rmd
       dimethenamid_2018.rmd
@@ -110,31 +110,28 @@
 
     
     
-Wissenschaftlicher Berater, Kronacher Str. 12, 79639 Grenzach-Wyhlen, Germany
Privatdozent at the University of Bremen
+Wissenschaftlicher Berater, Kronacher Str. 12, 79639 Grenzach-Wyhlen, Germany
 
 
 Introduction
-During the preparation of the journal article on nonlinear mixed-effects models in degradation kinetics (submitted) 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.
+During the preparation of the journal article on nonlinear mixed-effects models in degradation kinetics (Ranke et al. 2021) 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.
 This vignette is an attempt to satisfy this need.
 
 
 
 Data
-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 (EFSA 2018) were transcribed from the risk assessment report (Rapporteur Member State Germany, Co-Rapporteur Member State Bulgaria 2018) which can be downloaded from the EFSA register of questions.
+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 (EFSA 2018) were transcribed from the risk assessment report (Rapporteur Member State Germany, Co-Rapporteur Member State Bulgaria 2018) which can be downloaded from the Open EFSA repository https://open.efsa.europa.eu/study-inventory/EFSA-Q-2014-00716.
 The data are available in the mkin package. 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.
 Also, datasets observed in the same soil are merged, resulting in dimethenamid (DMTA) data from six soils.
  library(mkin)
-dmta_ds <- lapply(1:8, function(i) {
+dmta_ds <- lapply(1:7, function(i) {
   ds_i <- dimethenamid_2018$ds[[i]]$data
   ds_i[ds_i$name == "DMTAP", "name"] <-  "DMTA"
   ds_i$time <- ds_i$time * dimethenamid_2018$f_time_norm[i]
   ds_i
 })
 names(dmta_ds) <- sapply(dimethenamid_2018$ds, function(ds) ds$title)
-dmta_ds[["Borstel"]] <- rbind(dmta_ds[["Borstel 1"]], dmta_ds[["Borstel 2"]])
-dmta_ds[["Borstel 1"]] <- NULL
-dmta_ds[["Borstel 2"]] <- NULL
 dmta_ds[["Elliot"]] <- rbind(dmta_ds[["Elliot 1"]], dmta_ds[["Elliot 2"]])
 dmta_ds[["Elliot 1"]] <- NULL
 dmta_ds[["Elliot 2"]] <- NULL
@@ -154,20 +151,20 @@
   error_model = "tc", quiet = TRUE)
 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):
 -plot(mixed(f_parent_mkin_const["SFO", ]))
+plot(mixed(f_parent_mkin_const["SFO", ]))
 
 Using biexponential decline (DFOP) results in a slightly more random scatter of the residuals:
 -plot(mixed(f_parent_mkin_const["DFOP", ]))
+plot(mixed(f_parent_mkin_const["DFOP", ]))
 
 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:
 -plot(mixed(f_parent_mkin_const["DFOP", ]), test_log_parms = TRUE)
+plot(mixed(f_parent_mkin_const["DFOP", ]), test_log_parms = TRUE)
 
 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).
 The remaining trend of the residuals to be higher for higher predicted residues is reduced by using the two-component error model:
 -plot(mixed(f_parent_mkin_tc["DFOP", ]), test_log_parms = TRUE)
+plot(mixed(f_parent_mkin_tc["DFOP", ]), test_log_parms = TRUE)
 
 
 
@@ -177,175 +174,184 @@
 
 
 nlme
-The nlme package was the first R extension providing facilities to fit nonlinear mixed-effects models. We use 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. However, 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.
+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. However, 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.
  library(nlme)
 f_parent_nlme_sfo_const <- nlme(f_parent_mkin_const["SFO", ])
-#f_parent_nlme_dfop_const <- nlme(f_parent_mkin_const["DFOP", ])
-# maxIter = 50 reached
+# f_parent_nlme_dfop_const <- nlme(f_parent_mkin_const["DFOP", ])
 f_parent_nlme_sfo_tc <- nlme(f_parent_mkin_tc["SFO", ])
 f_parent_nlme_dfop_tc <- nlme(f_parent_mkin_tc["DFOP", ])
-Note that overparameterisation is also indicated by warnings obtained when fitting SFO or DFOP with the two-component error model (‘false convergence’ in the ‘LME step’ in some iterations). 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.
+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.
+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.
 -f_parent_nlme_sfo_const_logchol <- nlme(f_parent_mkin_const["SFO", ],
-  random = pdLogChol(list(DMTA_0 ~ 1, log_k_DMTA ~ 1)))
-anova(f_parent_nlme_sfo_const, f_parent_nlme_sfo_const_logchol) # not better
-#f_parent_nlme_dfop_tc_logchol <- update(f_parent_nlme_dfop_tc,
-#  random = pdLogChol(list(DMTA_0 ~ 1, log_k1 ~ 1, log_k2 ~ 1, g_qlogis ~ 1)))
-# using log Cholesky parameterisation for random effects (nlme default) does
-# not converge here and gives lots of warnings about the LME step not converging
-The model comparison function of the nlme package can directly be applied to these fits showing a similar goodness-of-fit of the SFO model, but 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.
- anova(
   f_parent_nlme_sfo_const, f_parent_nlme_sfo_tc, f_parent_nlme_dfop_tc
 )
                         Model df    AIC    BIC  logLik   Test L.Ratio p-value
-f_parent_nlme_sfo_const     1  5 818.63 834.00 -404.31                       
-f_parent_nlme_sfo_tc        2  6 820.61 839.06 -404.31 1 vs 2   0.014  0.9049
-f_parent_nlme_dfop_tc       3 10 687.84 718.59 -333.92 2 vs 3 140.771  <.0001
+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  <.0001
+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.
++f_parent_nlme_sfo_const_logchol <- nlme(f_parent_mkin_const["SFO", ],
+  random = nlme::pdLogChol(list(DMTA_0 ~ 1, log_k_DMTA ~ 1)))
+anova(f_parent_nlme_sfo_const, f_parent_nlme_sfo_const_logchol)
+f_parent_nlme_sfo_tc_logchol <- nlme(f_parent_mkin_tc["SFO", ],
+  random = nlme::pdLogChol(list(DMTA_0 ~ 1, log_k_DMTA ~ 1)))
+anova(f_parent_nlme_sfo_tc, f_parent_nlme_sfo_tc_logchol)
+f_parent_nlme_dfop_tc_logchol <- nlme(f_parent_mkin_const["DFOP", ],
+  random = nlme::pdLogChol(list(DMTA_0 ~ 1, log_k1 ~ 1, log_k2 ~ 1, g_qlogis ~ 1)))
+anova(f_parent_nlme_dfop_tc, f_parent_nlme_dfop_tc_logchol)
+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.
 The selected model (DFOP with two-component error) fitted to the data assuming no correlations between random effects is shown below.
 -plot(f_parent_nlme_dfop_tc)
+plot(f_parent_nlme_dfop_tc)
 
 
 
 
 saemix
-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 performed using an interface to the saemix package available in current development versions of the mkin package.
-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.
-The convergence plot for the SFO model using constant variance is shown below.
+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.
+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.
  library(saemix)
-f_parent_saemix_sfo_const <- mkin::saem(f_parent_mkin_const["SFO", ], quiet = TRUE,
-  transformations = "saemix")
+saemix_control <- saemixControl(nbiter.saemix = c(800, 300), nb.chains = 15,
+    print = FALSE, save = FALSE, save.graphs = FALSE, displayProgress = FALSE)
+The convergence plot for the SFO model using constant variance is shown below.
++f_parent_saemix_sfo_const <- mkin::saem(f_parent_mkin_const["SFO", ], quiet = TRUE,
+  control = saemix_control, transformations = "saemix")
 plot(f_parent_saemix_sfo_const$so, plot.type = "convergence")
 
 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.
-+ f_parent_saemix_sfo_tc <- mkin::saem(f_parent_mkin_tc["SFO", ], quiet = TRUE,
-  transformations = "saemix")
+  control = saemix_control, transformations = "saemix")
 plot(f_parent_saemix_sfo_tc$so, plot.type = "convergence")
 
 When fitting the DFOP model with constant variance, parameter convergence is not as unambiguous (see the failure of nlme with the default number of iterations above). Therefore, the number of iterations in the first phase of the algorithm was increased, leading to visually satisfying convergence.
-+ f_parent_saemix_dfop_const <- mkin::saem(f_parent_mkin_const["DFOP", ], quiet = TRUE,
-  control = saemixControl(nbiter.saemix = c(800, 200), print = FALSE,
-    save = FALSE, save.graphs = FALSE, displayProgress = FALSE),
-  transformations = "saemix")
+  control = saemix_control, transformations = "saemix")
 plot(f_parent_saemix_dfop_const$so, plot.type = "convergence")
 
-The same applies to the case where the DFOP model is fitted with the two-component error model. Convergence of the variance of k2 is enhanced by using the two-component error, it remains more or less stable already after 200 iterations of the first phase.
--f_parent_saemix_dfop_tc_moreiter <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
-  control = saemixControl(nbiter.saemix = c(800, 200), print = FALSE,
-    save = FALSE, save.graphs = FALSE, displayProgress = FALSE),
-  transformations = "saemix")
-plot(f_parent_saemix_dfop_tc_moreiter$so, plot.type = "convergence")
-
-The four combinations can be compared using the model comparison function from the saemix package:
+The same applies in the case where the DFOP model is fitted with the two-component error model. Convergence of the variance of k2 is enhanced by using the two-component error, it remains more or less stable already after 200 iterations of the first phase.
 -compare.saemix(f_parent_saemix_sfo_const$so, f_parent_saemix_sfo_tc$so,
-  f_parent_saemix_dfop_const$so, f_parent_saemix_dfop_tc_moreiter$so)
+f_parent_saemix_dfop_tc <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
+  control = saemix_control, transformations = "saemix")
+plot(f_parent_saemix_dfop_tc$so, plot.type = "convergence")
+ The four combinations and including the variations of the DFOP/tc combination can be compared using the model comparison function from the saemix package:
++compare.saemix(
+  f_parent_saemix_sfo_const$so,
+  f_parent_saemix_sfo_tc$so,
+  f_parent_saemix_dfop_const$so,
+  f_parent_saemix_dfop_tc$so)
 Likelihoods calculated by importance sampling
      AIC    BIC
-1 818.37 817.33
-2 820.38 819.14
-3 725.91 724.04
-4 683.64 681.55
-As in the case of nlme fits, the DFOP model fitted with two-component error (number 4) gives the lowest AIC. The numeric values are reasonably close to the ones obtained using nlme, considering that the algorithms for fitting the model and for the likelihood calculation are quite different.
+1 796.37 795.33
+2 798.37 797.13
+3 713.16 711.28
+4 666.10 664.01
+As in the case of nlme fits, the DFOP model fitted with two-component error (number 4) gives the lowest AIC. Using more iterations and/or more chains does not have a large influence on the final AIC (not shown).
 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.
--f_parent_saemix_dfop_tc_moreiter$so <-
-  llgq.saemix(f_parent_saemix_dfop_tc_moreiter$so)
-AIC(f_parent_saemix_dfop_tc_moreiter$so)
-[1] 683.64
--AIC(f_parent_saemix_dfop_tc_moreiter$so, method = "gq")
-[1] 683.7
--AIC(f_parent_saemix_dfop_tc_moreiter$so, method = "lin")
-[1] 683.17
-The AIC values based on importance sampling and Gaussian quadrature are quite similar. Using linearisation is less accurate, but still gives a similar value.
++f_parent_saemix_dfop_tc$so <-
+  llgq.saemix(f_parent_saemix_dfop_tc$so)
+AIC(f_parent_saemix_dfop_tc$so)
+[1] 666.1
++AIC(f_parent_saemix_dfop_tc$so, method = "gq")
+[1] 666.03
++AIC(f_parent_saemix_dfop_tc$so, method = "lin")
+[1] 665.48
+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.
 
 
 
 nlmixr
-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 First Order Conditional Estimation with Interaction (FOCEI), and the SAEM algorithm as implemented in nlmixr.
-First, the focei algorithm is used for the four model combinations and the goodness of fit of the results is compared.
-+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.
+First, the focei algorithm is used for the four model combinations. A number of warnings are produced with unclear significance.
+ library(nlmixr)
 f_parent_nlmixr_focei_sfo_const <- nlmixr(f_parent_mkin_const["SFO", ], est = "focei")
 f_parent_nlmixr_focei_sfo_tc <- nlmixr(f_parent_mkin_tc["SFO", ], est = "focei")
 f_parent_nlmixr_focei_dfop_const <- nlmixr(f_parent_mkin_const["DFOP", ], est = "focei")
 f_parent_nlmixr_focei_dfop_tc<- nlmixr(f_parent_mkin_tc["DFOP", ], est = "focei")
--AIC(f_parent_nlmixr_focei_sfo_const$nm, f_parent_nlmixr_focei_sfo_tc$nm,
-  f_parent_nlmixr_focei_dfop_const$nm, f_parent_nlmixr_focei_dfop_tc$nm)
-                                    df    AIC
-f_parent_nlmixr_focei_sfo_const$nm   5 818.63
-f_parent_nlmixr_focei_sfo_tc$nm      6 820.61
-f_parent_nlmixr_focei_dfop_const$nm  9 728.11
-f_parent_nlmixr_focei_dfop_tc$nm    10 687.82
++aic_nlmixr_focei <- sapply(
+  list(f_parent_nlmixr_focei_sfo_const$nm, f_parent_nlmixr_focei_sfo_tc$nm,
+    f_parent_nlmixr_focei_dfop_const$nm, f_parent_nlmixr_focei_dfop_tc$nm),
+  AIC)
 The AIC values are very close to the ones obtained with nlme which are repeated below for convenience.
 -AIC(
-  f_parent_nlme_sfo_const, f_parent_nlme_sfo_tc, f_parent_nlme_dfop_tc
+aic_nlme <- sapply(
+  list(f_parent_nlme_sfo_const, NA, f_parent_nlme_sfo_tc, f_parent_nlme_dfop_tc),
+  function(x) if (is.na(x[1])) NA else AIC(x))
+aic_nlme_nlmixr_focei <- data.frame(
+  "Degradation model" = c("SFO", "SFO", "DFOP", "DFOP"),
+  "Error model" = rep(c("constant variance", "two-component"), 2),
+  "AIC (nlme)" = aic_nlme,
+  "AIC (nlmixr with FOCEI)" = aic_nlmixr_focei,
+  check.names = FALSE
 )

-                        df    AIC
-f_parent_nlme_sfo_const  5 818.63
-f_parent_nlme_sfo_tc     6 820.61
-f_parent_nlme_dfop_tc   10 687.84
-Secondly, we use the SAEM estimation routine and check the convergence plots for SFO with constant variance
+Secondly, we use the SAEM estimation routine and check the convergence plots. The control parameters also used for the saemix fits are defined beforehand.
++nlmixr_saem_control <- saemControl(logLik = TRUE,
+  nBurn = 1000, nEm = 300, nmc = 15)
+The we fit SFO with constant variance
  f_parent_nlmixr_saem_sfo_const <- nlmixr(f_parent_mkin_const["SFO", ], est = "saem",
-  control = nlmixr::saemControl(logLik = TRUE))
+  control = nlmixr_saem_control)
 traceplot(f_parent_nlmixr_saem_sfo_const$nm)
 
-for SFO with two-component error
+and SFO with two-component error.
  f_parent_nlmixr_saem_sfo_tc <- nlmixr(f_parent_mkin_tc["SFO", ], est = "saem",
-  control = nlmixr::saemControl(logLik = TRUE))
+  control = nlmixr_saem_control)
 traceplot(f_parent_nlmixr_saem_sfo_tc$nm)
 
-For DFOP with constant variance, the convergence plots show considerable instability of the fit, which can be alleviated by increasing the number of iterations and the number of parallel chains for the first phase of algorithm.
+For DFOP with constant variance, the convergence plots show considerable instability of the fit, which indicates overparameterisation which was already observed earlier for this model combination.
  f_parent_nlmixr_saem_dfop_const <- nlmixr(f_parent_mkin_const["DFOP", ], est = "saem",
-  control = nlmixr::saemControl(logLik = TRUE, nBurn = 1000), nmc = 15)
+  control = nlmixr_saem_control)
 traceplot(f_parent_nlmixr_saem_dfop_const$nm)
 
-For DFOP with two-component error, the same increase in iterations and parallel chains was used, but using the two-component error appears to lead to a less erratic convergence, so this may not be necessary to this degree.
+For DFOP with two-component error, a less erratic convergence is seen.
  f_parent_nlmixr_saem_dfop_tc <- nlmixr(f_parent_mkin_tc["DFOP", ], est = "saem",
-  control = nlmixr::saemControl(logLik = TRUE, nBurn = 1000, nmc = 15))
+  control = nlmixr_saem_control)
 traceplot(f_parent_nlmixr_saem_dfop_tc$nm)
 
-The AIC values are internally calculated using Gaussian quadrature. For an unknown reason, the AIC value obtained for the DFOP fit using the two-component error model is given as Infinity.
+The AIC values are internally calculated using Gaussian quadrature. For an unknown reason, the AIC value obtained for the DFOP fit using constant error is given as Infinity.
  AIC(f_parent_nlmixr_saem_sfo_const$nm, f_parent_nlmixr_saem_sfo_tc$nm,
   f_parent_nlmixr_saem_dfop_const$nm, f_parent_nlmixr_saem_dfop_tc$nm)
                                    df    AIC
-f_parent_nlmixr_saem_sfo_const$nm   5 820.54
-f_parent_nlmixr_saem_sfo_tc$nm      6 835.26
-f_parent_nlmixr_saem_dfop_const$nm  9 842.84
-f_parent_nlmixr_saem_dfop_tc$nm    10 684.51
+f_parent_nlmixr_saem_sfo_const$nm   5 798.68
+f_parent_nlmixr_saem_sfo_tc$nm      6 808.88
+f_parent_nlmixr_saem_dfop_const$nm  9 815.95
+f_parent_nlmixr_saem_dfop_tc$nm    10 669.57
 The following table gives the AIC values obtained with the three packages.
  AIC_all <- data.frame(
+  check.names = FALSE,
   "Degradation model" = c("SFO", "SFO", "DFOP", "DFOP"),
   "Error model" = c("const", "tc", "const", "tc"),
   nlme = c(AIC(f_parent_nlme_sfo_const), AIC(f_parent_nlme_sfo_tc), NA, AIC(f_parent_nlme_dfop_tc)),
   nlmixr_focei = sapply(list(f_parent_nlmixr_focei_sfo_const$nm, f_parent_nlmixr_focei_sfo_tc$nm,
   f_parent_nlmixr_focei_dfop_const$nm, f_parent_nlmixr_focei_dfop_tc$nm), AIC),
   saemix = sapply(list(f_parent_saemix_sfo_const$so, f_parent_saemix_sfo_tc$so,
-    f_parent_saemix_dfop_const$so, f_parent_saemix_dfop_tc_moreiter$so), AIC),
+    f_parent_saemix_dfop_const$so, f_parent_saemix_dfop_tc$so), AIC),
   nlmixr_saem = sapply(list(f_parent_nlmixr_saem_sfo_const$nm, f_parent_nlmixr_saem_sfo_tc$nm,
   f_parent_nlmixr_saem_dfop_const$nm, f_parent_nlmixr_saem_dfop_tc$nm), AIC)
 )
 kable(AIC_all)
 
 Degradation.model Error.model
 nlme
 nlmixr_focei
 saemix
 
 
 SFO const
 818.63
 818.63
 818.37
 820.54
 
 SFO tc
 820.61
 820.61
 820.38
 835.26
 
 DFOP const
 NA
 728.11
 725.91
 842.84
 
 DFOP tc
 687.84
 687.82
 683.64
-
-
+
+
@@ -355,34 +361,34 @@ f_parent_nlmixr_saem_dfop_tc$nm    10 684.51
-
-
-
-
+
+
+
+
-
-
-
-
+
+
+
+
-
-
-
+
+
+
-
-
-
-
+
+
+
+
 Degradation.model Error.model Degradation model Error model
 nlme
 nlmixr_focei
 saemix
 

 SFO
 const 818.63 818.63 818.37 820.54 796.60 796.62 796.37 798.68
 
 
 SFO
 tc 820.61 820.61 820.38 835.26 798.60 798.61 798.37 808.88
 
 
 DFOP
 const
 NA 728.11 725.91 842.84 750.91 713.16 815.95
 
 
 DFOP
 tc 687.84 687.82 683.64 684.51 671.91 666.60 666.10 669.57
 
 
 
@@ -397,6 +403,9 @@ f_parent_nlmixr_saem_dfop_tc$nm    10 684.51
 
 EFSA. 2018. “Peer Review of the Pesticide Risk Assessment of the Active Substance Dimethenamid-P.” EFSA Journal 16 (4): 5211.
 
+
+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.” Environments 8 (8). https://doi.org/10.3390/environments8080071.
+
 
 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.” https://open.efsa.europa.eu/study-inventory/EFSA-Q-2014-00716.
 
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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
index 469ebafd..18b546e9 100644
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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
index d26bcc09..6a0c05c5 100644
Binary files a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_tc-1.png and b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_tc-1.png differ
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
index 6edeb794..ed978664 100644
Binary files a/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/plot_parent_nlme-1.png and b/docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/plot_parent_nlme-1.png differ
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);
+  }
+});
-- 
cgit v1.2.1


From 047d048b89e167fb354b45cd7c6b719b9f4cdd28 Mon Sep 17 00:00:00 2001
From: Johannes Ranke 
Date: Fri, 17 Sep 2021 08:47:09 +0200
Subject: Put the AIC comparison in a subsubsection

---
 docs/dev/articles/web_only/dimethenamid_2018.html | 46 ++++++++++++-----------
 1 file changed, 25 insertions(+), 21 deletions(-)

(limited to 'docs/dev/articles')

diff --git a/docs/dev/articles/web_only/dimethenamid_2018.html b/docs/dev/articles/web_only/dimethenamid_2018.html
index b35d8210..26b352e1 100644
--- a/docs/dev/articles/web_only/dimethenamid_2018.html
+++ b/docs/dev/articles/web_only/dimethenamid_2018.html
@@ -101,7 +101,7 @@
       Example evaluations of the dimethenamid data from 2018
                         Johannes Ranke
             
-            Last change 16 September 2021, built on 16 Sep 2021
+            Last change 17 September 2021, built on 17 Sep 2021
       
       Source: vignettes/web_only/dimethenamid_2018.rmd
       dimethenamid_2018.rmd
@@ -114,7 +114,7 @@
 
 
 Introduction
-During the preparation of the journal article on nonlinear mixed-effects models in degradation kinetics (Ranke et al. 2021) 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.
+During the preparation of the journal article on nonlinear mixed-effects models in degradation kinetics (Ranke et al. 2021) 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.
 This vignette is an attempt to satisfy this need.
 
 
@@ -124,7 +124,7 @@
 The data are available in the mkin package. 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.
 Also, datasets observed in the same soil are merged, resulting in dimethenamid (DMTA) data from six soils.
 -library(mkin)
+library(mkin, quietly = TRUE)
 dmta_ds <- lapply(1:7, function(i) {
   ds_i <- dimethenamid_2018$ds[[i]]$data
   ds_i[ds_i$name == "DMTAP", "name"] <-  "DMTA"
@@ -258,14 +258,14 @@ f_parent_nlme_dfop_tc       3 10 671.91 702.34 -325.96 2 vs 3  134.69  <.0001
  f_parent_saemix_dfop_tc$so <-
   llgq.saemix(f_parent_saemix_dfop_tc$so)
-AIC(f_parent_saemix_dfop_tc$so)
-[1] 666.1
--AIC(f_parent_saemix_dfop_tc$so, method = "gq")
-[1] 666.03
--AIC(f_parent_saemix_dfop_tc$so, method = "lin")
-[1] 665.48
+AIC_parent_saemix_methods <- c(
+  is = AIC(f_parent_saemix_dfop_tc$so, method = "is"),
+  gq = AIC(f_parent_saemix_dfop_tc$so, method = "gq"),
+  lin = AIC(f_parent_saemix_dfop_tc$so, method = "lin")
+)
+print(AIC_parent_saemix_methods)

+    is     gq    lin 
+666.10 666.03 665.48 
 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.
 

 
@@ -273,19 +273,19 @@ f_parent_nlme_dfop_tc       3 10 671.91 702.34 -325.96 2 vs 3  134.69  <.0001
 nlmixr
 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.
 First, the focei algorithm is used for the four model combinations. A number of warnings are produced with unclear significance.
-+ library(nlmixr)
 f_parent_nlmixr_focei_sfo_const <- nlmixr(f_parent_mkin_const["SFO", ], est = "focei")
 f_parent_nlmixr_focei_sfo_tc <- nlmixr(f_parent_mkin_tc["SFO", ], est = "focei")
 f_parent_nlmixr_focei_dfop_const <- nlmixr(f_parent_mkin_const["DFOP", ], est = "focei")
 f_parent_nlmixr_focei_dfop_tc<- nlmixr(f_parent_mkin_tc["DFOP", ], est = "focei")
-+ aic_nlmixr_focei <- sapply(
   list(f_parent_nlmixr_focei_sfo_const$nm, f_parent_nlmixr_focei_sfo_tc$nm,
     f_parent_nlmixr_focei_dfop_const$nm, f_parent_nlmixr_focei_dfop_tc$nm),
   AIC)
 The AIC values are very close to the ones obtained with nlme which are repeated below for convenience.
-+ aic_nlme <- sapply(
   list(f_parent_nlme_sfo_const, NA, f_parent_nlme_sfo_tc, f_parent_nlme_dfop_tc),
   function(x) if (is.na(x[1])) NA else AIC(x))
@@ -297,35 +297,35 @@ f_parent_nlme_dfop_tc       3 10 671.91 702.34 -325.96 2 vs 3  134.69  <.0001
   check.names = FALSE
 )
 Secondly, we use the SAEM estimation routine and check the convergence plots. The control parameters also used for the saemix fits are defined beforehand.
-+ nlmixr_saem_control <- saemControl(logLik = TRUE,
   nBurn = 1000, nEm = 300, nmc = 15)
 The we fit SFO with constant variance
-+ f_parent_nlmixr_saem_sfo_const <- nlmixr(f_parent_mkin_const["SFO", ], est = "saem",
   control = nlmixr_saem_control)
 traceplot(f_parent_nlmixr_saem_sfo_const$nm)
 
 and SFO with two-component error.
-+ f_parent_nlmixr_saem_sfo_tc <- nlmixr(f_parent_mkin_tc["SFO", ], est = "saem",
   control = nlmixr_saem_control)
 traceplot(f_parent_nlmixr_saem_sfo_tc$nm)
 
 For DFOP with constant variance, the convergence plots show considerable instability of the fit, which indicates overparameterisation which was already observed earlier for this model combination.
-+ f_parent_nlmixr_saem_dfop_const <- nlmixr(f_parent_mkin_const["DFOP", ], est = "saem",
   control = nlmixr_saem_control)
 traceplot(f_parent_nlmixr_saem_dfop_const$nm)
 
 For DFOP with two-component error, a less erratic convergence is seen.
-+ f_parent_nlmixr_saem_dfop_tc <- nlmixr(f_parent_mkin_tc["DFOP", ], est = "saem",
   control = nlmixr_saem_control)
 traceplot(f_parent_nlmixr_saem_dfop_tc$nm)
 
 The AIC values are internally calculated using Gaussian quadrature. For an unknown reason, the AIC value obtained for the DFOP fit using constant error is given as Infinity.
-+ AIC(f_parent_nlmixr_saem_sfo_const$nm, f_parent_nlmixr_saem_sfo_tc$nm,
   f_parent_nlmixr_saem_dfop_const$nm, f_parent_nlmixr_saem_dfop_tc$nm)
                                    df    AIC
@@ -333,8 +333,12 @@ f_parent_nlmixr_saem_sfo_const$nm   5 798.68
 f_parent_nlmixr_saem_sfo_tc$nm      6 808.88
 f_parent_nlmixr_saem_dfop_const$nm  9 815.95
 f_parent_nlmixr_saem_dfop_tc$nm    10 669.57
+
+
+
+Comparison
 The following table gives the AIC values obtained with the three packages.
-+ AIC_all <- data.frame(
   check.names = FALSE,
   "Degradation model" = c("SFO", "SFO", "DFOP", "DFOP"),
-- 
cgit v1.2.1


From 5c15ef747568b3a9a9c094b6aa546dc80e3aa87a Mon Sep 17 00:00:00 2001
From: Johannes Ranke 
Date: Mon, 27 Sep 2021 20:10:01 +0200
Subject: intervals() methods, more DFOP/tc variants

---
 docs/dev/articles/web_only/dimethenamid_2018.html  | 274 +++++++++++++++++----
 .../f_parent_nlmixr_saem_dfop_const-1.png          | Bin 174055 -> 195559 bytes
 .../figure-html/f_parent_nlmixr_saem_dfop_tc-1.png | Bin 162039 -> 167023 bytes
 .../f_parent_nlmixr_saem_dfop_tc_10k-1.png         | Bin 0 -> 156319 bytes
 .../f_parent_nlmixr_saem_dfop_tc_1k-1.png          | Bin 0 -> 162039 bytes
 .../f_parent_nlmixr_saem_sfo_const-1.png           | Bin 142453 -> 145173 bytes
 .../figure-html/f_parent_nlmixr_saem_sfo_tc-1.png  | Bin 144010 -> 150391 bytes
 .../figure-html/f_parent_saemix_dfop_tc_10k-1.png  | Bin 0 -> 39487 bytes
 .../figure-html/f_parent_saemix_dfop_tc_mkin-1.png | Bin 0 -> 44861 bytes
 .../f_parent_saemix_dfop_tc_mkin_10k-1.png         | Bin 0 -> 38868 bytes
 10 files changed, 230 insertions(+), 44 deletions(-)
 create mode 100644 docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_dfop_tc_10k-1.png
 create mode 100644 docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_nlmixr_saem_dfop_tc_1k-1.png
 create mode 100644 docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc_10k-1.png
 create mode 100644 docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc_mkin-1.png
 create mode 100644 docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc_mkin_10k-1.png

(limited to 'docs/dev/articles')

diff --git a/docs/dev/articles/web_only/dimethenamid_2018.html b/docs/dev/articles/web_only/dimethenamid_2018.html
index 26b352e1..aa84435d 100644
--- a/docs/dev/articles/web_only/dimethenamid_2018.html
+++ b/docs/dev/articles/web_only/dimethenamid_2018.html
@@ -101,7 +101,7 @@
       Example evaluations of the dimethenamid data from 2018
                         Johannes Ranke
             
-            Last change 17 September 2021, built on 17 Sep 2021
+            Last change 27 September 2021, built on 27 Sep 2021
       
       Source: vignettes/web_only/dimethenamid_2018.rmd
       dimethenamid_2018.rmd
@@ -174,7 +174,7 @@
 
 
 nlme
-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. However, 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.
+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.
  library(nlme)
 f_parent_nlme_sfo_const <- nlme(f_parent_mkin_const["SFO", ])
@@ -182,7 +182,7 @@
 f_parent_nlme_sfo_tc <- nlme(f_parent_mkin_tc["SFO", ])
 f_parent_nlme_dfop_tc <- nlme(f_parent_mkin_tc["DFOP", ])
 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.
-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.
+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.
  anova(
   f_parent_nlme_sfo_const, f_parent_nlme_sfo_tc, f_parent_nlme_dfop_tc
@@ -216,6 +216,8 @@ f_parent_nlme_dfop_tc       3 10 671.91 702.34 -325.96 2 vs 3  134.69  <.0001
  library(saemix)
 saemix_control <- saemixControl(nbiter.saemix = c(800, 300), nb.chains = 15,
+    print = FALSE, save = FALSE, save.graphs = FALSE, displayProgress = FALSE)
+saemix_control_10k <- saemixControl(nbiter.saemix = c(10000, 1000), nb.chains = 15,
     print = FALSE, save = FALSE, save.graphs = FALSE, displayProgress = FALSE)
 The convergence plot for the SFO model using constant variance is shown below.
 @@ -229,35 +231,65 @@ f_parent_nlme_dfop_tc       3 10 671.91 702.34 -325.96 2 vs 3  134.69  <.0001
   control = saemix_control, transformations = "saemix")
 plot(f_parent_saemix_sfo_tc$so, plot.type = "convergence")
 
-When fitting the DFOP model with constant variance, parameter convergence is not as unambiguous (see the failure of nlme with the default number of iterations above). Therefore, the number of iterations in the first phase of the algorithm was increased, leading to visually satisfying convergence.
+When fitting the DFOP model with constant variance (see below), parameter convergence is not as unambiguous.
  f_parent_saemix_dfop_const <- mkin::saem(f_parent_mkin_const["DFOP", ], quiet = TRUE,
   control = saemix_control, transformations = "saemix")
 plot(f_parent_saemix_dfop_const$so, plot.type = "convergence")
 
-The same applies in the case where the DFOP model is fitted with the two-component error model. Convergence of the variance of k2 is enhanced by using the two-component error, it remains more or less stable already after 200 iterations of the first phase.
+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.
  f_parent_saemix_dfop_tc <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
   control = saemix_control, transformations = "saemix")
 plot(f_parent_saemix_dfop_tc$so, plot.type = "convergence")
- The four combinations and including the variations of the DFOP/tc combination can be compared using the model comparison function from the saemix package:
+
+We also check if using many more iterations (10 000 for the first and 1000 for the second phase) improve the result in a significant way. The AIC values obtained are compared further below.
 -compare.saemix(
+f_parent_saemix_dfop_tc_10k <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
+  control = saemix_control_10k, transformations = "saemix")
+plot(f_parent_saemix_dfop_tc_10k$so, plot.type = "convergence")

+
+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.
++f_parent_saemix_dfop_tc_mkin <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
+  control = saemix_control, transformations = "mkin")
+plot(f_parent_saemix_dfop_tc_mkin$so, plot.type = "convergence")
+
+As the convergence plots do not clearly indicate that the algorithm has converged, we again use a much larger number of iterations, which leads to satisfactory convergence (see below).
++f_parent_saemix_dfop_tc_mkin_10k <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
+  control = saemix_control_10k, transformations = "mkin")
+plot(f_parent_saemix_dfop_tc_mkin_10k$so, plot.type = "convergence")
+
+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:
++AIC_parent_saemix <- saemix::compare.saemix(
   f_parent_saemix_sfo_const$so,
   f_parent_saemix_sfo_tc$so,
   f_parent_saemix_dfop_const$so,
-  f_parent_saemix_dfop_tc$so)
+  f_parent_saemix_dfop_tc$so,
+  f_parent_saemix_dfop_tc_10k$so,
+  f_parent_saemix_dfop_tc_mkin$so,
+  f_parent_saemix_dfop_tc_mkin_10k$so)
 Likelihoods calculated by importance sampling
-     AIC    BIC
-1 796.37 795.33
-2 798.37 797.13
-3 713.16 711.28
-4 666.10 664.01
-As in the case of nlme fits, the DFOP model fitted with two-component error (number 4) gives the lowest AIC. Using more iterations and/or more chains does not have a large influence on the final AIC (not shown).
++rownames(AIC_parent_saemix) <- c(
+  "SFO const", "SFO tc", "DFOP const", "DFOP tc", "DFOP tc more iterations",
+  "DFOP tc mkintrans", "DFOP tc mkintrans more iterations")
+print(AIC_parent_saemix)
+                                     AIC    BIC
+SFO const                         796.37 795.33
+SFO tc                            798.37 797.13
+DFOP const                        713.16 711.28
+DFOP tc                           666.10 664.01
+DFOP tc more iterations           666.15 664.06
+DFOP tc mkintrans                 682.26 680.17
+DFOP tc mkintrans more iterations 666.12 664.04
+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 improve the fit a lot. When the mkin transformations are used instead of the saemix transformations, this large number of iterations leads to a goodness of fit that is comparable to the result obtained with saemix transformations.
 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.
-+ f_parent_saemix_dfop_tc$so <-
-  llgq.saemix(f_parent_saemix_dfop_tc$so)
+  saemix::llgq.saemix(f_parent_saemix_dfop_tc$so)
 AIC_parent_saemix_methods <- c(
   is = AIC(f_parent_saemix_dfop_tc$so, method = "is"),
   gq = AIC(f_parent_saemix_dfop_tc$so, method = "gq"),
@@ -273,19 +305,19 @@ f_parent_nlme_dfop_tc       3 10 671.91 702.34 -325.96 2 vs 3  134.69  <.0001
 nlmixr
 In the last years, a lot of effort has been put into the nlmixr package which is designed for pharmacokinetics, where nonlinear mixed-effects models are routinely used, but which can also be used for related data like chemical degradation data. A current development branch of the mkin package provides an interface between mkin and nlmixr. Here, we check if we get equivalent results when using a refined version of the First Order Conditional Estimation (FOCE) algorithm used in nlme, namely the First Order Conditional Estimation with Interaction (FOCEI), and the SAEM algorithm as implemented in nlmixr.
 First, the focei algorithm is used for the four model combinations. A number of warnings are produced with unclear significance.
-+ library(nlmixr)
 f_parent_nlmixr_focei_sfo_const <- nlmixr(f_parent_mkin_const["SFO", ], est = "focei")
 f_parent_nlmixr_focei_sfo_tc <- nlmixr(f_parent_mkin_tc["SFO", ], est = "focei")
 f_parent_nlmixr_focei_dfop_const <- nlmixr(f_parent_mkin_const["DFOP", ], est = "focei")
 f_parent_nlmixr_focei_dfop_tc<- nlmixr(f_parent_mkin_tc["DFOP", ], est = "focei")
-+ aic_nlmixr_focei <- sapply(
   list(f_parent_nlmixr_focei_sfo_const$nm, f_parent_nlmixr_focei_sfo_tc$nm,
     f_parent_nlmixr_focei_dfop_const$nm, f_parent_nlmixr_focei_dfop_tc$nm),
   AIC)
 The AIC values are very close to the ones obtained with nlme which are repeated below for convenience.
-+ aic_nlme <- sapply(
   list(f_parent_nlme_sfo_const, NA, f_parent_nlme_sfo_tc, f_parent_nlme_dfop_tc),
   function(x) if (is.na(x[1])) NA else AIC(x))
@@ -297,48 +329,70 @@ f_parent_nlme_dfop_tc       3 10 671.91 702.34 -325.96 2 vs 3  134.69  <.0001
   check.names = FALSE
 )
 Secondly, we use the SAEM estimation routine and check the convergence plots. The control parameters also used for the saemix fits are defined beforehand.
--nlmixr_saem_control <- saemControl(logLik = TRUE,
-  nBurn = 1000, nEm = 300, nmc = 15)
++nlmixr_saem_control_800 <- saemControl(logLik = TRUE,
+  nBurn = 800, nEm = 300, nmc = 15)
+nlmixr_saem_control_1000 <- saemControl(logLik = TRUE,
+  nBurn = 1000, nEm = 300, nmc = 15)
+nlmixr_saem_control_10k <- saemControl(logLik = TRUE,
+  nBurn = 10000, nEm = 1000, nmc = 15)
 The we fit SFO with constant variance
-+ f_parent_nlmixr_saem_sfo_const <- nlmixr(f_parent_mkin_const["SFO", ], est = "saem",
-  control = nlmixr_saem_control)
+  control = nlmixr_saem_control_800)
 traceplot(f_parent_nlmixr_saem_sfo_const$nm)
 
 and SFO with two-component error.
-+ f_parent_nlmixr_saem_sfo_tc <- nlmixr(f_parent_mkin_tc["SFO", ], est = "saem",
-  control = nlmixr_saem_control)
+  control = nlmixr_saem_control_800)
 traceplot(f_parent_nlmixr_saem_sfo_tc$nm)
 
 For DFOP with constant variance, the convergence plots show considerable instability of the fit, which indicates overparameterisation which was already observed earlier for this model combination.
-+ f_parent_nlmixr_saem_dfop_const <- nlmixr(f_parent_mkin_const["DFOP", ], est = "saem",
-  control = nlmixr_saem_control)
+  control = nlmixr_saem_control_800)
 traceplot(f_parent_nlmixr_saem_dfop_const$nm)
 
 For DFOP with two-component error, a less erratic convergence is seen.
-+ f_parent_nlmixr_saem_dfop_tc <- nlmixr(f_parent_mkin_tc["DFOP", ], est = "saem",
-  control = nlmixr_saem_control)
+  control = nlmixr_saem_control_800)
 traceplot(f_parent_nlmixr_saem_dfop_tc$nm)
 
-The AIC values are internally calculated using Gaussian quadrature. For an unknown reason, the AIC value obtained for the DFOP fit using constant error is given as Infinity.
-+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.
++f_parent_nlmixr_saem_dfop_tc_1000 <- nlmixr(f_parent_mkin_tc["DFOP", ], est = "saem",
+  control = nlmixr_saem_control_1000)
+traceplot(f_parent_nlmixr_saem_dfop_tc_1000$nm)
+
+Here the fit looks very similar, but we will see below that it shows a higher AIC than the fit with 800 iterations in the burn in phase. Next we choose 10 000 iterations for the burn in phase and 1000 iterations for the second phase for comparison with saemix.
++f_parent_nlmixr_saem_dfop_tc_10k <- nlmixr(f_parent_mkin_tc["DFOP", ], est = "saem",
+  control = nlmixr_saem_control_10k)
+traceplot(f_parent_nlmixr_saem_dfop_tc_10k$nm)
+
+In the above convergence plot, the time course of ‘eta.DMTA_0’ and ‘log_k2’ indicate a false convergence.
+The AIC values are internally calculated using Gaussian quadrature.
+ AIC(f_parent_nlmixr_saem_sfo_const$nm, f_parent_nlmixr_saem_sfo_tc$nm,
-  f_parent_nlmixr_saem_dfop_const$nm, f_parent_nlmixr_saem_dfop_tc$nm)
-                                   df    AIC
-f_parent_nlmixr_saem_sfo_const$nm   5 798.68
-f_parent_nlmixr_saem_sfo_tc$nm      6 808.88
-f_parent_nlmixr_saem_dfop_const$nm  9 815.95
-f_parent_nlmixr_saem_dfop_tc$nm    10 669.57
+  f_parent_nlmixr_saem_dfop_const$nm, f_parent_nlmixr_saem_dfop_tc$nm,
+  f_parent_nlmixr_saem_dfop_tc_1000$nm,
+  f_parent_nlmixr_saem_dfop_tc_10k$nm)
+                                     df    AIC
+f_parent_nlmixr_saem_sfo_const$nm     5 798.69
+f_parent_nlmixr_saem_sfo_tc$nm        6 810.33
+f_parent_nlmixr_saem_dfop_const$nm    9 736.00
+f_parent_nlmixr_saem_dfop_tc$nm      10 664.85
+f_parent_nlmixr_saem_dfop_tc_1000$nm 10 669.57
+f_parent_nlmixr_saem_dfop_tc_10k$nm  10    Inf
+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.
 
 
 
 Comparison
-The following table gives the AIC values obtained with the three packages.
-+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).
+ AIC_all <- data.frame(
   check.names = FALSE,
   "Degradation model" = c("SFO", "SFO", "DFOP", "DFOP"),
@@ -368,7 +422,7 @@ f_parent_nlmixr_saem_dfop_tc$nm    10 669.57
 796.60
 796.62
 796.37
-798.68
+798.69
 
 
 SFO
@@ -376,7 +430,7 @@ f_parent_nlmixr_saem_dfop_tc$nm    10 669.57

 798.60
 798.61
 798.37
-808.88
+810.33
 
 
 DFOP
@@ -384,7 +438,7 @@ f_parent_nlmixr_saem_dfop_tc$nm    10 669.57
 NA
 750.91
 713.16
-815.95
+736.00
 
 
 DFOP
@@ -392,10 +446,142 @@ f_parent_nlmixr_saem_dfop_tc$nm    10 669.57
 671.91
 666.60
 666.10
-669.57
+664.85
 
 
 
++intervals(f_parent_saemix_dfop_tc)
+Approximate 95% confidence intervals
+
+ Fixed effects:
+            lower       est.      upper
+DMTA_0 96.2802274 98.2761977 100.272168
+k1      0.0339753  0.0645487   0.095122
+k2      0.0058977  0.0088887   0.011880
+g       0.9064373  0.9514417   0.996446
+
+ Random effects:
+              lower     est.   upper
+sd(DMTA_0)  0.44404 2.102366 3.76069
+sd(k1)      0.25433 0.589731 0.92514
+sd(k2)     -0.33139 0.099797 0.53099
+sd(g)       0.39606 1.092234 1.78841
+
+ 
+       lower     est.    upper
+a.1 0.863644 1.063021 1.262398
+b.1 0.022555 0.029599 0.036643
++intervals(f_parent_saemix_dfop_tc)
+Approximate 95% confidence intervals
+
+ Fixed effects:
+            lower       est.      upper
+DMTA_0 96.2802274 98.2761977 100.272168
+k1      0.0339753  0.0645487   0.095122
+k2      0.0058977  0.0088887   0.011880
+g       0.9064373  0.9514417   0.996446
+
+ Random effects:
+              lower     est.   upper
+sd(DMTA_0)  0.44404 2.102366 3.76069
+sd(k1)      0.25433 0.589731 0.92514
+sd(k2)     -0.33139 0.099797 0.53099
+sd(g)       0.39606 1.092234 1.78841
+
+ 
+       lower     est.    upper
+a.1 0.863644 1.063021 1.262398
+b.1 0.022555 0.029599 0.036643
++intervals(f_parent_saemix_dfop_tc_10k)
+Approximate 95% confidence intervals
+
+ Fixed effects:
+            lower       est.      upper
+DMTA_0 96.3027896 98.2641150 100.225440
+k1      0.0338214  0.0644055   0.094990
+k2      0.0058857  0.0087896   0.011693
+g       0.9086138  0.9521421   0.995670
+
+ Random effects:
+              lower    est.   upper
+sd(DMTA_0)  0.41448 2.05327 3.69206
+sd(k1)      0.25507 0.59132 0.92758
+sd(k2)     -0.36781 0.09016 0.54813
+sd(g)       0.38585 1.06994 1.75402
+
+ 
+       lower     est.    upper
+a.1 0.866273 1.066115 1.265957
+b.1 0.022501 0.029541 0.036581
++intervals(f_parent_saemix_dfop_tc_mkin_10k)
+Approximate 95% confidence intervals
+
+ Fixed effects:
+            lower       est.      upper
+DMTA_0 96.3021306 98.2736091 100.245088
+k1      0.0401701  0.0645140   0.103611
+k2      0.0064706  0.0089398   0.012351
+g       0.8817692  0.9511605   0.980716
+
+ Random effects:
+                lower     est.   upper
+sd(DMTA_0)    0.42392 2.068018 3.71212
+sd(log_k1)    0.25440 0.589877 0.92536
+sd(log_k2)   -0.38431 0.084334 0.55298
+sd(g_qlogis)  0.39107 1.077303 1.76353
+
+ 
+       lower     est.    upper
+a.1 0.865291 1.064897 1.264504
+b.1 0.022491 0.029526 0.036561
++intervals(f_parent_nlmixr_saem_dfop_tc)
+Approximate 95% confidence intervals
+
+ Fixed effects:
+            lower       est.      upper
+DMTA_0 96.3059406 98.2990616 100.292183
+k1      0.0402306  0.0648255   0.104456
+k2      0.0067864  0.0093097   0.012771
+g       0.8769017  0.9505258   0.981067
+
+ Random effects:
+             lower     est. upper
+sd(DMTA_0)      NA 1.724654    NA
+sd(log_k1)      NA 0.592808    NA
+sd(log_k2)      NA 0.010741    NA
+sd(g_qlogis)    NA 1.087349    NA
+
+ 
+          lower     est. upper
+sigma_low    NA 1.081809    NA
+rsd_high     NA 0.032051    NA
++intervals(f_parent_nlmixr_saem_dfop_tc_10k)
+Approximate 95% confidence intervals
+
+ Fixed effects:
+           lower       est.     upper
+DMTA_0 96.426510 97.8987836 99.371057
+k1      0.040006  0.0644407  0.103799
+k2      0.006748  0.0092476  0.012673
+g       0.879251  0.9511399  0.981147
+
+ Random effects:
+             lower       est. upper
+sd(DMTA_0)      NA 3.7049e-04    NA
+sd(log_k1)      NA 5.9221e-01    NA
+sd(log_k2)      NA 3.8628e-07    NA
+sd(g_qlogis)    NA 1.0694e+00    NA
+
+ 
+          lower     est. upper
+sigma_low    NA 1.082343    NA
+rsd_high     NA 0.034895    NA
 
 
 
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-- 
cgit v1.2.1


From ff83d8b2ba623513d92ac90fac4a1b0ec98c2cb5 Mon Sep 17 00:00:00 2001
From: Johannes Ranke 
Date: Tue, 5 Oct 2021 17:33:52 +0200
Subject: Update docs

---
 docs/dev/articles/web_only/dimethenamid_2018.html | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

(limited to 'docs/dev/articles')

diff --git a/docs/dev/articles/web_only/dimethenamid_2018.html b/docs/dev/articles/web_only/dimethenamid_2018.html
index aa84435d..13b0f98e 100644
--- a/docs/dev/articles/web_only/dimethenamid_2018.html
+++ b/docs/dev/articles/web_only/dimethenamid_2018.html
@@ -101,7 +101,7 @@
       Example evaluations of the dimethenamid data from 2018
                         Johannes Ranke
             
-            Last change 27 September 2021, built on 27 Sep 2021
+            Last change 27 September 2021, built on 05 Okt 2021
       
       Source: vignettes/web_only/dimethenamid_2018.rmd
       dimethenamid_2018.rmd
@@ -151,20 +151,20 @@
   error_model = "tc", quiet = TRUE)
 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):
 -plot(mixed(f_parent_mkin_const["SFO", ]))
+plot(mixed(f_parent_mkin_const["SFO", ]))
 
 Using biexponential decline (DFOP) results in a slightly more random scatter of the residuals:
 -plot(mixed(f_parent_mkin_const["DFOP", ]))
+plot(mixed(f_parent_mkin_const["DFOP", ]))
 
 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:
 -plot(mixed(f_parent_mkin_const["DFOP", ]), test_log_parms = TRUE)
+plot(mixed(f_parent_mkin_const["DFOP", ]), test_log_parms = TRUE)
 
 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).
 The remaining trend of the residuals to be higher for higher predicted residues is reduced by using the two-component error model:
 -plot(mixed(f_parent_mkin_tc["DFOP", ]), test_log_parms = TRUE)
+plot(mixed(f_parent_mkin_tc["DFOP", ]), test_log_parms = TRUE)
 
 
 
@@ -205,7 +205,7 @@ f_parent_nlme_dfop_tc       3 10 671.91 702.34 -325.96 2 vs 3  134.69  <.0001
 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.
 The selected model (DFOP with two-component error) fitted to the data assuming no correlations between random effects is shown below.
 -plot(f_parent_nlme_dfop_tc)
+plot(f_parent_nlme_dfop_tc)
 
 
 
-- 
cgit v1.2.1


From c0638c84568d475b3b059e2c6e593e6f03b846bc Mon Sep 17 00:00:00 2001
From: Johannes Ranke 
Date: Tue, 11 Jan 2022 19:57:58 +0100
Subject: Update static docs

---
 docs/dev/articles/web_only/dimethenamid_2018.html  | 286 ++++++++++-----------
 .../f_parent_nlmixr_saem_dfop_const-1.png          | Bin 195559 -> 183868 bytes
 .../figure-html/f_parent_nlmixr_saem_dfop_tc-1.png | Bin 167023 -> 165931 bytes
 .../f_parent_nlmixr_saem_dfop_tc_10k-1.png         | Bin 156319 -> 153748 bytes
 .../f_parent_nlmixr_saem_dfop_tc_1k-1.png          | Bin 162039 -> 154763 bytes
 .../f_parent_nlmixr_saem_sfo_const-1.png           | Bin 145173 -> 142217 bytes
 .../figure-html/f_parent_nlmixr_saem_sfo_tc-1.png  | Bin 150391 -> 151002 bytes
 .../figure-html/f_parent_saemix_dfop_const-1.png   | Bin 55927 -> 52351 bytes
 .../figure-html/f_parent_saemix_dfop_tc-1.png      | Bin 43674 -> 42286 bytes
 .../figure-html/f_parent_saemix_dfop_tc_mkin-1.png | Bin 44861 -> 45118 bytes
 .../f_parent_saemix_dfop_tc_mkin_moreiter-1.png    | Bin 0 -> 43391 bytes
 .../figure-html/f_parent_saemix_sfo_const-1.png    | Bin 55667 -> 54513 bytes
 .../figure-html/f_parent_saemix_sfo_tc-1.png       | Bin 50848 -> 50300 bytes
 13 files changed, 137 insertions(+), 149 deletions(-)
 create mode 100644 docs/dev/articles/web_only/dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc_mkin_moreiter-1.png

(limited to 'docs/dev/articles')

diff --git a/docs/dev/articles/web_only/dimethenamid_2018.html b/docs/dev/articles/web_only/dimethenamid_2018.html
index 13b0f98e..a2ea5c8d 100644
--- a/docs/dev/articles/web_only/dimethenamid_2018.html
+++ b/docs/dev/articles/web_only/dimethenamid_2018.html
@@ -101,7 +101,7 @@
       Example evaluations of the dimethenamid data from 2018
                         Johannes Ranke
             
-            Last change 27 September 2021, built on 05 Okt 2021
+            Last change 11 January 2022, built on 11 Jan 2022
       
       Source: vignettes/web_only/dimethenamid_2018.rmd
       dimethenamid_2018.rmd
@@ -151,20 +151,20 @@
   error_model = "tc", quiet = TRUE)
 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):
 -plot(mixed(f_parent_mkin_const["SFO", ]))
+plot(mixed(f_parent_mkin_const["SFO", ]))
 
 Using biexponential decline (DFOP) results in a slightly more random scatter of the residuals:
 -plot(mixed(f_parent_mkin_const["DFOP", ]))
+plot(mixed(f_parent_mkin_const["DFOP", ]))
 
 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:
 -plot(mixed(f_parent_mkin_const["DFOP", ]), test_log_parms = TRUE)
+plot(mixed(f_parent_mkin_const["DFOP", ]), test_log_parms = TRUE)
 
 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).
 The remaining trend of the residuals to be higher for higher predicted residues is reduced by using the two-component error model:
 -plot(mixed(f_parent_mkin_tc["DFOP", ]), test_log_parms = TRUE)
+plot(mixed(f_parent_mkin_tc["DFOP", ]), test_log_parms = TRUE)
 
 
 
@@ -205,7 +205,7 @@ f_parent_nlme_dfop_tc       3 10 671.91 702.34 -325.96 2 vs 3  134.69  <.0001
 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.
 The selected model (DFOP with two-component error) fitted to the data assuming no correlations between random effects is shown below.
 -plot(f_parent_nlme_dfop_tc)
+plot(f_parent_nlme_dfop_tc)
 
 
 
@@ -217,50 +217,54 @@ f_parent_nlme_dfop_tc       3 10 671.91 702.34 -325.96 2 vs 3  134.69  <.0001
 library(saemix)
 saemix_control <- saemixControl(nbiter.saemix = c(800, 300), nb.chains = 15,
     print = FALSE, save = FALSE, save.graphs = FALSE, displayProgress = FALSE)
-saemix_control_10k <- saemixControl(nbiter.saemix = c(10000, 1000), nb.chains = 15,
+saemix_control_moreiter <- saemixControl(nbiter.saemix = c(1600, 300), nb.chains = 15,
     print = FALSE, save = FALSE, save.graphs = FALSE, displayProgress = FALSE)
 The convergence plot for the SFO model using constant variance is shown below.
  f_parent_saemix_sfo_const <- mkin::saem(f_parent_mkin_const["SFO", ], quiet = TRUE,
   control = saemix_control, transformations = "saemix")
-plot(f_parent_saemix_sfo_const$so, plot.type = "convergence")
+plot(f_parent_saemix_sfo_const$so, plot.type = "convergence")
 
 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.
  f_parent_saemix_sfo_tc <- mkin::saem(f_parent_mkin_tc["SFO", ], quiet = TRUE,
   control = saemix_control, transformations = "saemix")
-plot(f_parent_saemix_sfo_tc$so, plot.type = "convergence")
+plot(f_parent_saemix_sfo_tc$so, plot.type = "convergence")
 
 When fitting the DFOP model with constant variance (see below), parameter convergence is not as unambiguous.
  f_parent_saemix_dfop_const <- mkin::saem(f_parent_mkin_const["DFOP", ], quiet = TRUE,
   control = saemix_control, transformations = "saemix")
-plot(f_parent_saemix_dfop_const$so, plot.type = "convergence")
+plot(f_parent_saemix_dfop_const$so, plot.type = "convergence")
 
 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.
  f_parent_saemix_dfop_tc <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
   control = saemix_control, transformations = "saemix")
-plot(f_parent_saemix_dfop_tc$so, plot.type = "convergence")
+plot(f_parent_saemix_dfop_tc$so, plot.type = "convergence")
 
-We also check if using many more iterations (10 000 for the first and 1000 for the second phase) improve the result in a significant way. The AIC values obtained are compared further below.
 -f_parent_saemix_dfop_tc_10k <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
-  control = saemix_control_10k, transformations = "saemix")
-plot(f_parent_saemix_dfop_tc_10k$so, plot.type = "convergence")
-
+# The last time I tried (2022-01-11) this gives an error in solve.default(omega.eta)
+# system is computationally singular: reciprocal condition number = 5e-17
+#f_parent_saemix_dfop_tc_10k <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
+#  control = saemix_control_10k, transformations = "saemix")
+# Now we do not get a significant improvement by using twice the number of iterations
+f_parent_saemix_dfop_tc_moreiter <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
+  control = saemix_control_moreiter, transformations = "saemix")
+#plot(f_parent_saemix_dfop_tc_moreiter$so, plot.type = "convergence")
 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.
  f_parent_saemix_dfop_tc_mkin <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
   control = saemix_control, transformations = "mkin")
-plot(f_parent_saemix_dfop_tc_mkin$so, plot.type = "convergence")
-
-As the convergence plots do not clearly indicate that the algorithm has converged, we again use a much larger number of iterations, which leads to satisfactory convergence (see below).
+plot(f_parent_saemix_dfop_tc_mkin$so, plot.type = "convergence")

Degradation.model	Error.model	nlme	nlmixr_focei	saemix
SFO	const	818.63	818.63	818.37	820.54
SFO	tc	820.61	820.61	820.38	835.26
DFOP	const	NA	728.11	725.91	842.84
DFOP	tc	687.84	687.82	683.64

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).

-f_parent_saemix_dfop_tc_mkin_10k <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
-  control = saemix_control_10k, transformations = "mkin")
-plot(f_parent_saemix_dfop_tc_mkin_10k$so, plot.type = "convergence")

saemix_control_muchmoreiter <- saemixControl(nbiter.saemix = c(3200, 300), nb.chains = 15,
+    print = FALSE, save = FALSE, save.graphs = FALSE, displayProgress = FALSE)
+f_parent_saemix_dfop_tc_mkin_muchmoreiter <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
+  control = saemix_control_muchmoreiter, transformations = "mkin")
+plot(f_parent_saemix_dfop_tc_mkin_muchmoreiter$so, plot.type = "convergence")

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:

 AIC_parent_saemix <- saemix::compare.saemix(
@@ -268,9 +272,9 @@ f_parent_nlme_dfop_tc       3 10 671.91 702.34 -325.96 2 vs 3  134.69  <.0001
   f_parent_saemix_sfo_tc$so,
   f_parent_saemix_dfop_const$so,
   f_parent_saemix_dfop_tc$so,
-  f_parent_saemix_dfop_tc_10k$so,
+  f_parent_saemix_dfop_tc_moreiter$so,
   f_parent_saemix_dfop_tc_mkin$so,
-  f_parent_saemix_dfop_tc_mkin_10k$so)

+ f_parent_saemix_dfop_tc_mkin_muchmoreiter$so)

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 improve the fit a lot. When the mkin transformations are used instead of the saemix transformations, this large number of iterations leads to a goodness of fit that is comparable to the result obtained with saemix transformations.

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.

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.

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.

Secondly, we use the SAEM estimation routine and check the convergence plots. The control parameters also used for the saemix fits are defined beforehand.